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Spectral Detection: Technologies and Applications—2nd Edition
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Spectral Detection: Technologies and Applications—2nd Edition

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Optics and Lasers".

Deadline for manuscript submissions: 30 July 2025 | Viewed by 359

Special Issue Editors

Prof. Dr. Xihui Bian

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Guest Editor
School of Chemical Engineering and Technology, Tiangong University, Tianjin 300387, China
Interests: chemometrics methods; rapid nondestructive detection of edible oil; quality control of traditional Chinese medicine; near infrared spectral analysis; Raman spectral analysis; ultraviolet-visible spectral analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Jin Yu

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Guest Editor
Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
Interests: laser absorption spectroscopy; solid-state lasers; laser micromachining
Special Issues, Collections and Topics in MDPI journals
Dr. Qunbo Lv

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Guest Editor
Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China
Interests: spectral imaging; spectral image processing; Raman spectral analysis; Fourier transform spectrometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Spectral detection technology has always been a research hotspot in the field of detection. Because of its non-contact, fast, efficient, and dynamic characteristics, spectral detection can be completed without sampling and sample preprocessing. Thus, it is widely used in national defense, space remote sensing, food detection, biomedicine, and other engineering fields. In recent years, with the development of science and technology, the application of spectral detection technology has expanded to a new dimension. To this end, we have set up a Special Issue, entitled "Spectral Detection: Technplogies and Applications". This Special Issue aims to investigate the latest advances and trends in spectral detection technology and its applications. Topics of interest include, but are not limited to, the following:

  • Hyper-spectral detection;
  • Multispectral detection;
  • Infrared spectral analysis;
  • Near-infrared spectral analysis;
  • Raman spectral detection;
  • Spectral imaging;
  • Spectral sensing;
  • Laser spectroscopic detection;
  • High-resolution spectral detection;
  • Chemometric methods and their application in spectral analysis.

Prof. Dr. Xihui Bian
Dr. Jin Yu
Dr. Qunbo Lv
Guest Editors

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Keywords

  • multispectral detection
  • hyper-spectral detection
  • spectral analysis
  • spectral imaging
  • spectral sensing

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Research

30 pages, 22071 KiB  
Article
Analysis of Optical Errors in Joint Fabry–Pérot Interferometer–Fourier-Transform Imaging Spectroscopy Interferometric Super-Resolution Systems
by Yu Zhang, Qunbo Lv, Jianwei Wang, Yinhui Tang, Jia Si, Xinwen Chen and Yangyang Liu
Appl. Sci. 2025, 15(6), 2938; https://doi.org/10.3390/app15062938 (registering DOI) - 8 Mar 2025
Viewed by 223
Abstract
Fourier-transform imaging spectroscopy (FTIS) faces inherent limitations in spectral resolution due to the maximum optical path difference (OPD) achievable by its interferometer. To overcome this constraint, we propose a novel spectral super-resolution technology integrating a Fabry–Pérot interferometer (FPI) with FTIS, termed multi-component joint [...] Read more.
Fourier-transform imaging spectroscopy (FTIS) faces inherent limitations in spectral resolution due to the maximum optical path difference (OPD) achievable by its interferometer. To overcome this constraint, we propose a novel spectral super-resolution technology integrating a Fabry–Pérot interferometer (FPI) with FTIS, termed multi-component joint interferometric hyperspectral imaging (MJI-HI). This method leverages the FPI to periodically modulate the target spectrum, enabling FTIS to capture a modulated interferogram. By encoding high-frequency spectral interference information into low-frequency interference regions through FPI modulation, an advanced inversion algorithm is developed to reconstruct the encoded high-frequency components, thereby achieving spectral super-resolution. This study analyzes the impact of primary optical errors and tolerance thresholds in the FPI and FTIS on the interferograms and spectral fidelity of MJI-HI, along with proposing algorithmic improvements. Notably, certain errors in the FTIS and FPI exhibit mutual interference. The theoretical framework for error analysis is validated and discussed through numerical simulations, providing critical theoretical support for subsequent instrument development and laying a foundation for advancing novel spectral super-resolution technologies. Full article
(This article belongs to the Special Issue Spectral Detection: Technologies and Applications—2nd Edition)
►▼ Show Figures

