Optical spectrum analyzers and typical applications in astronomy and remote sensing

A spectrometer is an instrument used for spectral analysis of optical signals, enabling the determination of the spectral composition of emitted, absorbed, or scattered optical radiation by substances. It allows for the measurement of parameters such as wavelength, intensity, and profile, among others. Within the realm of astronomical and remote sensing instruments, the optical spectrum analyzer (OSA),¹ or spectrometer, holds significant importance. Spectrometers can be classified into several types, including prism, grating, Fourier transform (such as Michelson, Mach–Zehnder, and Sagnac interferometers), tunable filter (such as Fabry–Pérot, acousto-optic and liquid crystal tunable filters) spectrometers, as well as reconstructive spectrometers² (comprising spectral response and spectral-to-spatial mapping types). In Sec. II, we present a systematic introduction to the fundamental principles, classifications, and typical applications of spectrometers in the fields of astronomy and remote sensing. In Sec. III, we construct a generalized reconstructive spectrometer model and introduce the principles behind spectral mapping, reconstruction, and imaging. Section IV delves into the important parameters of spectrometers, including spectral range, bandwidth, spectral resolution or spectral resolving power (SRP), étendue, and calibration from a theoretical standpoint. In Sec. V, we explore the diverse applications of spectrometers. Finally, in Sec. VI, we provide concluding remarks and outline future prospects.

The APEX and PRISMA spectrometers are employed in remote sensing applications for soil, water, and atmosphere. The APEX instrument consists of VNIR (Visible-Near-Infrared) and SWIR (Short-Wave-Infrared) channels, realized by CaF₂/ZnS and CaF₂/sapphire prisms, respectively. The spectral range for VNIR is 380.5–971.7 nm (334 bands), while for SWIR, it is 941.2–2501.5 nm (198 bands). On the other hand, the PRISMA instrument uses three prisms to achieve VNIR and SWIR channels with a spectral range of 400–1010 nm (66 bands) and 920–2505 nm (174 bands), respectively. The CSIM spectrometer is utilized for long-term measurements of solar spectral irradiance (SSI) to understand how solar variability affects Earth’s climate. The CSIM system incorporates a fused silica triangular prism that disperses the incoming light. By rotating the prism, the dispersed light is detected by Si (200–950 nm), InGaAs (900–1700 nm), and extended InGaAs (1600–2800 nm) detectors, covering a spectral range of 200–2800 nm. This range accounts for over 97% of the total solar irradiance.

The Féry prism¹⁰ is characterized by its curved surfaces and is defined by parameters such as the curvature radii of its front and rear light transmission surfaces, its thickness (which represents the light transmission distance inside the prism), and the apex angle (which is the angle between the two tangents at the intersection of the light and the prism’s curved surfaces). Due to its design, the Féry prism exhibits several advantageous properties, including collimation, aberration correction, and imaging. There are two main types of Féry prisms: catadioptric and transmissive.

The catadioptric Féry prism spectrometer finds typical applications in various instruments, such as the Solar Prism Spectrometer (SPS)¹¹ shown in Fig. 2(a), the Spectral Irradiance Monitor (SIM) for the Solar Radiation and Climate Experiment (SORCE) mission,^12,13 NASA’s Total and Spectral Solar Irradiance Sensor-1 (TSIS-1) Spectral Irradiance Monitor (SIM) hosted on the International Space Station (ISS),¹⁴ and the TSIS-1 Hybrid Solar Reference Spectrum (HSRS).¹⁵ 

The SPS utilizes a fused quartz prism, with radii of curvature of 423 and 440 mm, a thickness of 12.08 mm, and an included angle of 33.44°. It is equipped with a scanning four-exit-slit structure, consisting of one UV, two VNIR, and an IR channel. These channels cover spectral ranges of 250–400 nm, 400–1000 nm, and 1000–2500 nm, respectively. The full-width half-maximums (FWHMs) for these channels range from 0.7 to 3.5 nm, 3.5–35.0 nm, and 28.5–41.2 nm, respectively. It is worth noting that the FWHM varies with wavelength according to Eqs. (1) and (2). The SPS is used in the study of solar physics, weather forecasting, and climate change.

The SORCE-SIM instrument is designed to measure x rays, ultraviolet rays, visible light, and near-infrared radiation emitted by the sun that reaches the Earth. It enables the study of long-term climate change, natural fluctuations, atmospheric ozone, and UV-B radiation. The instrument covers a spectral range of 200–2700 nm with a spectral resolution ranging from 0.25 to 33 nm. To achieve this, the SORCE-SIM employs a fused quartz prism, with radii of curvature of 421.48 and 441.27 mm, respectively. The prism has a central thickness of 12.30 mm and an included angle of 34.35°.

The TSIS-1-SIM is designed to continuously monitor solar spectral irradiance (SSI) over the spectral range of 200–2400 nm. It has a spectral resolution of 2 nm (<280 nm), 5 nm (280–400 nm), and 45 nm (>400 nm). In recent years, the TSIS-1-HSRS has been developed using a modified spectral ratio method to normalize very high spectral resolution solar line data to the absolute irradiance scale of the TSIS-1-SIM and the CSIM. The TSIS-1-HSRS spans 202–2730 nm, covering an integrated energy that exceeds 97% of the total solar irradiance. Its accuracy ranges from 0.3% to 1.3%, and its spectral resolution ranges from 0.001–0.01 nm.

The catadioptric Féry prism is known to suffer from significant image astigmatism, and the curved spectral plane can pose challenges for planar array detectors. Consequently, the transmissive Féry prism is often preferred in various applications, including the BASS^16,17 (Broadband Array Spectrometer System) shown in Fig. 2(b), the NIHTS^18–20 (Near-Infrared High-Throughput Spectrometer) installed on the 4.3 m Discovery Channel Telescope LDT depicted in Fig. 2(c), and the FPIS^21,22 (Féry prism Infrared Spectrometer) illustrated in Fig. 2(d).

The BASS system incorporates an aplanatic optical design with transmissive Féry prisms made of NaCl and CaF₂. The CaF₂ prism has radii of curvature of 84.923 and 59.621 mm, a thickness of 30 mm, and an included angle of 27.29°. The spectral range covered by the BASS is 2.9–6.5 and 6.5–13.5 µm, respectively. This system is employed to study the infrared spectroscopy of celestial bodies such as α Orionis, planetary nebulae and comets. In contrast, the NIHTS utilizes a ZnS transmissive Féry prism with a maximum thickness of 44 mm and a 96 in. single slit. It covers a spectral range of 0.86–2.45 µm, and its optical throughput is ∼40%. The NIHTS is designed for observing time-varying celestial bodies, such as the Kuiper Belt, asteroids, and brown dwarfs. The FPIS employs a BaF₂ transmissive Féry prism with radii of curvature of 58.71 and 84.16 mm, respectively, and a thickness of 27.66 mm. It covers a spectral range of 1000–1800 cm⁻¹ with a spectral resolution of 0.5–5.5 cm⁻¹. The FPIS utilizes a high-brightness synchrotron radiation infrared light source, which significantly increases the light energy. This allows for the use of a micrometer-level entrance aperture to achieve high spectral resolution and luminous flux. The integration time is 1–4 µs, and the time resolution is 30 µs. The FPIS is particularly suitable for studying the dynamic processes in biological macromolecules, such as the conformational changes of retinal chromophore proteins.

An example of a significant application of blazed gratings is the Reflection Grating Spectrometer (RGS),^23,24 which is installed on the XMM-Newton satellite by the European Space Agency, as depicted in Fig. 3. The RGS employs 182 reflection blazed gratings, with a groove density of 645.6 lines/mm. It has a first-order blaze wavelength of 1.5 nm and a blaze angle of 0.6989°. The RGS achieves a high SRP ranging from 100 to 500 across a wide spectral range of 0.6–3.8 nm in the extreme ultraviolet band. Its primary purpose is to observe galaxy clusters and detect K-shell spectral transitions of elements such as C, N, O, Ne, Me, and Si, as well as L-shell spectral transitions of Fe.

The echelle grating²⁵ is a type of Littrow grating with a larger groove spacing compared to the wavelength. It features a larger blaze angle, greater angular dispersion, and the ability to utilize higher diffraction orders, allowing for higher spectral resolution compared to ordinary blazed gratings. However, it should be noted that echelle gratings typically have a smaller FSR compared to ordinary blazed gratings. Echelle gratings have found various applications in astronomy and remote sensing. Notable examples include the GMT-Consortium Large Earth Finder (G-CLEF)²⁶ on the Giant Magellan Telescope (GMT), as depicted in Fig. 4(a); the mid-infrared channel of the ExoMars2016 Mars probe Atmospheric Chemistry Suite (ACS);²⁷ the Cryogenic Near-Infrared-Spectro-Polarimeter (CryoNIRSP)^28–30 on the Daniel K. Inouye Solar Telescope (DKIST) currently been constructed at the Haleakala Observatory, as shown in Fig. 4(b); and the High-Resolution Spectrograph (HIRES) in the European Extremely Large Telescope (ELT).^31,32

The G-CLEF instrument incorporates three echelle gratings, each measuring 300 × 1200 mm², with a groove density of 31.6 lines/mm. Cross-dispersion is a process that disperses light in a direction perpendicular to the main dispersion axis, spatially separating the light or separating it based on another property orthogonal to the wavelength axis. In the G-CLEF system, to achieve cross-dispersion and generate a two-dimensional continuous spectrum, two volume holographic gratings with groove densities of 910 and 370 lines/mm are employed. The G-CLEF covers a spectral range of 350–540 and 540–1000 nm, enabling observations of low-mass exoplanets, stellar abundances, and high-redshift phenomena. The ACS-MIR utilizes an echelle grating with a groove density of 3.03 lines/mm and a blazed angle of 63.43°. The diffraction orders used range from 142 to 258. Cross-dispersion is accomplished using two ordinary blazed gratings of 361 and 180 lines/mm. The ACS-MIR covers a spectral range of 2.3–4.3 µm and is designed to detect trace gases, such as C₂H₆, HCl, H₂S, N₂O, CH₄, and ¹³CH₄, with a sensitivity of less than 1 ppm. Its goal is to explore the planetary chemistry and search for life-related information on Mars. The CryoNIRSP incorporates an R2 echelle grating with a ruled width of 408 mm and a diffraction order range of 12–107. It covers a spectral range of 530–4651 nm and is utilized to study the solar magnetic field and its thermodynamic properties.

