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10.2.4.7. Houghton-Cassegrain: designing   ▐    11. Solar telescope
 

10.2.4.8. Houghton-Cassegrain vs. Schmidt- and Maksutov-Cassegrain

In the conclusion, a comparison with near-optimized catadioptric two-mirror systems with spherical mirrors and an /3 primary is made: the SCT, MCT, and three HCT varieties: one standard aplanatic (symmetrical), with a pair of equal lens surface curvatures of opposite sign, the other with plano-symmetrical, and the third with asymmetrical, or all four surface radii different (FIG. 208).


FIGURE 208: Basic design comparison between five different 200mm /3/10 full-aperture catadioptric systems. On the LA plot, the orange is the r-line, and the pale blue is h-line. The coma blurs are reduced by a factor of 0.5. The circle represents the Airy disc diameter. Numerical data is given in the following table.                       SPECS: 1 2 3 4 5 
 

     /3/10
    SYSTEMS
 
    e-line
      RMS error
     h-line
       RMS error
     r-line
       RMS error
0.5 field
     RMS error
    best field
    curvature
 SCT 0.002 0.037 0.013 0.35(coma) -440mm
 MCT 0.023 0.05 0.03 0.05 -460mm
 HCT symmetrical 0.008 0.065 0.035 0.02 -460mm
 HCT plano-symm. 0.007 0.06 0.04 0.38(coma) -440mm
 HCT asymmetrical 0.004 0.05 0.03 0.05 -450mm

TABLE 14: Basic performance data for near-optimized two-mirror telescopes featuring the three main types of a full-aperture corrector: Schmidt, Maksutov and Houghton. The color errors are for the field center, and the 0.5 degree field radius error is for the best image surface. The three HCT systems are with correctors made of two different glass types, for improved chromatic correction. All systems have spherical mirrors.

Either Houghton or SCT-type correctors are capable of excellent axial correction for the optimized wavelength, while the Maksutov already (with an /3 primary) shows higher order spherical not correctable without adding special aspheric surface terms. While the rest of systems could, with perfect surfaces, achieve even better axial design correction than those given in the table, Maksutov remains just under - very respectable - 1/50 wave RMS axial e-line correction. It indicates that the primary mirror relative aperture limit for highly corrected MCT telescopes is at ~/3 level.  Off-axis, the SCT and the plano-lens HCT are clearly inferior to the rest of systems, due to uncorrected system coma. Best field curvature is nearly identical in all five systems, and astigmatism is generally low.

Chromatism-wise, the SCT is clearly ahead, with the combined h-line and r-line error of ~1/20 wave RMS (note that it is for the corrector with 0.707 neutral zone; the seemingly popular 0.866 neutral zone version has the error doubled). Achromatized asymmetrical HCT and the MCT are about equal with a nearly doubled combined error of the SCT. The two remaining HCT systems, one standard and the other with plano-lenses, have nearly identical combined error of ~0.1 wave RMS, which is about double the SCT error, and about 25% more than the other two systems. It should be noted that even the lower end systems in this comparison still have exceptional chromatic correction. For instance, the combined h-line and r-line RMS wavefront error of the standard 4" /15 doublet achromat is ~3.4 wave (~3 waves for the h-line alone).

From another perspective, taking a popular definition of apochromatic correction for refractors that, in regard to color correction, requires ~1/2 wave P-V at the g-line (436nm),  or better, and translating that into ~0.15 wave RMS limit, all five of our contenders are much better, with the g-line error ranging from 0.024 (SCT) to 0.057 (standard HCT) wave RMS.

The MCT has lowest secondary spectrum, but due to its underlying residual higher-order spherical, its wavefront error is larger across the spectrum. Single-glass Houghton correctors suffers from considerable more chromatism than their achromatized version. The standard, aplanatic HCT system has the combined (h+r)/2 error of 0.46 wave RMS (0.36@h+0.1@r), or 4-5 times more when made of a single glass. The single-glass plano-symmetrical HCT has the combined RMS error of ~0.23 wave (0.18@h+0.05@r), or more than double the achromatized corrector. The asymmetrical Houghton corrector benefits similarly from achromatizing: its single-glass version has 0.115 wave combined RMS error (0.09@h+0.025@r), more than two times greater. Better chromatic correction in the latter can be achieved by allowing more of spherical aberration (still very low), so these numbers are somewhat flexible.

It should be noted that Schmidt corrector can also be achromatized, which more than halves its chromatic error. However, with the Schmidt achromatizing involves more than just picking up a different glass type: it requires working two surfaces each nearly twice as strong as a single surface of the non-achromatized corrector, and cementing the elements. Likewise, achromatic Maksutov requires significant amount of additional work, unlike the Houghton, which can be achromatized simply by making it out of two different glass types.

The reason why the MCT is not competing to the SCT at the level of very compact systems with ~/2 primary is that its residual higher-order spherical would make it practically unusable with that fast mirror. To a smaller degree, it is a problem with the HCT, which for high-level correction requires ~/2.5 primary, or slower. Neither HCT nor MCT have the convenience of a relatively easy to apply higher-order surface term, offered by the aspheric Schmidt corrector. As their surfaces become strongly curved - which is in particular characteristic of the Maksutov corrector - there is simply no remedy for the quickly raising higher-order spherical.

Even with an /2 primary, the SCT is still at ~0.08 wave RMS g-line error, while its combined h/r error is 0.18 wave RMS. The MCT with an /2 primary has combined h/r error of 0.35 wave RMS, but its real problem is that its 6th order spherical can't be significantly lower than ~0.15 wave RMS with this fast primary. The symmetrical aplanatic HCT has similar problem; however, if it is allowed to have about as much coma as the SCT, it achieves 0.037 wave RMS level - perhaps somewhat better - at the optimized e-line, and a ~0.4 wave RMS combined h/r RMS error. Plano-symmetrical HCT with an /2 primary has about double the coma of the SCT, thus at least partial aspherizing of the secondary is almost mandatory (another option, as mentioned, is a system designed with an integrated sub-aperture coma corrector). With the 0.33 wave RMS combined h/r error and about as good e-line correction as desired, it is second only to the asymmetrical HCT and SCT. In combination with an integrated sub-aperture coma-corrector, plano-symmetrical HCT is very much attractive, both, from the standpoint of ease of fabrication and performance level.

Overall, in the /2-/3 primary range, Houghton corrector in its best form is close second to the Schmidt, and has more advantages than disadvantages when compared to the Maksutov corrector. Hence, there is no detectable factual reason for the nearly complete absence of Houghton-style two mirror systems in the world of actual telescopes.


10.2.4.7. Houghton-Cassegrain: designing   ▐    11. Solar telescope

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