Figure 1

Figure 1
<p>Schematic diagram of FPI principle [<a href="#B26-applsci-15-02938" class="html-bibr">26</a>].</p> Full article ">Figure 2
<p>Diagram of MJI-HI system structure.</p> Full article ">Figure 3
<p>Schematic diagram of combined interference principle: (<b>a</b>) object spectrum <span class="html-italic">B</span>(<span class="html-italic">ν</span>) and (<b>b</b>) its interferogram <span class="html-italic">I</span><sub>0</sub>(Δ) and (<b>c</b>) FPI-modulated spectrum <span class="html-italic">B</span>(<span class="html-italic">ν</span>)<span class="html-italic">T<sub>FPI</sub></span>(<span class="html-italic">ν</span>) and (<b>d</b>) its interferogram <span class="html-italic">I</span><sub>2</sub>(Δ).</p> Full article ">Figure 4
<p>(<b>a</b>) The schematic diagram of the FPI non-parallelism error in the direction perpendicular to the optical axis and a locally magnified schematic diagram of the flatness error. (<b>b</b>) The schematic diagram of the distribution of the non-parallelism error along the optical axis.</p> Full article ">Figure 5
<p>(<b>a</b>) The comparison and local magnification of the FPI transmittance spectra under ideal conditions (<span class="html-italic">T<sub>FPI</sub></span>) and with parallelism errors (<span class="html-italic">T<sub>FPI</sub></span><sub>-</sub><span class="html-italic"><sub>para</sub></span>); <span class="html-italic">T<sub>FPI</sub></span> and <span class="html-italic">T<sub>FPI</sub></span><sub>-</sub><span class="html-italic"><sub>para</sub></span> are decomposed into (<b>b</b>) the DC component, (<b>c</b>) fundamental frequency component, (<b>d</b>) second harmonic component, and (<b>e</b>) third harmonic component, with corresponding comparisons and local magnifications. Here, <span class="html-italic">z</span> is defined as 2<span class="html-italic">πν</span>2<span class="html-italic">r</span><sub>0</sub><span class="html-italic">β<sub>FPI</sub></span> in Equation (12), and the curves ±2<span class="html-italic">a<sub>m</sub>J</span><sub>1</sub>(<span class="html-italic">mz</span>)/(<span class="html-italic">mz</span>) can be regarded as the envelopes of the fundamental frequency and higher harmonic components of <span class="html-italic">T<sub>FPI</sub></span><sub>-</sub><span class="html-italic"><sub>para</sub></span>.</p> Full article ">Figure 6
<p>(<b>a</b>) The comparison and local magnification of the FPI transmittance spectra under ideal conditions (<span class="html-italic">T<sub>FPI</sub></span>) and with parallelism errors (<span class="html-italic">T<sub>FPI</sub></span><sub>-<span class="html-italic">flat</span></sub>); <span class="html-italic">T<sub>FPI</sub></span> and <span class="html-italic">T<sub>FPI</sub></span><sub>-<span class="html-italic">flat</span></sub> are decomposed into (<b>b</b>) the DC component, (<b>c</b>) fundamental frequency component, (<b>d</b>) second harmonic component, and (<b>e</b>) third harmonic component, with corresponding comparisons and local magnifications. Here, the curves ±2<span class="html-italic">a<sub>m</sub></span>exp[−(<span class="html-italic">mπσ</span>Δ<span class="html-italic"><sub>D</sub>ν</span>)<sup>2</sup>] can be regarded as the envelopes of the fundamental frequency and higher harmonic components of <span class="html-italic">T<sub>FPI</sub></span><sub>-<span class="html-italic">flat</span></sub>.</p> Full article ">Figure 7
<p>The curves of <span class="html-italic">a′</span><sub>0</sub> to <span class="html-italic">a′</span><sub>3</sub> as functions of <span class="html-italic">R</span><sub>0</sub>. The zero points of <span class="html-italic">a′<sub>m</sub></span> with respect to <span class="html-italic">R</span><sub>0</sub> are indicated by arrows, representing that at these points, <span class="html-italic">a<sub>m</sub></span> is less affected by changes in <span class="html-italic">R</span><sub>0</sub>.</p> Full article ">Figure 8
