Spot-diagrams and data of Multi-Schiefspiegler designs

		Design 1 - A spot - diagram describes the collimation of a parallel bundle of light within the image plane. In this case it is calculated for a bundle of light rays parallel to the optical axis and for 4 tilted bundles (tilt angle 0.25° each) entering the aperture from 4 different directions.  The circle around the central spot represents the diameter of the Airy-disc.  All image errors, which concentrate the rays within the circle are not detectable.  This design of a Multi-Schiefspiegler with 150 mm aperture and f/11 results in a diffraction limited image quality within 0.5° field of view.

		Design 2 - A second design with 140 mm aperture was calculated with f-ratio f/11. The corresponding spot-diagram is displayed on the left side.  A diffraction limited image quality is obtained near the field centre. Due to the higher f-ratio the off-axis image errors are slightly larger than that of design 1. The geometrical and optical data for design 2 are given in the table below. In contrast to design 1 the focal length of the parabolic mirror has been reduced from a f/9.6 mirror to a f/9.2 mirror which is responsible for the higher f-ratio of the telescope. The radii of the first and second mirror remain unchanged. This design allows a compact telescope tube with a total length of about 620 mm.

		Design 3 - Design No. 3 describes the optical layout of a Multi-Schiefspiegler with 200 mm aperture (f-ratio f/10.8). The spot-diagram (left side) demonstrates the high image quality for 0.5° field of view.  This design uses a parabolic mirror with f/ratio f/8.55. This construction is rather compact with a tube length of 960 mm. The weight of the telescope is about 15 kg.

Data of the Multi-Schiefspiegler designs (1-3)

Design No. Aperture f-ratio focal length	No. of reflection	mirror diameter	Radius of mirror	Distance to next surface	mirror tilt	conic constant k
1	1	150	-7200	535	-8.60°	0
150	2	160(132)	7200	495	+8.06°	0
f/11	3	150(140)	-2430	505	+2.75°	-1 (-0.88)
1668 mm	4	(80)	7200	777	-13.95°	0
2	1	150(140)	-7200	500	-9.20.°	0
140	2	150(122)	7200	465	+8.50°	0
f/11.1	3	125	-2300	475	+3.00°	-1 (-0.85)
1554 mm	4	(76)	-7200	745	-14.90°	0
3	1	200	- 11000	713	-9.10°	0
200	2	200 (160)	11000	679	+8.51°	0
f/10.75	3	200 (190)	- 3250	691	+2.55°	-1 (-0.90)
2144 mm	4	(120)	11000	1024	-13.93°	0
The designs given above are only examples of optical layouts. It can not be excluded that other layouts result in more optimised designs with respect to certain parameters.	All length are given in mm, values are rounded. (diameter) describes the diameter of the illuminated surface area of the corresponding mirror which is needed to ensure an unvignetted field of view of 0.5°	The f-ratios belong to the free aperture of the primary mirror and are only valid for images near the field centre. This value is slightly reduced off-centre.	Negative radii describe concave mirrors, positive values denote convex mirrors. The angle of reflection is twice the mirror tilt.	The conic constant k is defined as k = - (eccentricity)2. The numbers in brackets give the exact value of k to compensate for spherical aberration.

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