Apochromatic Telephoto Telescope- - Optical Design

(Nel caso qualcuno volesse la versione in italiano di questo post  basta che mi lasci un commento o mi madi una mail)

Image you want a refractor apochromatic with mid  aperture and a good field of view. You want as well a powerful telescope but less long than its nominal effective focal length.
The prescription are:

Effective Focal Length  :        1000.038 (in air at system temperature and pressure)
Effective Focal Length  :        1000.038 (in image space)
Back Focal Length       :        346.0243
Total Track             :        770.0004
Image Space F/#         :        9.091257
Paraxial Working F/#    :        9.091257
Working F/#             :        9.090858
Image Space NA          :       0.0549149
Object Space NA         :        5.5e-009
Stop Radius             :              55
Paraxial Image Height   :        17.45573
Paraxial Magnification  :               0
Entrance Pupil Diameter :             110
Entrance Pupil Position :               0
Exit Pupil Diameter     :        63.06786
Exit Pupil Position     :       -573.3451
Field Type              : Angle in degrees
Maximum Field           :               1
Primary Wave            :       0.5875618
Lens Units              :   Millimeters
Angular Magnification   :        1.744153

Then we have an apochrmatic refractor 110 mm aperture, 1000 mm focal length F/9. The system is long only 770 mm thanks to the telephoto design ( see a previous post).

Optical design

Let's take a look to the lens design





The aphochromatic field of wiew is 2 degrees diagonal.
The system is optimized in the visible band 0.486 - 0.656 micron. 


The design includes of 6 lenses. The firsts 4 lenses are the convergent part of the telephoto design, the last two lenses are a negative group, their role is to make the system reach the desired focal legnth: 1000 mm. The system is fairly telecentric within almost 1 degree FoV.




Lenses 1, 2 and lenses 3,4 would like to be cemented doublets but I perfer to keep them separated doublets. The reason of that is mainly the cost and the risk of a well done cemented doublet  respect to 2 single leses. Moreover the first doublet is made of two glasses with much different TCE and this could generate glasses stress and deteriorate the performances in case of violent change in temperature.

The focal plane has a diagonal about 34.9 mm. A high level commercial grade astro photographic camera (Atick, Sbig or whatever) can fit this focal plane. Also a good eyepiece can probably be applied. The Airy disk has a diameter about 13 micron. To samaple correctly the PSF it is needed a camera with pixels about 6/7 micron.The diffraction limited MTF value is 0.55 for a spatial frequecy about 67.5 that correspond to 2 pixels about 7 micron.



The glasses used for this design are quite a lot expensive. The correction of the second order chromatism is perfromed by abnormal relative dipsersion glasses (optical designs with this kind of glasses included in the design are commecialy called "ED"). 

 Performances

The sytem performs at the limit of diffraction within the field of view.. The glasses and the lens design can correct  spherical, coma and asigmatism up to 0.1 waves over most of the FoV and for each wave length in the band.



Distotion is indeed neglictable (-0.05% 5 pixels every 10000 pixels!), field curvature is better than 100 micron.

Tolerances

Tolerances for this design are not loose but for sure doable. This maks the system a bit expensive in almost all the parts: the metalwork, the lenses manufacturing and the system assembly/alignment.
Tolerances are  tuned to allow the MTF@Nyquist drop from 0.55 down to 0.2 within a likelihood of the 90%.



Radi of curvature: +-5/7 fringes
Lenses thickness and air gaps: +-0.1 mm
Surface quality: +-0.5 fringes

Glasses Index and Abbe standard Schott grade are enough (index 3*10E-05; abbe 0.2% )
Lenses alignment is challenging, the tilts on both axes must be better than +-0.01 degrees (1/2 arcminute).

Conclusion

This design is not bad, it has brilliant performances even if is a bit expensive to build, but it is just an exercices. Actually we could probably drop three lenses and relax the tolerances removing the TelePhoto constrain.This gives us a typical commercial apo refractor with less extreme performances but much cheaper.





The design looks like that and the performances in term of MTF are below.




Probably spending a bit more time on the design I could get it better. As I said before now the total track is 1007 mm than now the telescope is longer than its own focal length.
It is funny to check that the design evolved to a Cooke triplet design with 2 positive crown lenses and a negative flint. Indeed to kill the chromatism the flint is a special one. Not bad, with the cooke triplet you can't get wrong :-).