The ELT-HIRES incorporates four R4 echelle gratings with groove densities of 67.00, 34.50, 16.00, and 11.95 lines/mm. These gratings operate at diffraction orders of 72–87, 68–140, 68–146, and 72–86, respectively, enabling the U, BVRI, ZYJH, and K modules. Each of the U, B, V, R, I, Z, Y, J, H, and K arms has a specific spectral range: 330–405, 400–467, 483–555, 549–674, 666–833, 827–955, 950–1128, 1128–1356, 1435–1800, and 1877–2405 nm, respectively. Additionally, each arm utilizes a transmission grating as a cross-disperser with groove densities of 2240, 2490, 1860, 1410, 1000, 1240, 930, 730, 465, and 360 lines/mm, respectively. The ELT-HIRES possesses SRPs for different modes: 100 000 for HR-modes, 150 000 for UHR-modes, and 20 000 for MR-modes. The primary scientific objectives of the ELT-HIRES are the detection of bio-signatures in Earth-like exoplanets and the direct observation of cosmic expansion re-acceleration.

The volume holographic grating (VHG) is produced using high-precision holographic photography technology,³³ resulting in a grating with high density, a large production area, high dispersion, high SRP, and low stray light. However, according to the standard grating equation (sin θ = λm/d), a holographic grating with a higher diffraction order (m) and a smaller grating pitch (d) will have a larger m/d or diffraction angle (θ) than an echelle grating, which can lead to high-order dispersion interference. VHGs find applications in systems such as the Faint Object Camera and Spectrometer (FOCAS)^34,35 on the 8.2 m Subaru Optical Telescope, as shown in Fig. 5(a), the Dark Energy Spectroscopic Instrument (DESI)³⁶ for the Stage IV ground-based dark energy experiment on the Mayall 4 m Telescope, and the Raman Spectrometer for MMX (RAX), which is part of the JAXA Martian Moons eXploration (MMX) mission scheduled for launch in 2024.³⁷ 

The FOCAS incorporates a grism structure consisting of a VHG measuring 110 × 106 mm², which is sandwiched between two right-angle prisms. The spectral range covered by FOCAS is 200–2500 nm. It is used to investigate the formation, evolution, and large-scale structure of high-redshift quasars and galaxies. On the other hand, the DESI employs three VHGs to realize three spectral channels. Each VHG is sandwiched between two fused quartz plates, as depicted in Fig. 5(b). The three gratings have groove densities of 1103.5 ± 21, 1157.4 ± 21, and 992.5 ± 21 lines/mm, respectively. The spectral ranges covered by the three channels are 360–593, 566–772, and 747–980 nm, respectively. DESI is used to observe dark energy in the large-scale structure of the universe.

The flat-field holographic concave grating (FHCG) possesses the capability to both diffract and image incident light onto a plane, making it a valuable tool for detecting array CCDs. One notable application of the FHCG is in the extreme ultraviolet spectrometer (EUVS),^38,39 as depicted in Fig. 6. The EUVS utilizes a gold-plated concave variable line spacing (VLS) grating with a groove density of 2400 lines/mm, an area of 46 × 26 mm², a curvature radius of 15 920 mm, a blaze angle of 1.9°, and a blaze wavelength of 30 nm. With the FHCG, the EUVS is capable of covering a spectral range of 10–130 Å, enabling the study of high-temperature fusion plasma radiation, including elements such as H, B, C, O, Fe, and W.

The convex grating^40,41 is well-known for its strong spectral bending and its ability to correct optical aberrations, such as astigmatism and coma. These characteristics make it a popular choice for spectrometer applications. The Offner structure⁴² is a commonly used design in convex grating spectrometers, which find extensive applications in astronomy and remote sensing. Examples of these applications include the Visual and Infrared Mapping Spectrometer (VIMS-V)^43–45 on the Cassini Saturn probe depicted in Fig. 7(a), the Advanced Hyperspectral Imager (AHSI)⁴⁶ on China's GF-5 satellite shown in Fig. 7(c), and the Asteroid Exploration Spectrometer (AES)⁴⁷ illustrated in Fig. 7(d).

The VIMS-V spectrometer utilizes a convex grating that is holographically recorded in a Rowland circle configuration, as shown in Fig. 7(b). The grating features a rectangular laminar groove profile, with 67.5% and 32.5% of the surface area covered by grooves with depths of 300 and 440 nm, respectively. The spectral range of the VIMS-V spans from 300 to 1050 nm. This instrument is employed to create spatial maps of the distribution of minerals and chemicals on the surfaces of Saturn, its rings, and its moons.

The AHSI spectrometer employs an improved Offner structure that incorporates a meniscus lens positioned at the location of the convex grating. This lens helps to correct for spectral bending, additional astigmatism, and field curvature caused by the ultra-long slit (60 mm). The dispersion width of the AHSI reaches 30 mm, while its swath width is 60 km and its spatial resolution is 30 m. The instrument’s spectral range spans from 400 to 2500 nm, with 330 spectral channels. The spectral resolution is higher than 5 nm in the VNIR channel and 10 nm in the SWIR channel. The AHSI is renowned for its ability to detect and identify ground objects, making it well-suited for precision applications, such as ecological environment monitoring, land and resource surveying, and oil/gas exploration.

The AES spectrometer employs a convex grating with a spectrally partitioned structure, as depicted in Fig. 7(e). The radius of curvature of the grating is given by $R2=Δl/mgΔλ$⁠, where Δl, m, g, and Δλ represent the width of the spectral plane, the diffraction order, the groove density of the grating, and the spectral range, respectively. The central and outer regions of the grating correspond to the VNIR and SWIR channels, respectively, with groove densities of 118 and 40 lines/mm. The blazed angles for these regions are 1.25°/3.5° and 1.9°, respectively. The spectral range of the AES spans from 0.4 to 1 µm in the VNIR channel and from 1 to 2.7 µm in the SWIR channel. The spectral resolution is 3.63 and 9.64 nm for the VNIR and SWIR channels, respectively. The AES is primarily used for studying the evolution of the solar system by detecting asteroid bodies.

The working principle of a Fourier transform spectrometer (FTS) typically involves the utilization of interferometers, such as the traditional Michelson, Mach–Zehnder, and Sagnac interferometers.⁴⁸ These interferometers rely on the phenomenon of two-beam interference and make use of the mathematical concepts of Fourier transform. FTS offers various advantages, including high spectral resolution, wide spectral range, and the capability to measure the full spectrum simultaneously.

The ACE instrument is an FTS with a spectral range of 750–4400 cm⁻¹, offering a high spectral resolution of 0.02 cm⁻¹ and a FOV of 1.25 mrad. Its primary objective is to investigate atmospheric chemistry and dynamics, particularly related to stratospheric ozone depletion and the interplay between chemistry and climate change. The IASI instrument operates within an OPD range of −2 to 2 cm, covering a spectral range of 645–2760 cm⁻¹ with 8461 channels. It is employed for weather forecasting and climate studies, with the capability to detect various gases including CO, CO₂, N₂O, CH₄, SO₂, HNO₃, NH₃, OCS and CF₄. The ACS-TIRVIM instrument operates in both nadir and solar occultation modes, achieving maximum OPDs of ±1 and ±5 cm, respectively. The corresponding spectral ranges for these modes are 590–2000 and 590–5900 cm⁻¹. The instrument is dedicated to investigating atmospheric chemistry by measuring various molecular species. The HIRAS instrument features distinct channels for the Long-Wave-Infrared (LWIR), Middle-Wave-Infrared (MWIR), and SWIR spectral regions, with maximum OPDs of 0.8, 0.4, and 0.2 cm, respectively. The spectral ranges covered by these channels are 650–1135, 1210–1750, and 2155–2550 cm⁻¹. HIRAS is primarily employed to monitor atmospheric temperature, water vapor, and greenhouse gases, contributing to the improvement of numerical weather forecasting.

The standard Michelson interferometer suffers from a drawback where half of its energy returns to the light source, leading to interference with the spectral signal. This limitation can be overcome by employing an off-axis configuration, which introduces an angle between the interferometer and detector axes. Examples of instruments utilizing this approach include the Interferometric Monitor for Greenhouse Gases (IMG)^55,56 on the ADEOS satellite platform, as depicted in Fig. 8(a), and the imaging Fourier transform spectrometer SITELLE^57,58 installed on the Canada–France–Hawaii Telescope (CFHT), as shown in Fig. 8(b).

