With the continuous development of laser pulse width limits and improvement of peak power, the size of the pulse compression grating (PCG) must be further increased. However, the high-precision manufacturing and testing of large aperture and long focal distance off axis parabolic (OAP) mirrors required by reflective exposure systems, has presented a difficult challenge that restricts the manufacturing of large aperture gratings. The method based on computer generated holograms (CGH) does not require a complex design and setup, however, it introduces non-rotational symmetry and complex two-dimensional projection distortion. When correcting distortion, traditional marker point s and analytical methods have limited accuracy or complex calculations, which are not conducive to engineering applications. Therefore, this study proposes a distortion correction method based on numerical calculation, with the advantages of simplicity, versatility, and ease of programming. Based on the CGH test optical path, high-precision surface measurement can be achieved using system error calibration and distortion correction methods, laying the foundation for OAP mirror surface accuracy manufacturing and subsequent establishment of large aperture reflective exposure systems.

Initially, a Φ800 mm folding mirror is adopted to effectively shorten the optical path length, enabling development of a CGH measurement optical path on an 18 m vibration isolation air flotation optical table (Fig.2), and design a beam expansion system that matches the measurement aperture of the interferometer and CGH. Subsequently, the measurement errors introduced by the main optical elements in the optical path, excluding the interferometer, including CGH, beam expansion system, and fold mirror, are analyzed in detail, and the errors introduced are calibrated and removed. Thereafter, to ensure that the machining coordinate system matches the testing coordinate system, to achieve the precise positioning and convolution of the removal function and figure error, it is necessary to correct the distorted surface map measurement. Therefore, the mapping relationship between mirror, CGH, and CCD coordinate points is established based on the imaging distortion model (Fig.9). Finally, according to the corrected surface map, the OAP mirror is fabricated using Magnetorheological Finishing (MRF) technology.

. Once the measurement optical path is established, the surface map measured by the interferometer was compared with that measured by the coordinate measurement machine (CMM). Except for the projection distortion in the interferometric measurement results, the distribution of other features is basically consistent (Fig.3). When the CGH calibratable errors, beam expander system, and fold mirror are superimposed, the measurement optical path system error is 11 nm RMS (Fig.8). After error compensation, the measurement optical path error does not exceed RMS 5.4 nm (Table 5). Among them, the fold mirror figure error is the main error source. The coordinate positions and positional errors of the distortion correction points are listed (Table 6). The maximum correction error is 1.96 mm, which is smaller than the testing interferometer measurement resolution. This measurement accuracy meets the of magnetorheological computer numerical control (CNC) machining positioning accuracy requirements. Post processing, the OAP mirror figure error after distortion correction is PVr: 0.130λ, RMS: 0.013λ (Fig.11). By comparing the surface map distributions before and after distortion correction, it can be observed that the corrected surface map distribution and values are fundamentally consistent with those uncorrected s, and with the mirror coordinates. This result provides a good basis for subsequent light field exposure analysis and performance evaluation.

For the measurement of a 1650 mm×1120 mm long focal distance OAP mirror, an Φ800 mm fold mirror is introduced to shorten the CGH compensation measurement optical path. Using error analysis and calculation, the calibratable error in the optical path is projected onto the CCD, and then calibrated and removed, thereby achieving improved measurement accuracy. Considering the projection distortion error caused by simultaneous measurement, a correction method based on ray tracing and imaging distortion model fitting is proposed. Compared with traditional methods, the proposed method is extremely suitable for numerical programming calculations. Once processing verification completes, the figure accuracy can converge to RMS 0.013λ, and meet the requirements of high-precision OAP mirror specifications and manufacturing, laying a foundation for the subsequent establishment of large aperture reflective exposure systems.