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基于离散余弦变换最小二乘法实现数字全息再现像的相位解包裹
葛宝臻^1,2,崔鹏^1,2,吕且妮^1,2,魏耀林^1,2
(1.天津大学精密仪器与光电子工程学院，天津300072 ;2.天津大学光电信息技术科学教育部重点实验室，天津300072)

摘要:

采用离轴菲涅尔数字全息系统对栅格进行了全息图的数字记录和数字再现，并用离散余弦变换(DCT)最小二乘法对数字全息再现像进行了相位解包裹处理。在此基础上，增加了后处理过程,即对原始包裹相位的相应点加上或减去2-的整数倍,与此最小二乘算法所求得的解包裹相位进行比较,使二者之差的绝对值达到最小，将原始包裹相位做处理后的相位值作为解包裹相位的最后结果。对栅格的解包裹相位三维图和原子力显微镜扫描获得的三维图的对比测量和分析结果证明了经后处理的解包裹相位精度得到了有效提高。

关键词: 数字全息相位解包裹最小二乘算法后处理

DOI：

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基金项目:高等学校博士学科点专项科研基金(20050056010);天津大学青年教师基金(985Q200624)

Implement of phase unwrapping of digital holographic reconstruction image by discrete cosine transform least square method

GE Bao-zhen^1,2,CUI Peng^1,2,LV Qie-ni^1,2,WEI Yao-lin^1,2

(1. College of Precision Instruments and Optoelectronics Engineering, Tianjin University，Tianjin 300072, China ;2. Key Laboratory of Opto-electronics Information and Technical Science, Ministry of Education, Tianjin University，Tianjin 300072, China )

Abstract:

With Fresnel off-axis digital holography system, digital hologram (rf grid was recorded and reconstructed numerically. And the phase unwrapping of the reconstructed phase image was done, first by discrete cosine transform (DCT) least square method, and then post-processing, namely, an integer multiple of 2it was added to or deducted the corresponding point of the original wrapped phase. Tliis result was compared with that of phase unwrapping by DCT least square method，and until the smallest absolute value difference was obtained. The phase value processed (rf the original wrapped phase was taken as the final result of phase unwrapping. Measurement and analysis were performed about 3D image from phase unwrapping image of the grid and atomic force microscope. Hie results show that the precision of phase unwrapping can be improved by post-processing.

Key words: digital holography phase unwrapping least square method post-processing