The IMG instrument utilizes a 30° off-axis Michelson interferometer with a maximum OPD of 10 cm and a spectral range of 660–3030 cm⁻¹. It is specifically designed for monitoring greenhouse gases, such as CH₄, H₂O, N₂O, CO₂, and O₃. On the other hand, the SITELLE instrument incorporates a 15.5° off-axis Michelson interferometer, covering a spectral range of 350–900 nm. Its primary application is the study of galaxy cluster radiation and the analysis of nebular jet models, including phenomena such as the double peaks of [OII] 3726, 29 in Orion and [NII] λ6584 in the M1-67 nebula star WR124, which exhibits an escape velocity of 190.0 ± 7.4 km/s.

The SRP of the FTS can be significantly enhanced through the incorporation of gratings, as demonstrated by the Imaging Fourier Transform Spectrometer working in the far UV (IFTSUV)⁵⁹ depicted in Fig. 9(a) and the Compact Ultrahigh-Spectral-Resolution Imaging Spectrometer (CUSRIS)⁶⁰ shown in Fig. 9(b).

The IFTSUV instrument replaces the beam splitter of the Michelson interferometer with two reflection diffraction gratings, each having a density of 3600 lines/mm. This modification enables the instrument to achieve a maximum OPD of 1.784 253 mm and over a spectral range of 80–145 nm. It achieves a high SRP of 24 000 and is primarily utilized for studying the solar dynamic evolution and characteristics by observing the Ly-α 121.567 nm line. On the other hand, the CUSRIS instrument replaces one of the mirrors in the Michelson interferometer with a Littrow structured grating consisting of 106 lines/mm. When combined with a Fabry–Pérot cavity, it achieves a maximum OPD of 12.5 mm and an ultra-high SRP of 1 000 000, equivalent to a standard Michelson interferometer with a maximum OPD of 100 cm.

The FTS based on a time-modulated Michelson interferometer can achieve a large OPD and high SRP by scanning the moving mirror. However, this scanning mechanism introduces complexity, instability, and maintenance requirements to the system. In contrast, a spatially modulated FTS eliminates the requirement of a scanning component, leading to improved reliability and ease of maintenance. Notable examples of spatially modulated FTS include the Stepped Mirror Fourier Transform Spectrometer (SM-FTS)⁶¹ shown in Fig. 10(a), the Ultra-High-Resolution Interferometric Spectrometer (UHRIS)⁶² shown in Fig. 10(b), and the Caméra Hyperspectrale de Démonstration (CaHyD)⁶³ shown in Fig. 10(c).

The SM-FTS replaces the two mirrors of the Michelson interferometer with two stepped mirrors. One mirror has 19 tall steps, while the other has 24 small steps. This configuration allows the SM-FTS to generate 456 OPD samples in space and achieve a maximum OPD of 6.3 cm. The resulting SRP is ∼65 000 at 6357 cm⁻¹, which is comparable to a time-modulated spectrometer. The SM-FTS is primarily used for detecting greenhouse gases in low-Earth orbit, ∼700 km above the Earth’s surface. Similarly, the UHRIS utilizes a static Michelson interferometer with two stepped mirrors. One mirror has 25 tall steps, and the other has 25 small steps. This setup enables the UHRIS to generate 625 OPD samples in space, with a maximum OPD of 10 cm. By combining with a scanning Fabry–Pérot interferometer (FPI) with specific parameters, such as a cavity length of 2.5 cm, a scanning step of 25 nm, and 50 scanning steps, the SRP can reach 1 000 000 at the center wavenumber of 4000 cm⁻¹. The CaHyD instrument is installed on a moving aircraft, such as a helicopter flying at an altitude of 2240 m and a velocity of 25 m/s. It achieves OPD scanning by continuous acquiring ground scene images through three sine filters with different periods, resulting in three distinct OPD signals. The CaHyD instrument achieves an OPD range of −20 to 40 µm and a spectral resolution of 250 cm⁻¹. Its purpose is to detect the vertical atmospheric spectrum along a 2 km transmission path.

The spatially modulated Michelson interferometer can be implemented using various components, such as a single mirror, a Wollaston prism, or a liquid crystal. In this configuration, the incident light is divided into two spatially separated beams that overlap and interfere on the detector. The OPD in this setup varies linearly with the deflection distance of the beams. Notable examples of spatially modulated Michelson interferometers include the Single-Mirror Fourier Transform Infrared Spectrometer (SM-FTIR)^64,65 shown in Fig. 11(a), the Wollaston Prism Fourier Transform Spectrometer (WP-FTS)^66,67 shown in Fig. 11(b), the Time Division Fourier Transform Imaging Spectropolarimeter (TD-ISP),⁶⁸ and the Birefringent Liquid Crystal Fourier Transform Spectrometer (BLC-FTS)⁶⁹ shown in Fig. 11(c).

The Michelson interferometer suffers from a loss of half the light throughput and high incoherent intensity. In contrast, the Mach–Zehnder interferometer (MZI)⁷⁰ exhibits a lower incoherent intensity (A) and utilizes nearly all of the light throughput, resulting in a significantly enhanced signal-to-noise ratio (SNR). This characteristic makes it particularly advantageous for satellite remote sensing applications. An example is the Mach–Zehnder Fourier Transform Spectrometer (MZFTS)^73,74 installed on the James Clark Maxwell Telescope (JCMT), as depicted in Fig. 12(a). The MZFTS utilizes two beam splitters to enable optical double input and double output. It operates in the submillimeter spectral range at wavelengths of 350, 450, 750, and 850 µm. With a maximum OPD of 1.2 m, it achieves a spectral resolution of 0.005 cm⁻¹ or 150 MHz. The MZFTS is employed for studying planetary atmospheres, molecular clouds, and extragalactic sources. Another example is the On-Chip Fourier transform Spectrometer (OCFTS)⁷⁵ depicted in Fig. 12(b), which utilizes TE-mode rectangular silicon-on-insulator (SOI) waveguides and employs digital microfluidic technology. By gradually introducing silicone oil into a 3 m hollow sensing arm to scan the OPD, it achieves a maximum OPD of 0.57 mm and a spectral resolution of 3.1 nm in the spectral range of 1.5–1.7 µm.

The Sagnac interferometer is a transverse shearing interferometer characterized by its triangular common optical path structure. An example of this is the Sagnac Interferometer Fourier Transform Spectrometer (SIFTS),⁷⁸ as depicted in Fig. 13(a). It splits the incoming light into two beams that are spatially misaligned. The separation distance, denoted as l, is related to the displacement, a, of mirror 2, with $l=2a$⁠. Consequently, the two beams overlap and interfere on the detector, forming an interference pattern with an increasing OPD from the center to both sides. With a maximum OPD of 8 mm, the SIFTS achieves a spectral resolution of 238 cm⁻¹ at a wavenumber of 6451 cm⁻¹. Signal padding can extend the spectral range up to 27 cm⁻¹.

The Sagnac interferometric spectrometer (SIS) with a compact half-pentaprism structure is particularly well-suited for aerospace and harsh mechanical environments. An example of this is the China’s Chang’e−1 Lunar Exploration Sagnac Fourier Transform Spectrometer (CE1-SFTS),^79–81 presented in Fig. 13(b). The CE1-SFTS has a maximum OPD of 15.37 µm, corresponding to a spectral resolution of 325.25 cm⁻¹ in the spectral range of 0.48–0.96 µm, utilizing 32 channels. This spectrometer is employed for studying the chemical composition and mineral distribution of the lunar surface. Similarly, the Ultraviolet Sagnac Fourier Transform Spectrometer (UV-SFTS),⁸² which shares a similar structure with the CE1-SFTS, achieves a maximum OPD of 64 µm. This corresponds to a spectral resolution of 78.125 cm⁻¹ in the UV band ranging from 250 to 400 nm. The UV-SFTS is particularly significant due to the numerous challenges involved in developing an ultraviolet imaging spectrometer, including low incident power, large chromatic aberration, and relatively low quantum efficiency of imaging sensors in the UV band.

Furthermore, the Sagnac Fourier Spectrometer (SAFOS)⁸³ incorporates a transmission grating with a groove density of 1200 lines/mm into the Sagnac optical path, as illustrated in Fig. 13(d). This configuration forms a spatial heterodyne spectrometer (SHS). The diffraction beam of the grating at a specific diffraction order β generates a small angle divergent beam, with its optical axis positioned at the center of the diffraction wavelength λ₀. The angular dispersion can be expressed as Δβ/Δλ = g/cos β, where g represents the groove density. By scanning a wide range of input angles α, it obtains a series of interferograms with an angle accuracy better than 0.01°. The SRP can reach 40 000 in the spectral range of 230–530 nm.

The spectrometers commonly utilize three types of tunable filters: Fabry–Pérot (F–P), acousto-optic, and liquid crystal tunable filters.

A single high-finesse F–P étalon with a small FSR can achieve high spectral resolution or a small FWHM. However, it requires a filter with a bandwidth of FSR/2 to separate specific interference orders, which can be challenging. Additionally, the transmissivity of a single F–P étalon is influenced by the reflectivity and cavity absorption, leading to the need for low finesse to achieve a large optical throughput. By combining two or more F–P étalons, the finesse requirement of each étalon can be reduced, resulting in improved effective FSR, spectral purity, out-of-band suppression performance, and optical throughput of the system.⁸⁵ Two notable examples utilizing this approach are the GREGOR Fabry–Pérot Interferometer (GFPI)^86,87 on the German 1.5 m Gregor solar telescope [Fig. 14(a)] and the Visible Light Tunable Filter (VTF)⁸⁸ on the DKIST [Fig. 14(b)].

