Optical Design For a 32 Inch, All-Spherical Relay Cassegrain Telescope Presented at Stellafane 2004 By: Scott Milligan 11/23/2018 Astroverted Optics

Motivation for this project 20” Mersenne telescope exhibited by Clyde Bone at 199X Stellafane. Seated observing position in a large aperture instrument working at F/5! But: Mersenne suffers from double field of view, and/or excessive central obstruction. Also requires fabrication of 2 parabolic mirrors.

20” F/8 Mersenne: primary field of view

20 “ F/8 Mersenne: secondary field of view

What is a Relay Cassegrain Telescope? A telescope offering: A reflective “Front end” A relatively compact, folded optical path. Relay optics re-image an intermediate image of the scene to an accessible location. Addition of relay optics solves the double FOV vs. central obscuration problem inherent with the Mersenne design. Relay designs can use all-spherical optics.

An Example: 32” F/6 Relay Cassegrain telescope

The “Classical-Cassegrain crunch” Once EFL & BFD are chosen, obscuration ratio and primary F/# are closely (and unfavorably) coupled.

An F/6 Cassegrain with a 44% central obscuration

An F/6 Cassegrain with a 25% central obscuration

Some advantages of relay telescopes: Can achieve excellent imaging on-axis over a wide range of F/# (F/4 – F/20). Accessible image location without requiring large central obstruction. Fully baffled without vignetting an extended field of view. All-spherical designs eliminate requirement to fabricate & test aspheric surfaces.

Material to be removed when figuring: three different Paraboloids compared

And a few drawbacks… Off-axis imagery is (typically) limited by field curvature associated with the use of positive focal length relay lens optics. Added complexity of design requires careful analysis of, and attention to fabrication and alignment tolerances. Collimation tolerances can be tighter than for equivalent, traditional Cassegrain. Spectral bandwidth may be limited in comparison with all-reflective designs.

Historical Development of Relay Telescopes Inventor Year Comments H. Dall, B.Cox 1947, 1962 D.K.”twitcher” with corrected relay R. Buchroeder 197X All-spherical, XX elements D. Dilworth 1976 All-spherical, 16” Built & shown at Stellafane R. Sigler 1982 All-Spherical, simplest possible construction

Limitations of prior work Dall & Cox designs difficult to correct for secondary spectrum w/o using expensive glasses. Dilworth & Sigler designs offer no control over off-axis astigmatism. These limitations motivated a search for an improved relay design.

Milligan Relay Cassegrain Uses the Dilworth & Sigler designs as a starting point. Improves correction for secondary spectrum and spherochromatism to achieve better than Diff. Ltd. Imaging on-axis over an extended spectral range 420-900 nm. Improves off-axis imagery by balancing field curvature with over-corrected astigmatism. Creates a near telecentric exit pupil for ideal matching with modern wide field eyepieces.

Primary Design Goals All-Spherical optics 32” aperture, working at F/6 Central obstruction ≤ 25% Use no exotic, “un-obtanium” glasses. Illuminate a 46 mm image circle without vignetting. Excellent on-axis imagery over a wide spectral band 400-900 nm. Improved Off-axis imagery (wrt prior art). Accessible focal plane.

Description of Layout Spherical F/3 primary Plano-CC Mangin-Type secondary Cemented doublet field lens Two singlet relay lenses

Analysis: On-axis OPD Fans

Analysis: Spot Diagrams

Analysis: Lateral Color

Analysis: Field Curvature

Analysis: MTF curves

New design vs. several other existing designs: A 32” F/6 Ritchey-Chretien A 32” F/6 Classical Cassegrain A 32” F/6 Newtonian. A 32” F/7.9 Sigler-type Relay

Analysis: MTF for Several existing designs R-C MTF Cassegrain MTF Newtonian MTF Sigler Relay MTF

Avg. MTF @ 20 cy/mm for 5 Designs On-axis 6 mm 12.3 mm R-C 0.83 0.78 Milligan 0.87 0.81 0.60 Newt. 0.89 0.73 0.41 Cass. 0.68 0.35 Sigler 0.84 0.45 0.07

Design variations: field flattener works at F/8.6

MTF with field Flattener

Design variations: folded Nasmyth focus; primary is F/2.4

Design variations: folded “outrigger”

Conclusions Relay Cassegrain designs can achieve accessible eyepiece locations in large aperture scopes without requiring the user to tolerate a double FOV or a large central obstruction. A new all-spherical relay Cassegrain design is presented that substantially improves upon the imaging performance of previously published, similar designs.