Objective  The instrument transfer function, which accurately reflects the instrument's response characteristics in spatial frequency, is widely used in instrument specifications. Currently, flat test boards engraved with single-step features or sinusoidal features of different periods are commonly used to measure the instrument transfer function of interferometers. However, when it comes to calibrating the instrument transfer function for high-steep spherical/non-spherical mirror testing, there is an issue with using flat test boards.

  Methods  To address this problem, a method is proposed to calibrate the instrument transfer function for high-steep mirror testing on spherical surfaces using sub-aperture stitching, based on a spherical step test board. The spherical step test board is manufactured using ultra-precision turning technology, and the steps within the measuring apertures are located and sampled using gradient localization and rotation matrix operations. The power spectral density of the measured surface shape of the steps is obtained using Fourier transform methods, and then compared with the power spectral density of an ideal surface shape to obtain the instrument transfer function.

  Results and Discussions   By combining examples, a spherical step test board with a diameter of 100 mm, a curvature radius of 100 mm, and concentric circular step structures was subjected to stitching testing and data analysis. The experimental results show that within the spatial frequency range of 1 mm⁻¹, the average testing level of each sub-aperture for high-steep mirrors can reach 82.72%, indicating a good testing accuracy. However, as the spatial frequency approaches 1.5 mm⁻¹, the testing level decreases to only 40%−60% for each sub-aperture, indicating poorer performance of the instrument transfer function.

  Conclusions  This article proposes a method for calibrating the sub-aperture stitching instrument transfer function of high-steep mirror surfaces using a designed spherical step test board. In this method, a spherical test board with concentric circular ring step structure is used, which allows for the calculation of the instrument transfer function at different positions of each sub-aperture. The testing accuracy of each sub-aperture can be obtained, thereby achieving the overall calibration of the instrument transfer function.