#27055 Nov 28, 2015
it's sort of received wisdom in the history of telescope construction that the extraordinarily long focal lengths of the earliestrefractors were primarily intended to minimize chromatic aberration in theimage. this explanation is buttressed by the observation that both lensgrinding and glass casting were imperfect arts in the 17th century. to illustrate the scale of these scopes, the two "aerial" telescopes constructed by christiaan huygens were designed as follows: D = 200 mm, . = 52000 mm, N = 260, M = 208D = 220 mm, . = 64000 mm, N = 290, M = 256 it's clear that both these objectives produce an image that isdiffraction limited to the naked eye, since both have a numericalaperture greater than 250. in exit pupil terms, assuming the eye is theeyepiece, the magnification is greater than the aperture. (i can't find information on an eyepiece, although this many have only been a negative lens, after the galilean design.)
the focal lengthstrongly implies that magnification was the principal design criterion,and the limit on the telescope focal length was set by the "useful"magnification produced by the objective focal length, not bychromatic aberration. there is also anecdotal information to suggest the principal interest was in the magnification: according to wikipedia, c.1690 "Adrian Auzout proposed a huge aerial telescope 1,000 ft in length that he would use 'to observe animals on the Moon'." since magnification scales as a multiple of aperture but chromaticaberration as a power of the aperture, there should be a point where theeffect of one becomes more important than the other. that depends onthe relative nuisance effect of chromatic aberration, which is a visualquality that varies with the observer. given the ~20cm apertures at which huygens was constructing, is thefull 52 to 64 meter focal length necessary to reduce CA to acceptablelevels, or could a visually acceptable "achromatic" image be produced ata smaller numerical aperture?
#27059 Nov 29, 2015
Bruce, yes, both lenses are far away to be count as "achromatic".Attached please find couple pictures. First shows chromatic shift for Huygens's lens RSL 23. Please note focal shift ranges in left lower corner. Second image shows simulated color diffraction image @F/248 and for near perfect "achromatic" case.