telescopeѲptics.net
▪
▪
▪
▪
▪▪▪▪
▪
▪
▪
▪
▪
▪
▪
▪
▪ CONTENTS
◄
10.2.4.2. Houghton camera 2
▐
10.2.4.4. Secondary spectrum reduction
► 10.2.4.3. HoughtonNewtonianThe only difference between Houghton camera and a telescope in Newtonian configuration is in the focal length of the mirror, and position of the corrector. In general, corrector separation in HoughtonNewtonian is somewhat larger, to accommodate for a smaller obstruction by diagonal mirror. The two corrector types most interesting to amateurs are symmetrical aplanatic and planosymmetrical. The only remaining aberration with the former is mild field curvature (FIG. 198b). The latter retains low residual coma of little or no consequence for general observing, with similar mild field curvature (FIG. 198a). Follows its description in more details. For n=1.52, the corrector position for zero coma would be at 0.264R (Eq. 145). Moving it to a more practical location in the Newtonian arrangement, say, 0.43R, wouldn't change coma coefficient of the corrector (Eq. 138), but would change that of the mirror. Consequently, sum of the two coefficients is not zero anymore and, for spherical primary, it determines the system coma aberration coefficient as cs=(σ*σ)/R2, where σ and σ* are the zerocoma and the actual correctortomirror separation, respectively. In this case, cs=0.166/R2, which is 1/6 of the mirror coma aberration coefficient, given by 1/R2. This means that the system will have 1/6 of the mirror coma. For an ƒ/4.5 primary, that would result in the comafree linear field at the level of an ƒ/8.2 mirror. It is about half the coma of the comparable MaksutovNewtonian, and ~1/3 the coma of the SchmidtNewtonian. FIGURE 198: Ray spot plots for Houghtoncorrector systems in a Newtonian arrangement. (a) Planosymmetrical corrector type consists of a planoconvex and planoconcave element, thus does not cancel the system coma for every corrector location. However, this has little practical significance. At the location supporting diagonal flat in a regular Newtonian configuration (~0.85f in front of the mirror), some residual coma is visible in the spots, but hardly any in actual observing. (b) Symmetrical aplanatic corrector type, with two radii on four surfaces, also corrects for coma. Coma with planosymmetrical corrector can be cancelled if the corrector is moved halfway between the mirror and the focal plane (c), which would result in larger central obstruction, still acceptable for photographic purposes. The small circle represents the size of the eline (446nm) Airy disc. SPEC'S Chromatic correction is excellent, as long as the mirror is not significantly faster than ~ƒ/4.10.2.4.4. Twomirror Houghtoncassegrain telescope  aplanaticFullaperture Houghton corrector can also be used as a part of twomirror catadioptric system (FIG. 199). The only difference vs. singlemirror arrangement on the above is that the aberrations of the secondary are to be added. They are identical to those given for SchmidtCassegrain telescope. The HoughtonCassegrain has the advantage of allowing coma correction in an allspherical arrangement for any location of the corrector. However, for that it requires putting a curve on at least three out of four surfaces.
For lowerorder spherical aberration of the primary cancelled, the sum of the three aberration coefficients  for the corrector (Eq. 134 in general, Eq. 135 for q1=q2), primary and secondary mirror (Eq. 113)  has to be zero. The coefficient sum sH+s1+s2=sS, respectively, will result in the system PV wavefront error at the best focus of: Ws= ssD4/64 (146) with D being the aperture diameter. Presence of the glass refractive index n in Eq. 130131 indicates that spherical aberration can be cancelled only for a single wavelength. The nonoptimized wavelengths are affected by spherical aberration, resulting in spherochromatism. In combination with spherical mirror, needed corrector's aberration coefficient for zero spherical aberration at the optimized wavelength with the refractive index n is s=n(n1)(n+1+ι)/4(n+1)(n+ι)(n1+ι)R3=1/4R3 for the index differential ι=0 (from Eq.135, with q substituted by Eq. 136). Thus, the aberration coefficient for spherochromatism of the Houghton corrector is given by:
with ι being the index differential ι=nni, and R the mirror radius of curvature. Hence, the PV wavefront error of spherochromatism at the best focus for nonoptimized wavelengths (i.e. ι≠0) is: Ws=s'D4/64 (148) A good empirical approximation of the spherochromatism coefficient, yielding ~5% greater value, is given by s'~0.8ι/R3, or s'~ι/10ƒ3 in terms of the mirror radius of curvature, or focal length, respectively. Substituted in Eq. 148 it gives the PV wavefront error of spherochromatism at the best focus as: Ws~ Dι/640F3 (149) with F being the mirror focal ratio. Negative index differential for shorter wavelengths makes them overcorrected at the best focus, while longer wavelengths are undercorrected. Compared to the PV wavefront error of spherochromatism at best focus of the Schmidt corrector (Eq. 106), that of the Houghton is greater by a factor of ~1.6 for the Schmidt with the neutral zone at 0.707 the radius, and lower by a factor ~0.8 for the Schmidt with the neutral zone at 0.866 the radius. However, Schmidt corrector with 0.707 radius neutral zone has the advantage of best foci of all the wavelengths coinciding, ensuring virtually zero secondary spectrum. This is not the case with this form of the Houghton corrector (symmetrical aplanat type), which can have significant secondary spectrum. While there is no significant difference in spherochromatism level with other Houghton corrector types, their secondary spectrum is generally significantly smaller. Also, the comparison is for the lowerorder spherochromatism alone; at some point higherorder spherical becomes significant aberration contribution, again, in particular with the symmetrical aplanat type, and needs to be taken into account. These are comparisons for a singlemirror system, but they remain nearly unchanged for twomirror systems as well. The only difference is that the power of the corrector  and its chromatism  are somewhat lower, due to the aberration of the primary being partly offset by the secondary. While spherochromatism does contribute to the level of chromatism of the Houghton corrector, more of a limiting factor can be its secondary spectrum. This is definitely the case with the symmetrical aplanat type, while much less with the planosymmetrical and asymmetrical type, the later being limited by spherochromatism (FIG. 200). In comparison, Schmidt corrector has secondary spectrum practically cancelled, with the only source of chromatism being spherochromatism, while the Maksutov has nearly cancelled secondary spectrum, but suffers from strong higher order spherical at all wavelengths.
While not a factor with ordinary Newtonianstyle systems, chromatism level of twomirror Houghton systems sets the limit to how fast the primary can be at ~ƒ/3 with the aplanatic singleglass Houghton corrector (FIG. 201). Reduction in the chromatism can be obtained by allowing for a relatively small amounts of residual coma, allowing for more weakly curved lenses, as illustrated on FIG. 201c.
Fortunately, Houghton
corrector as an optical arrangement offers various possibilities for
significant reduction in the level of chromatism. Some that are most
appropriate are presented in more details in the following section. ◄ 10.2.4.2. Houghton camera 2 ▐ 10.2.4.4. Secondary spectrum reduction ►