The GFPI utilizes two cascaded F–P étalons with cavity lengths of 1.1 and 1.4 mm. These configurations achieve FWHM values of 3.43 and 2.73 pm, respectively, at a wavelength of 617 nm. The corresponding FSR values are 0.158 and 0.126 nm, resulting in a combined FWHM of 1.95 pm. The fineness of the system is 46, and the two cavities can change synchronously. The GFPI has a spectral range of 530–860 nm, offering a theoretical SRP of ∼250 000. The GFPI is utilized to study the dynamic evolution process of the solar atmosphere and magnetic field. Similarly, the VTF also employs a dual F–P étalon structure. It achieves a FWHM of 6–8 pm, with a specific value of 6 pm at 600 nm. The spectral range of the VTF spans from 520 to 870 nm. This instrument is used for studying the structure and dynamics of the Sun and its atmosphere.

The standard F–P interferometer (FPI) typically exhibits a low spectral contrast of less than 10³ due to uneven field amplitudes on multiple interference paths. These amplitudes are associated with the transmission intensity distribution, which is described by the Airy function in the far-field interference pattern. The low spectral contrast reduces fringe visibility and significantly limits the detection sensitivity of weak signals. To overcome this issue, the Single-Pass Fabry–Pérot Spectrometer (SPFPS)^89,90 [Fig. 14(c)] employs a spatial light modulator (SLM) to equalize the output field of the virtual imaging phased array (VIPA) using a semi-Gaussian distribution intensity mask. The VIPA has a FSR of 30 GHz or 1 cm⁻¹, a fineness of 40, and an optical throughput larger than 50%. This configuration significantly improves the spectral contrast by a factor of 1000 times, allowing for a spectral resolution of 0.08 cm⁻¹ or 800 MHz with an SRP of 800 000.

Compared to prism and grating-based spectrometers, the AOTF offers advantages such as a smaller volume, lighter weight, tunable wavelength, larger aperture, faster scanning speed, and higher diffraction efficiency. These characteristics make it particularly well-suited for astronomical and aerospace applications. For instance, the China’s Chang’e−3, 4, 5 AOTF (CE3, 4, 5-AOTF)^92–94 [Fig. 15(a)] spectrometers, the Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Venus (SPICAV)^95,96 on the Venus Express (VEX) orbiter [Fig. 15(b)], and the ACS-NIR²⁷ [Fig. 15(c)] employ AOTFs in their setups.

The CE4-AOTF, designed for lunar exploration missions, is equipped with two AOTFs featuring ultrasonic driving frequencies of 71.2–178.7 and 42–118.8 MHz, respectively. This configuration enables the CE4-AOTF to cover a spectral range of 450–950 and 900–2400 nm, with corresponding FWHM values of 2.8–6.4 and 4.2–9.6 nm, respectively. The SPICAV instrument utilizes two AOTFs with ultrasonic driving frequencies of 140–250 and 80–140 MHz, respectively. Its spectral range spans from 0.65 to 1.05 µm and 1.05–1.7 µm, with spectral resolutions of 7.8 and 5.2 cm⁻¹, respectively. The SPICAV instrument is primarily employed for observing Venus’s atmosphere, studying various components, such as H₂O, HDO, CO₂, and aerosols, through solar occultation, nadir, and limb observation modes. In the ACS-NIR instrument, an AOTF is employed to select the diffraction orders of the echelle grating, which has a blazed angle of 70° (R3), a groove density of 24.3 lines/mm, an effective area of 46 × 102 mm², and a diffraction order range of 48–105. The ultrasonic driving frequency in this instrument ranges from 64 to 156 MHz, while the spectral range covers 0.73–1.6 µm. The SRP achieved by the ACS-NIR ranges from 20 000 to 27 000.

W_λ represents the optical response bandwidth, μ_m is an initial integer guess determined by the transmission function and sparse representation, and Δλ_m is the spectral interval. The LCPS system covers a spectral range of 500–700 nm, with a FWHM of 0.2 nm at the wavelength of 650 nm. It has the capability to reconstruct any complex spectrum using an adaptive sparse dictionary, eliminating the need for a filter array.

In addition to the aforementioned conventional tunable filter-based spectrometers, a new on-chip thermally tunable spectrometer (TTS)⁹⁹ has been developed. The TTS relies on a thermally tunable ultra-high-Q resonator (precision filter) and a wideband resonator array (coarse filters) connected in cascade across N channels. This compact device, with a size of 0.35 mm², offers an ultra-high spectral resolution of 5 pm over a spectral range of 1545.8–1555.5 nm.

The reconstructive spectrometer utilizes reconstructive algorithms to map the incident spectrum either in the spatial or temporal domains to the intensity matrix of the detector array, similar to tomography techniques. There are two types of reconstructive spectrometers: spatial-domain and time-domain.² The spatial-domain reconstructive spectrometer consists of the spatial-domain spectral response (SDSR) reconstructive spectrometer and the spatial-domain spectral-to-spatial mapping (SDSM) reconstructive spectrometer. The time-domain reconstructive spectrometer includes the time-domain spectral response (TDSR) reconstructive spectrometer and the time-domain spectral-to-spatial mapping (TDSM) reconstructive spectrometer.

An example of the SDSR reconstructive spectrometers is the Single Nanowire Spectrometer (SNS),¹⁰⁰ as depicted in Fig. 17(a). It consists of a parallel In/Au electrode array on compositionally graded semiconductor CdS_xSe_1−x nanowires. Each adjacent pair of electrodes forms a photodetector with a distinct spectral response, resulting in the generation of 38 equations. The target spectrum is fitted using the adaptive Tikhonov regularization algorithm, also known as the restricted least squares method. The SNS covers a spectral range of 500–630 nm with a spectral resolution of 15 nm at a wavelength of 570 nm. Another example of the SDSR reconstructive spectrometer is a compressively strained InGaN/GaN multiple quantum well hetero-structure (MQWH),¹⁰¹ as shown in Fig. 17(b). It utilizes the built-in GaN pn junction to detect photocurrents and reconstructs the spectrum using a non-negative least-squares (NNLS) algorithm with total-variation regularization and an appropriate kernel function. The MQWH spectrometer covers a spectral range of 400–645 nm with a wavelength accuracy of 4–6 nm.

The SDSR reconstructive spectrometer typically employs a micro-structured spatial array filter to achieve different spectral responses. For instance, a photonic crystal slab (PC-slab) is integrated on top of a CMOS sensor array,¹⁰² as illustrated in Fig. 17(c). It contains a random basis of a 6 × 6 different pattern structures to generate distinct spectral responsivities. The incident spectrum can be reconstructed using least-square and compressive sensing methods. This spectrometer covers a spectral range of 550–750 nm with a resolution of ∼1 nm. Another spatial spectral filter array used is the F–P micro-cavities (FPMCs)¹⁰³ integrated onto an InGaAs detector chip, as shown in Fig. 17(d). Different cavity thicknesses correspond to different spectral responses. A compressed sensing-based accelerated proximal gradient (APG) algorithm is employed to reconstruct the spectrum. This spectrometer covers a spectral range of 900–1700 nm with a spectral resolution of 2 nm for a 50 pixel set. The photon counting reconstructive spectrometer (PCRS)¹⁰⁴ utilizes metasurfaces and superconducting nanowire single-photon detectors (SNSPD) and is fabricated on a silicon-on-insulator substrate. The PCRS can reconstruct the spectrum of mono-color light with a resolution of 2 nm in the wavelength range of 1500–1600 nm, with a detection efficiency of 1.4%–3.2%. Other similar spatial spectral filters include a 2D thin-film filter array,¹⁰⁵ étalon array,¹⁰⁶ quantum dot filters,^107,108 etc.

The SDSM reconstructive spectrometer utilizes different methods and random media to achieve spectral reconstruction. One example of such random media is the fiber-coupled integrating sphere (FCIS),^109,110 as illustrated in Fig. 18(a). The FCIS acts as an interferometer with a long OPD of several meters, producing wavelength-dependent speckle patterns that are captured by a camera. To calibrate the speckle wavemeter, an F–P interferometer (REF) is employed, and the transmission matrix method (TMM) is used for spectrum reconstruction. This spectrometer offers an ultra-high spectral resolution of 0.3 fm at a wavelength of 780 nm and covers a spectral range of 488–1064 nm. Another example of the SDSM reconstructive spectrometer is the Multiple Scattering Chip Spectrometer (MSCS)¹¹¹ depicted in Fig. 18(b). It utilizes a photonic crystal lattice with random air holes as the random medium. The random medium induces light scattering, which is detected by an annular detector array to obtain the intensity distribution. A matrix equation, I = TS, is employed for spectrum reconstruction. Nonlinear optimization techniques are applied to minimize $I−TS2$⁠. The MSCS covers a spectral range of 1250–1750 nm with a spectral resolution of 0.75 nm at a wavelength of 1500 nm.

The Micro-taper leaky-mode spectrometer (MTLMS)¹¹² is another variation, which employs a fiber taper tip to generate intricate leaky mode patterns within a 1 mm length. These patterns exhibit a distinct association with wavelengths and can effectively operate in the spectral range of 450–1000 nm. The MTLMS achieves an ultra-high spectral resolution of ∼1 pm. To analyzing the complex frames captured by the CMOS image sensor (CIS) and associate light pattern images with wavelength information, a combination of convolutional neural networks (CNNs) and a lightweight vision transformer (ViT) network is employed in the MTLMS.

