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Abstract
A novel tempo-spatially mixed modulation imaging Fourier transform spectrometer based on a stepped micro-mirror has the advantages of high throughput, compactness, and stability. In this paper, we present a method of image- and spectrum-processing and performance evaluation, which is utilized to obtain a high-quality reconstructed image without stitching gaps and a reconstructed spectrum with significantly reduced noise and side-lobe oscillation. A theoretical model of instrument line shape and signal-to-noise ratio is established to verify the effectiveness of non-uniformity sampling correction and spectral resolution enhancement. Meanwhile, the performance of the instrument was evaluated combined with experimental results.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a safe, real-time, and accurate monitoring technology, the imaging Fourier transform spectrometer (IFTS) can obtain two-dimensional image information and one-dimensional spectral information simultaneously. The image can guide the spatial position of the target while the spectra can analyze the composition and content of the target. Moreover, IFTS features high spectral resolution, high throughput, and high stability, with strong targeting, high sensitivity, high adaptability, and a longer working life [1].
According to different optical path difference (OPD) acquisition methods, IFTS is divided into three types: temporal modulation (TMIFTS), spatial modulation (SMIFTS), and tempo-spatially mixed modulation (TSMIFTS) [2]. TSMIFTS obtains the OPD in the spatial dimension and completes OPD accumulation in the time dimension. The interference system of TSMIFTS has no movable parts and slits. Therefore, TSMIFTS possesses high stability of SMIFTS and a high luminous flux of TMIFTS simultaneously.
TSMIFTS, due to the above characteristics, has garnered much interest, and currently has a variety of structures: Sagnac based [3], corner based [4], scanning-mirror based [5], and snapshot [6,7], popularized in many different fields. In TSMIFTS interference data processing, in 2010, Jian et al. researched the data processing process of a tempo-spatially mixed modulated polarization interference imaging spectrometer, which was modulated by polarized interference optoelectronic devices [8–11], and proposed a multi-spectral data reconstruction method [12,13]. In 2014, Kleinert et al. proposed a nonlinear spectral radiation calibration method to improve the accuracy of radiation measurement [14]. In 2017, Ferrec et al. used multiplicative decomposition to remove fringes from the interferogram [15]. In 2018, Yan et al. proposed a method of high spectral resolution channeled imaging spectropolarimetry based on a high-throughput tempo-spatially mixed modulated mode Savart interferometer, greatly increasing the reconstructed-spectrum resolution [16,17].
In 2014, we presented a TSMIFTS that used a stepped micro-mirror, instead of a high-precision moving mirror to obtain the OPD, greatly improving stability and ensuring high throughput and certain spectral resolution [18]. We also performed a laboratory imaging experiment; however, due to the new structure of the interference core that introduced the stepped micro-mirror, data processing and performance evaluation of the instrument was not completed and had many problems. For example, the uneven width and edge distribution of the sub-steps of the micro-mirror caused stitching gaps of the reconstructed images, and the uneven height distribution of the sub-steps of the micro-mirror caused wavenumber shifts of the reconstructed spectra. The existing methods [12–17] provide a reference value, but cannot solve the inherent problems of this instrument. In this paper, we propose a TSMIFTS based on a stepped micro-mirror with a greater number of steps to achieve higher spectral resolution. Problems related to data processing are considered and corresponding solutions are proposed. Moreover, for potential applications, we evaluate instrument-performance indicators and propose methods to move indicators close to their theoretical values.
2. Instrument structure and parameters
2.1 Structure and working principle
Figure 1(a) shows that the stepped micro-mirror TSMIFTS comprises a scanning mirror, a first imaging system, a plane mirror, a beam splitter, a compensator plate, a stepped micro-mirror, a second imaging system, and a detector with a cold stop.
Fig. 1. (a) Simplified configuration of the TSMIFTS based on 128-step micro-mirror. (b) Internal structure of the prototype.
The working principle of the system is that at a certain time the light emitted by the target object passes through the scanning mirror and first imaging system, forming two primary image points on the plane mirror and the stepped micro-mirror, respectively. The two primary image points are ultimately imaged through the second imaging system on the focal plane of the detector, after being reflected by the plane mirror and micro-mirror. The difference in height between the plane mirror and micro-mirror causes the OPD between the two beams reaching the detector to be different, thereby forming interference fringes on the detector. Therefore, image and spectral information regarding the target reaches the detector. Then the scanning mirror rotates, and the target is imaged on the next step surface, so the detector can obtain interference information concerning different OPDs of the target. After one scan period, the detector obtains a three-dimensional data cube containing two-dimensional spatial information and one-dimensional spectral information.
