## Generalized figure-control algorithm for large segmented telescope mirrors

JOSA A, Vol. 18, Issue 3, pp. 638-649 (2001)

http://dx.doi.org/10.1364/JOSAA.18.000638

Acrobat PDF (360 KB)

### Abstract

A fundamental discovery in segmented-mirror active optics is described: symmetrizing the geometry of the sensor–actuator array provides a computationally effective symmetrization of the mathematical description for the figure control of a Keck-type telescope mirror. The author establishes a universal mathematical control model and provides an efficient algorithm to solve this model equation set. This model can be applied to multifarious Keck-type mirror configurations with a similar sensor–actuator geometry design, no matter what kind of outline shapes and how many segments they have. With the underlying symmetry, a further extension of this algorithm is possible without increasing the number of parameters to be estimated for the recently proposed extremely large telescopes, such as the 30-m California Extremely Large Telescope (CELT) and the 100-m OverWhelmingly Large (OWL) telescope. Moreover, careful choice of boundary conditions in conjunction with the proper choice of minimization algorithm yields results that exceed the performance of the current existing techniques given by Nelson and Mast [Appl. Opt. **21**, 2631 (1982)]. This method allows noise performance analysis. Several computer simulation models for application of this algorithm are given for the Keck 10-m Telescope and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope’s (LAMOST’s) M_{A} (Reflecting Schmidt plate) and M_{B} (spherical primary mirror).

© 2001 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

(080.2720) Geometric optics : Mathematical methods (general)

(230.4040) Optical devices : Mirrors

(350.1260) Other areas of optics : Astronomical optics

**Citation**

Weiyao Zou, "Generalized figure-control algorithm for large segmented telescope mirrors," J. Opt. Soc. Am. A **18**, 638-649 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-3-638

Sort: Year | Journal | Reset

### References

- T. S. Mast and J. E. Nelson, “Figure control for a fully segmented telescope mirror,” Appl. Opt. 21, 2631–2641 (1982).
- R. C. Jared, A. A. Arthur, S. Andrede, A. Biocca, R. W. Cohen, J. M. Fuertes, J. Franck, G. Gabor, J. Llacer, T. Mast, J. Meng, T. Merrick, R. Minor, J. Nelson, M. Orayani, P. Salz, B. Schaefer, and C. Witebsky, “The W. M. Keck Telescope segmented primary mirror active control system,” in Advanced Technology Optical Telescope IV, L. D. Barr, ed., Proc. SPIE 1236, 996–1008 (1990).
- G. H. Golub and C. Reinsch, “Singular value decomposition and least squares solutions,” Numer. Math. 14, 403–420 (1970).
- R. Gilmozzi, B. Delabre, P. Diericky, N. Hubin, F. Koch, G. Monnet, M. Quatteri, F. Rigaut, and R. N. Wilson, “The future of filled aperture telescopes: is a 100 m feasible ?” in Advanced Technology Optical/IR Telescope VI, L. M. Stepp, ed., Proc. SPIE 3352, 778–791 (1998).
- G. Chanan, J. Nelson, C. Ohara, and E. Sirko, “Design issues for the active control system of the California Extremely Large Telescope (CELT),” presented at the Astronomical Telescopes and Instrumentation 2000 meeting, Munich, Germany, March 27–31, 2000.
- S. Wang, D. Su, Y. Chu, X. Cui, and Y. Wang, “Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation,” Appl. Opt. 35, 5155–5161 (1996).
- W. Zou, “The figure control of large segmented mirror telescope,” Master’s thesis (Chinese Academy of Sciences, Nanjing, China, 1996).
- W. Zou and Z. Zhang, “Generalized wave-front reconstruction algorithm applied in a Shack–Hartmann test,” Appl. Opt. 39, 250–268 (2000).
- J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Chinese ed. (Springer-Verlag, New York, 1994).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flanery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, New York, 1998), pp. 278–283.
- D. Su and Y. Wang, “Automatic correction of aberration in astro-optical system,” Acta Astron. Sinica 15, 51–60 (1974).
- D. Su, “A merit function composed by spot-diagrams and the damp least square method,” Opt. Instrum. Tech. No. 4, 1–12 (1980).
- D. Su, W. Zou, Z. Zhang, Y. Qu, S. Yang, L. Wang, and Y. Rao, “Experiment system of segmented-mirror active optics,” presented at the Astronomical Telescopes and Instrumentation 2000 meeting, Munich, Germany, March 27–31, 2000.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.