Hadamard spectrometers

Hadamard transform [17], For example the IR spectrum (512 data points) shown in Fig. 40.31a is reconstructed by the first 2, 4, 8,. .. 256 Hadamard coefficients (Fig. 40.38). In analogy to spectrometers which directly measure in the Fourier domain, there are also spectrometers which directly measure in the Hadamard domain. Fourier and Hadamard spectrometers are called non-dispersive. The advantage of these spectrometers is that all radiation reaches the detector whereas in dispersive instruments (using a monochromator) radiation of a certain wavelength (and thus with a lower intensity) sequentially reaches the detector. 

C M. Wehlburg, J. C. Wehlburg, S. M. Gentry, and J. L Smith, Optimization and characterization of an imaging Hadamard spectrometer, Proc. SPIE, 4381, p. 506-515, Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VII, Sylvia S. Shen, Michael R. Descour, Eds., (2001). 

Figure 4.1.15. Simplified (A) and detailed (B) schematic of a dispersive Hadamard transform spectrometer. In A the source provides radiation for the monochromator where the energy is dispersed for focusing onto the exiting mask. The post optics collect the radiation from the transparent slots in the mask and focus this radiation onto the detector. The figure in B is given to illustrate the complexity of a Hadamard spectrometer.

An instrumentation technique that utilizes the output from a monochromator, and that provides some of the benefits of multiplexed data acquisition, is known as a Hadamard transform spectrometer. This class of instrument can feature either a monochromator or a polychromator (equipped with a detector array). Hadamard transform instruments are available as custom-made devices, but none have been fully commercialized. 

D8. Decker, J. A., A new I.R.-spectrometer with multi slit array (Hadamard-Trans-form spectrometer). Int. Colloq. Spectrosc., 16th, Heidelberg 1, 102-106 (1971). 

Figure 11.27. Schematic of a Hadamard transform imaging Raman spectrometer. The mask is moved between CCD exposures by the stepping motor, and the cylindrical lens creates a line focus along the entrance slit to an imaging spectrograph. (Adapted from Reference 24.)...

Non-dispersive multiplex spectrometers include Hadamard transformation spectrometers and Fourier transform spectrometers and are particularly useful for the case of very stable sources. In both cases the information, such as intensities at various wavelengths, is coded by a multiplex system, so that it can be recorded with a conventional detector. A suitable transformation is then used to reconstruct the wavelength dependence of the information. In Hadamard spectrometry use is made of a codation of the spectrum produced by recombining the information with the aid of a slit mask which is moved along the spectrum [66],... 

R. Riesenberg, and U. Dillner, HADAMARD Imaging Spectrometers, SPIE s 44th Annual Meeting Exhibition, Optical Science, Engineering and Instrumentation, Denver, USA, Proceedings of SPIE, Vol. 3753, pp. 203-213, (18-23 July 1999). 

A. Wuttig, and R. Riesenberg, Sensitive Hadamard Transform Imaging Spectrometer with a simple MEMS,Prac. SPIE, 4881, pp. 167-178, (2003). 

Fig. 36. Optical layout of a 2047-slot Hadamard transform spectrometer (taken from Ref. >)...

In virtually all types of experiments in which a response is analyzed as a function of frequency (e.g., a spectrum), transform techniques can significantly improve data acquisition and/or data reduction. Research-level nuclear magnetic resonance and infra-red spectra are already obtained almost exclusively by Fourier transform methods, because Fourier transform NMR and IR spectrometers have been commercially available since the late 1960 s. Similar transform techniques are equally valuable (but less well-known) for a wide range of other chemical applications for which commercial instruments are only now becoming available for example, the first commercial Fourier transform mass spectrometer was introduced this year (1981) by Nicolet Instrument Corporation. The purpose of this volume is to acquaint practicing chemists with the basis, advantages, and applications of Fourier, Hadamard, and Hilbert transforms in chemistry. For almost all chapters, the author is the investigator who was the first to apply such methods in that field. 

Plankey et al have reported on the application of Hadamard transform spectrometry to the ultraviolet and visible spectral regions. The Hadamard technique utilizes the dispersed radiation from a conventional spectrometer. The radiation is passed through a coded mask, recombined, and recorded. The mask is composed of N slits, and N measurements are made with the mask in different positions. After measurement, N simultaneous equations must be solved with a Hadamard matrix to obtain the spectrum. The mask must be moved mechanically and reproducibly and a computer is used to solve the simultaneous equations. 

Filler monochromators are of use only for flame photometry. They make use of interference filters, which often have a spectral bandpass of a few nanometers or less. Multiplex spectrometers include Hadamard transform spectrometers and Fourier transform spectrometers, and are especially useful where very stable sources are needed. Hadamard transform instruments make use of a coding of the spectrum produced by recombining the information with the aid of a slit mask which scans the spectrum [48]. 

AOTF and LCTF function both in discrete and full-spectrum spectrometers in that both can move randomly to individual wavelengths within the operating range. Finally, prism, grating, FT-NIR, and Hadamard are discussed as strictly full-spectrum analyzers. 

Hadamard. Hadamard-transform NIR spectrometry (see Fig. 4.1.15) (HT-NIR) is based on the combination of multiplexing and dispersive spectrometers where the... 

R. M. Hammaker, R. A. DeVerse, D. J. Asunskis, W. G. Fateley. Hadamard transform near-infrared spectrometers. In Handbook of Vibrational Spectroscopy, J. M. Chalmers, P. R. Griffiths, eds. John Wiley Sons Ltd., Chichester, West Susses, UK, 1 453-460, 2002. 

D. C. Tilotta, R. M. Hammaker, W. G. Fateley. A visible-near-infrared Hadamard transform spectrometer based on a liquid crystal spatial light modulator array A new approach in... 

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