Under-sampled Image Quality Measurement Based on Virtual Knife Edge for Next Generation Palomar Spectrograph
The Next Generation Palomar Spectrograph(NGPS)is a broadband high-throughput medium-low resolution spectrograph with a focal ratio of f/15.7 and a slit field of view of 180"×10",which will be installed on the Cassegrain focus platform of the Hale telescope.NGPS generally consists of four channels,U,G,R and I respectively,covering a wide spectral range of 310～1 040 nm.The spectrograph is equipped with a 4 000×2 000 scientific grade CCD with single pixel size of 15 μm.The imaging quality of the astronomical spectrometer can be characterized by Point Spread Function(PSF)or Line Spread Function(LSF),but it is usually under-sampling on the spectrometer detector,which is difficult to measure directly.Therefore,it is necessary to manage to measure the image quality accurately under the condition of CCD under-sampling while in the debugging phase of the spectrograph.In this paper,the virtual knife edge method is introduced into the image quality measurement of the NGPS.A pixel boundary of CCD is set as a virtual segmentation edge.When the light source of the optical system moves gradually along the slit plane at a certain step length,the image spot is scanned along the direction perpendicular to the virtual knife edge,and meanwhile the CCD takes under-sampled images.By integrating the energy on one side of the virtual knife edge of the images,the intensity profile of integral region is obtained,and the Edge Spread Function(ESF)is acquired by Gaussian function fitting.The LSF is the derivative of ESF,then Full Width Half Max(FWHM)can be calculated from LSF.The LSF measured by the virtual knife edge method represents the energy distribution of the virtual line light source after passing through all optical elements,which can objectively evaluate the imaging quality of the optical system.Simulation and experimental research are carried out on the R channel optical system of NGPS,and the following work is done in the image quality test:first,the virtual knife edge method is introduced to measure the under-sampled image quality of the spectrometer;second,the virtual knife edge method is applied to measure the scale of the under-sampled light source.The classical straight edge method and direct oversampling measurement are compared and analyzed to verify good measurement accuracy of the virtual knife edge method.At 693 nm,the oversampled result of LSF is FWHM=7.05 μm measured by the straight edge method,and under-sampled result is FWHM=7.14 μm measured by the virtual knife edge method,with a measurement error of 1.3%.For 0.3"field of view scale,the under-sampled FWHM at 689 nm,693 nm and 701 nm measured by virtual knife edge method is 24.2 μm,27.7 μm and 30.8 μm,respectively.Consider the direct oversampling measurement as a reference,the accuracy of virtual knife edge reaches 98.3%,93.9%and 88.8%,respectively.The experimental results show that the virtual knife edge method can measure the image quality of spectrograph accurately when the detector is under severe under-sampled condition.It can be predicted that with further optimization of image quality of the spectrograph,the measurement accuracy will also be improved.The method combined with dispersion coefficient can also measure the resolution of spectrometer.The research work in this paper provides a reference for the application of this method in the field of image quality measurement of astronomical spectrograph.
Point spread functionLine spread functionVirtual knife edgeUnder-sampled imageImage quality measurement
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