DESIGN OF DOUBLE GAUSS SYSTEMS USING ASPHERICS

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B04770A001500060082-1
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 54
• Document Creation Date: December 28, 2016
• Document Release Date: September 26, 2005
• Sequence Number: 82
• Publication Date: May 1, 1967
• Content Type: REPORT

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DESIGN OF DOUBLE GAUSS SYSTEMS USING ASPHERICS
by
May 1967
NGA Review Complete
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DESIGN OF DOUBLE GAUSS SYSTEMS USING ASPHERICS
by
Submitted in Partial Fulfillment
of the
Requirements for the Degree
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The author wishes to acknowledge
for the assistance he has given throughout this study.
The author is also deeply indebted to the
for the use of their computer without which this
project may not have been possible. The final form of
this thesis was prepared under
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Page
I.
Introduction .................................
1
Ii.
Background of the Double Gauss Design ........
3
III.
Original Lens ................................
5
IV.
Optimized Spherical System -- Lens 1 .........
7
V.
Aspherics on Outer Surfaces -- Lens 2 ........
11
VI.
Aspherics on Inner Surfaces -- Lens 3 ........
15
VII.
Aspheric Corrector Plate -- Lens 4 ...........
19
VIII.
Another Double Gauss System ..................
23
IX.
Image Evaluation Techniques ..................
25
X.
Conclusions ..................................
28
XI.
Bibliography .................................
41
Appendix I ....................................
42
Appendix II ..................................
45
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Page
TABLE 1
-- Design Specifications for Lens 1.
8
TABLE 2
-- Design Specifications for Lens 2.
13
TABLE 3
-- Design Specifications for Lens 3.
17
TABLE 4
-- Design Specifications for Lens 4.
20
TABLE 5
-- Kidger-Wynne Spherical Design.
24
TABLE 6
-- Comparative Resolution Limits for
Various Double Gauss Designs.
30
TABLE 7
-- Image Errors Used in FLAIR.
42
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Page
FIGURE 1
-- Lens 1
- Optimized Spherical Lens.
9
FIGURE 2
-- Lens 2
- Aspherics on Outer Surfaces.
14
FIGURE 3
-- Lens 3
- Aspherics on Inner Surfaces.
18
FIGURE 4
-- Lens 4
- Aspheric Corrector Plate.
21
FIGURE 5
-- Transverse Aberration Plots for Lens 1.
31
FIGURE 6
-- Geometrical Frequency Response for
Lens 1.
32
FIGURE 7
-- Transverse Aberration Plots for Lens 2.
33
FIGURE 8
-- Geometrical Frequency Response for
Lens 2.
34
FIGURE 9
-- Transverse Aberration Plots for Lens 3.
35
FIGURE 10
-- Geometrical Frequency Response for
Lens 3.
36
FIGURE 11
-- Transverse Aberration Plots for Lens 4.
37
FIGURE 12
-- Geometrical Frequency Response for
Lens 4.
38
FIGURE 13
-- Transverse Aberration Plots for
Kidger-Wynne Spherical Design.
39
FIGURE 14
-- Geometrical Frequency Response for
Kidger-Wynne Spherical Design.
40
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The following is a study of the use of aspheric
surfaces in a Double Gauss photographic objective. In
addition to gaining some general familiarity with the
design of optical systems using large electronic com-
puters, the author has attempted to determine the im-
provement in image quality that might be realized through
the use of one or two aspheric surfaces, and to make
some recommendations regarding the optimum location of
the aspherics in the lens. The Double Gauss lens was
chosen because of its basic symmetrical shape, and most
conclusions stated here would apply equally well to
other objectives of similar form.
Four major design efforts will be presented in this
paper. These approaches differ in the use of the aspheric
surfaces. In many designs, the aspheric surfaces are
placed close to the aperture stop where they can be
used to correct spherical aberration without affecting
the off-axis aberrations. The four basic designs dis-
cussed in this report include an optimized spherical
lens and three lenses incorporating aspheric surfaces
(a) on the outside surfaces of the lens, (b) on the inside
surfaces surrounding the aperture stop, and (c) on one
surface of an aspheric corrector plate at the stop.
All design in this study has been aimed at achieving
reasonably observable modulation at high frequencies. In
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order to accomplish this, emphasis has been placed on
the realization of an image with a tight core at the
expense of having to accept some larger flare.
