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to a. Let t2 be the axial thickness of the outer ring, the resulting maximum stress is ffmax =7"^ A22Et2 < Cult, (3.74)

1+v where Cult is the ultimate stress.

Metal substrates conveniently allow the construction of a single piece mirror including the perimeter collar and ring. Several stainless steel mirrors have been built in Fe87Cr13 quenched alloy. The optical tests are in accordance with the analysis and provide diffraction-limited images (Fig. 3.26).

• Off-axis astigmatism correction by CTD concave mirrors: Vase form and meniscus form mirrors can be designed to provide the Astm 3 mode. Degenerated solutions using only four external forces have been found [22] (Sect. 7.4). With vase forms, a smooth modulation in cos 29 is also achieved by the axial thickness of the outer ring (Fig. 3.27).

Compared to the VTDs, these solutions are well adapted for glass or vitro-ceram substrates. Of the two CTDs, the vase form is preferred because the loading geometrical configurations are more compact than with meniscus form (Lemaitre [22]) (Fig. 3.25-Left). The folded arms in vase form can be shorter than for menis-cuses.

Four-force configurations of vase form have been built and tested (see interfer-ogram Fig. 7.4). The determination of the location and of the intensity of the four forces are given by (7.22a) and (7.23a).

Fig. 3.26 VTD class: Saddle aspherization of a concave mirror. Design: cycloid like - collar - ring as in Fig. 3.25-right. Fe87Cr13 quenched alloy. Aperture 2a = 80mm,R = 640mm, f/8 beams, i = 8.6°,A22 = -3.5110-5 mm-1, t0 = 4mm,t2 = 12mm. Astm3 mode is generated by four axial forces applied to outer ring at 9 = 0, n/2, n, 3n/2. (Up) Astigmatic focii and least confusion image before flexure. (Down) Airy disc after flexure (Loom)

Fig. 3.26 VTD class: Saddle aspherization of a concave mirror. Design: cycloid like - collar - ring as in Fig. 3.25-right. Fe87Cr13 quenched alloy. Aperture 2a = 80mm,R = 640mm, f/8 beams, i = 8.6°,A22 = -3.5110-5 mm-1, t0 = 4mm,t2 = 12mm. Astm3 mode is generated by four axial forces applied to outer ring at 9 = 0, n/2, n, 3n/2. (Up) Astigmatic focii and least confusion image before flexure. (Down) Airy disc after flexure (Loom)

Fig. 3.27 CTD - case 2: Vase-form configuration providing Astm 3 mode Z22 with only four axial forces applied at

Fig. 3.27 CTD - case 2: Vase-form configuration providing Astm 3 mode Z22 with only four axial forces applied at

3.5.7 Concave Diffraction Gratings and Saddle Correction

• Aberrations of constant-spaced-line concave gratings: A reflective concave grating simultaneously provides the imaging and dispersion modes. Since this is achieved without need of collimator and camera optics, the aberrations are expected to be much larger than those using plane grating systems. The theory has been developed by many authors, among them Zernike [34], Beutler [2], Namioka [24, 25], Welford [31, 30(b)], and is based on the determination of the length of optical path I from the stigmatic point source P to its image P' via a grating point G. Similarly to demonstrate Fermat's principle, the series expansion of I shall be stationary whatever the location of G at the grating surface (Fig. 3.28).

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