10.2.2.2. Wright camera

In 1935, just a few years after the introduction of the Schmidt camera, Franklin Wright (Berkley, California) presented his "short" alternative to the original arrangement. He placed Schmidt corrector at the focal plane (FIG. 171), and aspherized the mirror in order to cancel coma resulting from the altered stop position. While astigmatism remains present in the Wright camera, it conveniently combines with the mirror Petzval curvature to result in a flat best image surface. The Wright design logic can be followed with two simple relations. Knowing that mirror coma changes with a factor 1-(1+K)σ, where K is the mirror conic and σ the mirror-to-stop separation in units of the mirror radius of curvature, and that mirror's best astigmatic surface becomes flat with the stop separation σ=[1-√0.5(1-K)]/(1+K), zero coma requires σ=1/(1+K), which in turn, for the flat-field stop location requires √0.5(1-K)=0. Thus, to a third-order, for zero coma and flat astigmatic field K=1 (oblate ellipsoid) and σ=0.5. Reducing the conic K at this stop location would introduce both, coma and field curvature (the conic is a subject to minor changes in optimizing for the effect of higher-order off-axis aberrations, mainly coma).

FIGURE 171: Schmidt and Wright camera of identical apertures and focal ratio. Wright camera is only 1/2 the length of the Schmidt. However, from the practical standpoint, with twice as strong corrector as required for the Wright, the Schmidt would have relative aperture greater by a factor of ~1.25 and the tube longer by a factor of 1.6, not 2. And factoring in less than trivial amount of work needed to make Wright's strongly aspherized primary, even faster and shorter Schmidt could be made with similar amount of time and effort invested. The tube length difference between the two would become relatively small; the only advantage of the Wright camera would be its flat-field performance, and the absence of spider vanes. On the other hand, Schmidt camera would have far superior best field performance, less chromatism and significantly larger relative aperture. Considering that field curvature in the Schmidt can be easily corrected with a field flattener lens, Wright camera has quite limited appeal.

With mirror astigmatism changing in proportion to Kσ2+(1-σ)2, for the given values of K and σ, Wright camera astigmatism is 1/2 of the mirror astigmatism with the stop at the surface. That gives the P-V wavefront error (from Eq. 19-20) as W=(αD)2/8R = -Dα2/16F = -h2/16DF3, and the transverse error - as the diameter of the least circle of confusion - T=4FW=-h2/4DF2, where α is the field angle in radians, D the aperture diameter, R the mirror radius of curvature, h the linear height in the image plane and F the mirror focal ratio (the minus sign for transverse aberration indicates that the aberrated ray in tangential plane focuses shorter than perfect reference wavefront).

Glance at the properties of the corrector shows that needed aspheric coefficient b for cancelling spherical aberration of the Wright's primary mirror is doubled in comparison to the original Schmidt arrangement. To a third-order, it is given by b=2(K+1)[1-(Λ/16F2)]/R3, which is identical to Eq. 103, except that the mirror aberration coefficient for spherical mirror (1/R3) is now given in its general form: (K+1)/R3. Simpler relations, given by Rutten and Venrooij (p285) for Schmidt corrector camera system in general, give the corrector power (which is the needed aspheric coefficient b normalized to 1) as P=1/σ, and needed conic for an aplanat as K=(1/σ)-1. Doubled aspheric coefficient - or "power" - with respect to the standard Schmidt results in a doubled wavefront error (Eq. 106) and transverse aberration (Eq. 107.1) of spherochromatism. Considering low spherochromatism of the standard Schmidt, it becomes significant only at ~ƒ/2 and faster systems.

The need for more strongly aspherized corrector and, especially, strongly aspherized fast mirror (into a rather unpopular type of aspheric shape) is more of a disadvantage. On the good side, Wright camera is only about half the length of the standard Schmidt. Since the corrector nearly coincides with the image plane, it can support film/detector assembly, clearing the optical path from supporting vanes. Wright's flat-field performance is better than that of a comparable standard Schmidt. Its geometric off-axis blur size is smaller by a factor of two (FIG. 172), with the defocus blur diameter in the Schmidt - from Eq. 26, after substituting the image curve depth for L - being given by Bs= h2/2DF2.

FIGURE 172: Imaging performance of 200mm ƒ/2.4 camera in the Schmidt and Wright arrangements for 1° field radius (black circles are the Airy disc). On axis, Schmidt camera has the benefit of twice lower chromatism. Off-axis, flat-field performance is somewhat better with the Wright. However, best image surface of the Schmidt has significantly better field quality. The off-axis blur size in the Wright camera is mainly result of astigmatism, with the color error being relatively insignificant. It should be noted that both, Wright and Schmidt in this example, have 0.866 radius neutral zone placement. This means that non-optimized colors at the optimum focus are the circles of least confusion, with the blur/error ratio similar to that of defocus in achromats. With the neutral zone at 0.707 radius, the blur doubles, but the error halves. In such arrangement, Wright camera at ƒ/2.4 still have chromatism of a 4" ~ƒ/50 achromat. Practical upper limit to the relative aperture for the Wright camera is a function of the field size desired. For the system shown, the blur is already near 0.025mm 1° off-axis. What makes it worse is that the blur is astigmatic, meaning that it represents larger wavefront error than most any other aberrated blur (larger by a factor of 5.5 from spherical aberration blur at best focus, or 33% from defocus blur of the same size). Since the blur size changes in inverse proportion to the third power of the F# and in proportion to the aperture size, larger quality field requires either slower system or smaller aperture, or both. SPEC'S

In terms of the wavefront error, the flat-field P-V errors are identical in both, Schmidt and Wright, given by W=-h2/16DF3. However, while the off-axis error in the flat-field Schmidt results from defocus, in the Wright camera it is caused by astigmatism. Since the RMS/P-V error ratio is smaller by a factor of √0.5 for astigmatism, the actual quality flat-field radius in the Wright camera is larger by a factor of 1.4.

◄ 10.2.2.1. Schmidt camera: aberrations ▐ 10.2.2.3. Schmidt telescopes ►

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