High-precision large optical flats are indispensable in astronomical optics and space optics. For example, large optical flats can be used as standard inspection mirrors for large-aperture optical systems to achieve system calibration or as standard sub-aperture mirrors to splice and test larger-diameter flat mirrors. Therefore, it is of great significance to detect the surface shape of large optical flats accurately. Ritchey-Common test is a special oblique incidence interferometry. The Ritchey-Common test optical path only needs to be built with a well-polished concave spherical mirror, so it is easy to implement in the optical detection workshop. The beam emitted by the interferometer is obliquely incident on the test flat, and the angle between the main optical axis and the normal of the test flat is called the Ritchey angle and is denoted as θ. The Ritchey angle is a critical parameter in the Ritchey-Common test. At present, there are two main methods for measuring the Ritchey angle: 1) measuring the distance between the focal points of the system, the intersection point of the optical axis and the test flat, and the intersection point of the optical axis and the stand spherical mirror, and then calculating the Ritchey angle by the cosine formula; 2) using the edge detection method to analyze the ratio of the long and short axes of the wave aberration image to obtain the Ritchey angle. However, in practice, it is quite difficult to accurately measure the distance between three points with the traditional ranging method, and the measurement process is easily disturbed by human subjective factors. In addition, the edge detection algorithm has low sharpness of the edge area of the interferogram, which brings difficulties to accurate identification. Therefore, it is also difficult to obtain an accurate Ritchey angle. An inaccurate Ritchey angle leads to inaccurate detection of the flat. The measurement of the Ritchey angle is essentially a geometric angle calculation. Meanwhile, the laser tracker has a very outstanding advantage in the field of large-scale spatial geometric parameter measurement, and its distance measurement can reach micron accuracy. Therefore, to reduce the measurement error of the Ritchey angle in the Ritchey-Common method and improve the detection accuracy of the large optical flats, an in-situ detection method for the Ritchey angle based on a laser tracker is proposed in this paper.

In the in-situ detection method for the Ritchey angle based on a laser tracker, there are two technologies that need to be focused on: one is the accurate establishment of the space model of the test flat based on the laser tracker; the other is the precise positioning of the focus of the interferometer. For the first technology, the least squares fit method is applied to establish an accurate model. The coordinates of feature points on the test flat are obtained by laser tracker. Then, the complete spatial geometry model of the test flat will be obtained by fitting the feature points sampled on the surface and outer contour of the test flat. In the simulation section, the influence of the algorithm fitting errors, ranging errors, and angle measurement errors on the measurement of the Ritchey angle is analyzed by the analog measurement function based on the laser tracker. Moreover, to position the focus of the interferometer precisely, the functional relationship between the coefficient of Zernike power term and geometric defocus has been derived. In the next step, the Ritchey-Common test experiment is performed on the Φ430mm optical flat to verify the reliability of this method for surface shape detection. Meanwhile, the experiment of positioning the focus point of the interferometer is conducted to prove the correctness of the functional relationship between the coefficient of Zernike power term and geometric defocus. Finally, the effectiveness of this method is evaluated by comparing it with other methods for measuring the Ritchey angle.

Through numerical simulation, it is analyzed that the relative error of using this method to detect the Ritchey angle is not more than 0.017%. Compared with the traditional method using the image compression ratio of the pupil surface of the system to calculate the Ritchey angle, the error of the Ritchey angle is reduced from about 0.2° to below 0.005°. In the Ritchey-Common detection experiment of the Φ430mm plane mirror, two angles are selected for measurement, and the Ritchey angles are obtained as 39.18° and 21.12°. We will evaluate the surface shape of the test flats from both the RMS of the surface shape and the Zernike power coefficient of the test flat. After the surface shape of the test flat is detected, the detection error of the Zernike power coefficient of the plane mirror is reduced from 6.31% to 0.028% (Fig. 11). Additionally, the residual RMS between the detected surface shape of the flat using the method described in this paper and the true surface shape of the flat is 0.0206λ; the residual RMS between the surface shape detected by using the compression ratio measurement method and the real surface shape is 0.0236λ. Besides, we design an experiment to position the focus of the interferometer. As shown in the result, the variation trend of the Zernike power term coefficient with the spatial position of the SMR is highly consistent with the conclusion we have derived (Fig. 13). The experimental results indicate that the accuracy of the detection of the Ritchey-Common test and the accuracy of the measurement of the Ritchey angle have been improved significantly by using the in-situ detection method for the Ritchey angle based on a laser tracker.

In this paper, we propose an in-situdetection method for the Ritchey angle based on a laser tracker and derive the functional relationship between the Zernike power term coefficient and geometric defocus, achieving accurate positioning of the interferometer focus point. In the simulation part, we analyze the effect of the software error, the ranging error, and the angle measurement error of the laser tracker on the measurement accuracy of the Ritchey angle. During the experiment, we detected Φ430mm flat with the Ritchey-Common test. Compared with the compression ratio method for measuring the Ritchey angle, the method we proposed can more accurately measure the Ritchey angle in the Ritchey-Common test, thereby improving the surface shape detection accuracy of the flat, especially the Zernike power term coefficient of the test flat.