Accuracy characterization of Shack–Hartmann sensor with residual error removal in spherical wavefront calibration

Abstract

The widely used Shack–Hartmann wavefront sensor (SHWFS) is a wavefront measurement system. Its measurement accuracy is limited by the reference wavefront used for calibration and also by various residual errors of the sensor itself. In this study, based on the principle of spherical wavefront calibration, a pinhole with a diameter of 1 µm was used to generate spherical wavefronts with extremely small wavefront errors, with residual aberrations of 1.0 × 10−4 λ RMS, providing a high-accuracy reference wavefront. In the first step of SHWFS calibration, we demonstrated a modified method to solve for three important parameters (f, the focal length of the microlens array (MLA), p, the sub-aperture size of the MLA, and s, the pixel size of the photodetector) to scale the measured SHWFS results. With only three iterations in the calculation, these parameters can be determined as exact values, with convergence to an acceptable accuracy. For a simple SHWFS with an MLA of 128 × 128 sub-apertures in a square configuration and a focal length of 2.8 mm, a measurement accuracy of 5.0 × 10−3 λ RMS was achieved across the full pupil diameter of 13.8 mm with the proposed spherical wavefront calibration. The accuracy was dependent on the residual errors induced in manufacturing and assembly of the SHWFS. After removing these residual errors in the measured wavefront results, the accuracy of the SHWFS increased to 1.0 × 10−3 λ RMS, with measured wavefronts in the range of λ/4. Mid-term stability of wavefront measurements was confirmed, with residual deviations of 8.04 × 10−5 λ PV and 7.94 × 10−5 λ RMS. This study demonstrates that the modified calibration method for a high-accuracy spherical wavefront generated from a micrometer-scale pinhole can effectively improve the accuracy of an SHWFS. Further accuracy improvement was verified with correction of residual errors, making the method suitable for challenging wavefront measurements such as in lithography lenses, astronomical telescope systems, and adaptive optics.

Keywords

• shack–hartmann wavefront sensor
• spherical wavefront calibration
• residual aberration correction
• high-accuracy measurement of wavefronts