## Algebraic Reconstruction of a Small-Scale Wave Front

Applied Optics, Vol. 37, Issue 23, pp. 5421-5426 (1998)

http://dx.doi.org/10.1364/AO.37.005421

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### Abstract

We show that a small-scale wave front can be reconstructed by an algebraic procedure from its intensity distribution in the focal plane, except for the ambiguities of the piston phase and the point-symmetrical solution of the complex conjugate. Details of the reconstruction procedure for a 3 × 3 wave front are presented, and the effectiveness of this procedure for a contaminated case is shown by computer simulation. A method for overcoming the ambiguity problem resulting from the point-symmetrical solution is also suggested.

© 1998 Optical Society of America

**OCIS Codes**

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

(010.7350) Atmospheric and oceanic optics : Wave-front sensing

(100.3010) Image processing : Image reconstruction techniques

(100.3020) Image processing : Image reconstruction-restoration

(100.3190) Image processing : Inverse problems

(100.5070) Image processing : Phase retrieval

**Citation**

Tohru Takahashi, J. Christopher Dainty, and Hiroaki Takajo, "Algebraic Reconstruction of a Small-Scale Wave Front," Appl. Opt. **37**, 5421-5426 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-23-5421

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