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10.2.4.1. Houghton camera 1
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10.2.4.3. Houghton telescopes
► 10.2.4.2. Houghton camera: planosymmetrical correctorFor the fixed lens shape factor q, correction of aberrations is less flexible. Spherical can always be corrected, but zero coma requires particular corrector location (assuming stop at the corrector). The most interesting arrangement of this kind is a pair of planoconvex and planoconcave lenses with the lens shape factor q=1 for both elements (which means that the curved surface in both cases faces incoming light) of equal surface curvatures of the opposite sign. In this case, the lens element focal length (absolute value) cancelling spherical aberration of the mirror is, from Eq. 136, given by:
with R being, as before, the mirror radius of curvature. Needed radius of curvature (absolute value) for corrected spherical aberration for the two lenses is:
The lowerorder coma coefficient of the corrector is constant, given by ccr=[(n+1)/n(n1)]1/3/2R2, after substituting Eq. 144 into Eq. 138 and setting q=1. For zero coma, needed corrector location is, after setting Eq.140 to zero, given by:
with σ being, as before, the mirrortocorrector separation in units of the mirror r.o.c. For n=1.52, the zero coma corrector separation would be 0.264R (FIG. 193). FIGURE 193: General prescription for planosymmetrical Houghton corrector made of a pair of planoconcave and planoconvex lenses with equal curvatures of the opposite sign (planoconvex in front, curved sides of both lenses facing incoming light), can be made very simple for the Newtonian configuration. For given mirror radius of curvature R, needed surface radius of curvature (absolute value) for the two lenses is R1,3= (n1)f1,3 = (n1)[(n+1)/n(n1)]1/3R. Lens thickness should be sufficient to resist flexure, and the two lenses are in contact or nearcontact. Eq.145 gives needed separation for corrected coma. In general, it requires relatively large secondary, in proximity of D/2. In the Newtonian arrangement, with the corrector moved somewhat farther away from the mirror, in order to facilitate smaller obstruction by the diagonal flat, low residual coma remains, but it is insignificant for most practical purposes. Chromatic correction is not as good as with Schmidt corrector, but remains generally low with a singleglass corrector as long as mirror relative apertures do not exceed ~ƒ/2.5. It can be significantly reduced if corrector is made of two different glass types. Note that these expressions use the thin lens approximation for primary aberrations, therefore they are not necessarily sufficiently accurate. While they are adequate for ~ƒ/4 and slower mirrors, raytracing and optimization are recommended when the primary mirror is of large relative aperture (~ƒ/3, and larger). FIG. 194 illustrates Houghton camera performance at ƒ/3.
A few more words on interesting possibility of placing this type of the Houghton corrector between mirror and its focal plane, for cancelled spherical aberration and coma. Depending on the glass refractive index, the aplanatic corrector location is anywhere between ~0.7ƒ and ~0.5ƒ (ƒ=mirror focal length) from the mirror, for the glass index ~1.65 to ~1.5, respectively (Eq. 145). It offers good performance in an ultimately compact, easy to build cameratype instrument, with low astigmatism and, for most practical purposes, flat field (FIG. 195).
Another option of reducing the size of obstruction is inclusion of a simple subaperture corrector doublet to correct residual coma for stop positions farther away from the primary (FIG. 196). Aberration coefficients of the subaperture corrector are different than those given for the fullaperture, due to it being placed in a converging cone of light. Consequently, the position factor p for both lens elements of the subcorrector has its value changed according to Eq. 97.
Use of the integrated subaperture corrector yields even better results in a twomirror HoughtonCassegrain camera. Due to compensating effect of the secondary's field curvature, it is possible to design a flatfield anastigmatic aplanat, with excellent color correction (FIG. 197).
This is not the best possible configuration,
but it is illustrative of the level of correction achievable with this
type of systems. ◄ 10.2.4.1. Houghton camera 1 ▐ 10.2.4.3. Houghton telescopes ►