<p>(<b>a</b>) The comparison of the FPI transmittance spectrum under ideal conditions (TFPI) and under reflectance variation errors (<span class="html-italic">T<sub>FPI-R</sub></span>); TFPI and <span class="html-italic">T<sub>FPI-R</sub></span> decomposed into (<b>b</b>) the DC component, (<b>c</b>) the fundamental frequency component, (<b>d</b>) the second harmonic component, and (<b>e</b>) the third harmonic component for comparison.</p> Full article ">Figure 9
<p>Beams with different divergence angles produce different OPDs in the FTIS and FPI. Here, <span class="html-italic">θ</span><sub>0</sub> is the maximum divergence half-angle, and ψ is the azimuth angle. The red arrows indicate the phase differences caused by the central aperture light in the FTIS and FPI, respectively, and the black arrows indicate the phase differences caused by the edge aperture light in the FTIS and FPI, respectively.</p> Full article ">Figure 10
<p>Assuming a divergence angle of 1°, (<b>a</b>) FTIS with an OPD of 1 mm, (<b>b</b>) FTIS with an OPD of 2 mm, and (<b>c</b>) FTIS with an OPD of 3 mm: the overall comparison and local magnification of the FTIS double-beam interferometric spectrum.</p> Full article ">Figure 11
<p>(<b>a</b>) In FTIS, the mirror tilt error causes the wavefront (blue surface) to deviate from the ideal wavefront (yellow surface), tilting in the <span class="html-italic">φ<sub>FTIS</sub></span> direction with a tilt angle of 2<span class="html-italic">β<sub>FTIS</sub></span>; in FPI, the non-parallelism error causes the wavefront (blue surface) to deviate from the ideal wavefront (yellow surface), tilting in the <span class="html-italic">φ<sub>FPI</sub></span> direction with a tilt angle of 2<span class="html-italic">β<sub>FPI</sub></span>, where the Z-axis represents the optical axis. (<b>b</b>) The relative tilt direction along the optical axis between the FTIS mirror tilt error and the FPI non-parallelism error.</p> Full article ">Figure 12
<p>(<b>a</b>) The schematic diagram of the geometric relationship in polar coordinates between the vector (<span class="html-italic">β<sub>m</sub></span>,<span class="html-italic">φ<sub>m</sub></span>) and the vectors <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>x</mi> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mi>F</mi> <mi>T</mi> <mi>I</mi> <mi>S</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>x</mi> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mi>F</mi> <mi>P</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) the schematic diagram of the geometric relationship between the vector (<span class="html-italic">β<sub>−m</sub></span>,<span class="html-italic">φ<sub>−m</sub></span>) and the vectors <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>x</mi> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mi>F</mi> <mi>T</mi> <mi>I</mi> <mi>S</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>x</mi> </mrow> <mo>→</mo> </mover> </mrow> <mrow> <mi>F</mi> <mi>P</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 13
<p>(<b>a1</b>) Hitran data input spectrum and (<b>a2</b>) the error-free interferograms <span class="html-italic">I</span><sub>1</sub> and <span class="html-italic">I</span><sub>2</sub> obtained using MJI-HI; (<b>b1</b>) Gaussian function input spectrum and (<b>b2</b>) the error-free interferograms <span class="html-italic">I</span><sub>1</sub> and <span class="html-italic">I</span><sub>2</sub>; (<b>c1</b>) cosine function input spectrum and (<b>c2</b>) the error-free interferograms <span class="html-italic">I</span><sub>1</sub> and <span class="html-italic">I</span><sub>2</sub>; (<b>d1</b>) <span class="html-italic">B</span><sub>0</sub> = 1 input spectrum and (<b>d2</b>) the error-free interferograms <span class="html-italic">I</span><sub>1</sub> and <span class="html-italic">I</span><sub>2</sub>.</p> Full article ">Figure 14
