基于DCT算法的种子点相位解包算法

Seed Point Unwrapping Algorithm Based on DCT Algorithm

移相干涉术由于其高精度被广泛应用在光学元件的面形测量上,而由移相算法得到的相位数据被包裹在[-π,π]之间。基于区域生长理论的相位解包算法(种子点法)可以高精度地实现连贯区域的相位解包,基于离散余弦变换的最小二乘解包(DCT)算法可以实现矩形区域的相位解包,而实际测量中,经常会碰到被测件的有效区域为非矩形的分离区域。因此,在分析前两种算法优缺点的基础上,提出了基于DCT算法的种子点相位解包算法。首先运用DCT算法对整个包裹相位进行解包,然后运用种子点法分别解包各分离区域,再通过DCT算法求得的种子点干涉级次实现各分离区域解包相位的统一。实验结果表明,该方法克服了种子点法和DCT算法的缺点,可以准确、快速地实现分离区域干涉图包裹相位的解包,且比这两种算法具有更好的稳定性和更高的精度。

Phase-shifting interferometry is widely used in the surface measurement of optical elements as its high precision.The phases obtained from phase-shifting algorithms are wrapped between-π and π.The algorithm based on the region growing theory（seed point algorithm） can realize phase unwrapping of connected regions with high precision.The algorithm based on discrete cosine transform（DCT） algorithm can realize phase unwrapping of rectangular region.In practical measurements,the valid region of test flat is often non-rectangular and separated.On the basis of analyzing the advantages and disadvantages of the above algorithms,the seed point unwrapping algorithm based on DCT algorithm is presented.Firstly,the wrapped phases are unwrapped totally with DCT algorithm.Secondly,the wrapped phases of separated regions are unwrapped with the seed point algorithm respectively.Then they are unified with the interference orders obtained from DCT algorithm.The experimental results show that the algorithm overcomes the disadvantages of the seed point algorithm and DCT algorithm.It can unwrap the wrapped phases obtained from separated interferograms correctly and quickly,and it is more stable and more precise than the two algorithms above.