2.2 Overall parameters
The instrument uses a medium-wave infrared HgCdTe area array detector, with a response band of 3.7∼4.8 µm. The F# is 4. The pixel number is 320 × 256. The pixel size is 30 µm × 30 µm. The theoretical spatial resolution of the instrument is 0.833 m at 2000 m. The theoretical width is 213 m at 2000 m.
2.3 Stepped micro-mirror
Figure 2(a) shows the stepped micro-mirror prototype, with its partial enlargement shown in Fig. 2(b).
Fig. 2. (a) Prototype of the stepped micro-mirror (steps are all in the dotted line). (b) Partial enlargement of the stepped micro-mirror.
The micro-mirror is made by a micro-nano process, and the design parameters are shown in Table 1.
Table 1. Design parameters of the stepped micro-mirror
The sub-step height design is as follows: Let the optical signal wavelength range be $[{\lambda _{min}},{\lambda _{max}}]$, and the sub-step height of the step micro-mirror be d, then the OPD sampling interval is 2d. According to the Nyquist-Shannon sampling theorem, the sampling frequency should be greater than twice the maximum signal frequency, that is, the sampling interval should satisfy 2d ≤${\lambda _{min}}$/2, and the sub-step height of the micro-mirror should satisfy d ≤${\lambda _{min}}$/4. Substituting ${\lambda _{min}}$ into the working band of the instrument, 3.7∼4.8 µm, and get d ≤ 3.7/4 = 0.925 µm. With respect to adjustment-error influence and micro-mirror-processing precision, the OPD during sampling has a certain error, and a certain margin should be left for the sampling interval. Therefore, we set the sub-step height of the micro-mirror to 0.625 µm.
For non-uniformity sampling correction in subsequent data processing, we used a stylus profiler to measure the micro-mirror step height. The probe scanning distance of the stylus profiler was 32 mm, covering all steps from the lowest to the highest. The scanning speed was 100 µm/s and the scanning frequency was 100 Hz. Figure 3(a) shows the sub-step height distribution of the test data; the test data was processed summarized. Figure 3(b) shows the sub-step height distribution histogram, and the measured parameters are summarized in Table 2.
Table 2. Measured parameter of the stepped micro-mirror
3. Data processing
The data processing process takes place on the data cube to obtain the scene image and reconstructed spectrum, the flow of which is in Fig. 4. The image is divided into different image units according to the different interference orders. The next processing stage comprises two routes. The first route involves stitching and reconstructing the scene image. We stitch image units of the same order in each image according to scanning direction to obtain the sequence of scene images; we then fuse the images to finally obtain the scene image. The second route involves stitching the interferogram sequence and reconstructing the spectrum. We stitch image units of different orders of the same target in each image according to the OPD sequence, to obtain the target interference pattern sequence, and then perform dimensionality reduction, baseline correction, apodization, non-uniformity sampling correction, and a Fourier transform on the target interferogram sequence to obtain the reconstructed spectrum.
3.1 Image cutting
Image cutting forms the basis of subsequent data processing. In theory, the image-unit position corresponding to each interference order is determined by the geometric shape of the stepped micro-mirror. However, the low precision in micro-mirror manufacturing and the instrument adjustment error, may cause alignment errors in the optical system; therefore, the image-unit widths corresponding to different interference orders may be different and the Hough transform method is chosen for image-unit separation.
The Hough transform is an effective curve-detection method, converting images from coordinate space to parameter space, detecting curves that can be parameterized, and controlling detection length by setting thresholds, thus filtering out unwanted ones. After detecting the step edge using the Hough transform, and using micro-mirror parameters, interpolation obtains the undetected edge; the least-squares method fits the corresponding line—the edge of the interference image unit.
3.2 Image stitching
Due to the difference in the widths between the different sub-steps of the micro-mirror, if the interferogram units are simply combined in order, the resulting stitched image has a stitching gap. Therefore, we use feature-based image-stitching methods to stitch scene images, the main steps of which include feature extraction, image registration, and image fusion.
