Multispectral imaging can be applied to water quality monitoring, medical diagnosis, and other applications, but the principle of multispectral imaging is different from the principle of hyper-spectral imaging. Multispectral imaging is generally achieved through filters, so multiple photos are required to obtain spectral information. Using multiple detectors to take pictures at the same time increases the complexity and cost of the system. This paper proposes a simple multispectral camera based on lensless imaging, which does not require multiple lenses. The core of the system is the multispectral coding aperture. The coding aperture is divided into different regions and each region transmits the light of one wavelength, such that the spectral information of the target can be coded. By solving the inverse problem of sparse constraints, the multispectral information of the target is inverted. Herein, we analyzed the characteristics of this multispectral camera and developed a principle prototype to obtain experimental results.

Fourier transform spectroscopy with bandpass sampling (BPS-FTS) increases the interferogram sampling step and reduces sampling frequency, thereby reducing system implementation difficulty. However, this technology has only been introduced in principle and lacks analysis of the actual system error. In this paper, we present a theoretical analysis of the optical system diffraction effect, derive the bandpass spectrum bandwidth and interferogram sampling step under the influence of the diffraction effect, and conduct modeling and a simulation analysis with and without the diffraction effect. Through simulation, we found that when the diffraction effect was considered, the relative deviation of the recovered spectrum from the input spectrum was 1.30%, and the spectral similarity was 0.9669. However, without considering the diffraction effect, the relative deviation of the recovered spectrum from the input spectrum was 6.23%, and the spectral similarity was only −0.0056. The simulation results demonstrate that the diffraction effect has a significant influence on BPS-FTS interferogram sampling and recovery spectra. The results of this study have reference significance for their technical realization of BPS-FTS.

In this paper, the expression for the SNR has been developed through the imaging model. It is concluded that the image SNR decreases with the increase of the number of light-emitting points of the target under the same hardware conditions and experimental parameters. Using uniform bright squares of different sizes as the target, the SNR of the reconstructed image is calculated. Simulation and prototype experiments have proved the correctness of the conclusion. Based on this conclusion, a method of segmented area imaging is proposed to improve the reconstructed image quality. The quality of all the images using this method with Wiener inverse filtering, R-Lucy deconvolution, and ADMM is better than the image quality obtained by full-area imaging.

The identification of hazardous chemicals based on hyperspectral imaging is an important emergent means for the prevention of explosion accidents and the early warning of secondary hazards. In this study, we used a combination of spectral curve matching based on full-waveform characteristics and spectral matching based on spectral characteristics to identify the hazardous chemicals, and proposed a method to quantitatively characterize the matching degree of the spectral curves of hazardous chemicals. The results showed that the four hazardous chemicals, sulfur, red phosphorus, potassium permanganate, and corn starch had bright colors, distinct spectral curve characteristics, and obvious changes in reflectivity, which were easy to identify. Moreover, the matching degree of their spectral curves was positively correlated with their reflectivity. However, the spectral characteristics of carbon powder, strontium nitrate, wheat starch, and magnesium–aluminum alloy powder were not obvious, with no obvious characteristic peaks or trends of change in reflectivity. Except for the reflectivity and the matching degree of the carbon powder being maintained at a low level, the reflectivity of the remaining three samples was relatively close, so that it was difficult to identify with the spectral curves alone, and color information should be considered for further identification.

For traditional Fourier transform (FTS), its integral sampling usually meets the Spectral Modulation Transfer Function (SMTF) criterion. However, for bandpass-sampling Fourier transform spectroscopy (BPS-FTS), based on our analysis, the integral sampling condition derived from the Spectral Modulation Transfer Function (SMTF) is excessively stringent. In other words, the interval of the integral sampling time that fulfills the tolerance requirements for the reconstructed spectrum is very narrow. There are numerous integration sampling time intervals outside this range that still meet the tolerance requirements for the reconstructed spectrum. In this paper, through theoretical modeling, we propose a method based on average |SMTF| as the selection criterion for the integration sampling time. Through simulation analysis, it is evident that the intervals and range of the integral sampling time obtained via this method are more accurate, ensuring the tolerance requirements of the reconstructed spectrum. Under these intervals, when conducting integral sampling on the interferogram, the spectral deviation of the reconstructed spectrum is minimal, and the Spectral Correlation Mapper (SCM) is nearly equal to one. This indicates that compared with the SMTF criterion in traditional FTS, this method is more suitable for the characteristics of BPS-FTS. The analysis in this paper can provide theoretical and simulation support for the implementation of BPS-FTS.

Single-lens imaging systems can capture spectral information, but they are affected by aberrations, defocusing, and other factors, leading to spectral data overlap. It is then necessary to perform restoration on overlapped spectral data. The restoration method should not only deblur image information, but also recover spectral information for each wavelength band. In other words, the restoration process needs to handle both spatial and spectral information in parallel while ensuring that neither is distorted. In this study, while considering the characteristics of capturing overlapped information in a single-lens imaging system, a spectrum restoration method based on gradient prior information optimization is proposed. This method is shown to achieve high-quality restoration of both images and spectra. The feasibility of this algorithm is demonstrated through simulation and experimental verification, which show that the restoration quality of spectra using the proposed algorithm is improved compared to that achieved using the MTV algorithm.