任意形状孔径的干涉图时空移相方法

Spatiotemporal phase-shifting method for interferograms of apertures with arbitrary shape

移相干涉术作为一种高灵敏度的非接触式光学测量方法,在精密测量领域得到了广泛的应用。时空移相方法(spatiotemporal phase-shifting method,ST-PSM)作为一种高精确度的移相算法,可避免传统移相算法的周期误差。这使得该算法适用于存在背景光强不均匀、调制度波动以及移相误差的情况,同时也能测量畸变的干涉条纹图像。然而,该方法中的插值拟合步骤要求干涉图呈矩形区域,对于非矩形孔径的光学元件,无法测量其面形全貌。为突破该局限性,提出将干涉图延拓技术与该方法结合,移相干涉图经延拓成矩形后,再使用时空移相方法进行相位提取,以获得完整的面形信息。数值模拟及实验结果显示,就相同形状下的干涉图,经延拓后使用时空移相方法相较于未延拓测得的波面峰谷值与均方根值更精确。以圆形为例,经延拓后峰谷值由0.1236λ降至0.0446λ,均方根值由0.0117λ降至0.0109λ(λ=633 nm)。结果表明该方法可用于非矩形光学元件的精确测量。

Phase-shifting interferometry is a highly sensitive non-contact optical measurement method that has been widely used in the field of precision measurement.The spatiotemporal phase-shifting method(ST-PSM)is a phase-shifting algorithm known for its high accuracy,which can avoid periodic errors that are typical of traditional phase-shifting algorithms.This makes it suitable for use in the presence of uneven background light intensity,modulation fluctuations and phase-shifting errors,as well as for measuring distorted interferometric fringe images.However,the interpolation fitting step of this method requires the interferogram to be in a rectangular region,which makes it difficult to measure the complete surface shape of optical elements with non-rectangular apertures.To address this limitation,a novel approach that combined the interferogram spreading technology with the ST-PSM method was proposed.This involved spreading the interferogram into a rectangle,which enabled the ST-PSM method to extract the phase and obtain the complete surface shape information.Numerical simulations and experimental results show that for interferograms with the same shape,the peak-valley values and root mean square values of the wave surface measured by the ST-PSM method with spreading are more accurate than those obtained by using the ST-PSM method without spreading.Taking the circle as an example,the peak-valley value decreases from 0.1236λto 0.0446λafter extension,and the root mean square value decreases from 0.0117λto 0.0109λ(whereλis 633 nm).The above results demonstrate that the proposed method can be used for accurate measurement of non-rectangular optical elements.