JPRS ID: 9788 TRANSLATION ASTRONOMICAL OPTICAL SYSTEM PRODUCTION METHODS BY EDUARD ALEKSANDROVICH VITRICHENKO, ET AL.

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JPRS L/9788
11 June 1981
Trar~slation
ASTRONOMICAL OPTICAL SYSTEM PRODUCTION METHODS
.By
~ Eduard Aleksandrovich Vitrichenko, et al.
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.7PR5 L/9788
11 June 1981
ASTRONOMICAL OPTICAL SYSTEM PRODUCTION METHODS
Moscow METODY IZGOTOVLENIYA ASTRONOMICHESKOY OPTIKI in Russian 1980
(signed to press 14 Nov 80) pp 2-142, 196
["Astronomical Optical System Production Methods", by Eduard
Aleksandrovich Vitrichenko, Alek,sandr Mikhaylovich Prokhorov and
Yevgeniy Vasil'yevich Trushin, research performed under i:he auspices
of the Space Research Institute of the USSR Academy of Sciences, pub-
lished by Izdatel'stvo "Nauka", 1,000 copies, 196 pages, UDC 522.2]
CONTENTS
- Annotation 1
Foreword 2
Introduction 4
Chapter 1. Principles of the Automation of Astronomical Optical
System Production 9
Introduction 9
l. Surfacing and Time Control 11
2. Tool Speed Control 30
3. Tool Trajectory Control 31
4. Control of the Tool Force 3~
5. Requirements on Automatian Hardware 40
Conclusions 42
Chapter 2. Automated System Software 43
Introduction 43
1. Archit~cture of the Applied Prc~grams 47
2. Methods of Determining the Mactiine Tool Function and the Process
Constant SO
3. Determination of the Process Conditions 60
4. Determination of the Size of the Tool 66
Conclusions ~1
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Chapter 3. Experience in Working with the ZEBRA-1 Automated System 72
Introduction 72
- l. Technical Description of the ZF;BRA-1 System 74
'L. Manufacture of Series Mirrors 89
3. Paraholic Mirror Production 95
4. Manufacture of Lenses Under Pl~nt Conditions 97
5. Ana:lysis of the Advantages and Disadvantages of the System 98
Conclusions 100
Chapter 4. Automated ZEBRA-2 and ZEBRA-3 Systems 10'_'
Introduction . 102
l. Automated ZEBRA-2 System 103
2. Automated ZEBRA-3 System 105
3. Experience in Working with the ZEBRA-3 Automated System 107
Conclusions 110
Chapter 5. Prospective Automated Mettiods of Building Astronomical
Aspherical Official Systems 112
Intraduction 112
l. Preliminary Machining of Opticll SurfacES by the Point Contact
rlethod 120
2. Finishing and Asphericalization of the Optical Surfaces in the
Grinding and Polishing Process 124
3. Super-Precision Finishing of Optical Surfaces 129
Conclusions 135
Cor.clusion 136
Bib~iography 138
Table of Contents 148
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ANNOTATION
Thi~ book discusses the problem of making astronomical mirrors by the methods of
digital and analog control of the shaping process. The American CAOSand CCP
automated production systems and the Soviet ZEBRA system are described. Special
attention is given to the software for the production systems and communication
of the production pracess with the optical surface shape control procedure. The
texts of the programs used in the ZEBRA system are presented.
The book is designed for scientific workers and engineers employed in astronomical
= instrument making, postgraduates and students at the institutions of higher learn-
ing for the indicated specialties.
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FOREWORD
~ Tn 1974 the largest telescope in the world with a primary mirror diameter of
6 meters was put intc operation. With the building of this tQlescope, a large
number of scientific and technical problems were successfully solved. As fre-
quently occurs in practice, during the solution of certain problems new prob-
- lems arose requiring their solutions in turn. The main one of these problems can
be farmulated as follows: th~ creation of an automated "production control" sys-
tem tor the production of high-quality astronomical mirrors. The pioneering
lrticle by Brown [1971] on this question begins with the prophetic words: "In
the past, the manufacture of mirrors :Eor large telescopes was more an art than a
science. However, the role of sciencc~ is increasing from year to year and,
possibly, in the f.oreseeable f uture ttie entire problem as a whole will become
understandable and completely controliable."
_ The ~~reblem of the con' rol of astronomical mirrors i~ the subject of a large
nun~ber of articles and several monographs, among which is the book by .
D. T. Puryayev [1976] "Methods of Controlling Aspherical Optical Surfaces" and
the book by E. A. Vitrichenko [1980] "Methods of Studying Astronomical Optics";
the problem of automated technology was the subject of only a few articles, and
among the books it is possible to mention only the book by N. P. Zakaznov and
V. V. Corelik ~1978] "Aspher.ical Optical System Production." The situation is
worse with regard to the procedure for using the results of controlling the shape
_ of an optical surface for giving the processing conditions. Only unrelated informa-
tion is available on this question in individual articles.
Nevertheless, no one doubts that the production of precision optical surfaces
for the needs of astronomy (Gascoigne, 1973] and for other purposes of a practical
nature is an urgent problem [Michelson, 1976]. The urgency is so great that it
t~as Eorced the creation of a special laboratory under the USSR Academy of Sciences
which is engaged in the solution of this problem in close connection with indus-
try.
'l'h3s book sums up many years of activ:tty with respect to the development and
introduction of the automated sy~tem which the authors call ZEBRA into industry,
the basis for which is local control of the force of a small tool. A great deal
of attention has been given to the description and analysis of other approaches
to the solution of the problem. The principle of the method for control of the
local pressure of a tool on a part is discussed, and the software for the ZEBRA
automated system is presented.
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Th-is sy~Lem is designed for automated processing of optical surfaces based on
measuring the topo~raphy of the surfaces. The surface is studied by the control
methods, it is stored in an analog or digital unit, and then considering the
shape of this surface, the operation of removal of the material in the required
_ amount at the reqt�*:ed locations is executed by a program written on the basis
of an analysis of the surface topography by specially developed software.
- The work on this system was participaLed in by coworkers ~hose names the authc,rs
_ consider it their duty to mention: G. I. Amur, A. M. Bogudlov, L. G. Boytsov,
L. P. Vasil'yev, V. V. Gorelik, 0. A. Yevseyev, V. A. Zverev, V. A. Ivanov,
F. K. Katagarov, N. L. Komarov, V. A. Kokotushkin, V. V. Kostin, I. M. Kopylov,
Yu. K. Lysyannyy, A. N. Makarov, V. A. Malykhin, S. K. Mamonov, A. A. Sa~~chenko,
R. Z. Sagdeyev, S. Ye. Stepanov, G. S. Tsarevskiy.
This book is the first effort to analyze such a complex problem as the automation
of optical technology. The authors will be very grateful to the readers for
critical reraarks.

~
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~NTRODUCTION
'I1~e manufacture of a large-scale astronomical optical system is connected with
overcoming an entire series of difficulties which are caused primarily by the fact
tliatit is necessary to sustain a mathematical surface in the area of an optical
~ surface of several square meters with a precision reckoned in hundredths or a
mi cron .
Kecently the ideas have been advanced for the creation of optical telescopes from
several mirrors with an equivalent diameter to 25 meters [Pacini, Richter, Wilson,
1977].
The following factors, for example, prevent the solution of the problem: 1) im-
perfection of the optical machine tool, the effects of adjusting it [Mikhnev,
1973J and wear of the subassembly lead to various types of errors in the optical
surface; 2) thermal effects connected witih the process of energy release in the
- contact zone of the tool and the part and nontm iformity of heating of the part and
the tool during th~ surfacing process [Maksutov, 1948, 1979]; 3) nonimiform ity
of the hardness with respect to grindability over the surface of the billet itself
which is unavoidable for large dimensions, leads to different removal of material
imder equal conditions; 4) nonimiformity of feeding the abrasive suspension to the
- contact point of the optical part with the tool; 5) imperfection of the tool and
its layer introduce their own errors [Tsesnek, 1970].
'lhe e:~isting practice of optical systtam manufacturers is based o~i experience and
intuiti_on and not on exact information about ti~ production process. This is more
a misfortune than a fault, inasmuch as consideration of the numerous production
factors without a computer is impc~ssible, and involvement of a computer leads
to reexamination of the production process itself. The existing practice is ~ '
leading to the fact that the process of manufacturing optical s:trfaces is not
cunverging, that is, during the proce:~s of working on the part the practical
optician improves the quality of the part, but part of the time is involuntarily
spent on its improvement. For this reason the expenditures of time and means on
the manufacture of large optical surfaces turns out to be unju.stifiably large.
By the accepted operating procedure [~lorne, 1972] the quality of the finished
optical product depends directly on tlie qualifications of the practicing optician.
This introduces a subjective element into optical technology, it forces long
years of training experimental optical personnel, spending large amounts of
means on training them. The subjecti~~eness of classical technology leads to the
fact that, for example, one optician "can" manufacture a high-quality part, and
another cannot reach this quality in any surfacing time. It is clear that this
is entirely tm acceptable for the industrial method of production.
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The ohvious Way out of the developed situation can be automation of the shaping
process with the application of computer engineering means. In this case the
production process hecomes strictly converging, that is, in. each surfacing
s~~ssi~m the opticril surface will only improve, and this converging process be-
comc~~ iiidependent of the personal expr~rience of the practlcing optician.
7'he creation of a completely automatic device for the manufacture of optical su~-
faces could be very enticing. In this case feedback in r_al time must be
organi..zed between the surface shdpe control and the producti~n process. Unfor-
tunatQly, the optical surface shape control in real time is not only not imple-
mented, b ut there are not even any ideas as to how to do this in the near future.
- There are two bas2c reasons for this. The contact methods provide ins ufficienr
� precision, and contactless methods carinot be iinplemented inasi~:
~ch as the optical
surface is coated witti abrasive suspension. On the other hand, local energy
release at the contact spot leads to cleformation of the optical surface. It is
knuwn that after a production session time is required to remove the local thermal
stresses in the part (waiting time), Thus, measurements of the surface shape in
real time, even if they can be perforr:ied, will pertain to the "current" shape of
the o~~tical surface and not to the shape that will be obtained as a result of the
waitin g period. For the above-indicated reasons the production pr~cess can only
be atitomated and not automatic.
The se arch for ways to create an automatic technological process is possible with
basic alteration of the classical technology. Possibly it will be necessary to
use ion bombardment methods or vacuum deposition technology (see, for example,
[Shapochkin, 1961]). In these methods the optical surface remains free and avail-
able for cnntactless control of its shape in real time. However, along this path
there are also characteristic problems that are difficult to resolve.
~ Fecently the paper by Aysin, et al. [1979] appeared in which an effort was made
to control (measure) the shape of the optical surface during the surfacing of it
and to use the control results in real time to control the shaping process. The
experiment demonstrated that when grinding by the contact method precision of
3-5 microns can be achic~ved, Only the zonal component of the errors was measured;
~ the complete picture of the normal de~riations of the entire optical surface was
not constructed. The authors draw the conclusion of prospectiveness of the
approach.
Anotller path is possible for obtaining precision surfaces. Classical p~'lishing is
r.eprod�ced insufficiently pr.ecisely. If nonclassical procedures are used [author's
certificate No 87504, 1950], and high reproducibility of the process is achieved,
the;1 there is no further necessity for. controlling the shape of the surface in
- real time. These nonclassical procedures include ultrasonic polishing in a
liquid medium [author's certificate Na 85551, 1950] or an abrasive-liquid flaw
comoin ed with the mask method [autho-r's certificate No 199701, 1967). The results
of stu~iying the reprodiicibility of these methods are unknown to us.
Soviet projects aimed at shaping the control research can be divided into two
basic groups. The first group includE~s the work on creating equipment with
explic.it and implicit formers; the ser.ond group includes wo�rk on a multielement
tool :::nd a mask method.
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A simple furmer in the form ot a pl~ne was investigared by Agashin and
(;or~lik [author's certificate No 448119, 1974]. The farmer creates the possibil-
ity of manufacturin~; complex asphericil_ surfaces. Line machining of the surface
witti the application of a complex fonner was investigated by Alaverdyanets,
et al. [author's certificate No 37313:L, 1973]. The ideas of s p arallelogram
[auLhor~s certificate No 305041, 1971j or various types of lever.s [author's
certificate No 344970, 1972; author's certificate No 87504, 1950; author's certifi-
cate No 48775~J, 1975] are proposed in a number of Fapers. The rotations of the
tool and tt~e billet around various axes permitting manufacture of aspherical
surfaces were investigated by Gorelik, et al. [author's certificate No 333017,
1.972; author`s certificate No 325163, 1972; author's certificate No 2I7998,
1968]. A knife type tool [author's certificate No 343830, 1972] or a flexible
belt on guides [author's certificate No 460987, 1975] are explicit former. A
combination of lever mechanisms and a parallelogram permits the manufacture of
toruses znd barrels [author's certifi,~ate No 439380, 1974]. Direct copying to
scale was investigated by Granichin and Kaganov [author's certificate No 241254,
1969 ] .
