July 4, 1972
A. OFFNER
3,674,334
CATOPTRIC ANASTIGMATIG AFOCAL OPTICAL SYSTEM
Filed Jan. 4, 1971
1521: ‘(-120
TIQEL
10a
27 ' .4
INVENTOR.
A7216 ?ffizer
1
3%, KM
?TTORNEY.
United States Patent 0
1
3,674,334
Patented July 4, 1972
2
magni?cation different from unity, the system of this in~
3,674,334
vention can be made appreciably shorter than previously
known confocal parabola systems. This is illustrated in the
example, subsequently described in detail, wherein a Cas~
segrain f/ 2 system constructed in accordance with this in~
CATOPTRIC ANASTIGMATIC AFOCAL
OPTICAL SYSTEM
Abe Offner, Darien, Conn., assignor to The Perkin
Elrner Corporation, Norwalk, Conn.
Filed Jan. 4, 1971, Ser. No. 103,495
Int. Cl. G021) 17/06, 23/02
US. Cl. 350-55
1
vention to have an aperture of 400 has an overall length
of 333.333. In contradistinction an f/2 parabola system
of previously known design having an aperture of 400
would require an overall length of 800.
6 Claims
1O
ABSTRACT OF THE DISCLOSURE
A catoptric anastigmatic afocal optical system is formed
by two concave paraboloidal re?ectors of different powers
Further objects, advantages and features of the optical
system of this invention will be apparent from the follow
ing detailed description of illustrative embodiments shown
in the accompanying drawings in which:
and a convex hyperboloidal re?ector each adapted to re
FIGS. 1, 2 and 3 are schematic illustrations of three
ceive and focus radiant energy. A paraboloidal re?ector 15 varied forms of the system of this invention, and
and the hyperboloidal re?ector have their axes optically
FIG. 4 is a schematic illustration of a speci?c embodi
coincident and are positioned with the real focus of this
ment of a system of the form shown in FIG. 2.
paraboloidal re?ector at the virtual focus of the hyper
Referring to FIG. 1 a ?rst concave paraboloidal mirror
boloidal re?ector. The axis of the other paraboloidal re?ec
10 having a central aperture 11 therethrough is positioned
tor is optically coincident with the axis of the hyper
to receive substantially collimated radiant energy from a
boloidal re?ector and its real focus is coincident with the
distant object and re?ect it to a convex hyperboloidal
real focus of the combination of the ?rst paraboloidal re
mirror 12 positioned to re?ect the energy received and
?ector and the hyperboloidal re?ector. By having the sum
focus this energy through the aperture 11 to a plane mirror
13 that is behind the mirror 10.
of the powers of all the re?ectors equal zero; all third
order aberrations except distortion are zero; if the sum
As shown, the plane mirror 13 is at the real focus of
the hyperboloidal mirror 12, whose virtual focus is in
is not zero, third order aberrations, other than ?eld curva
dicated at 14. The paraboloidal mirror 10 and hyperbo
ture and distortion, are zero.
loidal
mirror 12 are arranged with their axes optically
m
coincident and are spaced so that the real focus of the
30
paraboloidal mirror 10 is at the virtual focus 14 of the hy
The present invention relates to afocal optical systems
and particularly to a catoptric anastigmatic afocal tele
perboloidal mirror 12. Thus a plane wave front normal
scopic optical system, which provides high magni?cation
to the axis of the paraboloidal mirror 10 and incident on
in a relatively short length as compared with previously
it is converted into a spherical wave with its center at the
focus of paraboloidal mirror 10 which is coincident with
known systems, and with which all third order aberrations
35 the virtual focus 14 of the hyperboloidal mirror 12. The
except distortion may be reduced to zero.
hyperboloidal mirror 12 then reshapes the spherical wave
In accordance with this invention a three mirror system
is formed by a Cassegrain system, which consists of a ?rst
to a spherical wave having its center at the real focus (i.e.,
concave paraboloidal mirror and a convex hyperboloidal
at plane mirror 13) of the combination of the paraboloid
mirror, arranged confocally with a second concave para 40 and the hyperboloid.