The first step is feature extraction, where the considerably robust scale invariant feature transform (SIFT) algorithm is used [19,20]. The SIFT algorithm must usually be divided into several steps: detecting and locating scale-space extreme points, determining feature-point directions, and generating feature descriptors. We only use the algorithm to determine extreme-point position. To detect stable extreme points in scale space, we adopt Gaussian difference scale space, using different scale Gaussian difference kernels for convolution generation of images:
The second step is image registration. We use the feature matching algorithm based on local maximum entropy to obtain the matching result with greatest credibility, via correlation matching of local feature points. Entropy [21] expresses the complexity or uncertainty of a system, and can be used to describe mutual information, representing the statistical correlation between two random variables. Image matching based on mutual information searches for the pair of points with the largest amount of mutual information among the two images to be registered, obtaining the feature-point matching pair of the image. For an m × n image module, entropy is:
where ${p_{ij}}$ represents the grayscale distribution of the image in (i, j) coordinates. If H(A), H(B) represent the entropy of images A and B, respectively, and H(A, B) represents the joint entropy of the two images, then the information amount is: The third step is image fusion. The stitched image has a number of vertical stitching gaps, periodically arranged. After a two-dimensional fast Fourier transform, the vertical stitching gap in the image peaks on the horizontal axis of the Fourier frequency domain energy spectrum. Therefore, we can choose the appropriate filter and multiply it with the previously obtained frequency domain energy distribution, so that the gap components in the frequency domain space can be filtered out. Finally, we perform an inverse Fourier transform on the filtered spectrum to obtain a spatial image without stitching gaps.3.3 Spectral reconstruction
Using the above stitching method, we stitch image units of different orders of the same target in each image according to the OPD sequence. The interferogram sequence of the target is thus obtained, meaning the spectrum can now be reconstructed. Due to the instrument’s structure, our spectral reconstruction method consists of: (1) dimensionality reduction, (2) baseline correction, (3) apodization, and (4) Fourier transform.
- (1) The dimensionality reduction of the interferogram sequence is represented by the following two equations:$${I_0} = \left[ {\begin{array}{ccc} {{I_{11}}}& \cdots &{{I_{1n}}}\\ {{I_{21}}}& \cdots &{{I_{2n}}}\\ \vdots & \cdots & \vdots \\ {{I_{m1}}}& \cdots &{{I_{mn}}} \end{array}} \right]\begin{array}{ccc} {{I_{1({n + 1} )}}}& \cdots &{{I_{1({n \times N} )}}}\\ {{I_{2({n + 1} )}}}& \cdots &{{I_{2({n \times N} )}}}\\ \vdots & \cdots & \vdots \\ {{I_{m({n + 1} )}}}& \cdots &{{I_{m({n \times N} )}}} \end{array}$$Equation (4) represents a two-dimensional interferogram sequence, the matrix in the box represents an image in a sub-step mirror, and N represents the number of sample points resampled. Equation (5) represents a one-dimensional interference intensity sequence after dimensionality reduction.
- (2) In baseline correction, the interference intensity sequence consists of two parts, the DC-component and the AC-component. Due to the linearity of the Fourier transform, the AC-component modulates the interferogram, determining the shape and peak position of the spectrum, but the DC-component has little effect. When error exists in the DC-component, it causes a baseline curvature of the interference intensity sequence. The least-squares method is used to fit the baseline of the interference intensity sequence, and then obtain the corresponding DC-components at different sampling points. Finally, the corresponding DC-component value is subtracted from the intensity value of each sampling point in the interference intensity sequence.
- (3) In apodization, the integral interval of the Fourier transform is infinite, but acquisition of the interferogram can only be performed in a limited interval, called the “sampling cutoff.” Sampling cutoff causes side-lobe oscillation in the spectrum, and the first side-lobe should be no more than 22% larger than the main peak. Therefore, the apodization function must apodize the interference intensity sequence to mitigate side-lobe oscillation. We use the Happ-Genzel function, which has little influence on spectral resolution. Let the sampling length be Δ:
- (4) We perform a fast Fourier transform on the interference intensity sequence to obtain the reconstructed spectrum.
