干涉测量波面重构DCT算法研究

Wavefront reconstruction of interferometry by DCT algorithm

采用一种空间移相干涉仪测量凹形非球面反射镜光学表面,使用偏振元件和多幅图像同步采集实现移相,并对测量得到的干涉条纹采用基于离散余弦变换的相位解包裹算法,对不连续相位分布采用非加权的最小二乘法进行优化目标函数,最终重构出被测光学表面的面形。这种结构形式的干涉仪具有一定的抗振能力,同时在数字图像处理上优化了算法,能够快速稳定地得到被测面形,而且对硬件要求不高。结果表明:这种算法能够适用于非实验室条件下的光学测量,在一定干扰条件下可以达到较高的测量精度。

We use a type of interferometer with space phase-shifting technique to measure the optical surface of the concave aspheric mirror in this paper. By using polarized elements and multi-image collected in synchronism we implement the phase-shifting process, and we adopt the phase unwrapping algorithm based on discrete cosine transform（DCT） onto the interferograms that we measured. For the discontinuous phase distribution, we adopt the un-weighted least square method to optimize the objective function, and finally reconstruct the wavefront surface of the measured optical surface. This type of interferometer has the capacity of anti-vibration, and can optimize the algorithm in the digital image processing procedure, so we can get the measured surface shape rapidly and steadily, and it is no need for high performance hardware. This approach can be used as optical measurement out of laboratory conditions, and we can get high measuring precision under the condition of disturbance existing.