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BACKGROUND OF THE DOUBLE GAUSS DESIGN
The Double Gauss lens is typical of many varieties
of photographic objectives being generally symmetrical
about an aperture stop in the center of the lens. The
original design work was done early in the nineteenth
century by C. F. Gauss, who "discovered that if a tele-
scope objective is made with meniscus crown and flint
elements separated by a small air gap having the shape
of a negative lens, the variation of spherical aberration
with wavelength could be eliminated."1 In 1888, A. Clark
suggested combining together two similar Gauss objectives
surrounding a central stop. Typical early examples were
the Ross Homocentric, the Meyer Aristostigmat, and the
Kodak Wide-Field Ektars, which operated at f/6.3 over a
total field of 701.
A great contribution to indoor photography was
realized in 1920, when H. W. Lee designed the Opic lens,
which covered a total field of 48? at f/2. This lens
incorporated two additional cemented surfaces and, thus,
a total of six elements. Examples of this type were the
Zeiss Biotar, the Leitz Summar, and the Kodak Ektar.
"With the advent of rare-earth glass having a very high
refractive index, the type has been still further improved,
1Kingslake, R., Lenses In Photography, A. S. Barnes
and Co., Inc., New York, 1963, p. 144.
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as in the 7" f/2.5 Aero Ektar; and the Kodak Cine Ektar
f/1.4 of the same general type is excellent for 16 milli-
meter motion picture photography. For taking 35 milli-
meter motion pictures, such modern lenses as the Cooke
Speed Pancho f/2 and the Bausch & Lomb Baltar f/2.3
are of this same fundamental type, and so are the best
high aperture motion picture projection lenses such as
the Super Cinephor f/2 and the Super Snaplite f/1.9."2
Very recently the Leitz Company of Wetzlar, West
Germany have announced the production of a f/1.2, 50
millimeter focal length Double Gauss lens using aspheric
surfaces.3 This lens, called the Noctilux, is the first
high speed aspheric lens to be mass-produced. It is to
be used with the Leica M2 or M3 body for 35 millimeter
photography. Although no design specifications were re-
ported, the lens is said to make use of new glasses of
very high refractive index. The number or position of
the aspheric surfaces was not given, but the lens is to
be sold for $678.4
2Kingslake, R., Lenses In Photography, A. S. Barnes
and Co., Inc., New York, 1963, p. 144.
3Crawley, Geoffrey, "The Aspheric f/1.2 50 mm Leitz
Noctilux," The British Journal of Photography, October 7,
1966, pp. 882-885.
4Desfor, Irving, "No-Flash Nighttime Lens," Christian
Science Monitor, February, 1967, p.7.
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sity of
All design in this study was done using the Univer-
lens design program FLAIR on the IBM
7044 computer at
The starting point of the design was a six element
Double Gauss system designed on the ORDEALS program. The
system under consideration was a 10 centimeter focal
length lens operating at f/2.1 and covering a total field
of 42 degrees. It was specified to function at a magnifi-
cation of -0.05, and a vignetting factor of 0.79 was
allowed at the zone and 0.70 at the margin.
This lens was typical of the Double Gauss type,
basically symmetric, composed of two groups of three ele-
ments centered about the aperture stop. Each group was
composed of one single element and a cemented doublet.
All surfaces were spherical in shape. The glasses used
were not catalogue glasses, but were very close to the
Schott glasses, SK 16, BAF14 10, SF 2, and F 2. Thus,
these glasses have been used throughout the further design
efforts. Note that the meniscus crown and flint elements,
described by Gauss in his original design theory, are
SK 16 and SF 2, in this design. BAFN 10 is a new glass
with high refractive index.
Both the ray trace curves and the geometrical fre-
quency response show the lens to have poor resolution.
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The axial response suffers predominantly from spherical
aberration, while the off-axis performance deteriorates
from large coma and astigmatism.
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The first attempt at improving the original lens in-
volved the use again of only spherical surfaces. All
radii and thicknesses were allowed to vary. A trial run
was made in which most of the group one and all the group
two image aberrations5 were minimized. The program was
successful in this effort as the merit function, composed
of the sums of the squares of all these image aberrations,
weighted evenly, was reduced by a factor of ten.
The basic shape of the lens remained unchanged.
Nevertheless, this design using minimization of the image
aberrations had a great deal of spherical aberration and
a curved tangential field which governed both the axial
and off-axial response. The resolution of this lens was
lower than that of the original lens. Thus, it could be
concluded that this technique of straight minimization of
all aberrations is not an adequate approach to the design
of an improved system.
In a second attempt at improving the spherical lens
system, the mean square deviations of the wavefront from
a perfect reference sphere were minimized. In addition,
5A11 aberration numbers refer to the FLAIR program.
Group one aberrations, numbers 1-16, 18, and group two
aberrations, 1-12,were minimized. Only certain color
aberrations were omitted. Hereafter, image aberrations
will be referred to in the form 1.5-8, where 1 represents
the group number and 5-8, the aberration numbers in that
group. An explicit interpretation of these image aber-
rations is given in Appendix I.