The time-domain spectral response (TDSR) reconstructive spectrometer provides a simpler, more affordable, and faster alternative to spatial-domain reconstructive spectrometers. It only requires a single detector and a tunable filter to obtain a complete set of spectral response functions. One example of a tunable filter used in TDSR spectrometers is the black phosphorus (BP),¹¹³ as depicted in Fig. 19(a). BP is a dark gray layered material, and its responsivity function $RD,λ$ or matrix R_D,λ $D1∼Dn,λ1∼λn$ at each wavelength λ_i is related to the electric displacement (D) of the BP. By using a response vector I = RS, the unknown incident spectrum (S) can be reconstructed by solving the matrix equation. The BP spectrometer (BPS) covers a spectral range of 2–9 µm with a FWHM of 90 nm and utilizes 81 photocurrent sampling points. Remarkably, the BPS is the world’s smallest spectrometer, with an active area footprint of only 9 × 16 µm². Another example of a tunable filter used in TDSR spectrometers is a single MoS₂/WSe₂ van der Waals junction (VDWJ)¹¹⁴ shown in Fig. 19(b). The VDWJ exhibits an electrically tunable transport-mediated spectral response, where different gate voltages correspond to different photo-responses of the van der Waals junction. Its spectral range spans from 405 to 845 nm with a spectral resolution of 3 nm and a peak wavelength accuracy of 0.36 nm.

By including the interference signals at all wavelengths and positions, a transmission matrix can be obtained, and the spectrum can be reconstructed by solving the transmission matrix Eq. (24). This TDSM reconstructive spectrometer operates within the optical communication band of 1540–1565 nm, offering an ultra-high spectral resolution of 0.4 fm, corresponding to a 2 µs probe pulse. It can resolve dynamic multi-wavelength signals with a time resolution of 25 µs.

All spectrometers can be considered as generalized reconstructive spectrometers (GRS), as depicted in Fig. 20. They operate in a manner similar to a tomography system.¹¹⁷ The GRS comprises two main procedures: the forward procedure for spectral mapping and the backward procedure for spectral reconstruction. In the forward procedure, the spectral mapping structure is constructed according to specific requirements. A calibrated or tunable narrowband light source is used to determine the transformation characteristics for each wavelength, resulting in the acquisition of a reference intensity matrix. Subsequently, the system measures the light source with an unknown spectrum, capturing the intensity matrix. In the backward procedure, the spectral reconstruction algorithm is employed to reconstruct the unknown spectrum based on the acquired intensity matrix.

The optical spectrum analyzer or spectrometer establishes a mapping relationship between the spectrum of the light source and the intensity measured by the detector. This mapping enables the analysis and characterization of the spectral content of the light source.

The prism or grating spectrometer projects the incident slit onto a detector array, where each position corresponds to a different wavelength, as illustrated in Fig. 21(a). Within the spectral resolution, this mapping follows a spatial-domain one-to-one mapping (SDOM), also known as bijection. On the other hand, the Fabry–Pérot, acousto-optic, or liquid crystal tunable filter spectrometers sequentially image each wavelength signal onto the detector array, exhibiting a time-domain one-to-one mapping (TDOM), as depicted in Fig. 21(b).

The Michelson or Mach–Zehnder interferometer Fourier transform spectrometer (FTS) generates varying optical path differences (OPDs) by scanning the moving mirror. Each OPD signal encompasses the entire wavelength information of the spectrum and is projected onto the detector array, as shown in Fig. 22(a). Consequently, it exhibits a time-domain holo-morphism mapping (TDHM). Additionally, spatial Fourier transform spectrometers can be constructed using Michelson, Mach–Zehnder, or Sagnac interferometers, along with Wollaston prisms and liquid crystals. These spectrometers project the two-beam interference signals onto the detector array, with the OPDs linearly changing along the interferogram. Each OPD contains the complete spectrum of wavelengths. Hence, within the spectral resolution, they fall under the spatial-domain holo-morphism mapping (SDHP), as shown in Fig. 22(b).

The spatial-domain reconstructive spectrometer transforms the incident spectrum into a spatial spectral distribution intensity matrix by utilizing a microstructure spatial spectral filter array or a detector array. Each unit of the detector array exhibits unique spectral responses, thereby falling under the spatial-domain holo-morphism mapping (SDHM), as depicted in Fig. 23(a).

The time-domain spectral-to-spatial mapping (TDSM) reconstructive spectrometer converts the incident spectrum into a wavelength-dependent temporal Rayleigh speckle intensity matrix by utilizing an AOM or an EOM for frequency scanning, as illustrated in Fig. 23(b). On the other hand, the time-domain spectral response (TDSR) reconstructive spectrometer transforms the incident spectrum into a wavelength-dependent intensity matrix using an electrically tunable spectral micro-responder, such as black phosphorus and van der Waals junction, as shown in Fig. 23(c). Therefore, both TDSR and TDSM reconstructive spectrometers fall under the time-domain holo-morphism mapping (TDHM).

The prism, grating, or tunable filter spectrometer operates based on a one-to-one mapping structure. It is represented by a white transparent box, allowing for direct acquisition of the spectrum without intricate reconstruction processes. The Fourier transform spectrometer (FTS), on the other hand, follows a holo-morphism mapping structure. It is depicted as a semi-transparent box with a straightforward mathematical relation involving Fourier transforms, enabling spectrum reconstruction through a simple inverse Fourier transform operation. The reconstructive spectrometer also falls within the holo-morphism mapping structure, but it is more complex than the FTS and cannot be described by a simple theoretical formula. It is represented by a gray box and requires more intricate algorithms, such as the least square method and the transfer matrix method, for spectrum reconstruction.

While area-array micro-detectors, such as CCD and CMOS sensors, are commonly employed in spectrometers, it is important to note that not all spectrometers utilizing these detectors are considered imaging spectrometers. Prism and grating spectrometers capture the image of the incident slit on the detector, while Fourier transform spectrometers capture the interferogram. Reconstructive spectrometers, on the other hand, capture the complex spectral mapping signals on the detector. In all these cases, the area-array detectors are primarily used for receiving spectral mapping signals and facilitating spectral reconstruction, rather than traditional imaging purposes.

The imaging spectrometer^118,119 is capable of capturing a three-dimensional data cube comprising two spatial dimensions (x, y) and one spectral dimension (λ), as depicted in Fig. 24(a). As a result, it enables comprehensive observation of spatial, spectral, and radiometric information. Depending on the method used to acquire the data cube, imaging spectrometers can be categorized as whiskbroom type, pushbroom type, filter type, and snapshot type.

The whiskbroom imaging spectrometer (WIS) employs a linear-array detector to collect spectral data from a single ground pixel. By flying along the aircraft orbit and scanning across the orbit in a whiskbroom fashion, it is possible to obtain the two-dimensional spatial information, as illustrated in Fig. 24(b). The pushbroom imaging spectrometer (PIS) uses an area-array detector to capture ground image information. One dimension is dedicated to spatial imaging, while the other dimension is utilized for spectrum acquisition. Flying along the aircraft orbit allows for the acquisition of two-dimensional spatial information, as depicted in Fig. 24(c). The filter imaging spectrometer (FIS) relies on an area-array detector to directly obtain ground image information. By tuning the filter, spectrum information can be obtained, as shown in Fig. 24(a). The snapshot imaging spectrometer (SIS) is capable of directly capturing the three-dimensional data cube, as depicted in Fig. 24(a).

The WIS offers the advantage of a large field of view (FOV) and relatively simple calibration. However, it includes moving parts, which can introduce system instability and complexity. In comparison, the PIS does not require any moving parts, resulting in a simpler and more compact structure. It provides higher SNR, superior spatial resolution, and simpler image processing compared to the WIS. The PIS is widely employed in astronomy and remote sensing applications and can be implemented using prism, grating, and Fourier transform spectrometers, such as APEX, PRISMA, AHSI, CUSRIS, UV-SFTS, and CE1-SFTS. The FIS enables simultaneous acquisition of two-dimensional spatial images and one-dimensional spectral information. It can be realized using tunable filter spectrometers, such as GFPI and CE4-AOTF. The SIS enables non-scanning, single capture imaging without the need for post-processing. This can be achieved through reconstructive spectrometers, such as SNS, PC-slabs, FCIS, and VDWJ. The SIS can also be implemented using the principle of diffractive rotation¹²⁰ and encoding reconstruction.¹²¹ To achieve 4D snapshot hyperspectral imaging (3D space + spectrum), structural lighting and 3D point cloud reconstruction can be employed.⁹⁷ For 4D video snapshot spectral imaging (2D space + spectrum + time), a prism spectrometer with multi-field slits can be utilized.¹²² Furthermore, the advanced deep learning broadband encoding stochastic hyperspectral camera¹²³ leverages artificial intelligence techniques for filter design and spectrum reconstruction. This innovative enables significantly faster signal processing (7000–11 000 times faster) and ∼10 times improved noise tolerance.

The prism spectrometer projects the entrance slit onto the detector array, capturing the spectral information. However, its spectral range is limited by the dispersion characteristics of the prism materials. For instance, the SPS utilize a fused silica prism, offering a wide bandwidth of 0.25–2.5 µm, as shown in Table I. On the other hand, the BASS employs a NaCl prism to extend the spectrum up to 13.5 µm. It is uncommon to use a prism for mid-infrared spectrometers due to the decrease in angular dispersion and spectral resolving power (SRP) with increasing wavelength.

