Shape error measurement using ray-tracing and fringe scanning methods: projection of grating displayed on a liquid crystal panel

We present an improved Hartmann test, which has high spatial resolution with respect to the measuring points, for measuring projection mirrors. In the method, grid lines with a sinusoidal transmittance distribution are displayed on a liquid crystal panel and illuminated with a collimated laser beam. The beam transmitted through the liquid crystal panel reflects off the mirror surface being tested and reaches a screen. A charge-coupled device camera detects the projected images, which contain information about the inclination of the surface being tested. Any error in the shape of the mirror surface is identified by integrating the inclination. To increase the spatial resolution, the fringe scanning method is performed by shifting the grid lines on the liquid crystal panel. The grid lines are optimized for the shape of the mirror being tested. Because the grid lines are displayed by an electrical method, the shifting operation is easy and rapid, and furthermore, the displacement can be done precisely. The shape error of an off-axis parabolic mirror made of plastic is measured by the proposed method.