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the distortion at full field (1.9), the axial color at
0.7 of the aperture (1.16), and the lateral color at 0.7
of the field (1.18) were corrected to zero. Again all the
radii and both glass and air thicknesses were allowed to
vary. In order to force more correction off axis, rela-
tive weightings of 0.75, 1.0, and 1.0 were given to the
axial case, the 0.7 field, and the edge, respectively.
The resulting design was again similar in shape,
although it became somewhat shorter. The lens, however,
showed great improvement in image quality. The ray trace
curves (see Fig. 5, page 31) showed none of the large
coma present in the original design and much less field
curvature. The lens, in general, is well corrected except
for the spherical aberration, which limits the axial
resolution and some astigmatism evident at off-axis points.
The geometrical frequency response corresponding to this
design is shown in Fig. 6, page 32.
SURFACE CURVATURE
THICKNESS
GLASS
1
0.1999
0.626
SK 16
2
0.0790
0.010
AIR
3
0.3106
1.020
BAFN 10
4
0.0261
0.171
SF 2
5
0.4377
1.394
AIR
6 S
0.0000
1.427
AIR
7
-0.3843
0.160
F 2
8
0.0094
0.901
BAFN 10
9
-0.2866
0.008
AIR
10
-0.0041
0.540
SK 16
11
-0.1523
6.559
AIR
OBJECT
DISTANCE
208.24
FOCAL
LENGTH
9.9328
BACK FOCAL LENGTH
6
.559
AXIAL LENGTH OF LENS
6.26
TABLE 1 -- Design Specifications for Lens 1.
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FIGURE I. LENS I - OPTIMIZED SPHERICAL DESIGN
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10
This technique of minimizing the mean square wave-
front deformations tended to produce a superior lens by
balancing the image aberrations rather than trying to
reduce the aberrations first and then perhaps trying to
balance their effect. In following designs, then, the
approach adopted was that of introducing aspheric sur-
faces in order to reduce the spherical aberration, while
trying to maintain approximately the same balance of the
off-axis aberrations present in this design.
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In this design the first and last surfaces were made
aspheric. In addition to all radii and thicknesses, the
fourth, sixth, and eighth order aspheric coefficients were
allowed to vary. Again the mean square wavefront devia-
tions were minimized while the distortion at full field
(1.9) and the axial (1.16) and lateral color (1.18)
were corrected to zero. The same weighting factors of
0.75, 1.0, and 1.0 were used across the field.
The lens produced by this design had an improved
axial resolution as would be expected. The zonal sagit-
tal resolution was increased at higher frequencies due
to the fact that the lens had a tighter core (there is
much less image aberration at small values of the aper-
ture). The zonal tangential resolution, however, and
especially the marginal tangential resolution was much
worse due to the introduction of a large amount of linear
coma and also oblique tangential coma.
In the following design attempts, this large coma
was reduced to approximately the same value as in the
spherical system. It was found that it was quite easy
to control the linear coma (1.6), producing the design
given below. The resolution obtained with this lens is
better than that for the lens using all spherical sur-
faces (See Fig. 7, page 33). Further attempts at trying
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to reduce the oblique tangential and sagittal spherical
aberration led to no improvement and seemed only to
disrupt the balance of image aberrations already obtained.
Better correction of the tangential field curvature as
well as the astigmatism at the zone and the margin was
possible, but only at the expense of the axial resolu-
tion.
The lens again had the same basic configuration as
the original spherical lens. Listed below are the design
parameters for this lens.
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1
0.2015(1)
0.711
SK 16
2
0.0770
0.010
AIR
3
0.3076
1.152
BAFN
10
4
0.0050
0.118
SF 2
5
0.4448
1.431
AIR
6
S
0.0000
1.441
AIR
7
-0.3989
0.247
F 2
8
0.0351
0.983
BAFN 10
9
-0.2925
0.004
AIR
10
0.0109
0.572
SK 16
11
-0.1357(11)
6.390
AIR
(i)
Z=Z (4) +Z (6) +Z (8) =aspheric sag
Z(4)=aY4=-.001895
Z(6)=bY6=+.002658 Y=2.94
Z(8)=cY8=-.000983
(ii) Z (4) =aY4=+.008123
Z(6)=bY6=-.005875 Y=2.57
Z(8)=cY8=+.002430
OBJECT DISTANCE 209.93
FOCAL LENGTH 10.0071
BACK FOCAL LENGTH 6.390
AXIAL LENGTH OF LENS 6.67
TABLE 2 -- Design Specifications for Lens 2.