3.4 Non-uniformity sampling correction
Due to the influence of the substrate material and manufacturing process, the height of each sub-step of the micro-mirror can be offset from the theoretical height, so the errors will be introduced into the OPD corresponding to each interference order. Set the height of the sub-step of the stepped micro-mirror to $\delta /2$ and the sampling point to N. Therefore, the sampling interval is $2\delta $ and the maximum OPD of the instrument is $N\delta $. According to Fourier transform infrared spectroscopy [22], for the n-th $(n = 0,1,\ldots ,N - 1)$ sampling point in the frequency domain, the wavenumber is ${\nu _{n0}} = 1/(N\delta )$. Set OPD errors to ${\varepsilon _i}(i = 1,2,\ldots ,N)$, the sampling interval in the frequency domain will turn into ${\nu _n} = 1/(N\delta + \sum\nolimits_{i = 1}^N {{\varepsilon _i}} )$. Its spectral intensity has the following relationship with the interference intensity in the OPD domain:
To correct the above phase error, we performed non-uniformity sampling correction as follows: First, set the height error of the i-th sub-step of the micro-mirror as ${\varepsilon _i}/2$, and the OPD error is ${\varepsilon _i}$ according to the interference principle. Then let $\Delta {R_i}(i = 1,2,\ldots ,N)$ represent the actual OPD matrix, $\Delta {E_i}$ the OPD error matrix, and $\Delta {I_i}$ the ideal OPD matrix, so that the non-uniformity sampling error correction process is:
- (1) Calculate the corresponding height error ${\varepsilon _i}/2$ based on the measured step-mirror height data (Section 2.3), and calculate the OPD error matrix as $\Delta {E_i} = {\varepsilon _i}$; then the actual OPD matrix is:
- (3) Substitute the ideal OPD matrix into Eq. (11) to find the ideal interference intensity sequence:
3.5 Spectral resolution enhancement
Due to the image noise and apodization algorithms, the resolution of the reconstructed spectrum is lower than the theoretical value. Therefore, after analyzing the spectral characteristics, we propose a spectral resolution enhancement algorithm based on empirical mode decomposition (EMD).
EMD is a signal decomposition method proposed by NASA’s Huang et al., which decomposes signals into different eigenmode functions according to frequency [23,24]. The eigenmode function must satisfy the following two conditions:
- (1) The number of times the signal passes through the zero point is equal to the number of poles, and if not equal, it is at most one.
- (2) The signal is locally symmetrical about the time axis, i.e., the mean value of the upper and lower envelopes at any point on the signal curve is zero.
4. Experimental results
The experimental location of this paper is 43° 50’ 53.76'’ north latitude, 125° 23’ 54.96'’ east longitude, and the target distance is 725 meters. To obtain the complete data cube of the target, the instrument must accumulate over a certain period of time to make the target traversing all interference orders via swing of the scanning mirror.
4.1 Data acquisition
To obtain the target interferogram from the zero OPD position to the maximum OPD position, the distance that the target moves on the micro-mirror should be less than or equal to the width of one sub-step mirror. To reduce scan time, the distance is set equal to the width of one sub-step mirror. According to the parameters of the first imaging system and the stepped micro-mirror, the scanning interval is calculated to be 0.024°. Then, we determine a scan direction and acquire an image after each scan interval of the scan mirror. After one cycle, we obtain a complete interference data cube, shown in Fig. 5.
4.2 Experimental results
After obtaining the target's interference data cube, we reconstruct the scene image. Using the method in Section 3.1, we perform a Hough transform and interpolation fitting on the interferogram to obtain the interferogram units, and the results are shown in Fig. 6(a). Then we use the method in Section 3.2 to stitch and fuse the interferogram units. The result of feature-based image stitching is shown in Fig. 6(b), and the result of image fusion is shown in Fig. 6(c).
Fig. 6. (a) Interferogram after Hough transform detection and interpolation. (b) Scene image after feature-based image stitching. (c) Scene image after image fusion.
Figures 6(a) and 6(b) show that the stitched image units match very accurately, and the image details in the red circle in Figs. 6(b) and 6(c) show that the stitching gaps and the transition between image units are greatly improved. Our method, therefore, is suitable for scene-image reconstruction of the instrument.
Next, we reconstruct the spectrum. We select a point in the scene as the target of spectral reconstruction (as shown in Fig. 7(a), select point A as the reconstructed target), then extract and stitch the image units of all orders in the order according to the OPD to obtain a two-dimensional interferogram sequence, as shown in Fig. 7(b).
Fig. 7. (a) Reconstructed target in the scene image. (b) Two-dimensional interferogram sequence of the reconstructed target.
We then use the methods in Sections 3.3, 3.4, and 3.5 to process the two-dimensional interferogram sequence. The result is shown in Figs. 8(a)–8(e).