In a number of papers simple tools have been proposed which permit the manufacture
of ;ispheric~il surfaces [author's certificate No 192651, 1967; author`s certificate
No 192650, ].961; author's certificate No 151580, 1966; author's certificate
No 182549, 1966]. A cam was proposed by Kaplan, et al. as a former [author's
certificate No 400443, 1973] and also by Karlin, et al [author's certificate
No 147937, 1962]. Complication~ of the trajectory of motion of the tool over the
i~illet were investigated by Kachkin and Chunin [author's certificate No 129499,
1960], Konyashkin, et al. [author's certificate No 314406, 1972], Skibitskiy
[author's certificate No 182019, 1966]. Special attachments and tools permitting
aspherical surfaces to be ma~hined were investigated by Khabirov [auth~r's certif-
icate No 427838, 1974], Kuznetsov and Sergeyev [author's certificate No 113952,
1957], Kumani.n, et al. [author's certificate No 214328, 1968]. The ideas of
cre;iting e:cplicit formers jointly with the ideas of the distribution of operations
by zones of the optical surface were studied by Lipovetskiy [author's certificate
No 317488, 1971; author's certificate No 325164, 1972], Khusnutdinov and
Kh abirov [author's certificate No 244142, 1969].
The original kinematics of motion of the tool with respect to the part were inves-
- ti.gated by Khusnutdinov [author's certificate No 239071, 1969; author's certifi-
cate No 258055, 1969; author's certificate No 463535, 1975; author's certificate
- No 395238, 1973] and also Chunin and Kachkin [author's certificate No 131632,
196~].
In spite of the great difference in technical solutions, all of the devices indi-
cated above have common advantages and deficiencies. The primary advantage
consists in tlia fact that the application of these methods and devices permits
th e sc~lution of the problems of manuf:3cturing aspherical surfaces. A common
, clelic.iency is l.ow precision of the su~rfaces obtained, which is unsatisfactory for
astronomi.cal optic.s. Tlie former must be not mechanical device but the normal
- cleviatio~s obtaineci by precision cont?-ol methods themselves. Many authors have
" not given sufficient attention to the methods of controlling the shape of the
optical surface. An indirect consequE~nce of this is the almost complete absence
- in scientific literature of an analys~s of these solutions in which the results
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of cluantitat.ive control of optical parts obtained by the proposed method are
presented.
Le~ us discuss the multielement tool. Two tools performing different functions
were investigated by Vladimirov and ti~-ef'yev [author's certificate No 103130,
_ 1954]. Ttie combination of the multielement tool witn a template was proposed by
Gorelilc and Denisov [author`s certificate No 283846, 1970]. A spring-heel tool
- developed by Semibratov and his students combines the pri,::-~nles of the multi-
elemenr. tool and the principle of operation distribution b~ zones [author's
certificate No 429931, 1974; author's certificate No 335080, 1972; author's
_ certiFicate No 427837, 1974]. Split flat springs [author's certificate
No 144737, 1962] and simply individual tools on a common base [author's certif.`..-
cate No 595073, 1978; 218687, 1968; author's certificate No 370014, 1973;
author's certificate No 360199, 1972] are used as the multielement tool. The
multielement tool pr.inciple is used iii the mask method [author's certificate
No 217999, 1968; Tsesnek, 1970].
- An analysie of the applicationof the i~ultielement tool in optical technology leads
to tlie same conclusions as the analys~:s of the application of inethods connected
~aith the template. In the literature we have found no information about the
- investigation of the shape of the optical surface made by a multiele~nt tool or
indications or recommendations for calculating the production processing conditions.
Only in the papers by Semibratov and his students were the first steps taken in
_ this direction [Semibratov, 1962; Semib ratov, Yefremov, 1976]. Comparisons of
- new methods described in the author's certificates with classical technology have
also not been made, b ut, nevertheless, this comparison alone can serve as a
decisive argument in favor of transition to the new technology.
Excessive criticism of the above-enumerated developments would be improper.
Moreover, it is known that many of them are used in industry and provide a large
effect. Hawever, most frzquently, in our opinion, this effect is achieved for
small parts (up to 100 nnn in diameter), with large steepness of the surface (more
than 10�) and with great asphericalness (more than 0.1 micron/~n). For astronom-
ical mirror~ the application of the at~ove-described methods is limited.
Ar~~erican and Soviet automated systems are described in this book in which the
f possible speeds is taken into account.
Tf~e file of speeds is output on magnetic tape which is read by a minicomputer
realizing tlie surfacing session. Afte~r completion of the surfacing session the
part a~ain goes to control .
In the paper by Jones [1977] special attention is given t~ `he shape of the to~l.
This most important problem has been studied insufficiently; therefore a more
- detailed discussion is presented of the results of the a~ithor of the article.
The operation of a small tool is stu~ied both by simulation on a computer and in
fu11-scale experiments. The machine cimulation of the operation of the small t-ool
was b ased on the following principles:
I:emoval of the material takes place orily as a result of rotation of the tooi
around its axis in the process of moving over the optical surface;
The removal of the material is a function of the distance from the center of the
tool ;
7'he tool moves over the surface of the part along a unit trajectory, and control
, of the removal of the material is achieved as a result of variable speed of this
displacement.
According to Semibratov's terminology, the control of the removal of the material
takes place as a result of the variable coverage factor which the author calls
the clwell function. If the tool makes N passes over the surface, then the total
_ material removed can be described by the equation
1~~~x,Y) =S(X,Y) = Nf~PT(u, v)R(x-u, y-.v)diriv, (1.4)
where R is the material removal profile which is related to the operation of the
sma].1 tool; T is the coverage factor; S(x,y) is the chart of the normal deviations
of tlle optical surface before the beginning of finishing operations; F(x,y) is
the chart of the normal deviations with respect to completion of the finishing
operation.
Simiilation consists in the fact that an arbitrary initial chart of normal devia-
tions is input to the computer memory, the program computes the proaess conditions
and calculates a new chart of normal deviati~i~s which will occur after realization
of the process conditions. The new ch art of deviations is initial for the next
cycle, and so on. The separate program described in the paper by Wagner and
Sliannon [1974] defines the material removal profile for a different structure of
t}ie small rotating tool.
Tn formul.a (1.4) the value of P denotes the product of the constant p ressure
times the process constant connected with the materials of the tool, the part and
the ah rasive. This vzlue can be taker? from under the integral sign, but it can
he considered as a function of ttie raclius of the tool for nonuniform pressure
.listribution.
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'1'he ~imulation program executed on the IBT1-370 computer has been used for many
purposes. One of them is the effect uf the nwnber of elementary polishers on
convergence of the technological process. The results of this simulation are
presented in Figure 1.10 where the coiifiguration of two types of tools is also
illustrated (see Figure 1.10, a). One of them consists of two elements 2.5 cm
in diameter with spacing between centers of 3.8 cm, and the other consists of
four elements of the same diameter, but with a spacing between centers of 6.4 and
3.8 cm. Profiles of the removal of material for these types of tools are pre-
- sented in Figure 1.10, b. The distance from the center of the tool is plottted
along the x-axis, and the amount of material removed, along the y-axis. From the
figure it is obvious that increasing ihe number of tool elements increases the
removal of material, but the removal profile changes insignificantly.
- f Q
0
~ ~ o-.-~-.-o
~B
~y omn.tQ ~ Z,S ~
Z, ~1~
b
- ~0 ~
O
4 Z O Z ~ ~ 2 D Z /9~cn
Figure 1.10. Rotating tools.
a-- geometric configurations ot two types of tools, b-- rate of
removal of material under the Lool platform. A11 dimensions in the
figure are given in cm.
Key:
1, relative units
I'he following model experiment was conducted for two types of tools presented
_ in T'igure 1.10, the results of which are presented in Figure l.ll. The order
number of the production session is plotted along the x-axis; the mean square
deviation of the optj.cal surface expressed in fractions of a wave length is
plotted along the y-axis. In the paper by Jones, the wave length is tal;en as
0.6328 micron.. Curve 1 pertains to a rotating tool having four elements;
c~~rve 2 indicates convergence of the finishing process for a two-element tool;
c.urve 3 is the conver~ence for an ideal tool, the removal profile of which is
~lescribed by an equilateral triangle and the apex of the triangle coincides
with the center of the tool. From the figure it is obvious that this ideal tool
- permits achievement of the best quality of optical surfaces. If a real tool
permits a surface to be obtained with mean square deviation of 1/20 of the wave
length in 6-8 cycles, an ideal tool leads to a surface with an error of 1/50 of
the wave length in 10 cycles, and further improvement of the surface is possible.
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-
� G/~
S,O
,10
4�s
q~p ~ ~ z
qos
~
qo~
0 Z f~ 6 B`!ON
Figure l.ll. Results of model calculations of the convergence
of the technological process fur different structural designs
of tools.
l, 2-- rotating tool with four and two working elements,
respectivel_y; 3-- model tool having the function of removing
material iri the form of a triangle
dG 'omn.t~.~~) .
90 Q b`
Z, O
- 7,0
O
f~ Z O 2 ~ 6 ~ 2~O Z~ 6
1,S
1,0 c
O, S
- O
B 6 4 Z O Z 4 6 B~,cn
Fisure 1.12. Retr,oval profiles of a material for various oscillation
amplitudes of the tool.
a-- tool does not oscillate; b-- oscillation ampli:tude is equal to
the tool radius; c-- oscillation amplitude is equal to twice the
radius of the tool element.
The distance from the center of the tool in cm is plotted on the
x-axis.
Key:
1. relative units
21
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G/.b
S,0 I
,/O i
O,
1
Q10 Z
QOS -
,
- Q0I
p 2 4 6 B !ON
~
Fi~;ure 1.13. Results of model calculations of the convergence of
a technological process for various amplitudes of the epicyclic
movement of the tool.
1-- tool does not oscillate, oscillation amplitude is equal
to the radius of the tool element, 3-- oscillation amplitude is
equal to twice the radius of the tool element.
In the given model experiment it was c:onsidered that the initial surface .is an
ideal plane, and the required surface is a sphere with a pointer of 1/10 of
' the wave lengtn. The coverage factor was taken proportional to the required
material removal, and the removal profile was selected so that half the material
subject to removal would be removed in one pass of the tool. Analogous results
were obtained also for other types of machined surf aces.
Thus, the described model tool leads to the conclusion that it is necessary to
use a material removal profile in the form of a triangle. This profile can be
obtained if the multielement rotating tool is given oscillating m~tion. In this
case th e tool rotates at high speed around its axis, and the tool axis rotates
with lower speed around a center.
Figure 1.12 shows the results of calculations of the removal profile of the
~ material by a two-element tool for thi�ee amplitudes of the oscillating motion.
On the figure it is obvious that the best profile is the one with oscillation
amplitude equal to the radius of the t:ool element inasmuch as in this case the
nrofile is clo~est to a triangle.
1n Figure l.l? results are nresented from model calculations of the convergence
of the technological process for three cases of oscillating movements. The tool
- is two-element, the spacing bet~aeen the centers of the elements is equal to twice
the radi.us of the tool. Just as shoul.d be expected, the best quality of surface
is achieved for oscillation amplitude equal to the element radius: in 10 sur-
facing cycles the mean square error dECreases to 1/50 of the wave length, and
further improvement of the surface is possible in this case. The conditions of
the model experiment arE the same as t:hose corresponding to Figure 1.10.
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rinally, the adopted configuration anc~ dynamics of the tool are illustrated in
Figi~re 1.14. The tool elements are de~monstrated in the figure by solid circles.
Both tools 3.5 cm in diameter rotate at high speed around the midpoint.
'1'Ile spacing between the centers of the tool is 3.8 cm, which insures a clear-
ance between edges of the tools of 0.3 cm, k.eeping them from contact. A separate
- drive provides for movement of the mic(point of the tool around a circle 3.8 cm
in diamete r.