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FIGURE 2. LENS 2 -ASPHERICS ON OUTER SURFACES
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In this design, the surfaces surrounding the stop
(numbers five and seven) were aspherized. Again all
radii, thicknesses, and three aspheric coefficients for
each aspheric surface were varied. The preliminary de-
sign effort made use of the minimization of group one
and group two image aberrations, choosing the proper
weights so as to achieve a reasonable balance between
them.
Important points in this design were the introduc-
tion of large positive tangential oblique spherical
aberration (2.2-3) and the maintaining of slightly posi-
tive tangential field curvature (1.12). The design ob-
tained in this manner showed good sagittal and tangential
frequency response. The circular response, however, was
considerably lower due to coma still present in the lens.
In later design attempts, a better balance of the coma
terms (2.10-12) was achieved, thus yielding a higher
circular frequency response. The next design attempts
involved the use of the mean square wavefront deformation
(MSWD) minimization technique. Due to the fact that the
frequency response on-axis was much greater than that
off-axis, relative weights of 0.2, 1.0, and 1.0 were
used for the axial case, 0.7 field, and full field, re-
spectively. The MSWD technique did little in regard to
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shifting the emphasis of correction from the axial to
off-axial points. Nevertheless, it did?find a different
balance of aberrations which produced a tighter core at
full field.
The final design obtained using aspheric surfaces
surrounding the aperture stop is basically similar to
that using aspheric surfaces on the outer surfaces. The
main difference, however, is the way in which resolution
varies across the field in the two cases. In the former
lens, the axial resolution is very high, while coma
limits the off-axis correction. The latter lens does
not exhibit such a pronounced comatic effect and its
resolution is more uniform across the field. See Figs.
9 and 10 on pages 35 and 36 for ray trace and modulation
transfer curves, respectively. Table 3 on the following
page gives design specifications for this lens.
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1
0.1944
0.653
SK 16
2
0.0705
0.001
AIR
3
0.2963
1.166
BAFN
10
4
-0.0315
0.283
SF 2
5
0.4390(i)
1.185
AIR
6
S
0.0000
1.444
AIR
7
-0.3877(ii)
0.160
F 2
8
-0.0032
1.061
BAFN 10
9
-0.2899
0.005
AIR
10
0.0286
0.550
SK 16
11
-0.1135
6.295
AIR
(i) Z=Z (4)+Z (6)+Z (8) =aspheric sag
Z(4)=aY4=+.004546
Z(6)=bY6=-.002348 Y=1.73
Z(8)=cY8=+.003722
(ii) Z(4)=aY4=-.005239
Z(6)=bY6=+.002828 Y=1.87
Z(8)=cY8=+.011646
OBJECT DISTANCE 210.24
FOCAL LENGTH 10.0088
BACK FOCAL LENGTH 6.295
AXIAL LENGTH OF LENS 6.51
TABLE 3 -- Design Specifications for Lens 3.
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FIGURE 3. LENS 3 - ASPHERICS ON INNER SURFACES
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The final lens design attempt involved the use of an
aspheric corrector plate placed in the aperture stop.
The thickness and plane back surface of the plate were
held constant, while the fourth, sixth, and eighth order
aspheric coefficients on the first surface of the cor-
rector plate were allowed to vary. In addition all other
curvatures and thicknesses were used as variables.
As a starting point for this design effort, a thin
plane parallel plate was inserted at the stop into the
spherical lens (lens 1) designed earlier. With the above
mentioned degrees of freedom, the mean square wavefront
deviations were minimized using weights of 0.0, 1.0 and
1.0 for the axis, zone, and edge, respectively. Further-
more, the spherical aberration (1.1-2) as well as the
distortion (1.9) and the axial (1.16) and lateral color
(1.18) were controlled. The lens obtained in this man-
ner had good axial correction, but the field curvatures
were large, and thus the off-axis response was poor.
In further design attempts, emphasis was placed on
the correction of field curvature and astigmatism; it was
relatively easy to achieve a good balance of the coma
terms. In the last designs the oblique tangential spheri-
cal aberration (2.2-3) was reduced yielding a well cor-
rected lens. Note also that the stop position was allowed
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to vary, but with little further improvement in image
quality. The resolution obtained in this lens was much
better than in all other designs and could be attributed
to the attainment of good field curvature, producing
an image with a tight core. See Figures 11 and 12 on
pages 37 and 38 for ray trace and modulation transfer
curves, respectively.
