Numerical Simulation and Experimental Demonstration of Error Compensation between Recording Structure and Use Structure of Flat-Field Holographic Concave Gratings
ZHOU Qian,ZENG Li-jiang,LI Li-feng
State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China
Abstract：A flat-field holographic concave grating can be the only optical element in a spectrometer. If the mutually compensating roles of the concave grating and the spectrometer are taken into account, the difficulty of fabricating concave grating can be reduced. When the holographic method is used to make concave gratings, it is very difficult to fix precisely the spatial distances between the two recording points and the vertex of concave gratings. In like manner, it is also difficult to fix precisely the location of the entrance slit or the CCD in using concave gratings in spectrometers. In other words, during the fabrication stage and the end-use stage of concave gratings, there are inevitable errors between the practical system structure parameters and the theoretical ones. The authors name them fabrication structure errors and end-use structure errors, respectively. Numerical simulation indicates that these two classes of errors will seriously deteriorate the spectral image quality. At present, there are few references describing the elimination of the fabrication and end-use errors of concave gratings. In this paper, a concave grating used in a compact chromatograph is analyzed as an example. By performing numerical simulations that take both fabrication structure parameters and end-use structure parameters into consideration, we found that in a large neighborhood around the design point, the two sets of parameters can mutually compensate. This means that even both sets are away from the optimized design points, as long as proper compensations are made, the spectral image quality of the spectrometer can be as good as designed. In other words, on the one hand, for a specific concave grating that has been made with some fabrication structure errors, we can move the CCD to find an appropriate location where the spectral image quality is as good as designed; On the other hand, for a decided end-use system which has some end-use structure errors, we can adjust the fabrication structure to make concave gratings that will generate good spectral images in this end-use system. The experiment results show that this method is an effective way to adjust the optical system for grating fabrication. The authors also give experimental results that agree with simulation results. Such compensation can reduce both the alignment difficulty and the required precision of fabrication structure parameters of concave gratings. It could also give theoretical guidance to the design and assembly of spectrometers.
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