FR equivalents for apo, semi-apo, achromatic?

Probably people have posted lots about this before- is there a table (or formula(e)) for stating or determining approximate performance equivalencies from apo to achromatic lenses versus focal ratio (maybe aperture as a third variable)? I just picked up an old 80mm Towa achromat (F/15). Curious....

Jess Tauber

I'm not sure about other aberrations, but I believe the focal ratio of a achro needs to be 5 times its diameter before it shows little or no color.

Which works out OK for small apertures (like your 3" f/15 Towa) but a 10" would need to be f/50! 8O

The simplest way is to go with polychromatic Strehl. If we assume that an apo should have it 0.95 or better in the visual spectrum (400nm-700nm), an achromat pretending to this low chromatic error should be at this level.

For the standard Fraunhofer, polychromatic Strehl is closely approximated by ~1.3(F/D)^0.25 for (F/D)<0.25, and by (F/D)^0.07 for 0.25<(F/D)<1, where F is the focal ratio number, and D the aperture diameter in mm.

For 80mm f/15 that gives polychromatic Strehl of 0.86. Considering that most standard achromats - including 4" f/12 - are bellow 0.8 PS, it could be regarded as a semi-apo level.

For 0.95 PS, the 80mm would have to be f/40. But it would be real close at ~f/30 already.

Vlad

jess tauber said:

Probably people have posted lots about this before- is there a table (or formula(e)) for stating or determining approximate performance equivalencies from apo to achromatic lenses versus focal ratio (maybe aperture as a third variable)? I just picked up an old 80mm Towa achromat (F/15). Curious....

Jess Tauber

Jess: Here's my take as an observer who has done some reading...

There are basically two rules of thumb for the color correction in an Achromat, the 3X rule and the 5X rule. These refer to the focal ratio of the scope divided by the scopes aperture as measured in inches. This ratio is sometimes referred to as the Chromatic Ratio. The way I state these rules is:

3X: An achromat whose focal ratio is at least 3 times the aperture as measured in inches will have acceptable color correction. For an 80mm scope this is about F/9.5. The standard 80mm F/11 has a "chromatic ratio" of about 3.5. I have owned several 80mm F/11s and all have had very similar color correction. There is some CA to be seen around bright targets like Venus, Jupiter and Rigel but it not overly distracting.

5X: An achromat whose focal ration is at least 5 times the aperture as measured in inches will have negligible chromatic aberration. For an 80mm Scope this is a Chromatic Ratio of F/15.7, for practical purposes your 80mm F/15 fits the 5x criteria. Other scopes that fit this are common 60mm at the 700mm focal length. A scope with a CR of 5 will show essentially no false color, for practical purposes it will not affect the viewing but with care can be detected. the 3 inch F/15's I have owned have been nice in this regard but of course do have the disadvantage of that nearly 4 foot long OTA. One of my favorite scopes in a 60mm F/13.3 Asahi-Pentax, CR= 5.6.


In Suiter's book, Startesting Astronomical Telescopes, he has an analysis that suggests that the 3x criteria essentially provides a half wave correction over the visible spectrum which the 5x is close to a quarter wave... Val or Roland I am sure can explain it better...

Bottom line: Your scope should provide nice contrasty, essentially color free views. Back in the 60's and 70's when those scopes were built, an 80mm was a serious scope and the designs were optimized to maximize the high magnification views. In an 80mm Format, it's pretty tough to beat an F/15 achromat. The downside is that long OTA and the mount required. These days, fancy glasses and real money can put similar performance into a 80mm F/7 or even shorter making for a compact widefield scope that is better all around...

But when all is said and done, the combination of the slow focal ratio and it's forgivingness of simple eyepieces combined with the essentially color free views makes the views through an 80mm F/15 memorable.

Best to your for the new year...

Jon