1
0.2016
0.671
SK 16
2
0.0796
0.005
AIR
3
0.3212
1.118
BAFN
10
4
0.0192
0.116
SF 2
5
0.4631
1.442
AIR
6
S
0.0000
0.069
AIR
7
0.0000(1)
0.303
BK 7
8
0.0000
1.108
AIR
9
-0.4420
0.159
F 2
10
-0.0185
0.830
BAFN 10
11
-0.3267
0.008
AIR
12
-0.0113
0.542
SK 16
13
-0.1666
6.614
AIR
(i) Z=Z (4) +Z (6) +Z (8) =aspher is sag
Z(4)=aY4=-.000363
Z(6)=bY6=+.002462
Z(8)=cY8=+.001963
Y=1.57
OBJECT DISTANCE
210.24
FOCAL LENGTH
10.0039
BACK FOCAL LENGTH
6.614
AXIAL LENGTH OF LENS
6.38
TABLE 4 -- Design Specifications for Lens 4.
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FIGURE 4. LENS 4 - ASPHERIC CORRECTOR PLATE
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Some additional design was done with the thickness
and the back curvature of the aspheric plate also allowed
to vary. In optimizing this lens the thickness of the
plate got quite large and the curvature of the back sur-
face became positive. This had the effect of putting
an extra negative lens behind the stop. The most inter-
esting observation noted in this design was that the
large thickness, in conjunction with the positive curva-
ture following it, had reduced the oblique sagittal spheri-
cal aberration (2.5) by a factor of two. This aberra-
tion is normally one of the most difficult to reduce in
any design. In spite of this reduced oblique sagittal
spherical aberration, the resolution with this thick
element in the stop was no better than that for lens 4.
The general method followed throughout the design
using the aspheric corrector plate was that of starting
with the minimization of the wavefront deviations and
then adding to the merit function certain specific geo-
metrical aberrations until the lens was controlled to an
adequate degree. This technique was found to give good
results and to give the designer a means of slowly con-
structing a desired merit function.
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M. J. Kidger and C. G. Wynne have recently published
their analysis of the design of Double Gauss systems con-
taining spherical surfaces.6 Their report includes sev-
eral Double Gauss lenses optimized at f/2 with a 401
total field. Chromatic aberration was balanced for the
C-F spectral region, and vignetting of 65% was allowed
at full field. Some of these designs were done for sys-
tems with a focal length of unity and with the object at
infinity.
For purposes of comparison, one of these optimized
designs, scaled to a 10 centimeter focal length, was
evaluated on the FLAIR program. Note that the shape of
this spherical lens is similar to those designed on FLAIR
except that the fifth element is thicker and biconvex
in this design. Note also that the choice of glass types
is different in this design. Kidger and Wynne allowed
the glass type to vary during the design, resulting in
the use of glasses very similar to the Schott glasses,
LaK 9, F 1, and SF 10.
Ray Trace curves and geometrical frequency response
for the Kidger-Wynne design are given in figures 13 and
14, on pages 39 and 40, respectively. In comparison with
6Kidger, M. J. and Wynne, C. G., "The Design of Double
Gauss Systems Using Digital Computers," Applied Optics,
Vol. 6, March, 1967, pp. 553-563.
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1
0.1534
1.244
LaK
9
2
0.0428
0.000
AIR
3
0.2698
0.977
LaK
9
4
0.1517
0.300
F 1
5
0.4007
2.235
AIR
6
S
0.0000
0.899
AIR
7
-0.2364
0.300
SF
10
8
0.1791
2.283
LaK
9
9
-0.1987
0.000
AIR
10
0.0690
1.258
SF
10
11
-0.0627
6.008
AIR
OBJECT DISTANCE
FOCAL LENGTH
10.0011
BACK FOCAL LENGTH
6.008
AXIAL LENGTH OF LENS
9.50
TABLE 5--Kidger-Wynne Spherical Design
the optimized spherical lens, Lens 1, the Kidger-Wynne
lens shows much better correction of spherical aberration
and, thus, a better axial response. The off-axis re-
sponse, however, deteriorates quickly due to very large
astigmatism. Although both the .7 field and full field
tangential ray plots show a reasonably tight core, the
sagittal curves are poor and, thus, the circular fre-
quency response is low. Note that a better balance of
resolution across the field could be attained by choosing
a slightly different back focus.
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IMAGE EVALUATION TECHNIQUES
Among the most common techniques of predicting image
quality is the optical or modulation transfer function.
The modulation transfer function (MTF) represents the
contrast at which a lens transmits spatial frequencies.
Since the frequency response of a lens is governed
by both diffraction and geometrical aberration considera-
tions, the precise evaluation technique must include both
of these effects. If the lens is corrected to the degree
that the spot size due to geometrical aberration consid-
erations is smaller than the Airy disk diffraction pat-
tern of the lens, then it is diffraction limited, and its
frequency response is well known. In terms of wavefront
error, which may be associated directly with geometrical
aberration analysis, the tolerance for this case is X/4.