<p>(<b>a1</b>–<b>a4</b>). Broadening of the displacement components of orders <span class="html-italic">m</span> = 0, 1, 2, and 3 caused by different non-parallelism; (<b>b1</b>–<b>b4</b>). broadening of the displacement components of orders <span class="html-italic">m</span> = 0, 1, 2, and 3 caused by different non-flatness.</p> Full article ">Figure 15
<p>(<b>a1</b>) Interferogram reconstruction result when the <span class="html-italic">FWHM<sub>D</sub></span> of <span class="html-italic">Defect</span><sub>1</sub> is λ<sub>min</sub>/4; (<b>a2</b>–<b>a4</b>) are its local enlargements; (<b>b1</b>) interferogram reconstruction result when the <span class="html-italic">FWHM<sub>D</sub></span> of <span class="html-italic">Defect</span><sub>1</sub> is λ<sub>min</sub>/2; (<b>b2</b>–<b>b4</b>) are its local enlargements; (<b>c1</b>) interferogram reconstruction result when the <span class="html-italic">FWHM<sub>D</sub></span> of <span class="html-italic">Defect</span><sub>1</sub> is λ<sub>min</sub>; (<b>c2</b>–<b>c4</b>) are its local enlargements. Here, <span class="html-italic">I</span><sub>0</sub> is the ideal interferogram, <span class="html-italic">I<sub>sup</sub></span> is the MJI-HI interferogram reconstruction result without using the improved method, and <span class="html-italic">I<sub>sup−imp</sub></span> is the MJI-HI interferogram reconstruction result using the improved method.</p> Full article ">Figure 16
<p>(<b>a1</b>) Interferogram reconstruction results when the <span class="html-italic">FWHM<sub>tilt</sub></span> of <span class="html-italic">g<sub>FTIS</sub></span> is λ<sub>min</sub>/4; (<b>a2</b>–<b>a5</b>) are its local enlargements; (<b>b1</b>) interferogram reconstruction results when the <span class="html-italic">FWHM<sub>tilt</sub></span> of <span class="html-italic">g<sub>FTIS</sub></span> is λ<sub>min</sub>/2; (<b>b2</b>–<b>b5</b>) are its local enlargements. Here, <span class="html-italic">I</span><sub>0</sub> represents the ideal interferogram, <span class="html-italic">I<sub>sup</sub></span> denotes the MJI-HI reconstructed interferogram under mirror tilt errors, and <span class="html-italic">I<sub>0-tilt</sub></span> is the interferogram obtained using FTIS with the same mirror tilt errors.</p> Full article ">Figure 17
<p>(<b>a</b>) When <span class="html-italic">B</span>(ν) = 1 is used as the input spectrum, the overall situation of the interferogram <span class="html-italic">I</span><sub>2</sub>; (<b>b–e</b>). When the tilt direction angle differences are 0°, 30°, 60°, and 90°, the response function convolution broadening of <span class="html-italic">I</span><sub>2</sub> occurs at ±<span class="html-italic">m</span>Δ<span class="html-italic"><sub>FPI</sub></span>; (<b>b1</b>–<b>b4</b>). When the tilt direction angle difference is <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub> =</span> 0°, the convolutional broadening of the response functions of the <span class="html-italic">m</span> = 0, ±1, ±2, ±3 order caused by the combined errors; (<b>c1</b>–<b>c4</b>). When <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub> =</span> 30°, the convolutional broadening of the response functions of the <span class="html-italic">m</span> = 0, ±1, ±2, ±3 order; (<b>d1</b>–<b>d4</b>). When <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub> =</span> 60°, the convolutional broadening of the response functions of the <span class="html-italic">m</span> = 0, ±1, ±2, ±3 order; (<b>e1</b>–<b>e4</b>). When <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub> =</span> 90°, the convolutional broadening of the response functions of the <span class="html-italic">m</span> = 0, ±1, ±2, ±3 order.</p> Full article ">Figure 18
