Abstract

The precision alignment of high-performance, wide-field optical systems is generally a difficult and often laborious process. We report a new merit function regression method that has the potential to bring to such an optical alignment process higher efficiency and accuracy than the conventional sensitivity table method. The technique uses actively damped least square algorithm to minimize the Zernike coefficient-based merit function representing the difference between the designed and misaligned optical wave fronts. The application of this method for the alignment experiment of a Cassegrain type collimator of 900mm in diameter resulted in a reduction of the mean system rms wave-front error from 0.283λ to 0.194λ, and in the field dependent wave-front error difference from ±0.2λ to ±0.014λ in just two alignment actions. These results demonstrate a much better performance than that of the conventional sensitivity table method simulated for the same steps of experimental alignment.

© 2007 Optical Society of America

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References

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  1. R. N. Wilson, "Aberration Theory of Telescopes," in Reflecting Telescope Optics I (Springer, Berlin, 1996), Ch. 3.
  2. M. A. Lundgren, and W. L. Wolfe, "Simultaneous Alignment and Multiple Surface Figure Testing of Optical System Components Via Wavefront Aberration Measurement and Reverse Optimization," in 1990 Intl Lens Design Conference, G.N. Lawrence, ed., Proc. of SPIE 1354, 533-539 (1990).
  3. J. W. Figoski, T. E. Shrode, and G. F. Moore, "Computer-aided Alignment of a Wide-field, Three-mirror, Unobscured, High-resolution Sensor," in Recent Trends in Optical Systems Design and Computer Lens Design Workshop II, R. E. Fischer, and R. C. Juergens, eds., Proc. of SPIE 1049, 166-177 (1989).
  4. Z. Bin, Z. Xiaohui, W. Cheng, and H. Changyuan, "Investigation on Computer-aided Alignment of the Complex Optical System," in Advanced Optical Manufacturing and testing technology, L. Yang, H. M. Pollicove, Q. Xin, and J. C. Wyant, eds., Proc. of SPIE 4231, 67-72 (2000).
  5. H. S. Yang, Y. W. Lee, E. D. Kim, Y. W. Choi, and A. A. A. Rashed, "Alignment methods for Cassegrain and RC telescope with wide field of view," in Space systems engineering and optical alignement mechanisms, L. D. Peterson, and R. C. Guyer, eds., Proc. SPIE 5528, 334-341 (2004).
  6. SVD, "Matlab function reference,"http://www-ccs.ucsd.edu/matlab/techdoc/ref/svd.html.
  7. E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).
  8. Zemax development corporation, "Optimization," in Zemax optical design program user's guide (2004), Ch.14.
  9. J. Meiron, "Damped Least-Squares Method for Automatic Lens Design," J. Opt. Soc. Am. 55, 1105-1109 (1965)
    [CrossRef]
  10. H. Lee, G. B. Dalton, I. A. Tosh and S.-W. Kim, "Computer guided alignment I: Phase and amplitude modulation of alignment-influenced optical wave front," Opt. Express 15,3127-3139 (2007)
    [CrossRef] [PubMed]
  11. H. S. Yang, S.-W. Kim. Y.-W. Lee and S. Kim are preparing a manuscript to be called "Extending the merit-function regression method for effective alignment of multiple mirror optical systems".

2007 (1)

2005 (1)

E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).

1965 (1)

Choi, S. C.

E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).

Choi, Y.-W.

E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).

Dalton, G. B.

Kang, M.-S.

E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).

Kim, E. D.

E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).

Kim, S.-W.

Lee, H.

Meiron, J.

Tosh, I. A.

J. Opt. Soc. Am. (1)

J. Opt. Soc. Kor. (1)

E. D. Kim, Y.-W. Choi, M.-S. Kang, and S. C. Choi, "Reverse-optimization alignment algorithm using Zernike sensitivity," J. Opt. Soc. Kor. 9, 67-73 (2005).