On the other hand, when the wavefront deformation becomes
X or 2X or greater, the geometrical image is larger than
the diffraction image, and the geometrical optical modu-
lation transfer function gives a good approximation to
the actual frequency response. Note also that if there
is an error, the geometrical response tends to differ
from the actual response on the pessimistic side at high
frequencies.7
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26
Validity of the Use of the Geometrical
Optical Frequency Response
The image evaluation presented in this report is of
two forms: (1) image aberration ray plots and. (2) geo-
metrical optical frequency response curves. The image
aberration ray plots show the actual transverse ray dis-
placements from the actual intersection point of the chief
ray and the image plane in the tangential and sagittal
fans for various field points. From these plots one may
get an approximate idea of the image spot size. If the
diameter of the image core at full field is approximately
50 microns, it may be seen that the lens is still far
from its diffraction limit (the diameter of the Airy disk
diffraction pattern is about 2.5 microns).
The calculation of optical path difference (OPD)
for the extreme ray at full field in lens 2 is given below.
(p
Ymax I
OPD = TA'(P)dp
At p = .7, X _ .5u,
OPD = 2.5 (.0025) _- .006 z 12A
10
Again it may be seen that the lens is far from being dif-
fraction limited. The geometrical optical frequency
response is thus reliable and has been used throughout
this study.
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Geometrical Optical Frequency Response
The geometrical optical frequency response subrou-
tine, as incorporated into the FLAIR program, calculates
the frequency response of a lens on-axis and off-axis
at the .7 zone and at full field. At each off-axis point,
the response is computed in both the sagittal and tan-
gential directions. In addition an averaged circular
response is also given (only the circular responses have
been included in this report). Each of these responses
is calculated for d, F, and C light and then averaged
with the weights 1.0, 0.25, and 0.25, respectively, for
the white light response.
The average circular frequency response is an aver-
age over all target orientations. This circular aver-
aging technique involves counting the number of rays
which intersect the image plane within a small circle
centered about the Gaussian image point. Since each ray
represents the light energy passing through an elemental
area of the aperture, by counting the fraction of the
total number of rays the fraction of the total light
energy passing through the system is found.8 This in-
formation, known as the radial energy distribution, is
then used in calculating the average circular frequency
response.
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Three aspheric double Gauss lenses have been designed
in this study in an attempt to improve upon the spheri-
cal lens. All lenses were designed with the same cri-
teria: f-number - 2.1, focal length - 10 centimeters,
total field of view - 42 degrees, and magnification -
-0.05. The designs differ primarily in the position and
number of aspheric surfaces.
Upon inspection of Table 6 on page 30, it is appar-
ent that the off-axis resolution limits given for Lens 4
are superior to those of the other lenses. An equal
amount of effort was put into achieving each of the de-
signs. It must be noted, however, that this fourth system
was the last one designed, and it is entirely possible
that the experience gained in the previous design work
gave the author a better understanding of the techniques
involved and, therefore, facilitated the design task.
Lens 3 has very good axial correction and further design
effort could perhaps produce a better balance of correc-
tion across the field. The conclusion to be drawn, then,
is that well corrected double Gauss lenses can be designed
with an aspheric plate in or near the aperture stop, but
that additional investigation is necessary before any
definite preference of position for the asphere can be
determined.
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29
Further investigation should be made regarding the
ability to achieve similar image quality with fewer than
three aspheric coefficients as variables. In any case,
the comparison of the resolution obtained with designs 1
and 4 shows the marked improvement attainable through the
use of aspheric surfaces. It may be assumed that as
such systems are designed, better techniques for their
fabrication will be found, and there will be more fre-
quent use of aspheric refracting systems.
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30
Relative
Field Height
Lens 1
Lens 2
Lens 3
Lens 4
Kidger-Wynne
0.0
20
60
100
70
65
0.7
20
27
29
70
9
1.0
18
50
29
50
7
Maximum %
Distortion
.05%
.07%
.10%
.05%
.230
Lens 1 - Spherical Design
Lens 2 - Aspherics on Outside Surfaces
Lens 3 - Aspherics on Inside Surfaces
Lens 4 - Aspheric Corrector Plate Near Stop
Kidger Wynne - Spherical Design
TABLE 6 -- Comparative Resolution Limits for Various
Double Gauss Designs. (Resolution limit was
determined by a modulation of 0.1 and is given
in Q/mm.)