boloidal mirror. Each of the three mirrors is adapted
The plane mirror 13 is tilted (e.g., at 90 degrees) to
to receive and focus radiant enegy. The ?rst paraboloidal
bend the energy received from the hyperboloidal mirror
mirror and the hyperboloidal mirror are positioned with
12 to a second paraboloidal mirror 15, which may have a
their axes optically coincident and are spaced so that the
different power from the ?rst paraboloidal mirror 10 and
real focus of the ?rst paraboloidal mirror is at the virtual 45 which re?ects a collimated beam of energy of a different
focus of the hyperboloidal mirror. The second parabo
diameter (smaller, as shown) than the beam entering the
loidal mirror is positioned with its axis optically coincident
system.
with the axis of the hyperboloidal mirror and its real focus
The mirror 13 makes the axis of the second parabo
coincident with the real focus of the combination of the
loidal mirror 15 coincident with the axis of the hyper
paraboloidal and hyperboloidal mirrors. With this arrange
boloidal mirror 12; thus the focus of the second parabo
ment, if the sum of the powers of the three mirrors is
loidal mirror 15 is concident with the real focus (i.e., at
zero, all third order aberrations except distortion are zero.
plane mirror 13) of the combination of the ?rst parabo
If the sum is not zero, the Petzval sum of the system is
loid and the hyperboloid. A spherical wave with its center
equl to the sum of the powers of the mirrors with reversed
at the real focus of the combination of the paraboloidal
sign and all third order aberrations, except ?eld curvature
mirror 10 and the hyperboloidal mirror 12 is therefore
and distortion are zero.
converted by the second paraboloidal mirror 15 to a plane
There are two particularly important’ advantages of
wave normal to the axis of the latter mirror.
this system over prior art systems consisting of two con
FIG. 2 shows a variation in which the powers of the
focal paraboloidal mirrors or re?ectors. The ?rst is that
mirrors are selected so that a convex hyperboloidal mirror
in this system, the sum of the powers of the mirrors can 60 12a is spaced in front of a concave paraboloidal mirror
be made equal to zero. When this is done, incident waves
10a a distance less than the focal length of the mirror 10a,
whose normals make an angle other than zero with the
with a plane mirror 13a at the real focus of the combina
optical axis are converted into plane waves, that is, the
tion of mirror 10a and mirror 12a to re?ect the energy
system is afocal for directions other than the axial direc
received therefrom to a second paraboloidal mirror 15a,
tion. The system consisting of two confocal paraboloids 65 the axis of which is at an angle to the axis of mirror 12a.
is afocal only in the axial direction. Plane incident waves
As in the FIG. 1 embodiment, the mirror 13a serves to
whose normals are at an angle, 0, with the optical axis are
make the axis of mirror 15a optically coincident ‘with the
converted into spherical waves with curvature equal to
axis of the mirror 12a.
the sum of the powers of the paraboloidal mirrors multi
In the' FIGS. 1 and 2 embodiments the arrangement of
plied by the factor (m0)2/2, where m is the telescopic 70 the hyperboloidal mirrors 12 and 12a, respectively, ob
magni?cation of the afocal system.
scure some of the collimated light conducted through the
A second important advantage is that for telescopic
system, either obscuring energy entering the system in the
3,674,334
The ?fth order aberrations have been included to show
that these also are quite small in this system in (which
the intermediate image is at ;f/ 2. Actual ray tracing
direction indicated in FIGS. 1 and 2 or leaving the system
if the energy is passed through the system in the opposite
direction.
through the system gives results that agree closely with
FIG. 3 illustrates a variation in which obscuration is
reduced to zero by arranging the mirrors o?’ axis and by
making the mirrors sections only of full mirrors. In this
variation the plane mirror is eliminated and the substan
the third and ?fth order predictions of the aberrations.
It will be appreciated that certain modi?cations may be
made in the structure and arrangement of the system of
this invention as illustrated by the several illustrative vari
ations described above without departing from the scope
tially collimated energy from a distant object is shown en
tering from the small aperture direction. Energy entering
this system is re?ected by a section 15b of a concave para
boloidal mirror to a section 12b of a convex hyperbo
10 of the invention de?ned by the following claims.
