Denoising analysis of spatial pixel multiplex coded spectrometer with Hadamard H-matrix

Abstract We present a multiplex coded Hadamard transform spectrometer with which Hadamard H-matrix is employed to encode the entrance pixels. Specifically, the Hadamard H-matrix is divided into two coding matrices, H + and H − ; here  H − = H − J ∕ 2 and H + = H + J ∕ 2 , where each element of J  equals 1. We analyzed its denoising capability and compared with the ordinary Hadamard spectrometer with cyclic-S matrix coded and slit spectrometers. The simulation and experiment show that the proposed Hadamard spectrometer with H-matrix outperforms Hadamard transform spectrometer with cyclic-S matrix, gaining about 2 dB of the signal-to-noise ratio.

[1]  M. Golay.  Multi-slit spectrometry. , 1949, Journal of the Optical Society of America.

[2]  M E Gehm,et al.  Single-shot compressive spectral imaging with a dual-disperser architecture. , 2007, Optics express.

[3]  Evaluation of a Hadamard-coded photodiode-array spectrometer under low illumination. , 1994, Applied optics.

[4]  A. Barducci,et al.  Theoretical aspects of Fourier Transform Spectrometry and common path triangular interferometers. , 2010, Optics express.

[5]  P. L. Richards,et al.  High-Resolution Fourier Transform Spectroscopy in the Far-Infrared , 1964 .

[6]  Shutao Li,et al.  Fast Acquisition and Reconstruction of Optical Coherence Tomography Images via Sparse Representation , 2013, IEEE Transactions on Medical Imaging.

[7]  Mark A Arnold,et al.  Solid-State Digital Micro-Mirror Array Spectrometer for Hadamard Transform Measurements of Glucose and Lactate in Aqueous Solutions , 2011, Applied spectroscopy.

[8]  Shutao Li,et al.  Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images , 2017, IEEE Transactions on Medical Imaging.

[9]  Jing Han,et al.  Denoising analysis of Hadamard transform spectrometry. , 2014, Optics letters.

[10]  Vanni Nardino,et al.  Radiometric and signal-to-noise ratio properties of multiplex dispersive spectrometry. , 2010, Applied optics.

[11]  D. Brady,et al.  Coded aperture spectroscopy with denoising through sparsity. , 2012, Optics express.

[12]  Michael J. Cree,et al.  Optical full Hadamard matrix multiplexing and noise effects. , 2009 .

[13]  Jean-Paul Chamonal,et al.  Infrared focal plane array with a built-in stationary Fourier-transform spectrometer: basic concepts. , 2008, Optics letters.

[14]  J. A. Decker,et al.  Experimental realization of the multiplex advantage with a hadamard-transform spectrometer. , 1971, Applied optics.

[15]  Jiang Yue,et al.  High-throughput deconvolution-resolved computational spectrometer , 2014 .