The spectral range of a grating is determined by the grating pitch and the blaze angle. As an example, the RGS utilizes a small blaze angle of 0.6989° and a blaze wavelength of 1.5 nm, enabling it to cover the x-ray band of 0.6–3.8 nm under grazing incidence. Similar to the prism, the grating is not commonly used for mid-infrared spectrometers. Although grating spectrometers have a small FSR, the spectral range can be expanded by scanning the incident slit. For instance, DKIST-CryoNIRSP operates in the diffraction order of 12–107, with an FSR of only tens of nm. However, it still achieves a wide spectral range of 530–4651 nm and a broad bandwidth of 4121 nm.

The Fourier transform spectrometer (FTS) offers a wide spectral range, known as the Fellgett advantage, limited only by the detector’s spectral response and the optical material’s performance. It is particularly suitable for mid-infrared wavebands that cannot be reached by prism and grating spectrometers. Examples of FTS applications in the mid-infrared range include ACE, METOP-IASI, ACS-TIRVIM, ADEOS-IMG, FY3D-HIRAS, and SM-FTIR. Furthermore, FTS can operate in the terahertz or submillimeter wavebands, as demonstrated by the JCMT-MZFTS, which employs a 0.3 K neutron transmutation-doped (NTD) bolometer to cover spectral bands at 350, 450, 750, and 850 µm. FTS can also be utilized in the remote ultraviolet waveband, such as the IFTSUV with a spectral range of 80–145 nm. Additionally, a larger maximum OPD corresponds to a wider bandwidth. For instance, the JCMT-MZFTS achieves a maximum OPD of 1.2 m, corresponding to a bandwidth of one hundred micrometers. In contrast, the CE-SFTS has an OPD of only 15.37 µm, resulting in a bandwidth of only a few hundred nanometers.

The F–P tunable filter spectrometer is commonly used in the visible spectral band, with examples such as TAURUS covering 430–570 nm, GFPI covering 530–860 nm, and DKIST-VTF covering 390–550 nm and 600–860 nm. The F–P étalon is typically tuned using a piezoelectric ceramic, and the tuning range determines the spectrometer’s bandwidth. For instance, TAURUS has an étalon tuning range of 2 µm, resulting in a bandwidth of only 140 nm. On the other hand, SPFPS utilizes a non-tunable VIPA, but it requires a single-longitudinal mode laser at 532 nm.

The spectral range of an acousto-optic tunable spectrometer is limited by the acousto-optic crystal TeO₂, which has a theoretical bandwidth of 0.35–5 µm. Examples include CE4-AOTF, SPICAVS, and ACS-NIR, which have spectral ranges of 450–2400 nm, 0.65–1.7 µm, and 0.73–1.6 µm, respectively. To achieve a wider spectral range, segmental ultrasonic tuning is often necessary, as implemented in the CE4-AOTF. It has an ultrasonic tuning range of 71.2–178.7 and 42–118.8 MHz, corresponding to spectral ranges of 450–950 and 900–2400 nm, with bandwidths of 500 and 1500 nm, respectively. Higher ultrasonic frequencies are required for longer operating wavelengths.

The spectral range of the liquid crystal tunable spectrometer (LCTS) is determined by the bandwidth of the liquid crystal utilized. Generally, the LCTS is designed to operate within the visible band. For instance, the LCPS covers a spectral range of 500–700 nm with a relatively narrow bandwidth of only 200 nm, as the tuning range of liquid crystal birefringence is limited in this particular case.

The spectral range of the reconstructive spectrometer depends on the specific material used. For example, the SNS has a spectral range of 500–630 nm, which is determined by the spectral response of the In/Au electrodes on the compositionally graded semiconducting CdS_xSe_1−x. The MQWH covers a spectral range of 400–645 nm, determined by the spectral response of the compressively strained InGaN/GaN multiple quantum well heterostructures. The PC-slabs operates within the spectral range of 550–750 nm, determined by the spectral response of the silicon-on-sapphire (SOS) substrate. The FPMCs has a spectral range of 900–1700 nm, determined by the spectral response of the monolithic integrated F–P cavity on an InGaAs detector chip. The FCIS covers a spectral range of 488–1064 nm, determined by the spectral response of the fiber-coupled integrating sphere. The MSCS operates within the spectral range of 1250–1750 nm, determined by the spectral response of the silicon-on-insulator (SOI) wafer material. The MTLMS covers a spectral range of 450–1000 nm, determined by the spectral responses of the multimode optical fiber and the CMOS detector utilized. The BPS has a spectral range of 2–9 µm, determined by the spectral response of black phosphorus. The VDWJ covers a spectral range of 405–845 nm, influenced by the wavelength-dependent absorption of MoS2 and WSe2 as well as the controllable charge carrier transport through the MoS2/WSe2 van der Waals junction interface. The CMTRS operates within the spectral range of 1520–1600 nm, determined by the spectral response of the optical fiber system.

The spectral resolution δλ or spectral resolving power (SRP), denoted by R = λ/δλ, determines the ability of a spectrometer to analyze spectra. The theoretical SRP of a prism spectrometer is limited by the size and nonlinear material dispersion of the prism. For instance, the APEX spectrometer utilizes CaF₂/ZnS and CaF₂/sapphire prisms, with maximum SRPs of 634 and 227, respectively. The material dispersion of the prism is typically negative, resulting in a larger SRP at lower wavelengths.

The Féry prism features curved surfaces that enable focusing and imaging. It exhibits a larger angular dispersion compared to a triangular prism. However, its radius of curvature (ROC) is typically small, resulting in smaller collimating lens f₁ and converging lens f₂ compared to an ordinary prism spectrometer. The small f₁ introduces limitations on slit diffraction, leading to reduced spectral resolution. Similarly, the small f₂ reduces the linear dispersion f₂dθ/dλ and, consequently, the spectral resolution. Moreover, the Féry prism has a smaller thickness and apex angle. Overall, considering these parameters, the Féry prism spectrometer achieves a larger or comparable SRP compared to a triangular prism spectrometer. For example, spectrometers such as SPS, BASS, TSIS-1-SIM, and SORCE-SIM employ Féry prisms, resulting in SRPs of ∼250, 100, 100, and 800, respectively. In contrast, th TSIS-1-HSRS utilizes a modified spectral ratio method to normalize solar line data with extremely high spectral resolution to the absolute irradiance scale of the TSIS-1-SIM and the CSIM, yielding an impressive SRP ranging from ∼202 000 to 273 000.

The SRP of a grating spectrometer is determined by the diffraction order (m) and the groove number (N) of the grating. However, the actual SRP is often lower than the theoretical value due to limitations imposed by the size of the clear aperture. Ordinary plane blazed gratings typically operate at m = 1 or 2 to avoid overlapping diffraction orders, which significantly restricts their SRP and applications. An important application that overcome these limitations is the RGS, which utilizes two grating arrays with a grating density of 645.6 lines/mm and a blazed angle of 0.6989° to achieve an SRP of 100–500.

In contrast, echelle gratings have a large blaze angle and divergence angle and can be fabricated on a larger surface area. This enables significant improvement in SRP through the use of high diffraction orders. For example, the G-GLEF employs an echelle grating with a groove density of 31.6 lines/mm and an area of 300 × 1200 mm², resulting in an SRP of 100 000. The ACS-MIR utilizes an echelle grating with a density of 3.03 lines/mm and dimensions of 107 × 240 mm², achieving an SRP of 30 000–50 000. The DKIST-CryoNIRSP employs an echelle grating with a width of 408 mm and operates at diffraction orders of 12–107, resulting in an impressive SRP of 116 275–132 500.

The volume holographic grating (VHG) is produced using holographic technology, but its diffraction efficiency tends to be low at high diffraction orders. Furthermore, the VHG has a smaller grating pitch compared to the echelle grating, leading to high-order dispersion interference. As a result, the VHG typically operates at the m = 1 diffraction order. However, the VHG offers advantages such as high groove density and a large surface area. Taking all these factors into account, the SRP of the VHG falls between that of an ordinary blazed grating and an echelle grating. For instance, the DESI utilizes a VHG with ∼1100 lines/mm to achieve an SRP of 1500–4000. Similarly, the Subaru-FOCAS employs a VHG measuring 110 × 106 mm², resulting in an SRP of 250–7000.

The flat-field concave grating functions similar to the Féry prism. For instance, in EUV applications, a concave grating with a groove density of 2400 lines/mm, a curvature radius of 235 mm, and an effective width of 46 mm is utilized, resulting in an SRP of 421.

The convex grating spectrometer utilizes the concentric three-reflection imaging system, such as the VIMS-V. The traditional Offner structure, which includes a large concave mirror, is employed, resulting in a decrease in the SRP. The VIMS-V incorporates a convex grating with a groove density of 27.661 lines/mm, achieving an SRP of 150–525. On the other hand, the GF-F-AHSI and EAS employ improved Offner structures that replace the large concave mirror with two small concave mirrors and introduce the Rowland circle configuration. As a result, their SRPs can reach 500 and 280, respectively.

The spectral resolution of the time-modulated Fourier transform spectrometer (FTS) is determined by the maximum OPD, which is dictated by the scanning range of the moving mirror. For instance, the METOP-IASI, ACS-TIRVIM, ADEOS-IMG, and FY3D-HIRAS are Michelson interferometer FTS systems with maximum OPDs of 2, 5, 10, and 0.2/0.4/0.8 cm, respectively. Their corresponding SRPs are ∼5400, 3333/45 385, 30 000, and 1800/1400/1000. On the other hand, the JCMT-MZFTS is a Mach–Zander interferometer FTS operating in the submillimeter waveband. It utilizes an OPD of 1.2 m, resulting in an SRP of 5700.