What is claimed is:
1. A catoptric anastigmatic afocal optical system com
prising: ?rst and second concave paraboloidal re?ectors
and a convex hyperboloidal re?ector adapted to receive
tion 12b and concave paraboloidal mirror section 10b is
at 16 which is also the real focus of mirror 15b. Energy is 15 and focus radiant energy, the ?rst paraboloidal re?ector
and the hyperboloidal re?ector being positioned with their
re?ected by the mirror 12b to the concave paraboloidal
axes optically coincident and being spaced so that the real
mirror section 10b whose focus is at the virtual focus of
focus of the ?rst paraboloidal mirror is at the virtual focus
mirror 12b and which in turn re?ects a collimated beam
of the hyperboloidal re?ector, and the second parabo
of the energy out of the system. As shown, the mirror
sections 10b and 1212 are arranged on one side of (below) 20 loidal re?ector being positioned with its axis optically
coincident with the axis of the hyperboloidal re?ector and
the optical axis OA while the mirror section 15b is on the
its real focus coincident with the real focus of the com
opposite side of (above) the optical axis.
bination of the ?rst paraboloidal re?ector and the hyper
FIG. 4 shows a speci?c example of a system in accord
boloidal re?ector.
ance with this invention, which is an embodiment of the.
2. The system of claim 1 in which the sum of the pow
form of the system shown in, and described with refer 25
loidal mirror which is spaced from the mirror section 15b
so that real focus of the combination of the mirror sec
ence to, FIG. 2. This is a 4x system with an intermediate
ers of said three re?ectors is zero.
image at f/ 2. The particulars are as follows:
3. The system of claim 1 in which the optical axes of
the hyperboloidal re?ector and of the second paraboloidal
re?ector are at an angle to each other and intersect, there
30 being a plane re?ector at said intersection making said
axes coincident.
Distance to
real focus
Type
4. The system of claim 3 in which the ?rst paraboloidal
re?ector has an aperture therethrough, the plane re?ector
and the second paraboloidal re?ector being behind and the
Distance to
virtual focus
hyperboloidal re?ector being in front of the ?rst parabo
loidal re?ector, and the hyperboloidal re?ector and the
plane re?ector being in optical alignment through said
aperture.
5. The system of claim 3 in which the hyperboloidal,
40 the plane and the second paraboloidal re?ectors are in
front of the ?rst paraboloidal re?ector, the plane re?ector
being between the hyperboloidal re?ector and the ?rst
paraboloidal re?ector.
Aperture Angular ?eld
diameter diameter, deg.
Object space .......................... _ .
400
2. 5
Image space .......................... . _
100
10
ABERRATIONS (IN RADIANS) IN IMAGE SPACE
3rd order
Spherical aberration .............. -_
Tangential coma _ . _ . . . _ .
Astigmatic d1?erence-.
Oblique sphe
50
5th order
—2. 2X10-8
2. 0X10-9
_ _ . . . . -_
2. 6X 10-8
2. 4X10-8
._
—5. 5X10-9
3. 8X10-5
__
0
—7. 4X10-?
-_
—4. 7X10-4
Tangential ..................................... ._
Radial ......................................... --
6. The system of claim 1 in which the re?ectors are
45 paraboloidal sections and a hyperboloidal section, respec
2. 7X10-5
55
Elliptic coma:
8. 8X 10-5
Radial ......................................... . .
2. 9X10'6
(4.85 X 10-8 radian)
This aberration does not a?fect the quality of the imagery
1,578,899
3,062,101
3,460,886
3/ 1926
11/ 1962
8/1969
Lohmann __________ __ 350-55
McCarthy _________ __ 350—-55
Rumsey _________ .... 350—55 X
OTHER REFERENCES
60
Ingalls, Telescopics 171 Scienti?c American, pp. 47
48, July 1944.
Holleran, Gleanings for ATM’s 27(4) Sky and Tele
scope, pp. 242-246, April 1964.
65
DAVID SCHONBERG, Primary Examiner
In this example, distortion is the only third order aberra
tion which is greater than about .01 are second
opposite side thereof.
References Cited
UNITED STATES PATENTS
—6. 1X10-5
4. 5><10-B
Tangential _____________________________________ . _
tively, in which the section of the ?rst paraboloidal re
?ector and the section of the hyperboloidal re?ector are
on one side of their coincident optical axes, and in which
the section of the second paraboloidal re?ector is on the
J. W. LEONARD, Assistant Examiner
of any direction in the ?eld. It affects only the magni?ca~
tion associated with di?erent directions.
70 350-294
US. Cl. X.R.