Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization

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.