An introduction to Hadamard spectrometry and the multiplex advantage

Abstract

A common data-acquisition problem is t h e need t o estimate, as accurately as possible, t h e frequency spectrum of a s i g n a l . The r e l a t i v e success of t h e many spectrum-estimation techniques a v a i l a b l e depends a g r e a t deal upon t h e c h a r a c t e r i s t i c s of t h e instrumentation.I n t h i s paper ( t h e f i r s t of a two-part sequence) we consider a special c l a s s of problems i n which t h e dominant noise source i n t h e spectrum measurements is t h e noise generated i n t h e d e t e c t o r i t s e l f . I n t h i s case, t h e "signal-to-noise r a t i o ' ' of t h e spectrum-estimates may be improved by a multiplexing technique known as Hadamard spectrometry. This paper describes t h e basic multiplexing procedure and t h e concomitant improvement i n t h e estimate of t h e spectrum.The second paper i n t h i s sequence, "Implementation Problems i n Hadamard Spectrometry , I ' by R.A. Dyer, e t 0 1 , presents some s p e c i f i c examples of system models, optimal post-processing, and s p e c t r a obtained v i a these techniques.

Dynamic diffraction gratings and a spectrometer demonstrator

“…The light that goes through the pinhole is collimated and guided through a linear variable bandpass filter (LVBF) that passes different spectral bands on different parts of the filter thus separating the spectral bands. The PMDG does a Hadamard transform [11] or line scan through the spectrum and the reflected light returns to the pinhole. The diffracted light does not hit the pinhole because of its slightly different incident angle on the collimator.…”

Optical alignment algorithm using Hadamard transformation

“…The Hadamard transformation is one of well known multiplexing techniques using spatial light modulator called Hadamard encoding mask, which makes the best enhancement of SNR for the reconstructed signals [4]. In the respect of the Hadamard transform applications, Hadamard spectrometry has been studied [5,6,7]. The multiplexing advantage offered by Hadamard transform spectrometry can improve the SNR at the output of a spectrometer.…”

“…It gives us each optical power for each channel of the multiple channel components with one detector avoiding one-by-one measuring no matter how many channels the optical components have. Moreover, the proposed alignment system has excellent signal-to-noise ratio (SNR) advantage as the number of channels increases by using multiplexing technique in the Hadamard transform [4,5,6,7]. We demonstrate the usefulness of the proposed alignment system for aligning multiple channel optical components through computer simulations.…”

Fast processing spectral discrimination for hyperspectral imagers based on interferometry

“…Alternatively, the interferogram is recorded transversally on the image sensors, as in Sagnac interferometers [5], and the hypercube is combined by rotating the interferometer. This third HSI class implements a multiplexing technique that could also be realized using Hadamard masks in dispersive spectrometers [6]. There is an intrinsic advantage in using multiplex spectrometers (also known as Fellgett advantage) when the noise is dominated by the detector noise; in this case the improvement of the signal to noise ratio is proportional to the square root of the number of bins when compared to scanning spectrometers [5,7].…”