A Region Monitoring Type Slitless Imaging Spectrometer

1. Principle of the Regional Monitoring Imaging Spectrometer

The developed instrument produces two images of the observed area: conventional imaging and dispersion graphs. The dispersion graph depicts the dispersion of the conventional graph along a certain direction. For simplicity, let us assume a series of object points $y_i$, each characterized by wavelengths ${\lambda }_j$, where i ranges from 1 to s, and j ranges from 1 to n. Figure 3 depicts the schematic of the conventional imaging graph, while Figure 4 presents the schematic of the dispersion graph, with each grid representing a pixel.

When a phenomenon occurs at point $y_i$, it can be inferred that the brightness at this point changes, and simultaneously, the spectral range ${\lambda }_1$-${\lambda }_n$ at this point alters. The regions of change in the two system images are illustrated by the red boxes in Figure 5 and Figure 6. Assuming the brightness change is ${\delta }_y$, and the spectral change in each band is ${\lambda }_{1y}$-${\lambda }_{ny}$, as depicted in Figure 5, the difference between the pre-phenomenon and post-phenomenon imaging graph represents the brightness change. Similarly, the difference between the dispersion graph before and after the phenomenon indicates the variations in each spectral band, denoted as $\delta$$\lambda$.

By subtracting the images captured before and after the occurrence of the phenomenon, two new images can be obtained, as displayed in Figure 7 and Figure 8.

We hypothesize that a flare occurs within the designated region. Based on empirical knowledge, flares exhibit significant spectral variations across certain bands. Thus, from Figure 7, we can pinpoint the spatial location of the flare, as all variations are concentrated within a single pixel. Additionally, Figure 8 allows us to quantify the spectral changes at that point, as these variations are distributed across a series of pixels.

2. Optical Design of Regional Monitoring Imaging Spectrometer

Given the discrepancies between the developed instrument and traditional imaging spectrometers, this study delves into our instrument’s optical design process. As outlined earlier, the developed instrument requires a conventional imaging image and a dispersion image, both at the same wavelength. Thus, a grating-based approach is considered, where the 0th order of the grating produces the conventional imaging image, and the ±1st orders produce the dispersion image. The instrument should be designed to facilitate the placement of a field stop and maintain good image quality.

The optical design requirements for such an instrument are proposed as follows:

• The instrument must simultaneously produce both images without overlap.
• Image quality must meet the specified standards. Assuming a 5-micrometer CMOS, the point spread function at 600nm wavelength must be within 5 micrometers. Consequently, the system’s F-number must be less than 5.
• The system requires an intermediate image plane to accommodate a square field stop, thus isolating the dispersion and imaging images without significantly increasing the overall system length.
• Image quality must meet specified standards.
• Avoid overlapping of spectra of different orders.

Based on these requirements, we design the structure illustrated in Figure 9, Figure 10 and Figure 11.

Figure 9 depicts the 0th order spectrum image produced by the grating, while Figure 10 illustrates the -1st order spectrum image. According to the grating equation, when the grating order is 0, the system exhibits no dispersion, and the incident angle equals the reflection angle, resulting in normal imaging. Conversely, the -1st order spectrum introduces dispersion, forming a dispersion image. Figure 11 depicts the system’s imaging, where the 0th and -1st order spectra are simultaneously captured. The lens portion of the system can be custom-designed or purchased to suit specific requirements.

3. Experimentation and Data Processing

3.1. Experimentation

A regional monitoring imaging spectrometer was constructed and tested to validate our instrument’s performance. Figure 12 to Figure 13 depict the physical layout of the optical system. The components presented in Figure 12 include the instrument’s entrance pupil, filter, parabolic mirror, reflectors, grating, imaging lens, and CMOS detector.

The experimental observations, as depicted in Figure 14, Figure 15 and Figure 16, involve continuous monitoring of a specific region, as displayed in Figure 14. Subsequently, the appearance of a target is illustrated in Figure 15. Following the emergence of the target, variations in the spectral region are observed, and the disparity before and after the target’s appearance is illustrated in Figure 16.

3.2. Data Processing

The spectral data of the target were obtained under identical brightness conditions using a specialized spectrometer, as shown in Figure 17.

Data extraction from Figure 17 yields the results depicted in Figure 18.

Applying a denoising strategy involving wavelet transformation and moving averages to Figure 18 results in obtaining Figure 19.