In I'igure 1.15 a comparison is made between the material removal profiles for
three diEferent: structural designs of the tool. Curve 3 corresponds to the finrl
version of rotating and oscillating tc~ols.
Tn the initial CGP system the coverage factor was selected equal to the required
material removal. However, later the correction was introduced considering the
difference between the required removal of material and that calculated for a real
- tool. Let us denote this difference for the i-~h surfacing se ction in terms of
Li; the required material removal is D, and the actual removal will be
expressed as the convolution of the coverage factor Ti with tool remAVal profile R:
Ei = D - Ti * R, (1.5)
_ wliere the aste~isk denotes the convolution operation. In equation (1.5) the
coverage factor Ti is determined by the method of successive approxima.tions

~ according to the ~ollowing algorithm. The value of the required material
removal is taken as the initial va.lue~
Tl = D. (1.6)
The residual chart of normal deviatioris will in the first approximation have the
fo rm
E1=D-D *R. (1.7)
In the second approximation
T2=D+E,, E2 =D-D*(2b -R)*R, (1.8)
cohere 8 is the delta function. The entire iterative process can be written in
the form of the exp ression
T; =T;_, +E;,~ =D*C;(R), E; =D-D+G,(R)*R.
(1.9)
The auxiliary function Gi(R) is definE~d by the recurrent formula
G1 =S, G~ =C~-1 +b -G~-i �R. (1.10)
The sign of convergence of the pro ces;; is smallness of the value S defined by the
expression yR _S~ ~E
I Gi
(1.11)
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at om~.~a,
~ !,O
~ n
Z~" ~ R~~ 1 0 / ~ LZ
~ I
~ ~ ~ O,
~f0 % ~ ~
~ ,I 1 i j ' 1
~ ~ o,zs ~ ~ ~ I
; ; ~ ~ I
~ 6 ~ Z O Z ~iR,cn
Figure 1.14. Diagram of the oscillating movement nf a rotating
tool.
1-- trajectory of the center of the polishing head on the optical
surface; 2-- trajectory of rotation of the tool elements relative
to the midpoint; 3-- trajectory of m~tion of the midpoint.
- Solid lines --tool elements
Figure 1.15. Rate of removal of material for tools of different
- structural designs.
1-- two rotating elements 2.5 cm in diameter; 2-- four rotating
- elements 1.5 cm in diameter; 3-- rotating and oscillating tools
with elements 3.5 cm in diameter
Key:
a. relative units
The results of model calculation of the convergence of the technological process
indicating the effect of the correction of the coverage factor are presented
in Figure 1.16. The model conditions are the same as when obtaining the results
- shown in Figure 1.10. Curve 1 corresponds to the case where a correction to the
coverage factor is introduced for a rotating two-element tool. Surface quality
with mean square error 0.11 of the wave length is achieved. Further improvement
of the surface turns out to be impossib le. Curve 2 indicates the convergence
process for a rotating tool, but without correction of the coverage f actor.
However strange, the best shape of the surface is obtained here, which can indi-
cate that for a rotating tool (without oscillation) the correction procedure can
be degenerate. Finally, the best results permitting achievement of the surface
with a mean square error of 1/SO of the wave length are illustrated by curve 4
which corresponds to the rotating and oscillating tools with correction of the
coverage factor.
In the CCP systems special attention is given to the selection of the optimal
trajectory of the tool over the optical surface. 1`wo requirements are imposed
on the trajectory: the constancy of the step size and absence of turning points.
These requirements are satisfied by aai Archimedes spiral. The tool begins
movement from the center of the part, the movement takes place from the center to
the edge and from the edge to the cen~ter without changing the direction~of rota-
tion. For calculation of the trajectory of the tool center along a circular or
elliptic spiral, the following iterat:ive procedure is used:
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, -
~f al
G/~ d~ om~.ea.

J !,0
S, 0 .
_ ,10 '
O,S ~ 1 O,S
~ ~
0,10 2 .
O, OS ~ _ 1
Z . ~
4
0,O10 G ~ 6 B 10 N .f ~9,cn
Figure 1.16. Results of model calculations of the convergence of
the technological process for different operating conditions of
the tool.
_ l, 2-- rotating tool with correction and without correction,
respectively; 3, 4-- rotating and oscillating tools without
correction and with correction of the removal profile, respectively
Figure 1.17. P(aterial removal function by the rotating and
oscillating tools.
1-- theoretical removal of thc~ material; 2-- experimental
removal profiles of the material
Key:
a. relative units
LS
- Ci - (~'i- t + 1 + Bi = 9(- i + 2L ~
2a 1 Ci + Ct-t
k = 1, R; = C~, (1.12)
for k~ 1, R~ = C~/(k~sin6; +cosB~)~~2,
x; = R;~ose; , Y; = R;sin9~ .
Here S is the spiral pitch which is co:zsidered to be positive for untwisting
spirals and negative for twisting spirals; L is the length of the trajectory
element, Ci is the distance from the part center to the i-th point on a steep
spiral, Ai is the position angle of the i-th point of the spiral, k is the ratio
- of. the major and minor axes of the ellipse if the spiral is elliptic, Ri is the
distance from the center of the part to the i-th point nf the elliptic spiral,
Yi and Yi are the rectangular coordinates of the i-th point of the elliptic
- sPiral with location of the X-axis along the major axis of the ellipse.
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Table 1.1
~LUnbe~~ of ~part
Characteristic No ~ ~No 2 No 3 No 4
Surface type Plane Plane Complex Hyperbola
Size, mm 380 in 813x883 305x330 1500 in
_ diamE~ter diameter
Material Servi.te Beryllium Servite ULE
Mean square error, microns
initial 0.14 0.25 1.0 0.83
final O.OOfi 0.03 0.1 0.05
Machine tool time, hours 4 65 99 -
In order to check the reproducibility of the removal of the material, trial
experiments were run in which the tool completed rectilinear movement. In
Figure 1.17 the line 1 indicates the theoretical removal profile; 2 indicates.
experimental profiles. From a comparison of them it is obvious that the repro-
ducibility of the technological process is on the order of 10%. Know ledge of
this factor is very important for determining the requirements on h a rd -
ware entering into the automated system designed for manufacture of the optical
system. In particular, the same order of accuracy or somewhat better (3-S%) must
be required of the means of monitoring the surface shape and the devices removing
- the material.
Laboratory experiments in the manufacture of optical surfaces which are compli-
cated for classical technology are of special value in the Jones papers [1975, 1977,
1978]. Information is presented in Table 1.1 on experiments performed using the
CCP. The provisional numbers of the optical surfaces are presented in the first
_ row.
The part 1 was a plane mirror made of servite. Practicing opticians well know how
- complicated it is to mak.e a high-quality plane surface. The diameter of the part
was 380 mm, the initial surface at a mean square error of 0.22 of the wave length;
after surfacing on the CGP system, 0.012. The wave length was taken equal to
- 0.6328 microns. The total polishing time was 4 hours of machine tool time.
- Figure 1.18 schematically shows the course of improvement of the optical surface.
, If the relation between tl:e mean square normal deviation ~ expressed in wave
length units and the surfacing time t(hours) are represented by a function of the
type
- a = voz"f , (1.13)
the value of z characterizes the convergence rate of the technological process.
According to Figure 1.18, the value oi" z=1.34. This convergence is rarely
achieved in classical technology. In addition, and this is even more important,
such precision for a plane surface is achieved by rare masters.
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G/~L
QO�f
~
0,10
~
O,OS
O, Ol ~
O 1 2 t, y,~l~
Figure 1.18. Experiment in finishing a servite mirror.
t-- surfacing time in hours, mean square deviation of the
surface in fractions of a wave length (wave length is 0.6328
micron)
Key :
- 1. t, hours
,I
~
~ � t >
~ y ~Y } ~V '
- v J r- 1. i
_ ~ ' + Y ~ .
5
J ' , T
� F:
f T
6 ~
; d . .
~
i w
~
, Figure 1.19. Experiment in finishing a servite mirror.
a-- interferograms of the optical surface before beginning the
finishing operation; b-- inte.rferogram of the surface after
' finishing in less than 4 hours of machine time.
' The mean square error o f the surface a/80.[sic].
; Figure 1.19 gives interferograms of the initial and final optical surfaces.
From a comparison of the interferograms significant impruvement of the surface,
in the given case by almost 20-fold, is obvious. If we ass ~ne that the area
distrib ution with respect to amplitude is subject to a gaussian la~a with disper-
sion of 0.012 wave lengths, the error amplitude for 95% of the mirror area does
not exceed 0.048 of the wave length. The obtained plane satisfies the Rayleigh
number which is formulated as a/8.
The mirror 2(see Table 1) is also plane. It is designed for use in a Newton
type telescope, and therefore the shape of the billets is in the form of an
ellipse with 813 and 883 mm axes. Th~ mirror material is beryllium, the billet
is lightened to a weight of 15 kg. Pc~lishing by diamond abrasive continued for
65 hours of machine time. In order tc~ avoid the effect of removal of the edge,
the billet was placed in an aluminum ring which by using special attachments was
installed flat against the part. The shape of the optical surface was meas ured
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l~y :i Fizeau interferometer. In one p'cocedure the interferometer permitted
measurement of only part of the optical surface 760 mm in diameter. Therefore
- infurmation about the entire surface ~aas obtained by comparing three interf~ro-
grauis, and three resuperimposed sectic~ns of the optical surface were matched so
as to actiieve the least mean square difference in the common sections. After
grinding and coating of the mirror th~ mean square error of the surface was
0.4 of the wave length. After completion of the surfacing of the CCP system the
mean square error of the entire surfac:e turned out to be 0.06 of a wave length,
and on a diameter of 760 mm, 0.048 of a wave length. The interferograms of the
central part of the mirror before and after treatment are shown in Figure 1.20.
The value of z characterizing the convergence rate of the technologi�cal process,
according to formula (1.13) is 1.033.
The manufacture of th-. mirror 3, which is a correctoi�, the optical surface of
- which does not have axial symmetry is of exceptional intel~st. Tre manufacture
of this part by classical procedures is connected with enormous difficulties. The
form ot the optical surface is a segment of a Schmidt reflectirig plate, and the
material is servite. The billet has the shape of an ellipse with axes of 305 and
330 mm. After the billeting operation and coating, the optical surface turned out
to be so complicated that the applicat:ion of automated scanning of the interfero-
grams turned out to be impossible (see Figure 1.21, a) . From the mirror a plane
was made which gives a mean square deviation from the required surface of 1.56 of
a wave length. During machining on tYie CCP, the quality of the interferograms .
became so good that it became possiblE~ to use the scanning procedure. In 17
sessions with a total duration of 99 tiours, the deviation became equal to 0.17
of a wave length with a requirement of. 0.2. Figure 1.21, b shows the interfero-
gram of the completed surface. In thE~ optical control system the wave front is
- reflected from the corrector twice; therefore the distance between the bands on
the interferograms is equal to a/4.
_ ~
r ~
{
~ ~ .1,~ ~
s~~f~
A
~ ~ii `
t 1 /x ~,~;Itl
1~~!!! ; '
t f
Figure 1.20. Interfe rograms oi a plane beryllium mirror before
surfacing (a) on the CCP syste~i and after completion of surfacing (b)
The procedure for manufacturing a large flexible aspherical mirror 4 is of intsrest
(see Table 1). The shape of the optic.al surface is hyperbolic, the part diameter
is 1500 mm with a billet thickness of 90 mm. The material is ULE which has a
small coefficient of linear expansion. During the process of surfacing and control
_ the mirror was set up for unloading, :;imulating behavior of the part under
conditions of weightlessness.
28
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. -
,~f , c~
_ ~
.-p~ ~
~j/~ ~ "~,a:-~
* _ F,~r~! . t
2 v~,~,
+~~i~5~~~~`-,"""':~ ~.x'a~~
.~.A~ ~ ii~i
j .~y~�-'r"..".:~y.~ .
~ . h, 1~~~"c.. '~",~".~a-~- : ~S
r
/~I y, ~ ~ y ~ .
t .y t N
'~lis~ti` ' w^`. ' ~~t
J ,.r~ ,~,~3, s,:~
'~,j
LC ~ I ~ I l ~.~~.:Y~Q~~~ ~ F ~
r ~.r~-.:s~ ~~...~c~.~= . a
'y~ = : ~
..v .--.-..r .rec r,
L _ .--.i ~,.~w,.+;,,; . -..-:Y�
~
~ 4
� ~ � : ~ .