Fig. 8. (a) Interference intensity sequence after dimension reduction. (b) Interference intensity sequence after baseline correction. (c) Interference intensity sequence after apodization. (d) Interference intensity sequence after non-uniform sampling correction. (e) Comparison of unoptimized spectrum and reconstructed spectrum.
After a series of interference data processing, we finally obtain the reconstructed spectrum. Figure 8(e) shows that the optimized spectrum by the above steps has significantly reduced noise and side-lobe oscillation than the unoptimized spectrum, which shows that our method in section 3.3 has obvious effects. It can also be seen from Fig. 8(e) that the peaks of the spectrum before and after the optimization are slightly different, which shows that the non-uniform sampling correction in section 3.4 has a certain improvement on the wavenumber shift of the spectrum.
However, because the composition of the selected spectral reconstructed target is undetermined, and the spectrum is mixed with many unknown atmospheric components, the resulting spectrum cannot evaluate instrument performance in terms of spectral resolution and signal to noise ratio (SNR). Therefore, follow-up experiments are required to evaluate this performance.
5. Instrument performance evaluation
5.1 Spectral resolution
Spectral resolution characterizes the ability of an instrument to resolve adjacent lines. The criterion for distinguishing two adjacent lines of equal intensity and half-height width is that they have a depression of not less than 20% of the peak value of the intensity value after synthesis [25,26]. The theoretical calculation formula is:
where $\Delta \upsilon $ is the spectral resolution in cm−1 and ${\delta _{max}}$ is the maximum OPD in cm. Substituting ${\delta _{max}} = 0.625 \times 2 \times 128 \times {10^{ - 4}} = 0.016\,\textrm{cm}$, the theoretical spectral resolution is obtained as 62.5 cm−1.To obtain the true spectral-resolution value, we use the instrument line shape (ILS). The calculation process is as follows: Because of the effect of window truncation caused by limited OPD of the instrument, the actual reconstructed spectrum is:
According to the above calculation, we design the following ILS measurement experiment: A point-source black body and a narrow-band filter, with a center wavelength of 4.26 µm and a bandwidth of 66$\textrm{c}{\textrm{m}^{ - 1}}$, form a light source, and three calcium fluoride lenses form a collimation system to simulate a collimated monochromatic light source with parallel incidence. The optical path design and experimental platform are shown in Fig. 9(a). Then, we process the experimentally measured data [Fig. 9(b)] to obtain an interference intensity sequence [Figs. 9(c) and 9(d)], obtaining ILS as shown in Fig. 9(e).
Fig. 9. (a) Simplified configuration of the ILS measurement system. (b) Two-dimensional interferogram sequence. (c) Interference intensity sequence. (d) Interference intensity sequence after data processing. (e) Instrument line shape.
Figure 9(e) shows that the main peak position of the ILS without non-uniformity sampling correction is 2398$\textrm{c}{\textrm{m}^{ - 1}}$, and the deviation from the theoretical value of 2347.4$\textrm{c}{\textrm{m}^{ - 1}}$ is 1.28%. After non-uniformity sampling correction, the ILS main peak position is 2364$\textrm{c}{\textrm{m}^{ - 1}}$, only 0.41% from the theoretical value, 2347.4$\textrm{c}{\textrm{m}^{ - 1}}$, indicating that non-uniformity sampling correction effectively corrects the wavenumber shift of the spectrum caused by the step-height shift. However, the half-width (spectral resolution) is 79$\textrm{c}{\textrm{m}^{ - 1}}$, quite different from the instrument index, 62.5$\textrm{c}{\textrm{m}^{ - 1}}$. This is probably because of the narrow band source that replaces the monochromatic source, leading to ILS broadening. Therefore, we further processed the interference data, to enhance the resolution of ILS to bring it closer to the theoretical value. After spectral resolution enhancement, the ILS spectral resolution reached 65$\textrm{c}{\textrm{m}^{ - 1}}$, very close to the theoretical value of 62.5$\textrm{c}{\textrm{m}^{ - 1}}$.
5.2 Signal to noise ratio
The signal to noise ratio (SNR) is also an important performance characterization parameter of the spectrometer, related to factors such as target radiation and reflection characteristics, background characteristics, atmospheric transmittance, optical system aperture, relative aperture, transmittance, detector responsiveness, quantum efficiency, and specific detection rate [29,30]. Because the final data obtained by the instrument includes both interference images and spectral information, the SNR of the interferogram and the SNR of the reconstructed spectrum must be measured simultaneously, where the interferogram SNR reflects original-image quality, and the reconstructed-spectrum SNR reflects the instrument’s spectral response performance.