The Pearson correlation coefficient is a statistical measure to assess the linear relationship between two variables. Ranging from -1 to 1, it quantifies their linear association by computing the covariance of the two variables. A coefficient of 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear relationship between the variables. Usually, a value greater than 0.8 indicates a strong correlation between the two data. The calculated Pearson correlation coefficient between the comparison item and denoised data is 0.9226, indicating that the instrument successfully measured the target’s spectral data.

4. Results

We developed a region-monitoring imaging spectrometer with instrument parameters reported in Table 1. The instrument continuously images a specific area, where the appearance of a target changes in the conventional image and dispersion graph. Thus, we acquired a segment of target spectral data by utilizing the altered dispersion spectrum. Furthermore, we obtained the denoised data using a denoising method involving wavelet transformation and moving averages. The Pearson correlation coefficient between the denoised and reference data was 0.9226, indicating a highly significant correlation. Hence, the instrument successfully measured the target’s spectral data.

5. Discussion

This study investigates a region-monitoring imaging spectrometer. We discuss the results concerning three aspects.

5.1. Discussion of Measurement Results

Firstly, regarding the measurement of target spectral data, although the calculated Pearson coefficient shows a strong correlation with the denoised and the reference data, there are visual discrepancies. We attribute these differences to several factors:

• Vignetting, which affects measurement outcome.
• Random noise from the CMOS camera in both measurements, which affects measurement accuracy.
• The instrument’s spectral resolution is related to the target’s width in the dispersion dimension. Due to the broader width of the target in the dispersion dimension, the spectral resolution is lower than that of the reference, resulting in less distinct peaks in the denoised data.

5.2. Discussion of Instrument Advantages

Subsequently, we discuss the advantages of the developed instrument over traditional slit-based imaging spectrometers:

• Higher energy utilization efficiency of the dispersion element. A significant portion of energy (approximately 60%) resides in the zero-order spectrum for gratings. Traditional slit-based imaging spectrometers do not utilize the zero-order spectrum for imaging, while the region-monitoring imaging spectrometer fully utilizes it.
• Higher energy utilization efficiency over the full field of view. Traditional slit-based imaging spectrometers can only utilize energy within the slit area due to the presence of the slit. In contrast, the region-monitoring imaging spectrometer can utilize energy across the entire field of view.
• Lower manufacturing and tuning complexity. Traditional slit-based imaging spectrometers often employ a structure comprising a front telescope and a rear spectrometer. For instance, an off-axis three-mirror telescope commonly used in astronomy requires three large-aperture non-spherical mirrors. The telescope and spectrometer independently correct aberrations, leading to a complex structure. In contrast, the region-monitoring imaging spectrometer can independently image, and the collimation structure of the telescope and spectrometer comprises two symmetrical parts of a parabolic mirror, simplifying the structure. Only a small-aperture transmission imaging system must be manufactured, significantly reducing manufacturing costs and tuning complexity.

5.3. Discussion of Instrument Disadvantages

We also aim to discuss the disadvantages of the proposed instrument compared to traditional slit-based imaging spectrometers:

• The instrument’s spectral resolution depends on the target width in the dispersion dimension; thus, there is no stable spectral resolution. The instrument’s spectral resolution may be relatively low when faced with larger targets.
• There are mutual constraints between the instrument’s field of view and wavelength range.
• The instrument cannot obtain spectral data for every point in the image but rather captures spectral data for points where changes occur within the monitoring range.

6. Conclusions

In contemporary society, sustained observation of specific regions is necessary. In the realm of astronomy, continual monitoring is imperative, awaiting the occurrence of certain phenomena. Similarly, military operations require ongoing surveillance of particular areas to track enemy movements. In the field of biochemistry, continuous observation of experimental samples is indispensable. Addressing these requisites, this study investigates a siltless-region monitoring imaging spectrometer. Firstly, the principles underlying this instrument’s siltless-region monitoring imaging spectrometer are elucidated. The optical design of this system is scrutinized, culminating in the development of a seamless-region monitoring imaging spectrometer. Operating within the wavelength range of 400-600nm, with a focal length of 100mm and employing 150 lines per millimeter transmission grating, it boasts a field of view of 3°×7°. A siltless-region monitoring imaging spectrometer is assembled to validate the instrument’s performance. Utilizing this apparatus enables sustained observation of a designated area, detecting spectral data corresponding to the emergence of targets within the region. The Pearson correlation coefficient between the denoised data and the comparison item is 0.9226, surpassing the threshold of 0.8, affirming the successful detection of target spectra. Thus, the instrument demonstrates its capability to monitor designated regions and acquire spectral data therein continuously.