~ V
~
~ ..~...-.~.r-�~
-
t,=
_ ~
. .
_3 I
Figure 1.21. Interferograms o~ an aspherical nonaxisymmetric
correction plate which is a se~,~ment of a Schmidt plate.
a-- before beginning of surfacing on the CCP; b-- after completion
of surfacing; c-- model of an interferogram calculated on a
- computer for an ideal plate with some inclination of the optical
axis.
On all of the interferograms the spacing between the bands is
a/4, where a=~.6328 micron.
The studies were performed in a vacuum corridor; a corrector was included in the
optical system. The initial mean square error of the optical surface was 1.35
of the wave length, and the final~mean square error was 0.074. Here the greatest
error amplitude is achieved for the ecige of the part (see Figure 1.22). If we
exclude the edge zone from the invest:tgation, the. error turns out to be 0.059
of the wave length. The radius of curvature of the mirror in the papers by Jones
is not indicated, it is only mentioned that the surface deviates significantly
- from a plane. The total duration of the surfacing is also not presented.
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~
t:
~ ~ ~
~ ~
' t;N 4 ; ~ } . 4,~';
~~4 ~ ~ ~ ~ ~ , r ~ ~'~~~E�a~
~ v ~ir ' k ~ j:(~ ; ~ ~9t `y9~
'ri S ~y~ j~~'./yf fii'tlk~~ 1';.
( I ~ ~T
_ 1, -
/
Figure 1.22. Interferograms o:E a hyperbolic mirror 1500 mm in
diameter before the beginning ~~f surfacing on the CCP (a) and
aFter completion of surfacing (b)
2. Tool Speed Control
The tool speed vector with respect to the part has three camponents: the rotation
rate of the part on the machine tool spindle, rotation part of the tool and speed
connected with harmonic movement of the upper element.
The control of the rotation rate of the par*_ is difficult in view of the fact that
astronomical measures have great mass. For chis reas~n significant variations
of the velocity are impossible, and small variations of the velocity create a
sma11 dynamic range of regulation which leads to long surfacing time. Neverthe-
less this type of control is exercised on the START type machine tools produced
in small series by industry. As a result of absence of software for designing the
process conditions and absence of mathods of controlling the shape of the optical
surface these machine tools in practice are not used. In a number of foreign
p~tents (see, for example, [patent No 3566544, ].971]) original methods of con-
trolling the speed of the part are~described, but these methods are hardly
appticable to large products.
In the classical optical machine tool the upper element bearing the tool under-
goes harmonic oscillations. The extre~me positions of the cools are in a special
position: here the linear. velocity i~ close to zero. Even if the law o~f motion
of the upper element is varied, the edge positions of it become singularities.
In order to create the possibility of controlling the movement of the carrier it
is necessary decisively to change the kinematics of the optical machine tool;
the part must not turn on the spindle; otherwise it becomes impossib le to eliminate
local errors; speed control software must be created.
Forced rotation of the tool is most f:requently used not to control the material
removal, but to stabilize the shaping process. If we use a variable rpm to
control the removal of the material, ~the effect of directional wear of the tool
appears, which in turn, creates "crat~~rs" on the part at the points of inc�eased
removal. This effect h~s the same physical meaning as "corrugation" of parts
during zonal control of the machining time. So far as we know, no work is being
done in this area.
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_ 3. Tool Trajectory Control
`L'his procedure was implemented Uy the American "Aytek" c~ompany [A.~pdr�, et ri l.,
- 1972]. On a specially built machine t.ool permitting displacement of tt?e sma].1
tool in two mutually perpendicular directions, a trajectory is realized which
pro vides for the required removal of material. This trajectory is calculated
~ in advance by the results of the monitoring, and it is output to pim ch tape, b;
means of which the tool is controlled by the calculated t~ajectory. The method
is successfully tested for manufacturing errors up to 1 meter in diameter. In
_ several hours of finishing it was possible to obtain surface quality with a mean
square normal deviation of a/40, which satisfies the Marechal criterion [Marechal,
1947J. The classical procedures are unable to obtain surfaces of this quality
and th e surfacing time is reduced by tens of times by comparison with the surfacing
time by classical technology. �
In contrast to classical technology, j.n the CAOS/XY system the part does not
rotate, but remains stationary. The t.ool has a possibility of completing any
movements over the optical surface with constant pressure. The size of the tool,
also in contrast to classical technology, is much less than the part diameter.
As a rule, the tool diameter is 1/3 or less of the part diameter. The complete
process cycle (session) consists of the follawing steps.
1. Obtaining interferograms of the optical surface subject to surfacing. Inas-
much as only the finishing step is considered, the optical surface is polished.
2. The interferogram is scanned either manually or using an automatic device,
and then the chart of normal deviations in the entire optical surface is constructed.
The chart is digitalized so that the entire surface will consist of hexagonals
adjacent to each other. Th.e normal deviation pertains to the center of the
hexagon.
3. Using a computer, the size of the tool is calculated so that the possibility
of eliminating the majority of errors in minimum time will be created. The tool
also is represented in the form of adjacent hexagons.
4. Using a computer the time is calculated during which the tool must surface
each of the hexagons of the optical surface until the error is eliminated. The
calculations are made under the assumption of constant speed of the tool with
respect to the part and constant force of the tool on the part.
S. Using the computer, a continuous trajectory is calculated for which the center
of the tool is in the process of its movement within the limits of each hexagon
during the time calculated in the prec:eding section. The coordinates of this
trajectory are recorded successively en magnetic tape.
6. The control of the tool trajectory is realized by a special device by the
coor.dinates recorded on the magnetic tape. Then the optical surface is investi-
gated again by the interferometer, and. the entire cycle is x�epeated until the
given quality of optical service is achieved.
In Figure 1.23,a, a chart of normal de.viations is provisionally illustrated which
- was constructed using lines of equal levels. In Figure 1.23,b, a chart of the
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same surface is presented, but separated into elementary areas having the shape
oL right hexagons. In the center ~r each area, the height of the material
subjec to removal is indicated in provisional units.
After ttle size of the tool is selected, its elemental areas are assigned some
removal fim ction which is nonuniform with respect to the tool area. In Figure
1.24 a schematic model of the tool and normal deviation chart are presented; the
removal of the material for each pass of the tool over the element of optical
- surface is shown in each elemental area by the numbers. In the given example
- it is proposed that the central part uf the tool remove twice as much material as
the periptieral element. The chart of normal deviations is constructed with simu-
lation of the tool trajectory. The boldfaced line outlines the position of the
tool, and the negative numbers indicate the amount of material removed at the
given time. '
~s was mentioned, in one process session it is impossible to completely eliminate
all of the errors inasmuch as the inverse problem does not have an accurate
solution. This inaccuracy of the solution is first of all connected with the
tinite size of the tool. The solution turns out to be a fact only for infinitely
small size of the tool and infinitely long surfacing time. Figure 1.25 illus-
trates what has been stated. The normal deviation chart is shown here which,
according to the calculations, remains after the production session. This chart
must have two characteristic features: the error amplitude must be several
times less than in the additional chart; the characteristic size of the errors
must be less than For the initial optical surface. The satisfaction of these con-
ditions is an indirect indication of the correctness of the calculated session.
Tl~e final result of simulating the movement of the tool is a chart indicating how
many times the center of the tool must hit the given elemental area. Such a
chart is shown in Figure 1.25, a.
The trajectory of motion of the tool satisfying the conditions of the required
removal of the material is presented in Figure 1.25, b.
Figure 1.26 shows a photograph of tiie CAOS/XY machine tool. The white broken
line ~~as obtained as follaws. A light (the experiment was performed in a dark
facility) was fastened to the carrier, and a prolonged exposure was made during
which t}ie carrier completed the movement calculated by the computer and recorded
on mzgnetic tape twice. This machine tool permits the parts to be machined to
1100 mm in diameter. A part 800 mm in diameter was installed on the machine tool
_ (see Figure 1.26). In the front plane of the figure, the guide along the Y axis
is visible, and in the rear plane, the control unit.
- 'I'tie results of the experiments on the CAOS/XY system demonstrated high effective-
ness oF the system both with respect *_o the achieved quality of the optical sur-
face and with respect to their manufacturing times. Thus, the spherical mirrors
600 mm in diameter with a radius of curvature of 3000 mm could be finished to
the sllape the mean squarF~ error of wh:ich from the nearest camparison sphere is
,~/40. `i'he interferogram of this surface is shown in Figure 1.27. An obstruction
on th~~ ed~e amounting to 5-8% of the ~art diameter is visible on the interfero-
gram. This obstruction is obtained also when using a large tool, so that the
Gma.ll. tool does not introduce additional errors when surfacing the edge zone.
32
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.
~ u
i ~e
~ ~i ~e z
i s ~ ~ .
~ i i
a ~ i z
d b
Figure 1.23. Schematic representation of an optical surface.
a-- mockup of the optical surface (H is the local mound on the
optical surface, L is a hole); b-- digital representation of
an optical surface in the form of hexagonal elemental areas.
~ _
~ o ~ o o �i ~ ~-i �i
i i~ ai n s i e s e i
�i -z
~ , e ai ~ a a> > z ~ v �i t~-~
, 'i 'i
- ~ a ~ o ~ ~i x n a �i -i' ~ i =i
~ , i s ~ ~ s a o~ o o ~
i z o o i �i �i -i o �i
d ~
~ z ~ z o o
'b c
Figure 1.24. Diagram of the machining of an optical surface using ;
the CAOS/XY system.
a-- schematic representation of the tool (the n~bers indicate the
removal material in provisional units); b-- schematic representation
of the part and operation of the tool; c-- optical surface after
the production session
i o i ~
0 0 ~ i o
- 1 6 9 12 S 0
0 0 7 7 1 0 0
0 ~ I 0 1 f:
0 0 0 0 ~
I 0 0 0
d b
_ Figure l.'L5. Relation between the shape of the optical surface arid
the method of moving the tool in the system.
_ a-- mockup of the optical surface; b-- path of the center of the tool
calculated by com~uter
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't'~} ti}f,~a:i,~!~{'t ~"""_'i
t,h ~ ~ a' 1't
~
_z:..
i~~'E
- };s'- +t` :~:l~l~..
h{'r;
'i`
k ~ . .I
~ur ~in.`k..a.
�
_
`4 ~
~
~ 1
~~w._ ~i
' Figure 1.26. Trajectory of motion of the tool on the CAOS/XY-
- machine tool permitting parts to be surfaced to 1100 ~ in diameter.
Figure 1.27. Interferogram of a spherical surface 600 mm in
- diameter with a radius of curvature of 3000 ~(the part is made on
_ the CAOS/XY A~achine tool).
~r� ,
kt* a
~j V~l
' ~~J . 11.
S ~ 5: ~ } Rr `V III
_ ~y } I III
I I I I
-
~
Figure 1.28. Interferograms of surfaees indicating correction of
astigmatism using the CAOS/XY ~machine.
a-- significant astigmatism; b-- the same surface after surfacing
for 13 hours.
- In the opinion of the authors, the CAQS/XY system cannot demonstrate high.effective-
ness on simple spherical surfaces. The main area of application of the system is
the creation of nonspherical and even nonaxisymmetric surfaces and also elimina-
tion of local errors. Astigmatism of the optical surface of an astronomical
mirror presents special danger for classical technology.
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Q O' b
,h~
Q7ifMM a 1.~ ~eo~ ,J~
~2~0� 90� 6 . 4~s _.----a
4 4s 4s Q?
s
� 270' 9D'
Q7S Q1S 6
-6JcM 0 6BcM
- ,JO
!BO'
Figuze 1.29. Diagram of the structure of an optical surface on
an extra-axial parabolic segment
a-- chart of normal deviations from the comparison sphere;
b surface cross sections.
A11 the values are given in mm
Figure 1.28 shows how the astigmatism was reduced significantly using the system.
The left interferogram belongs to the surface having astigmatism which opticians
could not eliminate by the methods of classical technology. In the righthand
figure there is an oscillogram of the same surface after 13 hours of surfacing.
From a comparison of the interferograms it is obvious that the astigmatism is
reduced significantly, although it is not completely eliminated. Neither the
part diameter nor the radius of curvature nor the nature of the shape of the
optical surface are indicated in the article.
For certain types of telescopes and for fast cameras of spectrographs, segments
of aspherical surfaces are needed. The existing practice of obtaining them con-
sists in manufacturing a symmetric aspherical surface, from which ~egments of the
required shape are then cut. The inefficiency of this method is obvious. The CAOS/XY
system permits segments of aspherical surfaces to be made.
