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Case Studies

Large flats

Large flats are often used in large telescopes and optical testing systems. A null test of flats is strictly limited by the interferometer aperture. To overcome this problem, the Ritchey-Common test67 and the skip-flat test68 have been

Power accumulation effect

Figure 21 Power accumulation effect.

proposed, where the flat is illuminated by spherical and planar test beams, respectively (both with oblique incidence). They are naturally suitable for testing elliptical aperture flats, but both suffer problems with accuracy and efficiency.68 Subaperture stitching interferometry seems promising to overcome these problems because it possesses the advantages of extended lateral and vertical ranges and enhanced lateral resolution. Regardless, stitching large flats is quite challenging. The basic problem arises from the accumulation effect of the second-order surface error, including the power and astigmatism, which was pointed out by Bray.69 As shown in Fig. 21, subapertures of an ideally spherical surface exhibit a constant power with piston and tilts removed, which is identical to the reference surface error of the TF. On the other hand, any uncalibrated reference power mingled in the subaperture measurements may be accumulated and enlarged, leading to an erroneous surface figure during the process of stitching. This error propagation is “quadratically dependent on component size without affecting overlap error.”34,69

In view of the second-order error accumulation, we propose to deal with different components of the reference surface error differently. The power and astigmatism are first calibrated with a modified three-flat method. The high-frequency component of the reference is approximately estimated by averaging the high- frequency components of subaperture measurements, and more subapertures give more precise estimation. The residual Zernike polynomial reference error is then compensated with a built-in procedure during the self-calibrated stitching process, as described in Eq. (34).

This case experimentally studies the effect of error reductions in stitching large flats. The aperture of the test surface is about 600 mm. A total of 81 subapertures are tested with a standard 4-in. interferometer, as shown in Fig. 22. The overlapping ratio defined in Eq. (1) is about 28.5% because l = 0.6 d.

Following the error reduction procedure, the subapertures are stitched together with the residual Zernike polynomial reference surface removed, which together

Arrangement of 81 subapertures

Figure 22 Arrangement of 81 subapertures.

with the second-order and the high-frequency components gives the complete map of the reference surface. The full aperture error of the test flat is obtained and given in Fig. 23 (RMS 0.072X, power -0.076X). It is consistent with the full- aperture test result obtained by a 24-in.-aperture interferometer, as shown in Fig. 24 (RMS 0.066X, power -0.096X). However, stitching without error reductions gives a significantly different result with a large positive power, shown in Fig. 25 (RMS 0.122X, power 0.374X). The erroneous positive power evidently results from accumulation of the power of the reference surface.

Stitched full-aperture map

Figure 23 Stitched full-aperture map.

Full-aperture test map

Figure 24 Full-aperture test map.

Stitched full-aperture map without error reductions

Figure 25 Stitched full-aperture map without error reductions.

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