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.
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! 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
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We discuss grating array spectral sensors as the most promising basic architecture for future high-end micro-spectrometers. New extensions of this architecture with 2D-detector arrays are presented. They increase the spectral resolution by sub-pixel imaging. Sub-pixel architectures allow miniaturization of the spectrometers and shift the limits significantly towards the diffraction limit to the grating. To fully employ this, the slit dimensions have to be in the order of a few wavelengths, for instance down to 2 ?m in the UV region, requiring micro-machined entrance apertures. Feasible entrance apertures are transmissive MEMS, such as static slit patterns, micro shutters or mechanical slit positioning systems.
Multi object spectrometers measure spectra of multiple objects simultaneously. Besides others, e.g. fiber positioning systems, there is a class of multi object spectrometers which is based on a dispersing imaging optics in connection with a slit masks. Two considered approaches for reconfigurable slit masks are two-dimensional MEMS arrays, such as micro mirror or micro shutter arrays, and slit positioning devices. After an introduction to multi object spectrometry with dispersing imaging optics we calculate the effective multiplex capabilities of multi object spectrometers based on 2D MEMS and on slit positioning devices for randomly distributed objects. The observation efficiency of multi object spectrometers based on 2D MEMS is compared to integral field spectrometers and to multi object spectrometers based on slit positioning devices. We find that for typical applications the efficiency of the slit positioning approach is nearly as good as the efficiency of the 2D MEMS approach. This makes slit positioning systems a serious alternative solution to 2D MEMS devices as long as they are easier to get.
High resolution images can be extracted from a set of differently sampled low resolution images. Usually such a set of images is generated by shifting a detector array device fractions of a pixel or by moving a whole optical system in an appropriate way. Subpixel information is then encoded in the set of taken images. Another way to generate encoded subpixel information is presented in this paper. Multiple fixed images are generated in the optical part of the detector device. The latter method is the method of choice for grating diode array spectrometers. A programmable entrance slit array (MEMS device, mechanical slit positioning system), which replaces the conventional single entrance slit, generates multiple undersampled images of the same spectrum. Every slit is imaged with a different, wavelength dependent imaging scale ratio and a different imaging scale ratio and a different wavelength-aberration-dependency. The subpixel analysis has to take this into account. It is accomplished by a shift-variant superresolution algorithm, a representation of the spectrometer's optical properties and a calibration algorithm which estimates these properties from measured known gas emission spectra. The superresolution algorithm itself is nonlinear and therefore capable of recovering data lost by aberration and pixel integration. An algorithm for subpixel analysis is developed and tested. Theoretical and experimental approaches of the subpixel analysis are presented. The method is proven experimentally on a double array spectrometer. The resolution can be increased up to the factor 7 with seven entrance slits.
The polarizer and the analyzer of the polarimeter are realized by Glan-Thompson-prisms which are characterized by a very high extinction. In this set-up only the object under test is located between the prisms, i.e. the polarization properties of the light are not distributed by optical components and high angle resolution is achieved. The disadvantage of these prisms is the use of the extraordinary ray causing an axial astigmatism. In the paraxial domain this astigmatism can be corrected by a simple cylindrical lens. However, this leads to a distorted scaling in the image, because the scaling in the active and the inactive direction of this lens is different. This disadvantage can be omitted by using a cylindrical optic which consists of at least two lenses having opposite sign of their focal length. The calculated result for this optic are verified experimentally.
An optical method for the determination of high spatial frequency grating profiles with visible light is presented. The theoretical background is the effective medium theory. By using an optical surface profiler, the change of the surface height in the grating region is measured in two different ways. The results can be used to determine the duty cycle and the groove depth in the case of a binary grating profile.