Objective With the expanding application of large aperture and complex optical systems, the demand for aspheres is also increasing. Aspheres whose surface deviates from the spherical surface prove more design freedom for optical systems than spherical surfaces, and help improve image quality and achieve a compact and lightweight design of optical systems. Without high- precision testing, there cannot be deterministic control and manufacturing. The widespread utilization of aspheres requires high- precision surface measurement as support, and the final manufacturing accuracy is mainly determined by the testing accuracy. Asphere testing has developed numerous solutions, among which non-interference methods usually have sound flexibility without high measurement accuracy, and some methods are contact measurement, which can easily damage the device under test. Interferometric measurement methods include null and non- null interferometry, among which null interferometry has limitations in measuring the dynamic range and flexibility. Non- null interferometry lowers the high requirements for wavefront compensation, thereby improving the dynamic range and universality of measurement. The subaperture stitching interferometry is the most widely employed among non- null interferometry. The combination of subaperture stitching interferometry and partial compensation can achieve high- precision and flexible asphere testing. We propose an aspheric subaperture stitching interferometry with a single- wedge variable compensator to provide a new solution for high- precision testing of aspheres. Methods The proposed method is an aspheric subaperture stitching interferometry with a single-wedge variable compensator, which can be adopted for flexible asphere interferometry. The standard converging spherical wave emitted by the interferometer is modulated by an optical wedge to reach the subaperture of the tested asphere. The optical wedge can realize translation and rotation along the optical axis direction. The scanning system includes modules of subaperture scanning and component alignment. During measurement, the direction of the output beam is changed by altering the axial position of the optical wedge to complete radial scanning of the subaperture ring from the center to the edge and reduce the motion complexity of the scanning module. Meanwhile, the spherical wavefront after being modulated by optical wedges can compensate for fundamental aberrations such as astigmatism and coma of asphere subapertures. All subapertures of aspheres are collected by tilting and rotating the optical wedge around the axis. Reverse optimization reconstruction is utilized to correct system return error and projection distortion for all subaperture data. Afterwards, the stitching algorithm using alternating calibration is employed to reconstruct the phase distribution with the subaperture data after system error correction. Results and Discussions The stitching algorithm using alternating calibration is utilized to obtain the full-aperture phase of the tested asphere. The six-dimensional positioning error obtained by stitching is shown in Table 2. The measured low-frequency phase of the tested asphere is shown in Fig. 16(a), and the peak-valley (PV) value and root-mean-square (RMS) are 0.4283 lambda and 0.1070 lambda respectively. The residuals of the proposed method and LuphoScan 260 are shown in Fig. 16(c), and the PV and RMS are 0.1259 lambda and 0.0273 lambda respectively. The phase distribution and residual show that the proposed aspheric subaperture stitching interferometry with a single-wedge variable compensator can achieve measurement accuracy of approximately lambda/8 (PV) for aspheres. The distribution of residuals is close to coma, and this may be caused by the following three reasons. Firstly, when a single optical wedge for asphere compensation stitching interferomety is employed, the optical wedge mainly compensates for the astigmatism and coma of the off-axis subaperture. In actual testing, the processing and installation errors of the optical wedge can cause the aberration compensation of the subaperture to deviate from the ideal design testing state, resulting in measurement errors. Secondly, it is necessary to align the testing system and ensure that the motion of the test mirror controlled by the scanning system during subaperture scanning measurement conforms to the subaperture planning route. In this experiment, the test mirror may tilt in the vertical direction, which usually introduces coma in the test phase. Thirdly, there are residuals in the calibration of the system retrace error and projection distortion, which are coupled into the retrieves phase. These problems will be our focus in the future. Conclusions We propose an aspheric subaperture stitching interferometry with a single-wedge variable compensator, providing a new solution for high-precision and flexible asphere testing. This method employs a single optical wedge as a subaperture aberration compensator, and compensates for the basic astigmatism and coma of the off-axis subaperture by adjusting the tilt angle of the optical wedge. Meanwhile, adjusting the axial position of the optical wedge can also achieve subaperture scanning at different off-axis positions. Finally, the stitching algorithm is adopted to complete the full-aperture phase reconstruction. Additionally, we analyze the wavefront aberration modulation mechanism of the optical wedge and propose a complete alignment method for the optical wedge pose system. The experimental results show that the proposed method has good consistency with the point scanning results of the 3D profilometer, and the full-aperture testing residual is about lambda/8 (PV). This indicates that the proposed method can yield high-precision asphere compensation stitching interferometry, and has a simple and flexible compensation structure, thus improving the measurement ability of subaperture stitching interferometry.