First we calculate the theoretical SNR value. The theoretical value of the interferogram SNR is derived as follows: Set the detector area to${A_d}$, the focal length of the optical system to f, the incident aperture to$D$, the atmospheric transmittance to ${\tau _a}$, the optical system transmittance to ${\tau _0}$; the target spectral radiance is ${L_\lambda }$. The luminous flux to the detector is:
The theoretical SNR value of the reconstructed spectrum is derived as follows [31]: The Fourier transform relationship between interference intensity $I(x)$ and spectral intensity $B(\sigma )$ is:
Measure and calculate the SNR true value, where measurement of the SNR true value of the interferogram is as follows: Choose the SNR at the 0-path difference with the largest interference intensity as the SNR of the interferogram:
where ${I_0}$ represents the interference intensity at the 0-path difference.Use the point source black body and the integrating sphere to simulate an approximately uniform surface light source; set the temperature to be the same as the theoretical calculation, then use the instrument to scan one cycle to obtain a time-dimensional 0-path difference interference intensity sequence. Calculate the mean and standard deviation of the sequence and substitute them into Eq. (30) to obtain the interferogram SNR.
Measure the true value of the reconstructed spectrum’s SNR as follows: Use the data obtained from the interferogram-SNR calculation to obtain the black body’s reconstructed spectrum; compare it with the theoretical (simulated) black body spectrum; substituting the data into the following formula, the spectrum’s average SNR is:
Fig. 10. (a) Interference data cube of blackbody. (b) Interference intensity sequence of blackbody. (c) Theoretical spectrum and reconstructed spectrum of blackbody.
It can be seen from Fig. 10(c) that the theoretical spectrum and the measured spectrum of blackbody are slightly different. This is due to the influence of some factors, such as the interference of the experimental environment, the non-uniform spectral response of the detector and the uneven transmittance of the anti-reflection coated lens during the spectral response range.
After calculation, the measured value of the interferogram SNR is: $SN{R_{xt}} = 189.3201$, and the measured value of the reconstructed-spectrum SNR is: $SN{R_{\sigma t}} = 22.8817$. Therefore, the interferogram SNR error is 7.42%, and the reconstructed-spectrum SNR error is 10.48%.
6. Conclusions
Several novel algorithms are used to process data related to the characteristics of a stepped micro-mirror to eliminate the image's stitching gaps, and the spectral noise and side-lobe oscillations to generate a high-quality reconstructed image and an impressive reconstructed target spectrum.
Moreover, to evaluate instrument performance and verify the validity of non-uniformity sampling correction and spectral resolution enhancement, the theoretical values of spectral resolution and the SNR are rigorously derived from the instrument parameters and characteristics. This derivation establish the conversion relationship between the interferogram SNR and the reconstructed-spectrum SNR. Experimental results shows that the main peak positions of the ILS before and after non-uniformity sampling correction are 2398$\textrm{c}{\textrm{m}^{ - 1}}$ and 2364$\textrm{c}{\textrm{m}^{ - 1}}$, differing by 1.28% and 0.41% from the theoretical value of 2347.4$\textrm{c}{\textrm{m}^{ - 1}}$, indicating that non-uniformity sampling correction does correct wavenumber shift. The spectral resolutions before and after spectral-resolution enhancement are 79$\textrm{c}{\textrm{m}^{ - 1}}$ and 65$\textrm{c}{\textrm{m}^{ - 1}}$, differing by 26.4% and 4% from the theoretical value, 62.5$\textrm{c}{\textrm{m}^{ - 1}}$, indicating that the spectral resolution enhancement based on EMD enhances spectral resolution. The interferogram SNR of the instrument is 189.3201 and its error from the theoretical value of 204.4829 is 7.42%. The reconstructed-spectrum SNR of the instrument is 22.8817 and its error from the theoretical value of 25.5604 is 10.48%. Further research will focus on data-processing optimization to improve the accuracy of the main-peak position of the reconstructed spectrum and bring the SNR closer to the theoretical value, thus enhancing the applicability of the instrument.
Funding
National Natural Science Foundation of China (61575193, 61627819, 61727818, 61805239); Jilin Scientific and Technological Development Program (20150520101JH, 20180201024GX, 20190303063SF); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2018254).
Disclosures
The authors declare no conflicts of interest.
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