Determining the wedge angle and optical homogeneity of a glass plate by statistically analyzing the deformation in the wavefront surface

By using a light-emitting diode as the probing light source and a Shack-Hartmann wavefront sensor as the recorder for the wavefront surface to execute a relative measurement, we present a useful method for determining the small wedge angle and optical homogeneity of a nominally planar glass plate from the wavefront measurements. The measured wavefront surface from the light source was first calibrated to be a horizontal plane before the plate under test was inserted. The wedge angle of the plate can be determined from the inclining angle of the regression plane of the measured wavefront surface after the plate was inserted between the light source and the wavefront sensor. Despite the annoying time-dependent altitude fluctuation in measured wavefront topography, the optical homogeneity of the plate can be estimated from the increment on the average variance of the wavefront surface to its regression plane after the light passes through it by using the Bienaymé formula.