中文摘要：

针对光学元件的面形测量,提出了一种被测件随机移相干涉面形测量法,用于降低移相干涉仪的成本,避免移相器老化产生的移相误差对面形检测精度的影响。该方法利用微位移驱动器驱动被测件在摩擦气浮复合导轨上移动进行随机移相并用相机采集若干幅干涉图;然后利用最小二乘迭代算法处理干涉图数据进而迭代出被测表面相位分布;最后进行一系列数据处理求解出被测件的面形结果。为了验证该方法的可行性,在实验室搭建了改进的斐索移相干涉系统,并选用一个凹面镜和一个平面镜作为被测件在搭建的系统上进行了实验测试,同时与同台仪器上的传统移相方法得到的测量结果进行了比对。结果表明：在激光光源波长λ为632.8nm的情况下,凹球面镜面形PV值和RMS值与传统移相方式测量结果相差0.001λ,和0.002λ;平面镜面形PV值和RMS值与传统移相方式的测量结果相差0.002λ和0.003λ,面形数据基本一致。该方法避免了移相器老化引入移相误差,降低了仪器成本,测量精度高。

英文摘要：

For the surface measurement of optical elements,a surface measurement method by the randomly phase shifting interferometry of measured element was proposed to reduce the cost of phase shifting interferometer and to avoid phase-shifting error caused by an aged phase shifter.A microdisplacement driver was used to drive a measured element to move on a friction type air-bearing slider to implement the random phase shift,meanwhile,several interfere grams were collected by a camera.Then,the interferograms were processed by least-square iteration algorithm and the phase distribution of the measured element surface was iterated.Finally,the surface measurement result was calculated by a series of data processing and the surfaces of measured elements were obtained.To verify the feasibility of the proposed method,a Fazi phase shift interferometer was improved and a concave spherical mirror and a plane mirror were used as measured elements to perform the comparative experiment between the article＇s method with the traditional phase shifting method on the same instrument.Experimental results indicate that when the laser wavelengthλis 632.8nm,the PVdifference and the RMS difference between the two results are only 0.001λand 0.002λ,respectively for the concave spherical mirror.Moreover,those between the two results are only 0.002λ,and0.03λ,respectively for the plane mirror.These surface data are basically consistent.Experimental results show that the measurement method avoids the phase-shifting error caused by the aged phase shifter,and it has high accuracy and low cost.