The spatially modulated FTS (SFTS) is a system that does not require a moving mirror. Instead, it projects the interference signals onto a detector array. The resulting interferogram contains an OPD distribution. Various implementations of SFTS, such as WP-FTS-SP, WP-FTS-NSP, TD-ISP, CaHyD, SM-FTIR, BLC-FTS, OCFTS, SIFTS, CE-SFTS, and UV-SFTS, achieve maximum OPDs of 19, 123, 30, 20, 810, 23.4 µm/210, 570, 1000, 15.37, and 23.44 µm, respectively. The corresponding maximum SRPs are 238, 257, 73, 100, 216, 60/633, 548, 208, 64, and 512, respectively. The relatively small maximum OPDs result in small SRPs for these systems. To enhance the SRP, the signal padding method can be used, where incoherent regions on the detector are filled with zeros. The technique is particularly effective for systems such as WP-FTS-SP, which achieves an SRP of 238 despite having an OPD of only 19 µm. This SRP is equivalent to the WP-FTS-NSP, which has no signal padding but a larger OPD of 123 µm. Another approach is the SM-FTS, which utilizes stepped mirrors to generate nearly 500 OPDs. The maximum OPD for this system is 6.3 cm, corresponding to an impressive SRP of 65 000. The Ma-PWS, on the other hand, employs 200 Mach–Zehnder waveguide arrays to form an interferometer. It achieves a maximum OPD of 7.3 cm and a corresponding SRP of 54 620.

The F–P tunable filter is known for its extremely narrow bandwidth, enabling spectrometers such as TAURUS, GFPI, DKIST-VTF, and SPFPS to achieve high SRPs. Specifically, these spectrometers have SRPs of 714 285, 250 000, 100 000, and 800 000, respectively. The bandwidth of the AOTF is limited by the ultrasonic frequency. The SRP of an AOTF is inversely proportional to the dispersion constant, the acousto-optic interaction length, and the central wavelength of the light. Consequently, the SRP of the VOTF is significantly lower than that of a tunable F–P filter spectrometer due to several limitations. For example, the CE4-AOTF and SPICAVS have SRPs of 250 and 326, respectively. Liquid crystal tunable spectrometers utilize the electronically induced birefringence of liquid crystals. The SRP of such a spectrometer is directly proportional to the maximum birefringence and the thickness of the liquid crystal. For instance, the LCPS utilizes a nematic liquid crystal with a thickness of 22 µm and a bandwidth filter with an FWHM of 9 nm. This configuration enables the LCPS to achieve an SRP of 3500.

The reconstructive spectrometer offers several advantages over traditional spectrometers as it is not limited by the size and clear aperture of optical elements. Additionally, it can achieve spectral resolutions equivalent to those of traditional spectrometers. The spectral resolution of a reconstructive spectrometer is primarily determined by the spectral interval of the spectral mapping intensity signals. For instance, the SNS has a spectral resolution of 15 nm at a wavelength of 570 nm, which is approximately equal to the spectral interval of the adjacent photodetector unit. The MQWH spectrometer achieves an SRP of 4–6 nm due to 16 different spectral encoders within a bandwidth of 245 nm, with each encoder covering about 15 nm. According to the Rayleigh criterion, the spectral interval is close to the spectral resolution. In the case of the PC-slabs, the spectral resolution is 1 nm due to 100 pixels with different spectral responses within a bandwidth of 200 nm. The FPMCs achieves a spectral resolution of 2 nm with 50 F–P microcavity pixels, corresponding to 400 InGaAs detectors with different spectral responses within an 800 nm bandwidth. The PCRS achieves a spectral resolution of 2 nm by utilizing 101 sample points within a bandwidth of 100 nm. The FCIS achieves a spectral resolution of 0.3 fm as the sparkle wavemeter can identify wavelength modulation with an amplitude of 0.3 fm. The MSCS has a spectral resolution of 0.75 nm, determined by the half-width at half-maximum (HWHM) of 0.6 nm, which depends on the required change in wavelength to generate an uncorrelated intensity distribution on the detectors. The BPS achieves a spectral resolution of 90 nm as the reconstructed laser spectrum has 81 photocurrent sampling points within a 3 µm bandwidth. The OTDR-RS achieves a spectral resolution of 0.4 fm, which is inversely proportional to the probe pulse width. With a probe pulse width of 2 µs, the spectral resolution increases 15 times to 0.4 fm using the correlation coefficient method. Finally, the CMTRS achieves a spectral resolution of 40 am, determined by the length of the single-mode fiber (SMF).

Furthermore, the SRP of a spectrometer can be significantly improved by incorporating gratings or F–P étalons. For instance, the MZ-SHS utilizes a diffraction grating instead of a mirror in the M–Z interferometer. With a maximum OPD of 1 cm, it achieves an impressive SRP of 34 705, surpassing that of a regular Mach–Zehnder spatially modulated spectrometer. The SAFOS system inserts a transmission grating into the Sagnac interferometer, reaching an SRP of 4000. The CUSRIS combines a tunable F–P interferometer and a spatially modulated static grating interferometer (SGI), resulting in an ultra-high SRP of 1 000 000. Similarly, the UHRIS combines a tunable F–P interferometer and a spatially modulated stepper mirror interferometer (SMI), achieving the same ultra-high SRP of 1 000 000. These systems are equivalent to a standard time-modulated Michelson interferometer with a maximum OPD of 100 cm. The ACS-NIR combines an AOTF with an echelle grating, resulting in an SRP of 27 000. In the case of the BLC-FTS, the insertion of an F–P cavity into the optical path increases the SRP from 73 to 633.

Generally, traditional spectrometers can be roughly ranked according to their SRPs from high to low as follows: F–P tunable filter, echelle grating, time-modulated Michelson interferometer, liquid crystal tunable filter, acousto-optic tunable filter, convex grating, concave grating, ordinary blazed grating, spatially modulated Fourier transform, and prism spectrometer. The SRPs of spectral response reconstructive spectrometers typically range from tens to hundreds, which is comparable to prism spectrometers, spatially modulated interferometric spectrometers, and convex grating spectrometers. However, reconstructive spectrometers are usually much smaller in size compared to traditional spectrometers. Spectral-to-spatial reconstructive spectrometers often achieve ultrahigh SRPs. For instance, the FCIS has an SRP of 2.6 × 10⁹, the OTDR-RS has an SRP of 3.875 × 10⁹, and the CMTRS has an SRP of 3.875 × 10¹⁰. These spectrometers employ wavelength-dependent speckle and wavelength modulation technologies with ultra-small amplitude. The MTLMS, based on microtaper leaky mode, achieves an SRP of over 450 000, comparable to that of an F–P tunable-based spectrometer or a time-spatially modulated Michelson interferometer, such as the CUSRIS and UHRIS. The MSCS, which is based on optical random scattering, achieves an SRP of 2000, comparable to an AOTF or liquid crystal tunable filter spectrometer.

Dispersive spectrometers operate by projecting the incident slit onto the spectral detection plane. The SRP increases with a narrower slit, but it results in a lower étendue. The étendue of a grating spectrometer can be approximated as Θ_G ≈ 0.81Al/Rf, where l represents the length of the incident slit, A is the cross-sectional area of the incident beam, f is the focal length of the collimating lens, and R is the SRP of the spectrometer. On the other hand, the FTS does not use a slit, allowing all light to pass through. This characteristic leads to high optical throughput, often referred to as the Jacquinot advantage. The étendue of an FTS can be expressed as Θ_FTS = 2πA/R. Consequently, we can derive that Θ_G/Θ_FTS ≈ l/10f, considering that l is typically much smaller than f. This demonstrates that the étendue of an FTS is significantly higher than that of prism and grating spectrometers. For instance, the étendue of the FPIS (Féry prism), VIMS-V (convex grating), and SM-FTIR (FTS) is ∼5.9 × 10⁻⁴ sr mm², 4.42 × 10⁻⁵ sr mm², and 0.26 sr mm², respectively.

The precise spectral calibration of a spectrometer is essential for determining the spectral response function (SRF) line shape of the instrument. The SRF line shape determines the central response wavelength and the spectral bandwidth (FWHM) of each detector pixel. Prism and grating spectrometers require high-resolution observations and polynomial fitting of multiple monochromatic light sources for wavelength calibration. In traditional spectrometers, spectral calibration primarily relies on line light sources, high-resolution monochromators, and tunable lasers. However, the characteristic spectral line method can only determine the position of the central wavelength and cannot measure the SRF line shape. Although the wavelength scanning method based on a monochromator or tunable laser can theoretically obtain fine SRF curves for all wavelengths, it is time-consuming and limited to selecting specific wavelengths for measurement.

