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10.2.2.1.
Schmidt camera: aberrations
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10.2.2.3. Schmidt telescopes
► 10.2.2.2. Wright and Baker camerasThe similarity between these two camera concepts is that they both use Schmidt corrector with aspherized mirror, although the form of mirror aspherizing is exactly the opposite. In addition, the Baker camera uses subaperture corrector as an integral system element. 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. 171A), 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 mirrortostop 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(1K)]/(1+K), zero coma requires σ=1/(1+K), which in turn, for the flatfield stop location requires √0.5(1K)=0. Thus, to a thirdorder, 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 higherorder offaxis aberrations, mainly coma). FIGURE 171A: Schmidt and Wright camera of identical apertures and focal ratio. Wright camera is only 1/2 the length of the Schmidt. However, from 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 substantial 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 flatfield 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+(1σ)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 PV wavefront error (from Eq. 1920) 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 thirdorder, 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 flatfield performance is better than that of a comparable standard Schmidt, although it is a mixed bag, considering its inferior axial correction due to spherochromatism. Its geometric offaxis blur size is smaller by a factor of two (FIG. 171B), 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.
In terms of the wavefront error, the flatfield PV errors are identical in both, Schmidt and Wright, given by W=h2/16DF3. However, while the offaxis error in the flatfield Schmidt results from defocus, in the Wright camera it is caused by astigmatism. Since the RMS/PV error ratio is smaller by a factor of √0.5 for astigmatism, the actual quality flatfield radius in the Wright camera is larger by a factor of 1.4. BAKER PARABOLIC CAMERA Among many of the designs invented by James Baker is a camera that uses paraboloidal mirror (K=1) with subaperture coma corrector. Since the latter also induces undercorrection, Baker placed a Schmidt corrector inside the focus of a paraboloid to offset the aberration. The coma corrector also nearly eliminates image curvature and astigmatism generated by the mirror, producing flat, highly corrected field. Originally, the camera was intended for imaging in a limited spectral range (as plots below indicate, green and blue, with the red and violet left out), but it can be modified to have nearperfect correction across the entire visual range, and somewhat into infrared.
The coma corrector also reduces mirror focal length by over 20%, making
mirror fabrication relatively easy for camera focal ratios down to ~ƒ/3.
The Schmidt corrector, however, is not as weak as its 4th order aspheric
parameter might suggests. Using Eq.
102 we find that the focus factor
Λ corresponding to the parameter and radius value is
5.06. And Eq. 101 gives the
maximum depth (for ρ=1) of nearly 0.03mm, which agrees with ray
trace (field lens induces 56% more spherical aberration than what the mirror
would have, if spherical, hence the corrector is that much
stronger than what it would have been for spherical mirror). Since the
factor
Λ is larger than 2, it implies that the neutral zone is
out of the surface, i.e. that the profile is a smooth convex aspheric.
What creates this profile depth is the radius value, which is disproportionally strong for the aspheric parameter. Its purpose is not correcting spherical aberration  that is determined by the parameter value alone  rather to minimize spherochromatism by determining longitudinal placement of nonoptimized wavelengths. In this particular arrangement, with very low spherochromatism due to the low aspheric parameter (i.e. relatively low amount of the aberration to correct), the primary role of putting the radius on the aspheric is to minimize lateral color error (change in the radius value affects the longitudinal chromatic foci, but not the lateral color error, since the corrector is at the aperture stop and its central portion is practically a plano parallel plate for this weakly curved surfaces). Without it, the needed corrector depth with the 0.707 neutral zone profile would have been less than 2 microns. Some other glass combinations may allow for the weaker, shallower profile  for instance, FPL53/FK5 has a good control of lateral color with the radius value of 155,000mm, resulting in 26% smaller depth.
