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The holographic reconstructing algorithm and its error analysis about phase-shifting phase measurement |
| LU Xiaoxu1, ZHONG Liyun2, ZHANG Yimo3 |
| 1.School of Information and Optoelectronic Science and Engineering, South China Normal University, Guangzhou 510631, China; 2.College of Life Science and Technology, Jinan University, Guangzhou 510632, China; 3.School of Precision Instrument and Optoelectronic Engineering, Tianjin University, Tianjin 300072, China; |
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Abstract Phase-shifting measurement and its error estimation method were studied according to the holographic principle. A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period (N-step phase-shifting function for short) was proposed. In N-step phase-shifting measurement, the interferograms are seen as a series of in-line holograms and the reference beam is an ideal parallel-plane wave. So the N-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave. In ideal conditions, the proposed method is a kind of synchronous superposition algorithm in which the complex amplitude is separated, measured and superposed. When error exists in measurement, the result of the N-step phase-shifting function is the optimal expected value of the least-squares fitting method. In the above method, the N+1-step phase-shifting function can be obtained from the N-step phase-shifting function. It shows that the N-step phase-shifting function can be separated into two parts: the ideal N-step phase-shifting function and its errors. The phase-shifting errors in N-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the N+1-step phase-shifting function. The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error estimation method. Meanwhile, the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.
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Issue Date: 05 September 2007
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