Abstract

We report on the surface figure measurement of a freeform, φ-polynomial (Zernike) mirror for use in an off-axis, reflective imaging system. The measurement utilizes an interferometric null configuration that is a combination of subsystems each addressing a specific aberration type, namely, spherical aberration, astigmatism, and coma.

© 2013 Optical Society of America

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References

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  1. J. C. Wyant and V. P. Bennett, Appl. Opt. 11, 2833 (1972).
    [CrossRef]
  2. P. Zhou and J. H. Burge, Appl. Opt. 46, 657 (2007).
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  3. M. C. Ruda, “Methods for null testing sections of aspheric surfaces,” Ph.D. dissertation (University of Arizona, 1979).
  4. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, Opt. Express 19, 21919 (2011).
  5. A. Offner, Appl. Opt. 2, 153 (1963).
    [CrossRef]
  6. H. Coddington, A Treatise on the Reflection and Refraction of Light, Part 1 (Cambridge University, 1829).
  7. C. Pruss and H. J. Tiziani, Opt. Commun. 233, 15 (2004).
  8. T. Scheimpflug, “Improved method and apparatus for the systematic alteration or distortion of plane pictures and images by means of lenses and mirrors for photography and for other purposes,” British patent GB 1196 (May12, 1904).
  9. K. L. Shu, Appl. Opt. 22, 1879 (1983).
    [CrossRef]

2011 (1)

2007 (1)

2004 (1)

C. Pruss and H. J. Tiziani, Opt. Commun. 233, 15 (2004).

1983 (1)

1972 (1)

1963 (1)

Bennett, V. P.

Burge, J. H.

Coddington, H.

H. Coddington, A Treatise on the Reflection and Refraction of Light, Part 1 (Cambridge University, 1829).

Fuerschbach, K.

Offner, A.

Pruss, C.

C. Pruss and H. J. Tiziani, Opt. Commun. 233, 15 (2004).

Rolland, J. P.

Ruda, M. C.

M. C. Ruda, “Methods for null testing sections of aspheric surfaces,” Ph.D. dissertation (University of Arizona, 1979).

Scheimpflug, T.

T. Scheimpflug, “Improved method and apparatus for the systematic alteration or distortion of plane pictures and images by means of lenses and mirrors for photography and for other purposes,” British patent GB 1196 (May12, 1904).

Shu, K. L.

Thompson, K. P.

Tiziani, H. J.

C. Pruss and H. J. Tiziani, Opt. Commun. 233, 15 (2004).

Wyant, J. C.

Zhou, P.

Appl. Opt. (4)

Opt. Commun. (1)

C. Pruss and H. J. Tiziani, Opt. Commun. 233, 15 (2004).

Opt. Express (1)

Other (3)

T. Scheimpflug, “Improved method and apparatus for the systematic alteration or distortion of plane pictures and images by means of lenses and mirrors for photography and for other purposes,” British patent GB 1196 (May12, 1904).

M. C. Ruda, “Methods for null testing sections of aspheric surfaces,” Ph.D. dissertation (University of Arizona, 1979).

H. Coddington, A Treatise on the Reflection and Refraction of Light, Part 1 (Cambridge University, 1829).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Sag of the secondary mirror surface with the piston, power, and tilt Zernike components removed revealing the astigmatic contribution of the surface, (b) sag with the astigmatic component additionally removed, and (c) sag with the spherical component additionally removed. With the piston, power, tilt, astigmatism, and spherical components removed, the asymmetry induced from the coma being added into the surface can be seen.

Fig. 2.
Fig. 2.

Layout of the optimized interferometric null to be coupled to a conventional Fizeau interferometer with a transmission flat. The interferometric null is composed of three nulling subsystems: an Offner null to null spherical aberration, a tilted geometry to null astigmatism, and a retroreflecting DM to null coma and any higher order aberration terms.

Fig. 3.
Fig. 3.

Simulation of the double-pass interferogram exiting the interferometric null (a) before and (b) after the deformable null has been applied at a testing wavelength of 632.8 nm.

Fig. 4.
Fig. 4.

Layout of the setup to create the comatic and higher order null on the DM surface. The setup uses a Shack–Hartmann wavefront sensor to run a closed-loop optimization to set the shape of the comatic null. The comatic null is also interrogated with a Fizeau interferometer.

Fig. 5.
Fig. 5.

(a) Comatic null surface measured by the interferometer and (b) the residual after the theoretical shape has been subtracted. The residual has a P-V error of 2 μm P-V.

Fig. 6.
Fig. 6.

Interferometric null configuration realized in the laboratory. A rotation stage with a rail affixed is used to create the tilted geometry. The test mirror is measured using a Zygo Fizeau-type interferometer.

Fig. 7.
Fig. 7.

(a) Initial surface error map of the test mirror with power and (b) with the power removed. The P-V error of the surface residual before and after the power is removed is 3.821 and 2.025 μm, respectively. (c) Final surface error map of the test mirror after the software null has been subtracted (c) before and (d) after the power has been removed. In this case, the P-V error is 3.230 μm before and 1.140 μm after the power has been removed.

Equations (1)

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λ4cos(α),

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