Figure 1.29 shows the shape of an aspherical segment. The deviation from the
- nearest sphere is about 300 wave lengths. The part diameter is 1360 mm. The
experiments were also performed on an aspherical segment 800 meters in diameter
with a radius of the maximum sphere of 5000 mm, asphericalness of 100 wave lengths,
the axis of symmetry was 75 mm from the end of the part. In both cases after
grinding, before finishing the local errors were 5-10% of the asphericalness.
I
Figure 1.30. Interferogram of an extra-axial aspherical surface
during the machining of it (the asphericalness is 300 wave lengths)
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- . - , . E;
.w.~.f. .f" ~ , .F' L"~"-'
5 '
~ . i : ~ ~
. ~ ~'er t,.. '
_ J " 3..,. ,w+"Ty" `r 'fn+'y
_ } A~-~ i.
~ s~ ~=.V.,... _
~
- .
~ ~ ~ ~
i ,
; '
Figure 1.31. CAOS/XY type mac~iine tool surfacing parts up to
- 2.5 meters in diameter
Figure 1.30 shows an interferogram of a surface with asphericalness of 300 wave
lengths obtained during the process of finishing.
Figure 1.31 shows the CAOS/XY machine tool permitting parts up to 2500 mm in
diameter to be surfaced. A sy~netric aspher.ical part 1000 mm in diameter was
made on it; the mean square error of the final surface was 1/10 wave length.
A still more important system for finishing astronomical mirrors was proposed by
another American company "Perkin Elmer" [Jones, 1977]. Here, a computer was
included in the control circuit, that is, the realization of the trajectory
originated with the computer.
The decisve advantage of the described systems is the possibility of eliminating
local errors and also the manufacture of parts of complex asymmetric shape, for
example, extra-axial paraboloids. The only, but very serious deficiency of this
system is the necessity for manufacturing a special optical machine tool.
- The manufacture of the special optical machine tool or special tool is a
necessary condition of realizing all of the cont rol methods described above.
This fact greatly complicates the application of these methods in industry inas-
much as two difficulties arise here.
The first of them is of an economic nature and is connected with the necessity
for replacing the machine tool fleet of industry which leads to large expenditures
of time and resources. These expenditures are paid for, but the return time is
large in connection with the enormous organizational difficulties. A second
difficulty is of a psychological nature, and overcoming it can turn out to be
even more complicated. The fact is t:bat in the "last decades optical machine tools
have changed little with respect to structure; the master opticians have become
accustomed to them atid have accumulated a great deal of experience in handling
them. If the machine tool fleet is replaeed by unfamiliar machine tools the
- accumulated experience is lost, and the necessity arises for retraining the
practicing opticians. This again requires great time and organizational
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expenditures and can greatly reduce the production output in the optical indus-
try for several years.
4. Control of the Tool Force
At the Leningrad Institute of Precision Mechanics and Optics an attachment has
been built which permits smooth variation of the force (pressure) of the tool on
- the part. The attachment is shown in Figure 1.32 and is Get up as follows
[Rusinov, 1973]. The optical part 7:is rotated on the spindle of the optical
machine tool. The grinder 8 is conne~~ted by a ball hinge 6 to the carrier 1 whi.:h
undergoes oscillatory movement. The shaft of the carrier 1 is suspended on the
carrier frame 4, which permits the grinder to rub freely against the optical sur-
face. New elements in the optical ma.chine tool are the weight 2, which perm;its
the creation of a constant force of the tool on the part which does not depet~d on
- the tool position; the second arm 3'~aith weight 5 attached to~it. During rocking
of the carrier, the arm of the weight 5 changes, which leads to variation of the
pressure P of the tool on the part by the law
A
P B+e+C, (1.14)
where the constants A, B and C are related to the masses of the weights 2 and 5
' and also to the arms of the levers in the system, e is the eccentricity, that is,
the shift of the center of the tool with respect to the center of thA part.
'L'tie control of the removal of the material using this device is possible only for
a special case. An analysis of formula (1.14) and conclusions of a general
nature contained in the book by Rusinov [1973, p 286] remain valid only in the
case where the machine tool function is equal to one for any value of the eccentric-
ity. For real optical machine too]s this is not done at all. In addition, non-
r,ionotonic errors characterisic of astronomical optical systems cannot be elinr-
inated even if the machine tool function is equal to one. We are primarily ta~k-

, ing about local errors without symmetry with respect to the center of the
p art . ~
4
' .,,1IINIII '
/�i~i s
.
/~6 , ~
! ~I~
2
~
B .
Figure 1.32. Device for monotonic variation of the force of the tool
~long the oPtical surface zone3.
1-- lever; 2-- weight; 3-- second lever; 4-- carrier frame;
i-- weight of the second leve�r; 6-- ball hinge;7 rotating part;
I, II extreme positions of the lever; 1, 8-- grinder.
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9 ~
_ ~ ~
r s I~I
~
Figure 1.33. Lever device for programmed pressure on the optical
surface zones '
- 1-- grinder; 2-- lever; 3-- ball hinge; 4-- weight; 5-- rotating
part
In formula (1.14) tlie value of e changes sign when the tool passes th ~ough the
center oE the part. An elementary analysis of fo nnula (1.14) indicates that the
radius of curvature of the part must increase in the surfacing process if it is
concave and decrease if it is convex.
In the book by Rusinov [1973] another method of controlling the force, digi-
tally, is described. The diagram of this device is shown in Figure 1.33. The
_ grinder 1 which is connected by a ball hinge to the lever 2 is installed on the
rotaCing part 5. One end of the lever 2 is fastened to the bearing so that the
lever can turn around the horizontal axis, and the weight 4 is fastened to the
other end of the lever. The magnitude and position of the weight 4 determine the
force of the tool on the part. It is possible to install several grinders of
similar type in various zones on the part, thus insuring programmed removal of
_ the material.
By this tool it is possible to eliminate any axisymmetric errors and apply differ-
ent asphEricalness. However, each of the tools will be directionally worn,
which leads to "corrugaticn" of the optical surface. In addition, the procedure
will not permit elimination of local errors. ~
In Soviet industry a tool has been being developed for many years which will
permit programmed variation of the fo.rce of the tool on the part using hydraulic
devices. The structural principle of the multielement tool is used [author's
certific:~te No 2186$7, 1968; author's certificate No 370014, 1973; author's
certiEicate No 360199, 19 72].
A diagram of the tool appears in Figu~re 1.34. The surfaced optical part 2 is
rotated on the spindle of the machine tool. The working elements 1 are connected
by ba11 tiinges to the pushers 3. The pushers can be displaced inside the
cylinders installed in a flexible diaphragm 4. In the upper part of the tool 5
cylinders are installed ~aith a liquid which regulates the magnitude of the
pressure of the tool 1 on the part 2. The tool does not rotate, b ut undergoes
oscillatory motion. For connection to the hydraulic devi.ce, flexible hose 6 are
used. There can be several operating elements. The device operates only if the
upper p art of the tool 5 is attached ;~o th at it has no freedom of movement along
the normal to the optical surFace.
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6 l .1
/ S 1
~
~
~
\ ~
` ~ ~ ~ ~
~ ~
! Z
- Figure 1.34. Diagram of -the t~ol permitting variation of force
in the surfacing process.
1-- operating tool, 2-- surfaced part, 3-- pusher, 4-- diaphragm,
5-- upper part of the tool, 6-- flexible hoses
It is possible ~o use the tool (see Figure 1.34) for axisyffinetric remo.val of
material. A deficiency is the impossibility of eliminating local errors. In
. addition, the system has one specific deficiency charact~ristic of multielement
tools, the working elements of which have~ different load. The fact is that
variation in load on one of the working elements leads to redistribution of the
load on the remaining elements which leads to instability of the development of
the forces. Theoretically the described element can also be used to eliminate
local errors. For this purpose it is necessary to install a sensor of the rota-
- tion of the angle of the optical part and use a computer to execute variable
forces on each of the tools in time. However, the hydraulic drives h ave law
speed. This leads to the fact that the f.orce will not be executed where needed.
Therefore the hydraulic drives must be replaced by electrodynamic drives, the
speed of which is one or two orders higher.
In one ot the first attempts to control the removal of the material by varying
the pressure [Dvornikov, et al., 19i,0] the control effect was not achieved. The
cause was that a f ull sized tool was used. It is obvious that in the pressure
control mode, just as in any other lo~~al retouching mode, it is necessary to use
a small tool, the theory of the application of which was developed in the papers
by Lysyannyy [1972, 1974] and Semibra,*_ov j1958]. The proportionality of the
removal of the material to the applied force has been checked more than once
[Kachalov, 1958J.
[Je have stated the following problem. By using local pressure control of the
small tool on the part in real time aitd using an ordinary optical machine tool,
let us obtain the possibility of making high-precisio~ optical surfaces, including
extra-axial, aspherical surfaces. SL-rictly speaking, the degree of complexity
_ of the optical sur~ace in our statement of the problem has no bearing on the
- technology inasmuch as for realization of tfie production we must know only the
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tolerznce of the part h(x,y), that is, the difference between thetrue and the
required shapes of the optical surfaces. The information about h(x,y) is
obtained in the contro]. subsystem.
In ord~r. to solve tlie stated problem ~_n accordance with (1.1) it is necessary
to create a force P(x,y) in real time according to the law
P~X.Y) =h ~x,Y)IKT~G~P)~ (1.15)
where p is the currenr. radius of the zone on the optical surface, the function
~,(p) determines the removal of material with constant pressure (hereafter, the
machitie tool function), K is the process constant (see (1.1)), T is the surfacing
time.
Formula (1.15) is accurate, but under the assumption that the size of the tool is
much less than the diameter of the part. In practice the tool has finite dimen-
- sions. However, the performed experiments in the case of this restriction turns
out to be insigniL-icant, and the given~approximation can be successfully used.
The size of the tool can be considered, b ut in this case the calculations of the
process conditions become so awkward that the necessity arises for using expensive
large computers for many hours of computation.
The most important adva:itages of the f'orce control method are the following: the
possibility of automating any series aptical machine tool without significant
modification of it; the use of an ordinary tool in the form of a free lapping tool;
si~ licity of automation with the application of a computer both in the adviser
mode and in the control mode; possibility of servicing parts of as complex a shape
' as one might like and elimination of the types of errors, including local errors;
as a result of classical kinematics the "corrugation" effects connected with the
application of a small tool are absent.
When using the given control procedure, as a result of convergenc~ of the sh aping
process, accelerat~.on of the finishing operation by tens of times is achieved,
and the possibility is created for ~mproving the shape of the optical surface by
several times by comparison with classical technology [Prokhorov, et al., 1978,
1979].
5. Req uirements on Automation Hardware
The most astonishing feature of optical technology is the possibility of creating
exceptional surfaces with respect to precision, using comparatively rough machine
tools. The same comment applies to the hardware which is used in the ZEBRA auto-
mated system.
Let know the normal deviations h(xry) of the existing optical surface .from the
reqt~ired surface where x,y are the coc,rdinates on the optical surface. Let the
no rnial. deviations be stored in a compiiter memory. Let us consider the requirements
on the hardware permitting eli~mination of the indicated errors by progaimned
alteration of the f.orce.
In addition to the ordinary optical inachine tool the hardware must include the
. following devices:
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Tool center position sensors with respect to the coordinate system on the
optical surface; one of the sensors dc~termines the current angle of rotation of
the spindle, and the othe-, the carrier;
A pressure (force) gauge for the tool on the part;
A servomechanism whict~ permits the fo~-ce of the tool on the part to be varied
in real time;
A control unit in which information is stored about th e relation between the
coordinates on the optical surface and the code of the servosignal. The control
lmit, the role of which can be played by the control computer, combines the
position sensor and pressure gauge and the servoelement of the system.
A common requirement an all of the elements of the automated system is sufficient
speed. Let us d~termine this value as fol~aws. Let vm be the maximum admissib le
speed of the tool with respect to the part. This speed exists inasmuch as it is
l:nown [Krupenkova, et al., ].973J that with an increase in speed the removal of
material begins to increase, and then it decreases sharply. Then let us assume
that the optical surface is characterized by a mean size of the irregularities Q.
Then the speed of the automated systera (the time constant) is defined by the
inequality
Trma]. profi:le alon~ two mutually perpendicular diameters of the optical
~~urfacE~; in the :I.eCthand column, for the horizontal diameter, in the righthand
column, for the vertical diameter. 0~1 the printout only the first three values
of the normal deviations are presented, but there should be KT of them.
