Reverse optimization reconstruction of aspheric figure error in a non-null interferometer

Abstract

Aspheric non-null testing, as an alternative to the traditional null testing, achieves more flexible measurements. However, figure-error reconstruction in non-null tests has always been difficult due to the presence of retrace error. A novel method with reverse optimization is proposed for aspheric figure-error reconstruction in a non-null interferometer. It is a generalized and effective approach based on system modeling and polynomial fitting. An optimization function is set with polynomial coefficients of the desired figure error as variables and those of the detected experimental wavefront as optimization targets. Through the reverse optimization process with iterative ray tracing, the optimal solutions can be extracted and the desired figure error is reconstructed with a simple fitting procedure. Numerical simulations verifying the high accuracy of the proposed method are presented with error considerations. A set of experiments has also been carried out to demonstrate the validity and repeatability of this method.

Determination of aspheric vertex radius of curvature in non-null interferometry

“…1. Detailed descriptions about the testing system can be found in our previous work [13,15,18], and a brief summary is present here. The interferometric system is based on a modified phase-shifting Twyman-Green setup.…”

“…Specifically, the null test for aspheric has no cat's eye position because an aspherical wavefront employing a non-null test has no confocal position and, in most cases, no cat's eye position. In partial compensating interferometry [13][14][15], there are neither confocal nor cat's eye positions. The aspheric position identification has been the great obstacle of VROC even in figure error measurement.…”

“…In our previous work, we developed a non-null interferometer for a general aspheric figure error test [13][14][15] with a partial null lens (PNL) [13,16,17]. A reverse optimization reconstruction (ROR) method [15] is proposed to retrieve the aspheric surface figure error based on system modeling with the nominal aspheric function.…”

“…A reverse optimization reconstruction (ROR) method [15] is proposed to retrieve the aspheric surface figure error based on system modeling with the nominal aspheric function. In this method, an optimization function is set up to change the aspheric figure error in a system model, making the resulting test wavefront in the model constantly approach the actual one from experiment.…”

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test

“…Various approaches have been proposed to ensure the accurate surface measurement [6,[16][17][18]. In the SCOTS, a laser tracker is used to calibrate geometrical relation between the camera and the illumination screen [19], similar to the alignment process an interferometric testing for aspheric surfaces [20]. The measurement accuracy comparable to traditional interferometric methods has been reported.…”