<p>(<b>a1</b>) Interferogram reconstruction result under combined errors when <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub></span> = 0°, with (<b>a2</b>–<b>a4</b>) showing local magnifications; (<b>b1</b>) interferogram reconstruction result under combined errors when <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub></span> = 30°, with (<b>b2</b>–<b>b4</b>) showing local magnifications; (<b>c1</b>) interferogram reconstruction result under combined errors when <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub></span> = 60°, with (<b>c2</b>–<b>c4</b>) showing local magnifications; (<b>d1</b>) interferogram reconstruction result under combined errors when <span class="html-italic">φ<sub>FTIS</sub></span> − <span class="html-italic">φ<sub>FPI</sub></span> = 90°, with (<b>d2</b>–<b>d4</b>) showing local magnifications; here, <span class="html-italic">I</span><sub>0</sub> represents the ideal interferogram, and <span class="html-italic">I<sub>sup</sub></span> denotes the MJI-HI reconstructed interferogram under joint errors.</p> Full article ">Figure 19
<p>(<b>a</b>) When the input spectrum is a cosine function with a periodic frequency of <span class="html-italic">k</span><sub>0</sub>, the overall interferogram <span class="html-italic">I</span><sub>2</sub> is shown, indicating the specific positions of <span class="html-italic">I</span><sub>2</sub>(<span class="html-italic">m</span>Δ<span class="html-italic"><sub>FPI</sub></span>), <span class="html-italic">I</span><sub>2</sub>(<span class="html-italic">m</span>Δ<span class="html-italic"><sub>FPI</sub></span> − <span class="html-italic">k</span><sub>0</sub>), and <span class="html-italic">I</span><sub>2</sub>(<span class="html-italic">m</span>Δ<span class="html-italic"><sub>FPI</sub></span> + <span class="html-italic">k</span><sub>0</sub>) within <span class="html-italic">I</span><sub>2</sub>. For divergence angles of 0°, 0.5°, 1.0°, 1.5°, and 2.0°, the convolution broadening of <span class="html-italic">δ</span> functions of the <span class="html-italic">m</span> = 0, 1, 2, 3 frequency-shift components due to collimation errors is observed at (<b>b1</b>–<b>b4</b>). Δ = <span class="html-italic">m</span>Δ<span class="html-italic"><sub>FPI</sub></span>, at (<b>c1</b>–<b>c4</b>). Δ = <span class="html-italic">m</span>Δ<span class="html-italic"><sub>FP</sub></span> − <span class="html-italic">k</span><sub>0</sub>, at (<b>d1</b>–<b>d4</b>). Δ = <span class="html-italic">m</span>Δ<span class="html-italic"><sub>FPI</sub></span> + <span class="html-italic">k</span><sub>0</sub>.</p> Full article ">Figure 20
<p>(<b>a</b>) Super-resolution spectra obtained using MJI-HI with divergence angles of 0°, 1°, and 2°; (<b>b</b>) local magnification at wavenumber 1.5 × 10<sup>4</sup> cm<sup>−1</sup>. Here, <span class="html-italic">B</span><sub>0</sub> represents the input spectrum, and <span class="html-italic">B<sub>sup-</sub><sub>θ</sub></span> denotes the super-resolution spectra obtained under different divergence angles using MJI-HI.</p> Full article ">Figure 21
<p>(<b>a1</b>–<b>d1</b>) The FPI reflectance spectra generated by curves 1–4 under PVs of 0%, 2%, 6%, and 10%, respectively. (<b>a2</b>–<b>a5</b>) Correspond to curve 1, (<b>b2</b>–<b>b5</b>) to curve 2, (<b>c2</b>–<b>c5</b>) to curve 3, and (<b>d2</b>–<b>d5</b>) to curve 4, illustrating the changes in the response functions of <span class="html-italic">m</span> = 0, 1, 2, 3 frequency-shift components due to reflectance variations.</p> Full article ">Figure 22
<p>Using <span class="html-italic">B</span><sub>0</sub> = 1 as the input spectrum, the super-resolution spectral results obtained under reflectance variation (<b>a</b>) curve 1, (<b>b</b>) curve 2, (<b>c</b>) curve 3, and (<b>d</b>) curve 4 with PV = 2%, 6%, and 10% are shown. Here, <span class="html-italic">B<sub>sup</sub></span><sub>-PV</sub> represents the super-resolution spectra obtained using MJI-HI under different FPI reflectance error levels.</p> Full article ">
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