Phase Shifting Grating-Slit Test Utilizing A Digital Micromirror Device With an Optical Surface Reconstruction Algorithm

Abstract

A novel optical surface testing method termed the grating-slit test is demonstrated to provide quantitative measurements and a large dynamic measurement range. Although it uses a grating and a slit, as in the traditional Ronchi test, the grating-slit test is different in that the grating is used as the object and the slit is located at the observation plane. This is an arrangement that appears not to have been previously discussed in the optical testing literature. The grating-slit test produces fringes in accordance with the transverse ray aberrations of an aberrated wavefront. By using a spatial light modulator as the incoherent sinusoidal intensity grating it is possible to modulate the grating and produce phase shifting to make a quantitative measurement. The method becomes feasible given the superior intensity grayscale ability and highly incoherent illumination of the spatial light modulator used. Since the grating is used as the object, there are no significant diffraction effects that usually limit the Ronchi test. A geometrical and a detailed physical analysis of the grating-slit test are presented that agree in the appropriate limit. In order to convert the measured transverse ray aberrations to the surface figure error, a surface slope sensitivity method is developed. This method uses a perturbation algorithm to reconstruct the surface figure error from the measured transverse ray aberration function by exact ray tracing. The algorithm takes into account the pupil distortion and maps the transverse ray aberration from the coordinate system of the observation plane to the coordinate system of the surface under test. A numerical simulation proves the validity of the algorithm. To demonstrate the dynamic range of the grating-slit testing method, two optical surfaces are measured. The first surface is a polished spherical mirror with 0.6 waves of aberration as measured with an interferometer. Using the concept of transverse ray aberration separation, the first surface is measured without a strict alignment requirement. The second surface is a concave ground optical surface with 275 waves of astigmatism. The measurements from the grating-slit test yield useable surface figure information that is in agreement with the results from other testing methods.