Calibration of a non-null interferometer for aspheric testing.

Abstract

Aspheric surface testing would be greatly expedited by eliminating the need for a null condition. To test in a non-null configuration, an interferometer must be capable of measuring steep wavefronts. These wavefronts contain aberrations introduced by the interferometer optics, so non-null measurements must be calibrated. Sub-Nyquist interferometry (SNI) enables measurement of large wavefronts. A simple Twyman-Green interferometer was constructed to conduct SNI and to explore the calibration problem. The characteristics of the interferometer were investigated, and wavefronts with several hundred waves of departure from a reference sphere were recorded and successfully reconstructed. A defocused sphere was used to demonstrate the need for calibration and to serve as a test subject for the calibration study. Reverse optimization was used to calibrate wavefront measurements. Experimental wavefront data were entered into the merit function of a lens design program, and optimization was employed to retrieve the prescription of the interferometer and the part shape. To simulate interference in the design program, the reference wavefront was stored in a Zernike phase surface on the image plane. The multiple configuration mode of the program was utilized to optimize several test configurations simultaneously, providing additional information to overcome a global optimization problem and to remove uncertainty in the part alignment. Errors introduced by pupil distortion were avoided by moving the stop to the plane of the sensor in the design program. Measurements from a defocused sphere were successfully calibrated using reverse optimization. A surface departure of 100λ was calibrated to better than λ/4 PV. Because the interferometer could not be characterized sufficiently for calibration of measurements from aspheres, simulations were conducted. A lens design program was used to develop an accurate model of an interferometer, including simulated fabrication, alignment, and characterization errors. Reverse optimization was applied using wavefronts generated by the model. Testing was simulated for several conic asphere surfaces. Reverse optimization yielded calibration to λ/4 PV for conic aspheres with surface departures as large as 300λ. The results suggest that it is feasible to calibrate non-null measurements of aspheric surfaces using reverse optimization.