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31
H-1.0
0.01
H =0.7
-0.01
0.01
H=0
-0.01
FIGURE 5. TRANSVERSE ABERRATION PLOTS FOR LENS I
Approved Fq gas%38Qfll'/2.~QrIA- gRDP78B04770A001150006'00$2Sf_ed
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1.0
0.8
0 0.6
0.2
0
I0
20
30 40 50 60 70 80
FREQUENCY (lines/mm)
FIGURE 6. GEOMETRICAL FREQUENCY RESPONSE FOR LENS 1
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0.01
H = 0
7
.
-0.01
0.01
H=0
-0.01
FIGURE 7. ((TRANSVERSiiE.r{l ABERRATION PLOTS FOR LENS 2
Approved Fgr Rgktie ~505/1 1y2T :r8rMRD148 1W81do6br60492 d
line to sagittal fan)
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10
20 30 40 50 60
FREQUENCY (lines/mm)
70
80
FIGURE 8. GEOMETRICAL FREQUENCY RESPONSE FOR LENS 2
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 pproved For Release 2005/11/21 : CIA-RDP78BO477OA001500060082-1
H= 1.0
H = 0.7
0.01
H=0
-0.01
FIGURE 9. TRANSVERSE ABERRATION PLOTS FOR LENS 3 l Approved(IFR6 P)ight; solid line
5r1 / : CIA RDP78BO4770A001f5 b66082=? d
 Approved For Release 2005/11/21 : CIA-RDP78BO477OA001500060082-1
1.0
0.8
Z
0.6
H
J
D
00.4
2
0.2
0
I0
20
I I I I 1
30 40 50 60 70
FREQUENCY (lines/mm)
80
FIGURE 10. GEOMETRICAL FREQUENCY RESPONSE FOR LENS 3
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-0.01
0.01
0.01
/
100,
H =0.7
H=0
-0.01
FIGURE II. TRANSVERSE ABERRATION PLOTS FOR LENS 4
(D light; solid line refers to tangential fan, dashed
line to sagittal fan)
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1.0
0.8
z
0 0.6
I --
J
D
0 0.4
2
0.2
0 10 20 30 40 50 60
FREQUENCY (lines/mm)
70
80
FIGURE 12. GEOMETRICAL FREQUENCY RESPONSE FOR LENS 4
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39
0.01
-0.01
0.01
-0.01
= 1.0
H=0
FIGURE 13. TRANSVERSE ABERRATION PLOTS FOR KIDGER-
WYNNE DESIGN (D light; solid line refers to
tangential fan, dashed line to sagittal fan)
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0.81--I WHITE LIGHT
H =0
11.0c" H= 1.0
f I I I I
0 10 20 30 40 50 60 70 80
FREQUENCY (lines/mm)
FIGURE 14. GEOMETRICAL FREQUENCY RESPONSE FOR KIDGER-WYNNE
DESIGN
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1. Buzawa, John. W., "Notes on the Design of Double
Gauss (Biotar) Lens Systems,"
2. Crawley, Geoffrey, "The Aspheric f/1.2 50 mm Leitz
Noctilux," The British Journal of Photography,
October 7, 1966.
3. Desfor, Irving, "No-Flash Nighttime Lens," Christian
Science Monitor, February, 1967.
4. FLAIR User's Manual,
5. Kidger, M. J. and Wynne, C. G., "The Design of Double
Gauss Systems Using Digital Computers," Applied Optics,
Vol. 6, March, 1967.
6. Kingslake, R., Lenses in Photography, A. S. Barnes
and Co., Inc., New York, 1963.
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TABLE 7
-- Image Errors Used in FLAIR
Relative Relative
Group I: Aperture Field
1.
Transverse
Spherical Aberration at
0.4
2.
Transverse
Spherical Aberration at
0.7
3.
Transverse
Spherical Aberration at
1.0
4.
Linear Coma
0.416
5.
Linear Coma
0.7
6.
Linear Coma
1.0
7.
Distortion
8.
Distortion
9.
Distortion
10.
Tangential F
ield Curvature
11.
Tangential F
ield Curvature
12.
Tangential F
ield Curvature
13.
Astigmatism
(T-S)
14.
Astigmatism
(T-S)
15.
Astigmatism
(T-S)
16.
F-C Axial Chromatic Aberration
0.7
17.
F-C Axial Chromatic Aberration
1.0
9FLAIR User's Manual,
10Extrapolation without the vignetting factor has
been taken into account for 4, 5, 6, 10 to 15.
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Relative Relative
Aperture Field
18. F-C Chief Ray Lateral Color
19. F-C Chief Ray Lateral Color
20. F-D Axial Chromatic Aberration 0.7
21. F-D Axial Chromatic Aberration 1.0
22. F-D Chief Ray Lateral Color
23. F-D Chief Ray Lateral Color
Group II:
1.
