The surface shape testing of optical aspherical components has guiding significance in advanced optical processing and manufacturing processes. The traditional Foucault knife-edge shadow testing method is extremely effective in detecting various optical surfaces, with advantages such as simple testing equipment, high-accuracy testing results, high-sensitivity surface error testing response, and convenient testing. Thus, it is still widely employed in aspheric surface testing. Previous research has made sound progress in the digitization and automation of knife-edge optical testing through digital image processing technology and automatic control technology, but both require adjusting the knife edge of the knife-edge instrument to the focal position of the mirror to be tested before proceeding with further testing work. Meanwhile, although the traditional method of adding a screen optimizes the testing of ring belt error, it is limited by factors such as screen shape and image processing. Additionally, traditional physical screens cannot be flexibly adopted and can only be slotted at fixed positions. The edges of the slotted screen will produce some diffraction effects, which is not conducive to the accuracy of the testing results and increases system complexity. Therefore, we propose a knife-edge testing method based on virtual screen modulation for quantitative testing of ring belt error. By utilizing the object and image relationship between physical screens by the object surface and virtual screen by the image surface, we achieve subring ring belt segmentation of multiple axial knife-edge shadow grams generated by the mirror surface to be measured. The axial focus positions corresponding to each ring belt are determined based on the evolution characteristics of the corresponding image gray level along the axis. Finally, automation and quantitative solutions of the entire surface shape are achieved to implement quantitative and efficient optical testing.

This method first sets up a series of circular screens δR₁, δR₂,… δR_n and performs circular screen segmentation on the entire mirror surface to be tested from the inside out, and all screen masks are superimposed to form a complete screen. Then, a series of P(z₁), P(z₂),…, P(z_m) are multiplied by the radial annular diaphragm mask δR₁, a series of shadow grams P are obtained for bandpass filtering Pδ1(z₁), Pδ1(z₂),…, Pδ1(z_m). Meanwhile, to ensure the testing accuracy, we first filter and denoise this series of shadow grams, and then calculate the image variance of these shadow grams. If the image with the smallest gray variance in this series of images is Pδ1(zR₁), it indicates that the focusing point corresponding to the R₁ ring is at zR₁ on the optical axis. Finally, the above steps are repeated by different ring belt screen mask functions to process the shadow map n in total n×m times, and the focal points zR_n corresponding to different ring belts R_n on the axis can be obtained. The characteristic of this method is to utilize a series of shadow grams to obtain the focal position of a specific ring belt, and to extract information using the grayscale changes caused by the z-direction position changes with higher accuracy.

We validate the feasibility of the method in the field of quantitative testing and compare the profile testing results of the proposed method with the interferometric testing results. The employed interferometry is a commercial interferometer from 4D company, PhaseCam 4030. The comparison shows that the consistency of the undulating positions of the ring belt is consistent, and the main ring belt position is located at 0.7191 and 0.7114 times of the radius, with a deviation of no more than 1%. The error of peak-to-valley (PV) and root-mean-square (RMS) values is around 7%, and PV values are 0.7748λ and 0.7207λ with a difference of 0.0541λ, which is about 30.0255 nm. RMS values are 0.0569λ and 0.0547λ with a difference of 0.0022λ, which is approximately 1.2210 nm. Combined with the previous overall surface map for interpretation, results show that the proposed method has good testing reliability and can guide optical processing and testing. To ensure the accuracy and reliability of the experimental results and the universality of the parameter selection of this method, we also analyze the experimental and image processing results under different parameters. The main focus is on the quantitative comparison and explanation of the influence of different ring belt segmentation numbers and shadow gram sampling intervals on the experimental results. Finally, experimental error analysis is conducted.

We propose and verify a quantitative and automated knife-edge optical testing method based on algorithm adding virtual mask screens. This method automatically collects multiple axial knife-edge shadow grams generated by the tested mirror surface at non-focal points and divides them into subrings. Meanwhile, the axial focal positions corresponding to each ring belt are determined based on the evolution characteristics of the image gray level along the axis to achieve a quantitative solution of the entire surface shape. By adopting image processing algorithms to control the position of the circular screen, different circular screens can be selected in sequence. Finally, this optimizes the problem that traditional solid screens are limited to being slit in a fixed position and unable to be flexibly applied, with increased system complexity. The experimental results demonstrate that this method can achieve high-precision and quantitative surface shape testing of optical components, with high efficiency and strong applicability. Thus, this study has strong guiding significance for optical shop processing and testing.