'I'he~ program then prints out the values which it calculates. The table called the
ERROR DISTRII3LITION FUNCTION BY SIZE contains the size of the error expressed in
mm in the lefth and column, and the probability of an error of this size in the
righthancl colu~. In the given ease ~he errors of 15 mm are encountered in SO%
of the cases, 30 mm errors in 31.8% o.f the cases,and so on.
The recommended size of the tool is 27.3 mm. The printout is printed for a model
example. ~1hen surfacing 300 mm spherical and parabolic mirrors reconanendations
were made for a tool size in the range from 50 to 100 mm. Before beginning work
c,~i the part, we manufactured two tools: one 100 mm in diameter and the other 50 mm
in diameter. The reco~anended tool size was rounded to the nearest of these two
- numbers, and the corresponding tool is used. For the majority of cases the 100 mm
tool was used.
The program calculates ksmooth~ in the given model example it is 0.5. If it
turns aut to be negative, a message is printed out which is given in the printout:
CONCLUSION: INVESTIGATF.D SURFACE NONSMOOTH. This message forces the optician to
think about many things. We have already discussed the importance of such a
nx.ssage, but we shall repeat the basic principles again. On the technological
level the nonsmooth surface cannot be significantly improved by a tool, the diam-
eter of which is greater than the sizes of the irregularities. Nevertheless, in
c.lassical technology there is a procedure for smoothing small irregularities.
'lhis procedure consists in using a full-size polisher in creating small specific
for.ces on the order of 1 g/cm2. This procedure is not excluded even when using
an automated system. This is all the more the case in that a small tool sometimes
emphasizes small errors or even creates them.
On the level of quality control of the optical surface when there is nonsmoothness
of it the situation can be created where the Hartmann method used here will in-
adequately describe this surface. In this case the results obtained by the
Hartmann method must be duplicated by another method having better resolution with
respect to the surface of the part. For example, it is possible to recommend the
Foucault-Philbert method which gives resolution an order better than the Hartmann
method.
Tlie nonsmoothness of the bptical surface has sig~ificant influence on the
approacl~ to the analysis of the dispe.rsion circle. If the error is small in size,
~ hut the derivatives on the optical surface are large, the geometric approach to
calculating the dispersion surface can give nonreproducible and inadequate
~ res~ilts. When calculating the disper:~ion circle by the wave methods it is impor-
_ tant to know tfie correlation radius o:c the surfar_e errors. With a small correla-
tion radius it is necessary to break down the optical surface into small ele-
mt~ntal areas which leads to large voltunes of calculations.
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Conclusions
T'he software of the automated system clesigned to finish astronomical mirrors
solves three basic p roblems. First, t_fie calculation o~ the process conditions
based on the data on the shape of the:optieal surface. Secondly, determination
of the process constants and the proeHSS functions, without the knowledge of
which it is impossib le to control the shaping process numerically. The process
conditions in the proposed control procedure are the forcP vector on the zones uf
the tool and the duration of the processing session.
By the process constants we mean K defining the absolute removal of material at
the center of the part per unit time by a imit force, and the machine tool func-
tion ~(p) giving the dependence of the relative removal of material on the
part radius.
The process constants can be more precisely determined during operation by con-
sidering the systematic corrections.
Thirdly, in the system the size of the tool is defined as the average size of the
- irregularities of the optical surface, and the degree of smoothness of the optical
surface is investigated. The last characteristic has important significance both
in technological aspect and when solving the quality control problems.
The software presented here cannot in any way be considered the only possible
or the complete software. It is possib le to propose a set of versions of the
systematic approach and also an entire series of areas of further development of
the system.
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CHAF'TER 3. EXPERIENCE IN WORKING WITT3 THE ZEBRA-1 AUTOMATED SYSTEM
Improvement of the quality of astronomical mirrors and shortening the time
_ r.equired to manufacture them are basic goals of astronomical instrument making
[Prokhorov, et al., 1978]. There can be only one way to solve this problem
the development and assimilation by industry of automated methods of optical
technology and the application of object~.ve quantitative methods of controlling
the shape of the optical surface and the dispersion circle created by the astro-
nomical mirror.
At the Space Research Institute of the USSR Academy of Sciences a prob lem labora-
tury for the development and introduction into industry of digital methods of
the control and manufacture of astronomical mirrors was created. The ZEBRA-1
_ automated complex was created. The c~mplex includes a procedure for quantitative
control of the shape of the optical surface of an astronomical mirror based on
the Hartmanii method and a technological subsystem which permits the u.se of digital
procedures to improve the shape of the optical surface. The system also includes
software described in the preceding chapter.
The experimental laboratory versions of the ZEBRA-1 system were developed, put
together and passed laboratory tests in 1975. In December 1976 this system went
into trial operation at several enterprises of the country.
_ In all of the organizations special groups of coworkers were created who partici-
pated actively in the development of the automated system. The introduction of
tlle development is taking place simultaneously with the development process.
_ 'rhis path reduces the time interval between completion of the development and its
assimilation by industry to a minimum. In.ad~ition, the joint work is generating
:in atmosphere of mutual understanding and permits the developers to consider the
level of modern production. The accumulated positive experience of the joint
work can certainly be recommended for application also in subsequent steps of
the development of automated systems.
Introduction
T_n industry there are many years of experience in the automation o~ the process
of shaping an astronomical optical system. It is esper.ially necessary to note
thc~ works of the schools of Semit~ratov j1958, 1962, 1970, 1972, I973, 1975] and
'Csesnek j1970]. The mcst signi~icant deficiency of the available development is
~ absence of quantitative methods of centrolling the st~ape of the surface. This
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~~rob l.em be~;1n to be given attention otily in recent years. It is quite clear that
without inEormation about the real su~cface it is impossible to develop an
autumated technological process. In the ZEBRA system a closed "control-m,~nuEac-
r.ure" cyc~le is realiz~d by using digit:al and analog equipment.
~nr,~f~er ~leficiency is the "mechanical" approach to the automation problem. With
this ~~~~proach optimal machine tools are 3eveloped which have a great variety o'=
- kinematic possibilities, but how to realize these possibi'ities for the control
of the removal of material remains unclear. Another version of the mechanical
approach is the creation of inechanical templates or tool.~ of complex shape.
The weak software of the production cycle is a large brake on the development ~~f
the automation of optical technology. In essence, the computers are used only to
calculate the shape of the mask.
'Ct~e most significant step along the path of automating the shaping process was
creation of the START and PLANETA type machine tool. In the START n:achine tool,
provision was made ror the possibility of varying the spindle speed as a function
of the position of the tool center with respect to the part center. As a result
of the fact that the contro'1 of the START machine tool is not provided with soft-
- ware and the machine tool is produced in small series, it has not beoome wide-
spread.
In the PLANETA type machine tool [Kuk;;, 1980], a special tool is used which is
made in the form of radial springs, tYie tension on which can be adjusted, thus
creatin~ the possibility of variation of the shape of the lapping surfaces. For
evaluation of the "corrugation" effect the tool is given oscillating movements
- of small amplitude. This machine tool also has failed to become widespread for
the same reasons as the START type machine tool.
The fact of the production of machine tools on an industrial level itself, the
Ilardware for the controlled process of manufacturing aspherical parts indicate
the urgent necessity for solving the automation problem.
- Above, tlie creation of automated technological systems for the manufacture of
large optical parts has been given a great deal of attention. The American
comPany "Aytek" has developed an origa_nal system which permits the manufacture
- ot complex optical surfaces with great- precision in a short time [Aspden, et al.,
]972]. Another American company "Perkin Elmer" has built a still more improved
system [Jones, 1977]. In both cases the technological process is computer-
controlled in real time, a quantitative interferometric control of the shape of
the oPtical surface is provided, and the systems software has been developed.
'I'l~e 'LI:BRA-1 system was developed by tFie Space Research Institute of the USSR
~cademy of Sciences in close cooperat~.on and with the participation of indus-
- trial enterprises. The general direct:ion of this work was by the Division of
Gener.al Physics and Astronomy of tfie IISSR Academy of Sciences. The electronic
_ part o� the ZEBRA-1 system was develoF~ed and implemented ~ointly with the
Izt~evsk Mechanics Tnstitute. The prograFnming of the software was basically done
I~y the University of Friendship of Peoples imeni Patrice Lumumba.
~ 73
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~-c;u ~.;t~ ~~~ci.at_ t ~~N: o~t.~~
1. Technical Description of the ZEBRA-1 Sy~tem
_ Tn this section a description is presented of the hardware used for implementa-
tion ~f the ZEBRf1-1 automated system jauthor.'s certificate No 701773, 1979].
'1'he system is designed for axisymmetric controlle:d removal of material.
Tl~e b ~
~ ~
S
9
d
~ ~n
000
I~igure 3.6. Circuit diagram of the force gauge (P measured force).
1-- AC generator, 2-- elastic element, 3-- measuring coil,
4-- ferromagnetic core, 5-- remagnetizing coil, 6-- amplifier,
7-- quadratic detector, 8-- time interval shaper, 9-- discharge
sliape r, 10 comparison circuit, 11 binary-decimal counter
Tn tl~e '/.EBRA-0 system when studying the time characteristic, a clamp is used
cl~~si~;necl For maximal forces of 3000 kg. In the ZEBRA-1 system the clamp was
dcsi~ned for 1000 kg; therefore the time characteristic of the ZEBRt~-1 system can
h~~ het te r.
I I~~~riiig prolonged testing oE an analoQous gauge it was discovered that it is impossi-
- t~lr tt~ use it as a result of its time and temperature instabilities. The
c~l~ctrc~nic part of the gauge is constructed on the principle of ineasurinR a direct
~~urrent, and the deficiencies of this ;~rinciple are generally known. This forced
c~nver5ion to the induction type displacement sensor which is free of time
instahilities.
Tn the dibita]. gauge the force is measured by meastiring the deformation of the
c, 1;~tn1,. This deformation l.eacls to variation of the distan~e hetween thc~ indr~ction
~~c~i 1, rulcl the e?.ectronic circuit of tTir~ sensor �ixes the inductance variation in
- t-iic~ Corm of code and analog signals. Tfie analo, output makes it possihle to use
- ~~ii~ital volt~neter for indication of the force, and the code output ptrmits the
~;~~u~e t~ be connected to the computer through the interface card. The possibility

_ of creatinh feedback with respect to the force arises.
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Ft~Et Od~FlC[:1f, [ SE: O~LI'
In V~ i~;ure 3.6 we liave a schemati:c diagram of the electronic force gauge [author's
certificate Vo 717571, ]980]. The system operates as follaws. The output
~~urrent of the generator 1 passes thr~~ugh the magnetic wall 3 and creates a
periodically varying ma~netic field, as a result of which the ferromagnetic core 4
is remagne~ized. Let us consider the case of the absence of a load P on the
clastic element 2. In this case a preliminary load on the core 4 is created
cis a result of the tension of the ele~nent 2. The emf pulses induced in the
r~magnetizing winding S are amplified by the amplifier 6 and go to the quadratic
detect~>r 7 and the time interval shaper 8. The spike shaper 9 brings the signal
to sc~me selection level. `rhe formed ~~ulses go to the input of the comparison
ci_rcuit 10. The signal from the ampl:ifier 6 also goes to the detector 7, which
incl.uctes a smoothing filter. From th~~ output of the detector 7 the signal goes
to the time interval shaper 8 which c~~mpares the voltage of the envelope with
some standard voltage and shapes the ~_ime interval during which the envelope
voltage exceeds the standard voltage.
The standard voltage and the initial tension of thE core 4 are selected so that
whe~ P=0 the length of the time interval will also be zero. Then P=0 the readings
~~f the counter 11 are also equal to zero, for the comparison circuit 10 is closed
hy the corresponding attention of the shaper 8.
I~or P~0 the vo"itage in the core 4 decreases as a result of bending of the elastic
element 2, ttle signal power from the remagnetizing winding 5 increases, the
envel.ope voltage increases and the pulse duration from the output of the shaper 8
increases. Correspondingly, the number of pulses reaching the counter 11
increases. Befor~ the beginning of the measurement the counter 11 is automati-
- cally set to 0 from the generator 1. The two law-order decades of the counter 11
are not indexed, and they are used as frequency devices. The dispersion of the
~lumbcr of spikes dues not exceed the ~iniformity of the two low-order decades and
cloes not influence the counter readings. ~
'fhe hasic advantage of the investigated device is absence of an analog to digital
conver~er which introduces its own errors. Another advantage is the functional
tlexihility. By varying the selection level and magnitude of the standard
voltages it is possible to obtain different characteristics of the gauge and
:;elect those which are most acceptable for the given operating con ditions. The
haut;e is easilv connected to a computer which makes it irreplaceable in the
'I.LBit~1-2 system.
