Ritchey Chrétien Corrector System Seymour Rosin

Kollsman Instrument Corporation, 80-08 45th Avenue, Elm-hurst 73, New York. Received 23 November 1965.

In two earlier papers1-2, the writer has described catadioptric systems of a relatively simple nature but corrected for all of the third-order aberrations. The refracting elements are small com­pared with the diameter of the system aperture. The system described below has the same general properties.

I t is well known that the classical form of Cassegrain system (paraboloid primary, hyperboloid secondary) has approximately the same amount of coma as a single paraboloid of equivalent focal length. By allowing the eccentricity of the primary to in­crease slightly and suitably changing the secondary to retain spherical aberration correction, we arrive at the well-known Ritchey Chrétien form in which coma is simultaneously cor­rected. The increase in field performance has recently been set forth in rather dramatic form by Schulte3, especially in Fig. 1 of his paper.

Fig. 1. Optical layout of system.

Table I. Design Data of System

α Ritchey Chrétien primary e = 1.0704. b Ritchey Chrétien secondary e = 2.7570, E F = 1120, BF =

39.74.

However, the Ritchey Chretien form is not completely cor­rected for the field, in that residual undercorrected astigmatism and field curvature still exist and their effects are apparent in Schulte's figure. This letter is for the purpose of giving the principles of designing a simple two element corrector for the Ritchey Chretien, comprised of spherical surfaces only.

In an earlier paper4, the writer has pointed out that a lens bounded by surfaces concentric with the image point does not contribute to the primary spherical aberration or coma, but has a substantial effect on astigmatism, equal to the algebraic sum of the Petzval contributions by those surfaces. The lens may be of glass if the desired contribution is towards undercorrection of the astigmatism or of air if toward overcorrection. Thus, if this concept were used to neutralize the Ritchey Chretien astigma­tism, an air lens is needed. Referring to Fig. 2 of Ref. 4, an all­iens is shown, the external surfaces of the bounding lenses being piano. I t was pointed out to the writer by Bechtold5 that aplanatic surfaces could be used in place of the piano ones for getting into and out of the two glass elements that bound the concentric air lens.

Once astigmatism is corrected, an extra degree of freedom is needed for the correction of field curvature. This is obtained by allowing the two elements to be of different index of refraction. The dispersion values of these elements may be chosen to mini­mize any color contributions introduced by their presence.

These principles were used on a specific Ritchey Chrétien sys­tem mentioned to the writer by C. G. Wynne as suitable for a ground based astronomical facility. The specifications were for an F / 4 primary and an F/10 system with an aperture of 266.7 cm.

The formula for the system is given in Table I. I ts layout is given in Fig. 1.

The third-order aberration coefficients are given in Table I I , assuming the system stop is a t the secondary mirror.

Note that, in Table I I , the aplanatic surfaces 3 and 6 have zero contributions to spherical aberration, coma, and astigmatism, and the concentric surfaces 4 and 5 zero contribution to spherical aberration, coma, and axial color. The identical contributions to astigmatism and curvature are shown for each of the concentric surfaces.

In the equations for the curvature of the sagittal and tangential fields where

and

we find from Table I I , for the Ritchey Chrétien alone,

April 1966 / Vol. 5, No. 4 / APPLIED OPTICS 675

Table II. Aberration Coefficients of System

and for the corrected system

I t is interesting to note that, in cases where the diameter of the lenses exceed 20 cm or so, and normal test plate techniques be­come inadequate, each of the glass elements and the two together as a pair may be tested separately by knife-edge methods, with­out the need for nulling refractive optics. For example, the negative lens can be tested by setting up a point source at a dis­tance corresponding to point 7. Rays will be refracted aplanati-cally through surface 6 and strike surface 5 normally, whence after reflection they will return upon themselves to the knife edge. The positive lens can use a point source at the center of surface 4 through which the rays will pass undeviated. Refraction through surface 3 will take place aplanatically, and a reflecting test sphere can be used to return them. Finally, after assembly into their cell, the pair can be knife-edged by a source at 7 and a reflecting test sphere placed beyond surface 3.

The design was derived by third-order methods alone. No rays have been traced since these will depend upon the exact equations for the Ritchey Chretien. If the primary is chosen as

an exact hyperboloid, the secondary may have polynomial terms to compensate for higher order spherical aberration. The labor of doing this calculation is not worth while until a specific design is to be constructed. Higher order effects from the aplanatic and concentric lens surfaces are likely to be quite small. How­ever, in advance of submitting for publication, an analysis of this system has been made by Schulte indicating that the major higher order aberration of this system arises from fifth-order astigmatism caused by nonbalancing and overcorrecting contributions from surfaces 3 and 6. These can be largely com­pensated by a slight readjustment of the concentric radii 4 and 5 without upsetting the concentric feature.

While the given design is relevant only to the specifications given, the method of employing these elements comprised of aplanatic and concentric surfaces should yield equally satisfactory results for Ritchey Chretien systems over a wide range of values.

References 1. S. Rosin, J. Opt. Soc. Am. 51 , 331 (1961). 2. S. Rosin, Appl. Opt. 3 , 151 (1964). 3. D. H. Schulte, Appl. Opt. 2, 141 (1963). 4. S. Rosin, J. Opt. Soc. Am. 49, 862 (1959). 5. E. W. Bechtold, private communication.

676 APPLIED OPTICS / Vol. 5, No. 4 / April 1966