Abstract

This paper provides some mathematical formulae for Risley beam steer control system that is used for free space optical interconnection system. Given the prisms' orientations, the analytic formulae can be used to calculate the pointing position. For the inverse problem, i.e., given the desired pointing position, the required prisms' orientations can be obtained efficiently by applying any numerical method for systems of nonlinear equations related to the formulae. Unlike some existing methods, these formulae are not first-order approximation but an accurate closed analytical form. It does not need a good initial guess on the motor positions required by some other methods. It also does not need a feedback loop to get the correct pointing position but it can be used in feedback implementation. This feature is especially important for systems that need to slew the beam to the desired position quickly and accurately.

© 2008 IEEE

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References

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1997 (1)

K. Hirabayashi, T. Yamamoto, S. Hino, Y. Kohama, K. Tateno, "Optical beam direction compensating system for board-to-board free space optical interconnection in high-capacity ATM switch," J. Lightw. Technol. 15, 874-882 (1997).

1995 (1)

G. C. Boisset, B. Robertson, H. S. Hinton, "Design and construction of an active alighment demonstrator for a free-space optical interconnect," IEEE Photon. Technol. Lett. 7, 676-678 (1995).

1994 (1)

1966 (1)

1944 (2)

K. Levenberg, "A method for the solution of certain problems in least squares," Quart. Appl. Math. 2, 164-168 (1944).

D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," SIAM J. Appl. Math. 2, 164-168 (1944).

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

G. C. Boisset, B. Robertson, H. S. Hinton, "Design and construction of an active alighment demonstrator for a free-space optical interconnect," IEEE Photon. Technol. Lett. 7, 676-678 (1995).

J. Lightw. Technol. (1)

K. Hirabayashi, T. Yamamoto, S. Hino, Y. Kohama, K. Tateno, "Optical beam direction compensating system for board-to-board free space optical interconnection in high-capacity ATM switch," J. Lightw. Technol. 15, 874-882 (1997).

Quart. Appl. Math. (1)

K. Levenberg, "A method for the solution of certain problems in least squares," Quart. Appl. Math. 2, 164-168 (1944).

SIAM J. Appl. Math. (1)

D. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," SIAM J. Appl. Math. 2, 164-168 (1944).

Other (6)

J. Lacoursiere, M. Doucet, E. O. Curatu, M. Savard, S. Verreault, S. Thibault, P. C. Chevrette, B. Ricard, "Large deviation achromatic Risley prisms pointing systems," Proc. SPIE (2002) pp. 123-131.

J. J. Degnan, "Ray matrix approach for the real time control of SLR2000 optical elements," 14th Int. Workshop on Laser Ranging San FernandoSpain (2004).

Optical Design Program User's Guide Zemax Development Corp. (2005) Zemax Development Corporation, Bellevue, WA.

R. L. Easton, Jr.Imaging Systems Laboratory II http://www.cis.rit.edu/class/simg232/lab2-dispersion.pdf.

User's Guide: Optimization Toolbox MathWorks (2004) The MathWorks, Inc., Natick, MA.

N. R. Conn, N. I. M. Could, P. L. Toint, Trust-Region Methods (SIAM, 2000).

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