Abstract

The interferometers with computer generated holograms (CGHs) have been used to measure off-axis aspherical mirrors. However, the conventional CGH interferometer could not produce a high lateral resolution because of the blur and the distortion of the interferogram of the test mirror caused by the nonzero order diffraction of the CGH. We further develop the application of CGHs concerning interferometers in order to improve the lateral resolution of the interferogram. In particular, we change the application of the CGH in such a way that the returned test beam passes through the CGH with zeroth order diffraction and demonstrates the performance of the CGH interferometer when used for the measurement of the primary mirror of the Okayama Astrophysical Observatory 3.8 m telescope project. As a result, our CGH interferometer produces a good interferogram with high resolution of 2.8 mm for the off-axis aspherical mirror with a size of 1.2 m. With improved usage of the CGH, we successfully demonstrated a high lateral resolution interferometer.

© 2012 Optical Society of America

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References

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  1. A. J. MacGovern and J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10, 619–624 (1971).
    [CrossRef]
  2. J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. C. Zhaoa, R. Zehnder, J. H. Burge, and H. M. Martin, “Testing an off-axis parabola with a CGH and a spherical mirror as null lens,” Proc. SPIE 5869, 586911 (2005).
    [CrossRef]
  6. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef]

2010 (1)

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[CrossRef]

2005 (1)

C. Zhaoa, R. Zehnder, J. H. Burge, and H. M. Martin, “Testing an off-axis parabola with a CGH and a spherical mirror as null lens,” Proc. SPIE 5869, 586911 (2005).
[CrossRef]

1982 (1)

1974 (2)

1971 (1)

Brangaccio, D. J.

Breckinridge, J. B.

Bruning, J. H.

Burge, J. H.

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[CrossRef]

C. Zhaoa, R. Zehnder, J. H. Burge, and H. M. Martin, “Testing an off-axis parabola with a CGH and a spherical mirror as null lens,” Proc. SPIE 5869, 586911 (2005).
[CrossRef]

Chen, C. W.

Gallagher, J. E.

Herriott, D. R.

MacGovern, A. J.

Martin, H. M.

C. Zhaoa, R. Zehnder, J. H. Burge, and H. M. Martin, “Testing an off-axis parabola with a CGH and a spherical mirror as null lens,” Proc. SPIE 5869, 586911 (2005).
[CrossRef]

Rosenfeld, D. P.

Smartt, R. N.

White, A. D.

Wyant, J. C.

Zehnder, R.

C. Zhaoa, R. Zehnder, J. H. Burge, and H. M. Martin, “Testing an off-axis parabola with a CGH and a spherical mirror as null lens,” Proc. SPIE 5869, 586911 (2005).
[CrossRef]

Zhao, C.

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[CrossRef]

Zhaoa, C.

C. Zhaoa, R. Zehnder, J. H. Burge, and H. M. Martin, “Testing an off-axis parabola with a CGH and a spherical mirror as null lens,” Proc. SPIE 5869, 586911 (2005).
[CrossRef]

Zhou, P.

J. H. Burge, C. Zhao, and P. Zhou, “Imaging issues for interferometry with CGH null correctors,” Proc. SPIE 7739, 77390T (2010).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Schematic layout of the optical elements in our interferometer. The CGH splits the incident light into the test and the reference beams, and changes the shape of the test wavefront into the off-axis asphere.

Fig. 2.
Fig. 2.

Primary mirror of OAO 3.8 m telescope. This mirror consists of 18 petal segmented mirrors. Each segment has an off-axis hyperbolic surface.

Fig. 3.
Fig. 3.

CGH patterns for the inner segment mirror (left) and for the outer segment mirror (right). Each line represents 30 lines in the real pattern. The CGHs consist of a pattern to measure the test mirror (A) and alignment patterns (B, C1, C2).

Fig. 4.
Fig. 4.

Illustration of the CGH interferometer system. The interferometer is mounted on the moving stage about 10 m above the test mirror. The illustration at top right shows details of the main part of the interferometer, and bottom right is the layout of around the test mirror.

Fig. 5.
Fig. 5.

Error map of the inner segment. The remarkable pattern with concentric steps across the whole of the error map is a footprint generated by the grinding process. The gray-scale covers ±750nm.

Fig. 6.
Fig. 6.

Example of the typical difference between the measured error map and the intermediate value of the four measurement maps. The gray scale covers ±40nm.

Fig. 7.
Fig. 7.

Difference between the error map measurements of a spherical mirror of 152.4 mm in diameter and 1828.8 mm in ROC obtained by the CGH interferometer and the Fizeau interferometer. The gray scale covers ±50nm. White rectangles at the left and bottom on the figure are the marks for positioning.

Fig. 8.
Fig. 8.

The part of the interference amplitude map with the small masks. The masks are 3.0mm×3.0mm square, and are pasted at 50 mm intervals.

Fig. 9.
Fig. 9.

Distortion plot obtained from the positions of the masks in the amplitude map. The error bars represent ±0.3pixel. The distortion is roughly ±0.2%, except for the central region of the mirror.

Fig. 10.
Fig. 10.

X (solid curve) and Y (dotted curve) cross-sections of the mask image. The thick curve indicates a simulated curve obtained at lateral resolution of 2.8 mm.

Tables (2)

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Table 1. Specification of the CGH Interferometer

Tables Icon

Table 2. Specifications of OAO 3.8 m Telescope Primary Mirror (Top) and Specifications and Goals of the Segment Mirrors (Bottom)

Equations (1)

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Δz=λ2π·tan1{2I0I120I2403(I240I120)},

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