Optimization of freeform cylindrical lens in Czerny-Turner spectrometer system to correct the astigmatism by using user defined error function

Abstract

In the traditional Czerny-Turner spectrometer, the off-axis reflected light from the spherical mirror including astigmatism due to the different focal lengths in tangential and sagittal planes. A method of using user defined surface (UDS) in CODE V to establish the freeform cylindrical lens to correct the astigmatism is proposed. By adding a freeform cylindrical lens that the curvature radius values at each positions before the CCD sensor, will achieve astigmatism correction during the broadband wavelength from 300nm to 800nm and improves system performance greatly, especially the power collection. Because of the special features of spectrometer that one object point will form multiple imaging points for the grating diffraction, a general auto optimization method offered by the software is valid. By calculating the RMS wavefront error under every worked wavelength, and get the weighted mean, one can use a user defined error function to evaluate the whole system imaging performance and optimize the freeform cylindrical lens. Dichotomization searching method is used during the parameters optimization. Result shows the performance of our Czerny-Turner spectrometer system with freeform cylindrical lens. Compared to the traditional Czerny-Turner spectrometer, the astigmatisms are well corrected and the power collection was enhanced 4.1 times.