Whitepeak Observatory, Tacoma, WA

Contrast Transfer Comparison Between Perfect and Rayleigh Criterion Unobstructed Systems



NOTE: all bars should be discernible in this grayscale calibration image for the illustrations to best convey the information they offer. The contrast differential should be visibly equal between the bottom 150 line blocks in the grid boxes on the right side of the above and below images. If either area is pure white or pure black, then your monitor is incorrectly adjusted.

(these images are large size BMPs for a reason--a smaller jpeg's compression would smear the grids rendering them useless as visual comparative aids.)

Telescope can be thought of as "contrast translators". As in the phrase "lost in the translation" all telescopes translate less contrast to their focal planes than exists in the actual target. The Modulation Transfer Function diagram is a graphic representation of how much contrast a particular system "loses in translation" due to various degrees of optical defect.

A telescope's MTF reflects its strehl rating, but the shape of the resultant MTF curve, and thus the telescope's contrast "translation" abilities, can vary widely depending upon the aberration that is predominant even though the strehl figure may remain constant. That said, the most common primary optical defect is spherical aberration of the lower orders. The Rayleigh Criterion specifically addresses spherical aberration. It sets a maximum standard for the permissible degree of spherical aberration allowed in an optic designated "diffraction limited" (maximum 1/4wave aberration at the focal plane). The Rayleigh Criterion thus provides a basis on which relative comparisons between a diffraction limited optic and a perfect optic can be made. (The Rayleigh Criterion is an optical quality standard; the Rayleigh Limit specifies the maximum stellar resolution of an optic which has been manufactured to the Rayleigh criterion.)

The lower strehl of a diffraction limited system (typically considered to correspond to 0.82 strehl) means it translates less contrast than a perfect system (strehl 1.00). But the loss is not uniform. The most dramatic contrast loss in a diffraction limited system is in gross resolution, of those features the most broadly defined (ex; large lunar crater wall shadows, broad rilles, the main belts of Jupiter). There is also a considerable deficit in those bright targets having very low innate contrast, such as belt detail on Saturn's disk. But the contrast deficit of the diffraction limited system becomes inconsequential upon high contrast targets (moon and double stars). As the scale of the finest lunar detail or double star separations approaches the resolution and contrast threshold below which the eye can no longer resolve or sense any contrast difference whatsoever, there is virtually no detectable difference between the resolution of a diffraction limited system and a perfect optical system. Here are some specifics:

Low contrast, bright target resolution: (ex. Saturn's disk): 98lp/mm max (visual threshold @5% contrast differential), 40% obstructed is -27% resolution (61lp/mm to 98lp/mm), 1/4 wave is 30% less aberrated at this point, therefore the loss in resolution of a diffraction limited system to the perfect system on threshold contrast targets is ~ 18%, This amounts to about a 1" aperture deficit in resolution. So, a 6" diffraction limited system will deliver essentially the same level of discreet planetary resolution as a perfect system of 5" aperture.

High contrast, bright target resolution: (ex.lunar formations defined by shadowing and double stars) maximum resolution (of 180lp/mm possible) is at 157lp/mm for a perfect system at a 5% contrast visual threshold; for a diffraction limited system this point lies at 153lp/mm. This amounts to a 2.5% deficit to the perfect system or about two hundredths of a second arc resolution loss--which is beyond the eye's ability to differentiate.

High contrast, dim target resolution: (deep sky) Here comparative contrast ranges from a negligible ~4% resolution gain to the perfect optic at the maximum resolution level (about 130lp/mm at a ~17% contrast differential) to ~10% contrast gain to the perfect optic at half that resolution (65 lp/mm). In the latter case, the perfect optic delivers about 57% contrast and the diffraction limited optic about 47%.

references used: Rutten & van Venrooij, "Telescope Optics"
Conrady, "Applied Optics and Optical Design", vol. one and two
Sidgwick, "Amateur Astronomer's Handbook"
Ceragioli, "A Survey of Refractive Systems for Astronomical Telescopes"


Discussion:

The above analysis strictly applies only between apochromatic refractors, one having perfect (or essentially so) optics and another that is aberrated to the Rayleigh Criterion (about 0.82 strehl). back to main page