Error Compensation Algorithm for Higher Surface Accuracy of Freeform Mirrors Based On the Method of Least Squares

Off-axis reflective optical systems have attractive advantages relative to their on-axis or refractive counterparts, for example, zero chromatic aberration, no obstruction, and a wide field of view. For the efficient operation of off-axis reflective system, the surface accuracy of freeform mirrors should be higher than the order of wavelengths at which the reflective optical systems operate. Especially for applications in shorter wavelength regions, such as visible and ultraviolet, higher surface accuracy of freeform mirrors is required to minimize the light scattering. In this work, we propose the error compensation algorithm (ECA) for the correction of wavefront errors on freeform mirrors. The ECA converts a form error pattern into polynomial expression by fitting a least square method. The error pattern is measured by using an ultra-high accurate 3-D profilometer (UA3P, Panasonic Corp.). The measured data are fitted by two fitting models: Sag (Delta Z) data model and form (Z) data model. To evaluate fitting accuracy of these models, we compared the fitted error patterns with the measured error pattern.