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Noise, fluctuation, and HADAMARD-transform spectrometry
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Paper Abstract

The HADAMARD principle is known in optics as a multiplex technique. It describes the mode with the most advantageous increase of the signal-to-noise ratio (SNR) in terms of scanning (Fellget advantage). The maximum increase of SNR, we call it gain, is (n+1)/(2On), where n is the number of multiplexing. It is valid in the case of pure detector noise. The multiplex encoding Hadamard pattern in case of n = 7 is 1110100, whereby 1 stands for a switched on channel performed by a field selector. The signals of all (switched on) channels are detected by a single detector. n measurement steps with a cyclic change of the pattern is necessary to perform the Hadamard transformation and to get the result of each individual channel. In case of n = 7 the theoretical gain is 1.51. For all possible multiplex pattern (1100000, 1110000 and so on) the gain is theoretically investigated. A multiplexing advantage (gain > 1) is reached only by the Hadamard pattern, the inverse Hadamard pattern and for (0111111)-pattern (gain=1.08). Most of the multiplex pattern are disadvantageous. The reason for maximum gain of the HADAMARD transformation is analysed theoretically. Signal fluctuations during the measurement caused by fluctuations of the illumination or by the object under test, reduce the multiplex gain, too. So the limits for realizing a gain are estimated theoretically. Essential is the transformation procedure and its influence on the error propagation. The results could be verified by experiments with array spectrometeres. Requirements are derived by numerical simulation concerning the stability of the signals to be multiplexed. It is simulated the needed stability of the signals with increasing order of multiplexing. So the increase of the multiplex gain is limited by signal fluctuations. A realized 96 channel spectral reader is presented as a modern application of an optical multiplexing arrangement. ! M. Harvid, N. J. A. Sloane, Hadamard Transform Optics, Academic Press, 1979 ! R.A. De Verse, R.M. Hammaker, W. G. Fately, J.A.Graham, J.D.Tate, "Spectrometry and imaging using a digital micromirror array" American Laboratory, Vol. 30, 21, pp. 112-120, 1998 ! R. Riesenberg, A. Wuttig, B. Harnisch, "Optical MEMS Technology for Multiplexing in High-End Micro-Scpectrometers", Proc. SPIE 4928, 6-14, 2002 ! A. Wuttig, R. Riesenberg, “Hyperspectral imager with a facile MEMS”, Proc. SPIE 4881A, 2002, to be published ! R. Riesenberg, G. Nitzsche, W. Voigt, 'HADAMARD Encoding and other optical Multiplexing', VDI-Berichte 1694, pp. 345-350, 2002 ! A. Wuttig, R. Riesenberg, G. Nitzsche, “Subpixel Analysis of Double Array Grating Spectrometer”, Proc. SPIE 4480, pp. 334-344, 2002 ! A. Wuttig, R. Riesenberg, G. Nitzsche, “Integral Field and Multi Object Spectrometry with MEMS”, Proc. SPIE 4480, pp. 367-376, 2002 ! R. Riesenberg, G. Nitzsche, A. Wuttig, B. Harnisch, “Micro Spectrometer and MEMS for Space” in “Smaller Satellites: Bigger Business?”, edited by M. Rycroft, N. Crosby, Kluwer Academic Publisher, pp. 403-406, 2002 ! R. Riesenberg, A. Wuttig, “Optical sensors with MEMS, slit masks and micromechanical devices”, Proc. SPIE 4561, pp. 315-322, 2001 ! R. Riesenberg, “MicroMechanical Slit Positioning System as a transmissive spatial Light Modulator”, Proc. SPIE 4457, pp.197-203, 2001 ! R. Riesenberg, J. Lonschinski, “HADAMARD-Minispectrometer made by a Micro Device”, Proc. “3rd Round Table on Micro/NanoTechnologies for Space”, ESTEC, Noordwijk, The Netherlands, pp. 291 - 297, 2000 ! R. Riesenberg, U. Dillner, "HADAMARD Imaging Spectrometers“, Proc. SPIE 3753, pp. 203-213, 1999 ! R. Riesenberg, Th. Seifert, "Design of spatial Light Modulator Microdevices - Micro Slit Arrays“, Proc. SPIE 3680, Part One, pp. 406-414, 1999 ! R. Riesenberg, W. Voigt, J. Schoneich, "Compact Spectrometers made by Micro System Technology“, Sensor 97, Proc. Vol. 2, pp. 145-150,1997

Paper Details

Date Published: 16 May 2003
PDF: 10 pages
Proc. SPIE 5111, Fluctuations and Noise in Photonics and Quantum Optics, (16 May 2003); doi: 10.1117/12.510052
Show Author Affiliations
Guenter Nitzsche, Institute for Physical High Technology (Germany)
Rainer Riesenberg, Institute for Physical High Technology (Germany)

Published in SPIE Proceedings Vol. 5111:
Fluctuations and Noise in Photonics and Quantum Optics
Derek Abbott; Jeffrey H. Shapiro; Yoshihisa Yamamoto, Editor(s)

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