Acta Photonica Sinica, Volume. 52, Issue 12, 1212003(2023)

High Precision Deflectometric Measurement Based on Pinhole Camera with an External Stop

Lu YE1,2, Xiangchao ZHANG1、*, Junhua WANG1, Min XU1, and Liehua ZHENG2
Author Affiliations
  • 1Shanghai Engineering Research Center of Ultra-precision Optical Manufacturing,Fudan University,Shanghai 200438,China
  • 2Shanghai Institute of Technical Physics,Chinese Academy of Sciences,Shanghai 200083,China
  • show less

    With the increasing requirements of complex shapes and high resolution of optical systems, the precision measurement of optical mirrors is of great challenge. In the grinding stage, a coordinate measurement machine is generally adopted, which is realized by contact measurement, but it suffers from long measurement time and low accuracy. In the polishing stage, laser interferometry is generally adopted. Due to its limited measurement range, a specially designed compensator is required for measuring an aspheric surface. Usually, it is impossible to achieve full aperture interferometric measurement of a surface with deep asphericity, especially when it has a large form deviation.Fortunately, the Phase Measuring Deflectometry (PMD) can overcome this problem, which has the advantages of fast measurement speed, low cost, high dynamic range and high flexibility. However, it also has limitations. First, the accuracy of system calibration directly affects the measurement accuracy. The camera is usually regarded as a pinhole camera. The internal and external parameters of the camera are obtained through complicated calibration. Images of a calibration plate are taken at different positions and poses, and the coordinates of each camera pixel are obtained accordingly. The traditional calibration method has a complicated process and it is greatly affected by the quality of the calibration plate. Moreover, camera calibration and geometric calibration are generally obtained separately, and there will be error coupling and propagation in the conversion of coordinate systems. Second, most industrial camera lenses adopt a symmetrical structure in order to eliminate aberrations. The aperture stop is located in the middle of the lens group. In order to directly specify the position of the camera stop, an external stop can be set at the front of the lens, which will greatly affect the camera's field angle and bring inconvenience to measurement. Third, a theoretical model is needed for the surface under test to estimate the position of measured points to solve the height slope ambiguity problem. Generally, a plane model or spherical model can be used as the initial guess, but large errors can be yielded when there exists severe deviations and the measurement accuracy is affected in turn.As a consequence, a pinhole camera lens is designed with external stop, which can be measured easily. The camera lens consists of four pieces, one of them is glued, and the lens has good image quality. The size of the standard spot diagram is much smaller than the size of Airy disk, and the distortion is 0.707%, which is superior to most commercial lenses. It eliminates the need for complicated camera calibration. Combined with the calibration of reflected light, the camera coordinates can be obtained quickly and accurately. The screen pixel coordinates can be conveniently converted to the workpiece coordinates by pre-calibration. In this paper, at least three non-collinear markers made of aluminum blocks are applied. The spatial position relationship between camera, screen and workpiece can be obtained by external devices such as a coordinate measurement machine, and the coordinate system is henceforth unified. The phase shift algorithm is used to establish the correspondences between camera and screen pixels. The coordinates of the intersection points between the reflected light and the off-axis aspheric surface were deduced by the formula. Finally, surface reconstruction can be achieved using the above data at one time, without the need for iterative calculation.An aluminum parabolic mirror with a diameter of 110 mm and a vertex curvature radius of 800 mm is used as the surface under test. Surface measurement is carried out by using the designed pinhole camera with an external stop and the calculating method of measured points. The experimental results show that the accuracy of the reconstruction results is of the same order of magnitude with the profilometer and laser interferometer, and the distribution of the obtained form deviations is consistent. In addition, low-order aberrations including power, coma and astigmatism can be accurately measured by deflectometry, which indicates that the geometric calibration accuracy is very high. The reconstruction results of deflectometry are subtracted pixel by pixel with the results by LuphoScan and interferometry, and the relative errors are 27 nm RMS and 20 nm RMS, respectively.Firstly, the material of tested mirror is aluminum, which is fabricated by a single point diamond turning machine. The central area is steep, and the entire surface can be captured by one spiral scan by LuphoScan, and the final surface datas are obtained by numerical interpolation. There will be a small deviation in some steepness areas due to sample size. Secondly, the profile data collected by the laser interferometer may not be of full aperture, and there may be data missing in the area with a large sphericity deviation at the edge. These two reasons can lead to the possibility of position dislocation in the surface alignment, and it is reasonable to believe that the actual measurement error should be less than 20 nm. This implies that the accuracy can meet the measurement requirements of optical mirrors from grinding to polishing stage.Deflectometry combines the advantages of coordinates measurement machines and interferometry, with high measurement accuracy, fast measurement speed, and a large dynamic range. It provides a reliable, economical and efficient tool for surface assessment in optical machining shop, and henceforth, and has a wide application prospect.

    Tools

    Get Citation

    Copy Citation Text

    Lu YE, Xiangchao ZHANG, Junhua WANG, Min XU, Liehua ZHENG. High Precision Deflectometric Measurement Based on Pinhole Camera with an External Stop[J]. Acta Photonica Sinica, 2023, 52(12): 1212003

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category: Instrumentation, Measurement and Metrology

    Received: Jun. 14, 2023

    Accepted: Aug. 1, 2023

    Published Online: Feb. 19, 2024

    The Author Email: ZHANG Xiangchao (zxchao@fudan.edu.cn)

    DOI:10.3788/gzxb20235212.1212003

    Topics