A computational spectrometer is a novel form of spectrometer powerful for portable in situ applications. In the encoding part of the computational spectrometer, filters with highly non-correlated properties are requisite for compressed sensing, which poses severe challenges for optical design and fabrication. In the reconstruction part of the computational spectrometer, conventional iterative reconstruction algorithms are featured with limited efficiency and accuracy, which hinders their application for real-time in situ measurements. This study proposes a neural network computational spectrometer trained by a small dataset with high-correlation optical filters. We aim to change the paradigm by which the accuracy of neural network computational spectrometers depends heavily on the amount of training data and the non-correlation property of optical filters. First, we propose a presumption about a distribution law for the common large training dataset, in which a unique widespread distribution law is shown when calculating the spectrum correlation. Based on that, we extract the original dataset according to the distribution probability and form a small training dataset. Then a fully connected neural network architecture is constructed to perform the reconstruction. After that, a group of thin film filters are introduced to work as the encoding layer. Then the neural network is trained by a small dataset under high-correlation filters and applied in simulation. Finally, the experiment is carried out and the result indicates that the neural network enabled by a small training dataset has performed very well with the thin film filters. This study may provide a reference for computational spectrometers based on high-correlation optical filters.

Bayer filter color cameras are more and more widely used in the field of aerospace remote sensing, but the Bayer filter causes great degradation in image quality; therefore, obtaining a means of achieving the high-precision measurement of the modulation transfer function (MTF) of Bayer filter color cameras is an urgent problem. In order to solve this problem, this paper develops a slanted-edge method via three steps: the detection of the slanted edge, the acquisition and processing of the edge spread function (ESF), and the acquisition and processing of the line spread function (LSF). A combination of the Canny operator and Hough transform is proposed for the detection of the slanted edge, which improves the fitting accuracy and anti-interference ability of the algorithm. Further, the Canny operator is improved by constructing an adaptive filter function and introducing the Otsu method, which can more effectively smooth the image and remove its false edges. A method of processing ESF data by combining cubic spline interpolation and Savitzky–Golay (SG) filtering is proposed, which reduces the effects of noise and the non-uniform sampling of ESF on MTF. A method of LSF processing using Gaussian function fitting is proposed to further reduce the effect of noise on MTF. The improved algorithm is verified by the MTF measurement test applied to a specific type of Bayer filter color space camera. The simulation and test results show that the improved slanted-edge method discussed in this paper has greater precision and a better anti-interference ability, and it can effectively solve the difficult problem associated with MTF detection in Bayer filter color space cameras.

Computational spectrometers based on coded measurement and computational reconstruction have great application prospects. This paper proposes a computational spectrometer that has a low cost, is easy to implement in hardware, and has high reconstruction accuracy. The proposed computational spectrometer uses low-cost but highly correlated polymethyl methacrylate (PMMA) material as broadband encoding filters, which could affect spectral reconstruction accuracy. To alleviate this issue, we decoupled the sensing matrix, which is the product of the measurement matrix and sparse base matrix, and subsequently optimized the sparse base matrix independently. Enlightened by the neural network method, an over-complete dictionary was trained based on the public spectral dataset, which was used as the required sparse base matrix for reconstruction. Through this method, we achieved good reconstruction results in simulation. In experiments, the spectrometer prototype can achieve a high-resolution spectral measurements, demonstrating the feasibility of a low-cost computational spectrometer based on the trained sparse base matrix.