The FTS benefits from the Connes natural frequency calibration, introduced by French physicist Connes. This approach utilizes monochromatic laser reference positioning technology to enable more accurate positioning of the OPD compared to traditional spectrometers. Various FTS systems leverage this advantage for improved performance:

The IFTSUV employs He–Ne laser interference signals to maintain alignment and sampling stability of the moving mirror, enabling fringe counting and precise OPD measurement. The ADEOS-IMG utilizes a highly stable He–Ne laser with a stability of 3 × 10⁷ to monitor scanning mirror displacement and determine the sampling interval for the interferogram. The JCMT-MZFTS relies on a He–Ne laser for OPD measurement and calibration. The METOP-IASI employs a laser stabilized at 1.54 µm on the acetylene gas absorption line to measure and calibrate the OPD. The ACS-TIRVIM uses a 760 nm DFB laser interference signal for accurate synchronization of interferogram sampling and spectral retrieval. The CFHT-SITELLE utilizes a high-stability 1550 nm laser, which is insensitive to the CCD detector, to continuously monitor and calibrate the OPD and mirror alignment. This allows for precise determination of reflector position and angle with an accuracy 1/1000 better than that achieved by laser interference fringes. The FY-3D-HIRAS employs a frequency-stabilized laser with a wavelength of 852.357 02 nm to sample the interferogram at equal intervals. The laser’s frequency is stabilized based on the gas battery absorption line of the instrument, achieving an accuracy of 0.515 ppm. The SM-FTS uses a 1573 nm tunable laser to monitor scanning mirror displacement, enabling accurate OPD measurement and interferogram sampling. By incorporating these laser-based calibration methods, FTS systems can achieve enhanced precision and accuracy in spectral measurements.

Spectrometers find a wide range of applications across various fields, but this paper focuses primarily on their applications in astronomy and remote sensing. These fields require spectrometers that can operate in harsh environments while considering factors such as cost, size, weight, and sensitivity of the collected signals. As a result, these spectrometers have strict requirements for performance parameters, including spectral range and resolution. The selected applications in this paper serve as suitable models for such spectrometers, demonstrating their capabilities in demanding scenarios.

Traditional triangular and Féry prisms continue to be extensively employed in astronomical observation projects. These prisms offer advantages such as high light transmittance, ease of adjustment, long-term stability, absence of spectral order overlap, and a large FSR. Consequently, they are well-suited for studying the Earth’s environment, the sun, and exoplanets, as demonstrated by projects such as APEX, PRISMA, CSIM, SORCE-SIM, TSIS-1-SIM, TSIS-1-HSRS, BASS, and NIHTS. In these cases, the requirements typically involve wide spectral ranges such as 250–2500 nm or 2.9–13.5 µm and low SRP such as 200. The prism spectrometer proves to be highly suitable for meeting these specifications.

The ordinary blazed grating (OBG) is currently rarely utilized due to its operation at low diffraction orders (m = 1 or 2) and low SRPs. However, in the field of astronomy, there is a remarkable application called the RGS, which employs 182 OBGs with a blaze angle of 0.6989°. This configuration allows the RGS to cover the extreme ultraviolet band spanning from 0.6 to 3.8 nm, which corresponds to the emission bands of K-shell (C, N, O, Ne, Me, and Si) and L-shell (Fe) transitions in galaxy clusters. This specific wavelength range proves to be challenging for prism spectrometers to effectively cover.

The echelle grating is characterized by a larger groove pitch, a larger blaze angle, higher angular dispersion, higher diffraction orders (m = 10–100), and a higher SRP compared to ordinary gratings. It finds frequent application in measuring stellar abundance, tracing gases, and observing solar spectral lines. Notable examples include the G-CLEF, ACS, and CryoNIRSP instruments. These applications demand a high SRP, typically ranging from 30 000 to 100 000. In such cases, prism and ordinary blazed grating spectrometers struggle to meet the required performance levels.

The volume holographic grating (VHG) is known for its exceptional manufacturing accuracy, high groove density, large area, high dispersion, and high SRP. However, its application is limited by high-order dispersion interference. In large-scale surveys such as DESI, the VGH’s high manufacturing accuracy and consistency in diffraction efficiency and wavefront errors are crucial. On the other hand, the VHG exhibits ideal diffraction efficiency for applications requiring higher dispersion, such as FOCAS.

The flat-field holographic concave grating combines the capabilities of diffraction and imaging, simplifying the structure of spectrometers. One notable example is the EUVS, an extreme ultraviolet spectrometer designed for high spectral resolution analysis of radiation from high-temperature fusion plasmas, including elements such as H, B, C, O, Fe, and W.

The convex grating with a concentric structure provides a simple and compact configuration, resulting in high-quality imaging, a high SNR, low spectral bending, and minimal optical aberrations. This grating type demonstrates exceptional capabilities in ground object detection and recognition, making it widely applicable in astronomy and hyperspectral remote sensing. Notable examples of its usage include Earth observation (e.g., AHSI), Saturn observation (e.g., VIMS-V), and asteroid body studies (e.g., AES).

The Fourier transform spectrometer (FTS) offers high light optical throughput as it does not have the limitations of a slit. This allows for multi-channel measurements, significantly enhancing the SNR. FTS systems are calibrated using narrow linewidth lasers, ensuring precise wavenumber accuracy. The spectral resolution can be improved by increasing the moving distance of the mirror, while the spectral range can extend into the far infrared. Consequently, the time-modulated FTS, based on the Michelson interferometer, has become a preferred choice for important astronomy and remote sensing applications, such as the ACS, SITELLE, and HIRAS. On the other hand, the spatial-modulated Michelson FTS is limited by its OPD and SRP, resulting in its infrequent usage in astronomy and remote sensing applications. However, the SM-FTS serves as a notable example that utilizes step mirrors to achieve a maximum OPD of 6.3 cm and an SRP of 65 000, which is comparable to that of a time-modulated FTS. Despite that the Mach–Zehnder interferometric spectrometer may not offer significant advantages over the Michelson interferometric spectrometer in the visible and infrared wavebands due to its complex structure, the MZFTS provides a notable alternative. The MZFTS is specifically designed as a dual-input dual-output M–Z spectrometer for the submillimeter band (350, 450, 750, and 850 µm). It achieves a maximum OPD of 1.2 m, which poses a challenge to achieve with a time-modulated Michelson FTS. The Sagnac interferometer, known for its compact half-pentaprism structure, is highly suitable for aerospace and harsh mechanical environments, such as the CE1-SFTS used in China’s first lunar exploration. However, its drawback lies in its relatively lower SRP.

The AOTF is characterized by its small volume, light weight, operational wavelength range, large aperture, fast scanning speed, and high diffraction efficiency. These features make it highly suitable for astronomy and remote sensing applications. For instance, the CE3, 4, 5-AOTF used in China’s subsequent lunar explorations (specifically, moon mineral exploration), the ACS (trace gas detection on Mars), and the SPICAV (Venusian atmosphere measurement) benefit from the AOTF’s capabilities. The F–P tunable filter spectrometer typically offers a very high SRP, making it indispensable for various astronomy and remote sensing applications. Instruments such as the VTF (scanning spectral lines of the solar atmosphere), GFPI (performing tasks similar to the VTF), and TAURUS (mapping velocity fields of astronomical emission-line sources) heavily rely on F–P tunable filters. On the other hand, liquid crystal tunable spectrometers have not yet seen similar significant applications in the field of astronomy and remote sensing.

In recent years, there have been significant advancements in miniaturizing reconstructive spectrometers, making them highly suitable for spectral applications in lab-on-chip systems. Although currently not utilized in astronomy and remote sensing, these compact devices hold great potential for future applications in these fields. Despite their small aperture and limited étendue, reconstructive spectrometers offer ultrahigh spectral resolution, making them an attractive choice. The combination of their small size and exceptional spectral resolution makes them promising candidates for future applications in astronomy and remote sensing.

This paper presents a comprehensive exploration of a wide range of spectrometers, including traditional spectrometers, such as prism, grating, Fourier transform, and tunable filter spectrometers, as well as reconstructive spectrometers, based on various optical spectrum analyzers. This Review carefully analyzes and compares important parameters, such as spectral range, spectral resolving power, spectral resolution, étendue, and calibration. It also constructs a generalized model for reconstructive spectrometers and provides a mathematical overview of the spectral mapping of these devices. Additionally, the study includes a discussion of hyperspectral imaging. The research emphasizes that traditional optical spectrum analyzers and spectrometers continue to play a crucial role in astronomy and remote sensing. Although the technologies employed in these traditional spectrometers are well-established, their structures can vary significantly depending on the specific applications. For example, gratings can be made from different materials, such as volume materials, optical fibers, films, waveguides, crystal lattices, and ultra-cold atoms, while still operating on the same diffraction principles. Similarly, other spectrum analyzers and spectrometers exhibit similar principles despite variations in their construction. In contrast, reconstructive spectrometers employ principles akin to tomography technology. They achieve a significant reduction in size without compromising spectral resolution, making them promising for future technological advancements particularly in chip-scale applications. Furthermore, spectral-to-spatial reconstructive spectrometers based on wavelength-dependent Rayleigh speckle and wavelength modulation technology can attain ultrahigh spectral resolutions on the femtometer or attometer scale. Although reconstructive spectrometers have not been widely adopted in astronomy and remote sensing thus far, their small size and ultrahigh spectral resolution make them highly anticipated for future applications. Spectral analysis remains a vital tool for understanding nature and the universe, and the spectrometers discussed in this paper are expected to serve as catalysts for future research, accommodating diverse imagination, requirements, and technical capabilities.

We express our gratitude to Professor Yanbiao Liao and Dr. Zongyin Yang for their valuable guidance and suggestions. This research received financial support from the Academy of Finland projects (Grant No. 336145) and (Grant No. 337656), the Key Laboratory of Space Active Opto-electronics Technology of the Chinese Academy of Sciences (Grant No. 2021ZDKF4), and the Shanghai Science and Technology Innovation Action Plan (Grant No. 22dz1201300).

The authors have no conflicts to disclose.

C. S. Yan: Conceptualization (lead); Investigation (lead); Methodology (lead); Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead). Y. W. Chen: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Supervision (equal); Writing – original draft (equal). H. M. Yang: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Supervision (equal); Writing – original draft (equal). E. Ahokas: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.