- 7'lie technical specifications of the implemented force gauge are as follows:
Operat:in� ran~e of ineasured for.ces 0-50 kg
I:lasti_c element displacement 30 microns '
Outpur code binary, parallel, six-bit
Cn f:ormation update time 30 microns
1'ower +5 volts +12 volts
P.educed relative error. no more than 2%
80
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(~OR OI~FICIAL C!SE: ONLI'
( 3) N~.
F/ T1 NI CT2-2 i9C! , i9G1 y3 V~
A 4 y / Y Y o0
; V6
T2 y Y
- R c G
c
U~.
S/ SZ GZ F4
~
3
1
~ ' D
1
e ~
~1) ~rz-~ Fz y~ ---A~2~z F,~ ~
Figure 3.7. Functional circuit diagram of the force gauge.
C1 master oscillator; STR-1 bi.nary counter; F1, F2
shapers; Y1-Y3 amplifiers; Tl, T2 triggers; RG1, RGZ
registers; Sl, S2 pulse shapers
f:ey :
1. ST2-1 3. AND1
_ 2. DP
The functional circuit diagram of the force gage is illustrated in Figure 3.7.
1'he quartz-stabilized master oscillator G1 generates s square pulse train with
a frequency of 8192 kilohertz. The si.gnal from the oscillator G1 goes to the
ST 2-1 light-bit binary counter used here as a frequency divider. The counter
- output is connected to the pulse shapE:r input F-2, the circuit of which contains
a low-frequency filter with cut-off f~requency of 35 kilohertz. The shaper F-2
creates a sinusoidal voltage with a fz~equency of 32 kilohertz which goes from
its output to the shaper Fl and the amplifier Y1.
The o~itput of the amplifier Yl is coniiected to the primary windings of the
deforniation gages. The shaped output voltage goes to the input of the trigger T1.
A reference v;,ltage is fed to the inpiit R of this trigger from the outp ut of the
shaper F1. The pulse duration at the output of the trigger T1 turns out to be
prop~rtional to the output voltage phase of the sensor shown in the figure by a
dotted rectangle.
A r~f.erenc�e voltage goes to the input C of the trigger T2 from the output of the
~hr.ipE,r F1. The output signal o~ the t:rigger T2, che frequence of which is
1f kilohertz, is used to control the 5T2-2 counter. Signals go to the comparison
~~ircuit AND1 from the outputs S1, T1 and T2. The signal from T2 realizes a
forhid for one period of the reference voltage, which is necessary to increase
the reliability of the circuit. From the output of the ANDl circuit, b unches
o C pu] ses are picked iip where the numt~er of pulses in the bunch is proportional
to the phase oF the voltage picked up from the sensor.
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I ;;tt 111~E'!('1A1. i~tiF: O\1.1'
'I'he bunch aF Puls~>s goes to the input of the six-bit binary counter ST2-2,and
~hen rhe hinary numher is entered in rarallel code in the register RG1 (the
r,i~;nnl:: X1-:;6). '1't~e write pulse is st:aped by the circuit S1, and the pulse to
c~lear rhe cuntents of the counter ST2-2, by tne circuit S2. The contents of the
rc};i st c~r I:C I go thrc,~i~;h the n~miber huse5 to the P4-6000 control computer (the
:;I~~,nr~l~ Y1.-YG). 'Che ~utputs af the register RC1 are also connected to the display
register RC2. ThE~n the logical levels Zl-Z6 go through the amplifier Y3 to the
light diodes Vl-V6. The entry is made in the register RG2 by a pulse from the
~;enerator C2, the (requency of which is 1-2 hertz. This frequency is selected
for convenience of visual monitoring of the readings of the light diodes indexing
the Eorce in binary code. The signal from the output of the trigger T1, the off-
duty factor of which is proportional to the phase shift, goes to the shaper F4
_ which includes the mean value detector. The output voltage is proportional to the
duration of the volts from the output T1 and the phase shift.
~
~
_ L
_ ~I -
~
~
_J
r~
rigure 3.8. ~xample of recording of forces by a pen recorder.
rorce amPlitude is 5 kg; Tl, T2 time resolutions of the leading
~ind trailing edges in a square pulse (the wiggles are connected with
the pen recorder)
ln th~ present execution of the sensor there are two deficiencies. The first of
them is insufficient dynamic range. The actually built sensors have a range of
- al~uut 5 which ] eads to great di Eficulties when calculating the process conditions.
It appears to i~s t}iat this deficiency can be eliminated. Another deficiency of
tiic sensor is unsuccessful mechanical reinforcement of it. As was discovered during
tt~e operziting process, the readings of the sensor depend strongly on the late ral
l.~ads un the tool. This is no accident; the DOSM type gauge is not designed to
- work uncler dynamic conditions. The way out of the situation is obvious: trans-
nut thc Corce to the gauge through the guides which take the lateral loads. It
is ~>c~ssible to propose another way out: replace the bracket of the DOSM by
devices which do not have deformations in the vertical direction imder lateral
lo~~ds. Such devices have been developed.
- ~n e~:.~mi~ 1e oE ~i recording of. forces obtained under operating conditions is pre-
Senred in Figure 3.8. A.force o~ 5 kg was assigned �or one of the zones of the
part. '1'he for~e t~uilcls to hal~ its rated value in a time on the order of 0.02 sec.
'1'hen cnnertc~d with the pen recorder. When removing the force, the decay time to half
amPlicude tai:es 0.06 seconds. It turns out that this delay is explained by the
mech~~nic.il inertia of the DOSM bracket. All of the remaining elements of the
forc~~ p~rt of the 7EBRA system have characteristic times of less than 0.01 se cond.
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rou o~~FICIAL USF. ONI_1"
I)tiring continued work with the force ~auge it was discovered that its readings
d.ifEer depending on the direction of n~otion of the carrier by '_0-30%. This
effect is connect~d with the influence. of lateral loads on the bracket of the
DOSM, which complicates the ad~ustment of the machine tool, but tfie development
of the forces takes pla~:e correctly.
The next important element of the ZEBT:A type system is the force servo. The
variable force of the tool on the part is progra~ed in t1-_ svstem. As the
device executing the force, a vibration electrodynamic stand (V~DS) which is
series manufactured industrially is u~ed. The stand is designed for vibration
testing of instruments; it is used as the force control element in the ZEBRA
system. For conversion of the device to a force element, a rectifying bridge
and smoothing filter are installed in the output signal circuit.
_ The use of the VEDS type device in an automated system as a force element opens
~lp broad possibilities for automating many types of optical machine tools pro-
duced industrially. These devices are made inversions with maximum forces from
10 to 1400 kg, which is sufficient foz� making astonomical mirrors of in practice
any climension. For the VEDS type device the two basic advantages over the force
~yst~m of the ordinary optical machine. tool are speed and simplicity of control.
"L1ie speed is provided by the electrodynamic principle of the force element. The
pneumatic drives used in optical machine tools have a time constant in the
ranbe of 0.1 to 1 second. The industrially produced hydraulic drives with
appropriate power at the output have a. still faster speed.
Tiie simplicity of controlling the VEDS is connected with the fact that the VEDS
i5 �
~ ~ / ~
4 \ z Jf~
/7 ~ \ y : /
- /6 S � ' 9
6 O~n ~a aa
~a~ s 6
- ~ I + y !1- Om>
~
, /.f ~ - - Nacoca
/4 ~ B I ? , ' J~ \1B
~ ~8~ !
~ ~ I 9 0~ naccr
~
!3 I .
' % /S ; !f~
� ~P ~ ~ !J'
!0 /6
1I ~ r +?y X
- _ 1O ~
Figure 5.7. Diagram of the spindle Figure 5.8. Diagram of a machine tool
assembly of a machine tool. with cylindrical hinge.
Key: a. from the pump Key: a. from the pump
As a result of the addition of the rotational and the reciprocal motions the tool
10 describes a curvilinear trajectory in space . The parameters of the
latter, which are determined by the amount of misalignment of the spindle shaf t 9
- with respect to the center of t he hinge 3, the radius of rotation of the t4o1 10
and the angle of inclination of the standard surface 5 to the spindle axis 9, is
selected so that this trajectory will coincide with the f lat cross section of the
machined surface passing through its apex. On communicating the indicated movement
to the billet and the tool and selecting the parameters of the trajectory of motion
of the tool, we obtain all of the conditions of shaping aspherical surfaces with
given parameters. The constant condition of clamping the spindle 9 with the tool
10 to the hinge 3 is insured by pressure of the liqu~.d on the shoulder 8 of the
spindle. Compressed air or gas can be used instead of the liquid to feed the
pockets 2, 17 of the ball hinge, the bearings 13 and 15 of the spindle and also to
clamp the spindle 9 to the hinge 3.
- In a number oF cases, predominately for machining large parts, a tool spindle
bearing a tool, for example, a grinding disc and a drive for it, can be installed
- on the spindle. Figure 5.8 shows the schematic diagram of the machine tool which,
- retaining the advantages of the preceding system, permits expansion of the range of
machined surfaces and elimination of ttie systematic errors in the surfacing. This
- is achieved by replacement of the ball hinge by a cylindrical hinge, the axis of
rotation of which is parallel to the a:cis of rotation of the tool spindle and by
creation of additional translational motion of the tool spindle to correcr the
prof ile erors.
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1 LY
- /~clcl 1 L i~m~i L ulUVUmciiL is created by vary:~nb the gap in the hydrostatic thrust bear-
i~ib oE ttie cylindrical hinge. This var.iation of the gap causes axial displacement
- ofi thc hinge, and the tool spindle togc:ther with it. The control of the additional
clisplacement can be connected with rot.ition of it and the systematic error.
In addition, a mechanism has been intr~~duced into the machine tool which can shift
the tool to any position within the liinits from 0 to 180� with respect to the tool
spindle axis, which permits variation of the direction of the axial motion of the

_ tool during the machining of the part and obtaining a nonmonotonic surface on it as
a result.
Let us consider the schematic diagram of the machine tool. In the housing 1(see
}?igure 5.8) of the spindle head, the spindle 4 is installed in the hydrostatic bear-
ings 2 and 3. A templet 5 with standard plane 6 is attached to this spindle. The
plane 7 conjugate to ttie plane 6 belongs to the cylindrical hinge 8 which is in-
stalled in radial hydrostatic bearings 9 and 10 and is supported on the hydrostatic
tlirust bearing 11.
Tlie planes 6 and 7 are separated by a hydrostatic layer of lubricant 12. The con-
~tant clamping of the spindle 4 against the cylindrical hinge 8 is realized by the
oil pressure on the shoulder 13 of the spindle 4.
A faceplate 14 is fastened to the free end of the spindle 4, on which the device 15
with the tool 16 is installed. The latter is located at a given distance from the
e~>indle axis 4. Rotation of the spindle 4 is realized from a rack type mechanism
- driven by the cylinder 17. Simultaneously with rotation of the spindle 4 the
cylinder 17 can act on ttie correcting device 18 which regulates the flow of liquid
Erom the pump to the thrust bearing 11. In accordance with the ~low rate of the
liquid in a thrust bearing 11, a defined gap is established.
Tlie billet 19 is fastened to the spindle 20 and is turned from a drive.
The machine tool operates as follows. In accordance with the given equation of an
- asptierical surface and the diameter of the surfaced part, the parameters of the
surFacing system are established:
1) the angle of inclination of the spindle 4 to the axis of rotation of the machined
- part, 2) sliif ting of the templet axis, 3) the radius of rotation of the tool, 4)
angle of turn of the tool attachment 15 with respect to the face plate 14.
- Trial surfacing of the part is carried out, and then its profile is checked. By
tl~e magnitude of the deviations from the theoretical profile a program is compiled,
For example, in the form of a former, for the correcting 18, and it is introduced
into this device. The program is user. to compensate f or the surfacing errors. The
cylinder 17 of rotation of the spindlE~ 4 matches the signal speed from the correc-
tin~; clevice by the amount of the axial. displacement of the cylindrical hinge 8
_ with t(ie angle of rotation of the spir.dle 4.