Oblique Tangential Spherical
(Pure) 0.7*VFZ
0.7
2.
Oblique Tangential Spherical
(Pure) 1.0*VFZ
0.7
3.
Oblique Tangential Spherical
(Pure) 1.0*VFE
1.0
4.
Oblique Sagittal Spherical
(Pure) 0.7
0.7
5.
Oblique Sagittal Spherical
(Pure) 1.0
0.7
6.
Oblique Sagittal Spherical
(Pure) 0.7
1.0
7.
Oblique Tangential Coma (Pure) 0.7*VFZ
0.7
8.
Oblique Tangential Coma (Pure) 1.0*VFZ
0.7
9.
Oblique Tangential Coma (Pure) 1.0*VFE
1.0
10.
Oblique Saggital Coma (Pure) 0.7
0.7
11.
Oblique Saggital Coma (Pure) 1.0
0.7
12.
Oblique Saggital Coma (Pure) 0.7
1.0
13.
Primary (i.e. F-C) Chromatic
Aberrations of "outer" rays
0.7*VFZ
0.7
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Relative
Aperture
Relative
Field
14.
Primary (i.e. F-C) Chromatic
Aberrations of "outer" rays
-0.7*VFZ
0.7
15.
Primary (i.e. F-C) Chromatic
Aberrations of "outer" rays
1.0*VFZ
0.7
16.
Primary (i.e. F-C) Chromatic
Aberrations of "outer" rays
-1.0*VFZ
0.7
17.
Primary (i.e. F-C) Chromatic
Aberrations of "outer" rays
1.0*VFE
1.0
18.
Primary (i.e. F-C) Chromatic
Aberrations of "outer" rays
-1.0*VFE
1.0
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DISCUSSION OF DESIGN PARAMETERS FOR
In a paper entitled "The Design of Double Gauss
(Biotar) Lens Systems,"ll John Buzawa discusses the con-
struction, design parameters, and design approach of
Double Gauss systems. Buzawa's study was done primarily
on the LGP 30 and IBM 7074 computers, the latter using
the ORDEALS program, where surface contributions to the
particular third and fifth order aberrations are avail-
able. Listed below are several of his suggestions and
mention of how the spherical and aspheric designs pre-
sented in this paper agree with them.
A. The outer convergent elements should be of ap-
proximately equal power unless there are restrictions on
back focus which require otherwise. This yields a more
symmetrical solution which is more easily corrected for
distortion and lateral color.12 Note that this is usually
accomplished in systems operating close to unit magnifi-
cation. For systems in which the object is at infinity,
the first element is usually a weak meniscus while the
last is biconvex.13 In the four designs discussed in this
11Buzawa, John W., "Notes on the Design of Double Gauss
(Biotar) Lens Systems,"
12lbid. p. 5.
13lbid. p. 6.
STAT
45
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report, the last element was always stronger (by about
twenty percent) than the first. These lenses were de-
signed to operate at twenty to one conjugates.
B. For uniform performance over a wide field, the
use of thin doublets with strong outer curves is sug-
gested. In such systems, the surfaces tend to be more
concentric about the stop yielding smaller variations in
image quality from the axis to the edge of the field.
Baker, in his patent #2532751, defines A as the ratio
of the distance between convex surfaces of the doublets
to the focal length. For f/2 systems with a total field
of view of 40?, A should be approximately 0.5. Longer
values of A, or thick doublets surrounding the stop,
result in larger high order astigmatism.14
Lenses 1-4 presented in this study have values of
A ranging between 0.506 and 0.541; the astigmatism in
these lenses is reasonably well corrected. In the design
by Kidger and Wynne, however, the second doublet contains
a thick positive element, indicated by the fact that
A = 0.699. This system is limited in off-axis resolution
by large astigmatism.
Again the power of the two doublets should be ap-
proximately equal with the exception of the case of
14Buzawa, John W., "Notes on the Design of Double
Gauss (Biotar) Lens Systems,"
F
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unusual back focus requirements.15 In each of the de-
signs discussed in this study, the first doublet is con-
siderably stronger (almost twice as strong for lens 3)
than the second doublet.
C. The central airspace should be greater than the
shorter of the two adjacent radii. A large central ar-
space tends to reduce the oblique spherical aberration due
to the fact the angle of incidence of the chief ray at
the surfaces surrounding the stop is reduced.16 This
effect was observed in the aspheric corrector plate de-
sign when the corrector plate was allowed to become thick,
yielding a design with greatly reduced oblique sagittal
spherical aberration.
15Buzawa, John W., "Notes on the Design of Double
Gauss (Biotar) Lens Systems,"
161bid. p. 3.
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