Fast and precise registration of quasi-planar free-form wavefronts

Quasi-planar free-form wavefronts are featured with vertical fluctuations of small amplitude and high frequency. They can be considered a plane superposed with waviness at the scale of a wavelength, which is the key to enabling control of the optical performance. This paper presents a method for fast and precise registration of quasi-planar free-form wavefronts to obtain the true difference between the test wavefront and the nominal one. We first adapt the planar subaperture stitching algorithm to the registration of two wavefronts with almost 100% overlap. This will usually fail because the registration result is very sensitive to lateral misalignment. Hence a fast and precise method is proposed to directly register two point sets in three-dimensional (3D) space. It is based on a novel procedure to calculate the closest distances of 3D points to another 3D point set. Then registration of a 320 mmx320 mm wavefront with the method is simulated and compared with the subaperture stitching method. Finally a corrective machining case is given to demonstrate the validity of the method to achieve high precision.