_ In this case the spindle 4 will simultaneously take two axial displacements: 1)
as a result of slipping of the standaY�d plane 6 with respect to the eccentrically
arranged surface plane 7 of the cylinc~rical hinge, 2) as a result of axial shift
of tYie cylinders 8 with variation of t:he clearance in the thrust bearing 11, in
accordance with the signal from the c:orrecting device 18.
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'L'he5~ two displacements are summed on the tool 16 providing it with complex tra-
jectory of motion which will be transft~rred to part 19 during its rotation.
1'lie precision of the shape of the mach:ined aspherical surface depends on the pre-
cision of all of the servomotions and c~specially, the clearances in their mechanisms.
In order to exclude the play and insure high precision of rotation, the bearings 2,
3, 9 ancl lU are made hydrostatic or aerostatic, which permits their use, in addition,
as guides for axial displacement of thta spindle 4 and the hinge 8.
On turning the spindle 4, the hinge 8 must also turn for self-adjustment of the
plane 7 with respect to the plane 6 of the templet S. In order to facilitate this
turning, the angle of inclination of tl.le plane fixed to the spindle axis is made
equal to 45�.
'rhe constancy of the clearance 15 is determined by the constant force of clamping
- ttie spindle 4~against the hinge 8 realized through the shoulder 13 of the spindle.
The mact~ine tool permits complex and concave aspherical surf aces to be machined
with a diameter to 300 mm with controlled parameters of these surfaces within the
ranges of p from 20 to 2000 mm, and e from 0.1 to 5.
2. Finishing and Asphericalization of the Optical Surfaces in the Grinding and
Polishing Process
It is unquestioned that exceptional results with respect to accuracy of the "classi-
cal" method used in industry for the manufacture of a spherical optical system are pri-
marily determined by the set of characteristics of its geometric prerequisites and
mutual lapping of the tool and the surfaced product.
Tlle method of surfacing close to the process which is widely used in industry for
the series manufacture of a spherical optical sy~tem is based on the studies of
the properties of planar cross sections of aspherical surfaces.
Figure 5.9 sliows the diagram of the machine tool [Author's Certificate No. 325163,
1972] realizing this procedure.
The lower unit of the machine tool is analogous to the usual optical grinding and
polishing machines. The billet 11 is fastened to the spindle 12 which has the
possibility of. turning.
The upper unit of the machine tool has a number of distinguishing features. The
carrier 2 is installed on the shaft 1 located on the bed with the possibility of
oscillatory motion around this shaft from the drive and simultaneous axial displace-
ment in the guides. The plate 3 with standard plane to which the working elements
7 are clamping using the spring 4 is hinged to the carrier 2. One end of the
spring 4 is supported on the flange of the working element 7, and the other in the
plate 6 installed in the cardan suspension 5 in the housing 9. The latter is in-
5talled in ttie bearings using rotation around the carrier snaft 2. The Working elements
7 are located in the plates 8, for example, along an Archimedes spiral (for more
uniform distribution of them) with the possibility of axial displacement. Using
~tie intermediare bushing 10 the plates 8 are connected to the housing 9. The ma-
cliine tool opetates as follows.
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'1'he bL.Ll~.~ 1.1 ~urns together with the spindle 12 from the drive. The working ele-
m~nts 7 are lapped to the machined surface of the billet using a free abrasive.
'1'h?e working elements, constantly clampE~d by the springs 4 against a standard plate
3 uncierKo rotational motion around the axis 2 of the drive together with the hous-
i~i~; 9. lluring surfacing the plate 3 i:~ freely oriented with respect to the ma-
ctiined surface. The ends of the worki~ig element 7 are displaced at any arbitrary
point in time along ellipses of constantly variable parameter which permits any
5~:concl-order surface to be machined.
In order to obtain defined surfaces of an ellipsoid and hyperboloid of rotation on
tlie machine tool it is necessary to se:Lect the corresponding position of the shaft
L.
'1'he surfaces of a paraboloid of rotation can be obtained if the carrier 2 is fas-
tened in the guides with the possibility of displacment of it relative to the
sl~indle axis 12.
Tlie shaping process on the proposed machine tool is controlled analogously to the
process used for tlie surfacing of a spherical optical system on the usual series-
produced machine tools.
Tlie application of ttie plane standard surface offers the possibility of making it
wi~11 iiigh o~tical precision. The preliminary shape of the working surfaces of the
tool and tlie billet can be sperical. Figure 5.10 shows the general view of a ma-
chine tool for machining parabolic surf aces.
Figur~ 5.11 shows the diagram of a device [Author's Certificate No 343830, 1972]
for machining cylindrical and gently sloping toric surfaces on optical grinding
and polishing machines. The plate 2 i:~ hinged to the carrier 1 of the machine tool.
'1'lit: attachment 5 with the billets is iiistalled on the plate on the shafts 15. In
~icldition, a parallelogram mechanism consisting of the cleats 12 and 14 which are
connected to eacti other by the bearings 3 and 13 is installed on the plate 2 in the
- bearings 4. 'The parallelogram mechanism is connected to the face plate 7 using two
cleats 8 wliich are fastened to the mechanism and to the face plate in the bearings
tl and 9. The tool 6 is fastened to the f ace plate 7 which is connected to the
spindle by means of the adaptor chuck 10.
f)uring operation two motions are transmitted frorn the machine tool simultaneously
to the device: 1) rotational from the spindle of the machine tool through the
~idaptor chuck 10, 2) reciprocal, from the carrier 1. The movement from the carrier
is divided into two movements of the tool 6 with respect to the billets required
C~~r sl~aping: 1) rectilinear from the parallelogram mechanism as a result of turn-
i~i~; of tl~e cleats 12 in the bearings 3 and 13; 2) oscillatory as a result of turn-
ing of. the cleats 8 with respect to thr~ axes 9 and 11.
'f.l~c: req~iired radius of the oscillatory motion is automatically insured by turning
- the tool 6 together with the plate 2 with respect to the parallelogram mechanism on
tlie hearings 4. Th~ machining of the ~ently sloping toric surfaces is insured by
turn:in~; the attachment S with the billets around the shafts 14.
Since the device is continuously turned on the tnachine tool spir~dle with respect to
the dir~cti.on of displacement of the c;arrier 1, the rectilinear and oscillatory
_ 125
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I
I '
. ~
. ~
I
J I , .
I
I
.
_ I .
Z
I .
~ I
~ ; j ~
,
.
~
s \
6 I I I I I
, I I I I I I I I
I I I I I I I I
B I I I I I I I I I I
I I I I I I I I
9 I ' I I
I I I I I I I I I I
I I I I I I ( I I
/
0 I i ~ ~ ~ ~ ~ ~ .
~li
,
- .
~ ~
~ ' \ ~ ~ Z` ~ ~
- .
~ ~ ~
!Z ~
Figure 5.9. ~Diagram of a machine tool for machining
aspherical surfaces.
~:O111F~Olll'l1CS of the movements of the tool vary continuously from the minimum value to
som~~ maximum value so that the decrease. in one component corresponds to the increase
Ln tlu uther.
The device is distinguished by simplicity and convenience of servicing. The smooth-
aiid the precision of the operating displacements of the device will permit the ma-
cllining oF cylindrical and gently sloping toric surfaces of increased precision with
its help.
I.et us also bric~L-ly discuss the new possibilities of active monitoring and automated
control of shaping wi?ich are opened up by using the geometric properties of the
machined surfaces for this process.
~ 126
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. u
1
F
z
.r s
i-
;
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S ~ �
~i,` ~:~r~.
~~.h`:. -
k
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h, ~ q i':+~1} % �L+t~'~ .
} . txt~ ` ~ ~ '.u'~`~
i~~ .."''~.`5~'~~
. . ~ ~ ~ ~i;FF~
_ x _ . . . . .
Figure 5.10. General view of a machine tool for machining parabolic
surfaces. 1-- billet, 2-- tool housing, 3-- working elements,
4-- carrier, 5-- working thrust bearings.
1 ' .
/
!
/J ? ~ . ~ i .
!6 .~r-� f
b ~ -
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6 1 ~
".."'illllll U~ j
~ i~ , a
~ ; /o ) [
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s ir . .
Figure 5.11. Diagram of the device Figure 5.12. Diagram of the
for machining cylindrical and machining of an aspherical
~ gently sloping toric surfaces. surface by a conical tool.
A study has already been made above of machine Cools in which the shaping of the
; aspherical surfaces was carried out as a result of mutual lapping nf numerous
operating elements on the rotating billet. These working elements underwent rota-
tional and rectilinear movements so that their edges, making contact with the
billet, moved along elliptic trajectories. The distance of all of these working
elements from the standard plane, according to the theoretical surfacing system
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(see Hibure 5.9) must be invariant during the shaping process. Using the known
contact, pneumatic and other sensors oi' linear displacements, these distances can
be measured witti high precision (fractions of a micron), and the results of the
measurements using the f eedback sysrem are automatically transmitted to the con-
trolling elements of the machine tool directly in the surfacing process. Analo-
gously, it is possible to control the position of the standard plane in the case of
hinged attacYunent of the tool to the axis of rotation during reciprocal motion of
the latter.
Another example indicating the possibilities of ac~.ive monitoring and automatic
control of the asphericalizatior~ of optical surf aces is presented in Figure 5.12.
According to the "classical" process in the investigated case the tool and the bil-
let have working surfaces of rotation which are during surfacing in the process of
mutual lapping using an interlayer of free abrasive. Let us provisionally call
the lapped part with convex surface a t~illet and the part with concave conical sur-
Eace, the tool. In reality any of them can be both tool and billet. As the billet
goes deeper into the cavity of the conical tool during surfacing, continuous angu-
lar rotation of it takes place, the magnitude of which is controlled using the
- simplest copying device with plane templet (in the case of mutual lapping of the
surface of a right cone and the surface formed by rotation of the arc of a loga-
rithmic spiral).
In the investigated case invariant properties of the logarithmic spiral moving with-
out slipping along a straight line are used for shaping.
'lhese properties consist in coincidence of the roulette formed by the pole of the
logarithmic spiral during rolling of it without sliding along a straight line,
with another straight line. The latter is inclined to the straight line along
which the spiral rolls at a def ined angle a, def ined by the spiral parameter and lo-
cated in the same plane with it.
According to the theoretical diagram of the surfacing process, the straight line
- wl~icti is the roulette of tl~e spiral whc~n moving along another straight line (the
generatrix of the conical tool) coincides with the axis of rotation of the conical
toul.
Theretore the sensor of linear displac~~ments rigidly connected to the shaft for
turning the lapped billet must be shifted along the standard plane coinciding with
th.is axis. The distances from the standard plane f ixed by this sensor can be
measured with precision indicated above, and they are automatically transferred to
the controlling elements of the machine tool in order to correct the shaping pro-
cess.
Tlius, the direction of obtaining an aspherical optical system investigated here and
based on using the geometric properties of the machined surfaces will make it
possible to use the experience available in industry from finishing spherical
surFaces during grinding and polishing, to make the process of mutual lapping
similar ta the ordinary processes of m;ichining as a result of the possibility of
active monitoring and control of the shaping.
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3. Super-pr~~cisi.on l~inishLng of Optic,~l Surfaces
llevic~~ for h4acliining an Optical Surfac~~ under the Effect of Ion Beams with the
ilartmanii Ion Method o� Control. The iun beam device, the diagram of which is pre-
sented in Figure 5.1"3 consists of a vacsuum chamber equipped with an ion beam source,
a process unit, a Hartmann control sysl:em and computer-control program system with
computer. In this diagram provision i~ made f or a system to monitor the tempera-
ture oL t}ie machined surface.
A vacuum ctiamber, tlie dimensions of which must provide for the location and the
technological displacement of an optical part 0.5 meters in diameter, is evacuated
to a vacuum no worse than 1�10-5 torr by oil-free pumps (turbomolecular, cryogenic
or mercury vapor).
Tt~e detailed drawings for the process equipment for ion beam surfacing of a part
~.5 meters in diameter which insures translational displacement of the part along
the ver.tical axis of the device and horizontal displacement along the axis of the
ion beam and rotatior~ of the optical part around its axis with the required preci-
sion, have been developed. The part for surf acing is located at a fixed angle 45�
to the tiorizontal. This angle is selected from arguments of optimal use of the
vacuum space of the process chamber while maintaining sufficient efficiency of the
ion beam.
Tl~e f.Low char t f or the surf acing with