Opt. Express (1)

Other (8)

Zemax development corporation, "Optimization," in Zemax optical design program user's guide (2004), Ch.14.

H. S. Yang, S.-W. Kim. Y.-W. Lee and S. Kim are preparing a manuscript to be called "Extending the merit-function regression method for effective alignment of multiple mirror optical systems".

R. N. Wilson, "Aberration Theory of Telescopes," in Reflecting Telescope Optics I (Springer, Berlin, 1996), Ch. 3.

M. A. Lundgren, and W. L. Wolfe, "Simultaneous Alignment and Multiple Surface Figure Testing of Optical System Components Via Wavefront Aberration Measurement and Reverse Optimization," in 1990 Intl Lens Design Conference, G.N. Lawrence, ed., Proc. of SPIE 1354, 533-539 (1990).

J. W. Figoski, T. E. Shrode, and G. F. Moore, "Computer-aided Alignment of a Wide-field, Three-mirror, Unobscured, High-resolution Sensor," in Recent Trends in Optical Systems Design and Computer Lens Design Workshop II, R. E. Fischer, and R. C. Juergens, eds., Proc. of SPIE 1049, 166-177 (1989).

Z. Bin, Z. Xiaohui, W. Cheng, and H. Changyuan, "Investigation on Computer-aided Alignment of the Complex Optical System," in Advanced Optical Manufacturing and testing technology, L. Yang, H. M. Pollicove, Q. Xin, and J. C. Wyant, eds., Proc. of SPIE 4231, 67-72 (2000).

H. S. Yang, Y. W. Lee, E. D. Kim, Y. W. Choi, and A. A. A. Rashed, "Alignment methods for Cassegrain and RC telescope with wide field of view," in Space systems engineering and optical alignement mechanisms, L. D. Peterson, and R. C. Guyer, eds., Proc. SPIE 5528, 334-341 (2004).

SVD, "Matlab function reference,"http://www-ccs.ucsd.edu/matlab/techdoc/ref/svd.html.

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Figures (8)

Fig. 1.
Fig. 1.

Picture of the KRISS 0.9-m collimator.

Fig. 2.
Fig. 2.

Measured rms WFE of primary (a) and secondary mirror (b) before integration

Fig. 3.
Fig. 3.

Measurement field numbering at the image plane. The number in parenthesis indicates the relative incident angle.

Fig. 4.
Fig. 4.

Effect of the interferometric measurement errors on decenter in X axis and tilt about Y axis. Note that the standard deviation decreases with the increase in the number of measurement fields.

Fig. 5.
Fig. 5.

The variation of MF as the field is shifted 0.02 degrees on the X-axis.

Fig. 6.
Fig. 6.

Alignment results at each alignment action. Each point is the mean WFE for 5 fields and the error bar is the maximum rms WFE difference (λ = 633 nm).

Fig. 7.
Fig. 7.

Field error calculated from MF regression run.

Fig. 8.
Fig. 8.

On axis rms WFEs of the KRISS collimator at each alignment action (λ = 633 nm).

Tables (1)

Tables Icon

Table 1. Misalignment calculation results using the sensitivity table method and MF regression method for several misalignment cases applied to the SM of KRISS collimator. We denote Dx and Dy for the decenters in X-axis and Y-axis, Tx and Ty for the tilts about X-axis and Y-axis and Df for the defocus of SM. Error indicates the difference between the actual misalignment and calculation. Note that the machine precision is 10-16 in double precision, when looking at error terms.

Equations (3)

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Δ Z = A Δ D
Δ Z = [ Δ Z 1 Δ Z n ] = [ Z 1 Z n ] [ Z 1 o Z no ] , A = [ δZ 1 δx 1 δZ 1 δx 1 δZ m δx n δZ m δx n ] and Δ D = [ Δx 1 Δx n ] = [ x 1 x n ] [ x 1 o x no ]
MF 2 = W i ( V i T i ) 2 W i ,

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