A Practical Deconvolution Computation Algorithm to Extract 1D Spectra from 2D Images of Optical Fiber Spectroscopy

Bolton & Schlegel presented a promising deconvolution method to extract one-dimensional (1D) spectra from a two-dimensional (2D) optical fiber spectral CCD (charge-coupled device) image. The method could eliminate the PSF (point-spread function) difference between fibers, extract spectra to the photo noise level, as well as improve the resolution. But the method is limited by its huge computation requirement and thus can not be implemented in actual data reduction. In this article, we develop a practical computation method to solve the computation problem. The new computation method can deconvolve a 2D fiber spectral image of any size with actual PSFs, which may vary with positions. Our method does not require large amounts of memory and can extract a 4 k × 4 k noise-free CCD image with 250 fibers in 2 hr. To make our method more practical, we further consider the influence of noise, which is thought to be an intrinsic ill-posed problem in deconvolution algorithms. We modify our method with a Tikhonov regularization item to depress the method induced noise. We do a series of simulations to test how our method performs under more real situations with Poisson noise and extreme cross talk. Compared with the results of traditional extraction methods, i.e., the Aperture Extraction Method and the Profile Fitting Method, our method has the least residual and influence by cross talk. For the noise-added image, the computation speed does not depend very much on fiber distance, the signal-to-noise ratio converges in 2-4 iterations, and the computation times are about 3.5 hr for the extreme fiber distance and about 2 hr for nonextreme cases. A better balance between the computation time and result precision could be achieved by setting the precision threshold similar to the noise level. Finally, we apply our method to real LAMOST (Large sky Area Multi-Object fiber Spectroscopic Telescope; a.k.a. Guo Shou Jing Telescope) data. We find that the 1D spectrum extracted by our method has both higher signal-to-noise ratio and resolution than the traditional methods, but there are still some suspicious weak features, possibly caused by the method around the strong emission lines. As we have demonstrated, our deconvolution method has solved the computation problem and progressed in dealing with the noise influence. Multifiber spectra extracted by our method will have higher resolution and signal-to-noise ratio, and thus will provide more accurate information (such as higher r