In recent years, there has been an increasing interest in miniature spectrometers for research and development. Especially, filter-array-based spectrometers have advantages of low cost and portability, and can be applied in various fields such as biology, chemistry and food industry. Miniaturization in optical filters causes degradation of spectral resolution due to limitations on spectral responses and the number of filters. Nowadays, many studies have been reported that the filter-array-based spectrometers have achieved resolution improvements by using digital signal processing (DSP) techniques. The performance of the DSP-based spectral recovery highly depends on the prior information of transmission functions (TFs) of the filters. The TFs vary with respect to an incident angle of light onto the filter-array. Conventionally, it is assumed that the incident angle of light on the filters is fixed and the TFs are known to the DSP. However, the incident angle is inconstant according to various environments and applications, and thus TFs also vary, which leads to performance degradation of spectral recovery. In this paper, we propose a method of incident angle estimation (IAE) for high resolution spectral recovery in the filter-array-based spectrometers. By exploiting sparse signal reconstruction of the L1- norm minimization, IAE estimates an incident angle among all possible incident angles which minimizes the error of the reconstructed signal. Based on IAE, DSP effectively provides a high resolution spectral recovery in the filter-array-based spectrometers.
Miniature spectrometers have been widely developed in various academic and industrial applications such as bio-medical, chemical and environmental engineering. As a family of spectrometers, optical filter-array based spectrometers fabricated using CMOS or Nano technology provide miniaturization, superior portability and cost effectiveness. In filterarray based spectrometers, the resolution which represents the ability how closely resolve two neighboring spectra, depends on the number of filters and the characteristics of the transmission functions (TFs) of the filters. In practice, due to the small-size and low-cost fabrication, the number of filters is limited and the shape of the TF of each filter is nonideal. As a development of modern digital signal processing (DSP), the spectrometers are equipped with DSP algorithms not only to alleviate distortions due to unexpected noise or interferences among filters but also reconstruct the original signal spectrum. For a high-resolution spectrum reconstruction by the DSP, the TFs of the filters need to be sufficiently uncorrelated with each other. In this paper, we present a design of optical thin-film filters which have the uncorrelated TFs. Each filter consists of multiple layers of high- and low-refractive index materials deposited on a substrate. The proposed design helps the DSP algorithm to improve resolution with a small number of filters. We demonstrate that a resolution of 5 nm within a range from 500 nm to 1100 nm can be achieved with only 64 filters.