Reference beam method for source modulated Hadamard multiplexing

Abstract

A hyperspectral imaging system is in development. The system uses spatially modulated Hadamard patterns to encode image information with implicit stray and ambient light correction and a reference beam to correct for source light changes over the spectral image capture period. In this study we test the efficacy of the corrections and the multiplex advantage for our system. The signal to noise ratio (SNR) was used to demonstrate the advantage of spatial multiplexing in the system and observe the effect of the reference beam correction. The statistical implications of the data acquisition technique, illumination source drift and correction of such drift, were derived. The reference beam correction was applied per spectrum before Hadamard decoding and alternately after decoding to all spectra in the image. The reference beam method made no fundamental change to SNR, therefore we conclude that light source drift is minimal and other possibly rectifiable error sources are dominant. The multiplex advantage was demonstrated ranging from a minimum SNR boost of 1.5 (600-975 nm) to a maximum of 11 (below 500 nm). Intermediate SNR boost was observed in 975-1700 nm. The large variation in SNR boost is also due to some other error source.

Optical full Hadamard matrix multiplexing and noise effects

“…As N ¼ 256, the theoretical maximum boost is ffiffiffiffi ffi N p ¼ 16. The shape of the SNR boost is similar to that of previous work [16] using S-matrix complement encoding. The light level and detector sensitivity both vary with wavelength.…”

“…where e t is the total random error in the estimate, i.e., the noise due to instrument and photon effects combined with the reference beam noise. In a previous paper [16] we found the total random error variance (MSE) for our system considering only instrument noise. Expanding to include photon noise variance we observe that the total MSE after reference correction is…”

“…Our prototype hyperspectral imaging system [8,16] fits the theoretical considerations described in Section 2. Figure 3 shows a diagram of the optical configuration.…”

“…Immediately after each row of H þ the corresponding row of H À is similarly wrapped and projected onto the sample and the corresponding entry of a À acquired. The spectra are contaminated by random additive instrument noise e and the additive combination of dark current, background, and stray light, all represented by T. The light source in our experimental setup has been shown to be stable during the data acquisition period [16]. Regardless we model the effect of light source drift during the data acquisition as multiplication by the diagonal matrix R. The jth diagonal element in R is hri j and represents the mean illumination at the time of the jth acquisition.…”

“…Only the reference beam is chopped [16], thus the raw measurements include light from both the sample and the reference beam. The reference beam measurements are easily obtained by subtracting the sample measurement from the raw measurement.…”