Wavefront optical spacing of freeform surfaces and its measurement using CGH interferometry

Abstract

For optical surfaces, the distance between the wavefront at ideal design position and that at real surface testing position along the wavefront propagation direction is an important parameter. It determines the on-axis curvature deviation and best-fit sphere radius of the surface under testing, and thus, affects the optical distance, effective focal length, and tolerance design of the optical system. We define the distance as wavefront optical spacing (WOS or spacing d). The analytical form of the WOS can be utilised in critical tolerance balancing, and its test results can aid in optical system redesign. Aiming at a computer-generated hologram (CGH) interferometric test, in this study, we propose the WOS concept and deduce the coupling relation between the surface error and spacing d, particularly in freeform surface conditions. A cat-eye CGH interferometric method was presented to test the spacing error within a precision of several microns. The simulation and error budget demonstrate that this method can measure the WOS of freeform surfaces. The experimental results indicate that the metrology accuracy is 10.2 ± 4.3 μm (P = 95%) (absolute accuracy), 4.5 μm (repeatability), and 2.1 ppm (relative accuracy).