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Aspheric Optical Systems
Nntt-sherhical lent Srirf;ice. are a to4'1 e/
Thaii~ii l;?n0 t,tt for Deer flit cc tviitrirre.~,
rliey only l'ecanu? ccnwonrical to tuaniifcnturn .i leu, ynlr~
Notre they are 111'pearint in htt,'ll-,1)(t'd vi,l
It is to I )csc.trtcs that hlstorv itti abut ?s the
first Suggestion that the use ofnon-tipil- ri(al
lens surfaces ma} reduce optical na-
tions. In the publication La I )a 1 ii::4 r f
1638 he discloses the geometrical Construc-
tion for a single lens free front sphcrical
abberation.'Theconstruction described had
one surface a portion of an ellipse, whilst
the other surface was spherical having its
centre of curvature at one of the loci of the
ellipse.
The ellipse together with the parabola
and the hyperbola arc simple examples of
what may be described as-aspheric or non-
sphcrical surfaces ofrevolution, each having
4 articular properties when used as refract-
ng or reflecting surfaces. They constitute,
with the circle, a set of curves described as
conic-sections, since` all of them may be
produced by cutting across a cone or
cylinder.
More generally, our aspheric surface can
be considered to be a deformation of a,
spherical surface of equal vertex radius.
The Affect of the deformation on a refract-
ing Or reflecting surface is to advance or
retarl an incident wave front relative to
ti action of the ~phcr e.i stir,.e(c h% itcelL
t'eneraI Surf.i( e ,+f rev,d iinoI 1. s\ nlmetrI-
I about an optical axis (till, axis bate
l,,scn as the x: direction) can be re presented
I,%- the equation x a\ bs; c\"
t~)r the purpose of calculation.
Whilst the conic-sections are more easily
ueterniined and perhaps easier to manu-
facture and test, them represent a limitation
iii the design of aberration-free optical
`"'stems.
For example, whilst the ellipse nay be
shown to produce a point on axis free
from spherical aberration, either the in-
cident o emergent beans must be parallel
to the leis axis.
Thus no correction is made for the ob-
lique ft+dd aberration of,- say coma and
astigmatism.
It is therefore'often preferable to utilise
more cmnplex surfaces other than conic-
sections in designing a system utilising
aspheric surfaces. This may.aid_ correction
of resid4als From elsewhere in the system
and thy' off-axial aberrations.' A good
examp " f this point is the Schmidt system
(page 8 . Whilst it is over three'hundred
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years since Descarte$ described his aplanatic
lens using an elliptical surface, and whilst
there appear to be obvious advantages in
designing certain systems with aspheric
surfaces, there are comparatively few lenses
available commercially of photographic
quality that utilise aspheric components.
The reasons behind this involve design,
manufacture and economics, to quote but
a few. Perhaps however the single major
drawback to progress in this aspect of
optics has been the difficulty in evolving
methods for producing aspherics consist-
ently, and to an equivalent quality of
tr#erical surfaces, at similar or competitive
st.
Prior to this century very little was done
by way of either design or manufacture of
surfaces other than conic-sections. In the
mid-17th century there was a period of
activity in which the limitations of the
refracting telescopes led to the inception of
the reflecting telescopes of Gregory, Casse-
grain and Newton. In the same period
Sir Christopher Wren suggested an engine
for the production of hyperbolic surfaces.
At this time little was understood as regards
beration of optical systems; however,
4,egorpy suggested that conic-sections
could improve a system otherwise em-
ploying spherical mirrors. Newton had
turned to reflecting systems in his belief
that refracting systems could not be cor-
iect&d for chromatic abberation. The
'simplicity of his system having a parabolic
reffec,tor, a plane mirror and ari eyepiece,
is sttchthat today, most amateur telescope
makers adopt it. (The partfolc mirror has
sir,e ptbptrties to the
se in that a
ellip~
FM O47 0A001
beam parallel to the axis is reflected to a
single focus free from spherical aberration)
More recently the development of
photographic lenses stimulated a greater
desire t,, produce aspheric surficcs. Little
is discl,~acd as to attcnipts prior to the
appear. tee of the (:Doke l'riplet le I )enn>s
Tavlot it the turn of this century, but
hetwe: i 1908 and I'+'? ('.irl L.eiss rook ottt
several patents with respect to both th,
design and manti facturc of lease s usiiw,
ashhrr,, surfaces. One of these' ulrscnh~s
a triplet characterised bN the fr.ttur ? that
the lust surface of the objective is clef Ornr ].
Earlier attempts by Zeus to ni.inutActt.rr
asph: Tics were concerned with the muntldl-
ing of components.
Many attempts since this tithe have been
concerned with moulding asphcrtc curves.
but little success has resulted her surfaces
of photographic lens quality. This process
however has an important application in
the manufacture of, components for con-
densing systems, where the quality of
imagery is quite crude compared to the
photographic image. Nearly ev&Ymodern
projector has some form of aspherie cor-
recting surface in the condensing system.
Many materials other than glass have been
moulded successfully, these include benzyl-
cellulose, pheno-plastics, polystyrenc, poly-
methyl-methacrylate, and epoxy resins.2.3
THE SCHMIDT SYSTEM
When Bernhardt Schmidt introduced the
system, that now bears his name, in 1930,
he sparked off a new line of thinking in
photographic optics. It was simple,' com-
prising only a thin aspheric corrector plate
and a spherical mirror. His diiscoyety lay
in the poaiittioning . of the corrector elate
ve to the mirror. He placed that plate
aperture stop at the centre of curva-
af the. mirror. The corrector plate is
parallel in form having one surface
rival to correct not only the axial
ical aberration but also tl;c oblique
defects. Schmidt's first c.imera
ed at f 1.75 having an aperture of 14
s with a focal length of 24 inches,
ing a 16? field.
focal plane of the earlier Schmidt
ns is intermediate between the plate
he mirror and is necessarily curved
x towards the mirror. Subsequent
icatio ave led to the focal plane
broc exterior to the mirror
udt-Cassegrain system) and attempts
been made to flatten the focal plane
acing a plano-convex lens at this
In essence however the Schmidt
n has provided a means of achieving
relative apertures with reasonable
ngles without the large mass of glass
ubsequent absorption and flare of
,rig systems.
of interest to exanliiic how Schmidt
his first correcting plate. In a simple
ous manner he cemented his plane-
d glass plate to a drum. By evacuating
in the drum he caused the plate to
ew h edths of an inch, and then
d andshed the distorted plate to
Iqw spherical curve in the normal
T. On readmitting the air and releas-
Strain the plate took on the aspheric
D4 one side.
e these early days, iniany methods
peen attempted in figuring Schmidt
;drs, these include, electromagnetic
applied in annular rings, and various
;,kchniques.4 .
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Apart from their astronomical uses,
Schmidt systems have found ni,anv other
applications, anion elst them projection
systems for tclevisicni purposes, where the
problem, of a curved t