Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization

Abstract

Miniature spectrometers provide a cost and size advantage over traditional spectrometers. However, unlike traditional spectrometers in which appropriate dispersive optics and/or interferometric devices are well-developed, miniature spectrometers usually do not have ideal (or close to ideal) wavelength-specific filtering mechanism to resolve the power of the input spectrum at specified wavelengths. Hence, the raw outputs from the filtering mechanism may not be adequate to represent spectra of measured objects. The nonideal filtering mechanism makes reconstruction process necessary. In this work, the method of Tikhonov regularization for stabilizing the solution of inverse problems is applied to a prototype filter-based nano-optic spectrum sensor from nanoLambda. L-curve criterion and generalized cross validation (GCV) criterion for adaptively selecting the regularization parameter are examined. Satisfactory results are obtained by exploiting non-negative constraints on the reconstructed spectrum, with the regularization parameter being selected by the L-curve criterion. As a result, low-cost miniature spectrometer on-a-chip can be realized.

Evaluation of Resolution Improvement Ability of a DSP Technique for Filter-Array-Based Spectrometers

“…The current literature [5][6][7] provides a few DSP techniques to reconstruct the original spectrum but not on improving the resolution of the spectrometer.…”

A sparse template selection algorithm for spectrum measurement using miniature filter array spectrum sensors

“…Among various means, filter-based spectrometers have been reported to be one of the promising approaches to realize miniature spectrometers [4]- [5]. The filter-based spectrometers utilize different filter functions to filter spectral energy emanating from a measurement object.…”

“…Traditionally, a system of linear equations can be solved from a view point of an over-determined problem, using a least-square criterion, a constraint least-square criterion such as non-negative constraint, or a regularized least-square criterion such as Tikhonov regularization [5]. However, the spectral resolution is potentially limited in the over-determined approach, since the number of unknowns, i.e., the resolvable spectrum information, has to be less than the number of equations, i.e., the observations.…”

“…The device of interest has 195 spectrum sensors integrated on a CMOS imager, and was previously introduced in [4][5]. The transmission functions of Schematic…”

Spectrum reconstruction for filter-array spectrum sensor from sparse template selection

“…[1][2][3] Among various means, filter-based spectrometers have been reported to be one of the promising approaches to realize miniature spectrometers. [4][5][6][7] The filterbased spectrometers utilize different filtering functions to filter spectral energy emanating from a measurement object. It has been demonstrated that the filter-based spectrometers are capable of being fabricated in a chip scale, and hence are compact and rugged.…”