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Abstract
An ultra-wide-angle high-spatial-resolution high-spectral-resolution snapshot imaging spectrometer (UWA-2HSR-SIS) is presented, which comprises a microlens array (MLA), multiple fiber bundles, a micro-cylindrical-lens array (MCLA), a cylindrical lens, a static grating interferometer (SGI), and an area-array detector. The MLA is arranged in a circular arc of 120° or more. The MCLA is arranged in a straight line. The SGI includes a fixed reflection grating in Littrow configuration, a beam splitter, and a fixed plane mirror. Each fiber bundle containing multiple optical fibers is coupled to a separate microlens of the MLA, subdividing the field angle of each microlens into multiple smaller field angles. The light passing through each subdivided smaller field angle of each microlens of the MLA is received by a separate part of the detector. The UWA-2HSR-SIS is a new concept that not only obtains both high spatial resolution and high spectral resolution based on a single sensor for the first time, but also has an ultra-wide field angle in the horizontal plane, can obtain spectral information covering the full spectral range of interest in real time, and is very stable against various disturbances. The UWA-2HSR-SIS has great potential for remote sensing electro-optical reconnaissance sensors in the visible and near-infrared region.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Spectral resolution, spatial resolution, spectral range, field of view (FOV) and scanning speed are the key performance parameters of imaging spectrometers [1–10]. Since the birth of imaging spectrometers, for a single sensor, high spectral resolution and high spatial resolution have never been achieved at the same time. All existing high-spectral-resolution imaging spectrometers have only low spatial resolution. How to obtain both high spatial resolution and high spectral resolution based on a single sensor is still an unsolvable problem in practice.
In another aspect, an ultra-wide FOV is very important for wide-angle search requirements especially in surveillance and reconnaissance. At present, the ultra-wide FOV for optical sensors is realized by four methods: (1) a fisheye lens [11–14], a catadioptric panoramic lens [15–19], or both [20,21]; (2) Monocentric multiscale cameras [22–28], which separates a lens system into a single primary lens and multiple small-scale secondary lens arrays; (3) Artificial compound eyes [29–35]; (4) Panoramic monocentric fiber-coupled imagers [36–40], which combine a panoramic monocentric lens with fiber bundles. However, none of the four methods mentioned above can obtain high-resolution spectral information.
In yet another aspect, an ultra-fast scanning speed is very important for rapid detection requirements of remote sensing electro-optical reconnaissance sensors, especially for resolving the time evolution of flame, plume and flash source spectra. The scanning nature makes the scanning Michelson-type interferometers or scanning Fabry-Perot interferometers [41–49] unsuitable for measuring the spectra of flame, plume and flash sources (e.g., the flash from an explosion, the missile plume, or the plume of a rocket). For remote sensing electro-optical reconnaissance sensors, the most ideal situation is to be able to acquire target information in real time. Therefore, the ability to obtain spectral information covering the full spectral range of interest in real time is also very important for airborne or spaceborne imaging spectrometers used in reconnaissance.
In the last aspect, high stability, small volume, low mass and power are also very important for airborne or spaceborne electro-optical reconnaissance sensors. The static optical sensors without any moving parts are compact and very stable against a variety of disturbances [50–63]. Some static spectrometers can obtain high spectral resolution, but cannot obtain spatial information and cannot obtain ultra-wide FOV [50–56]. Some snapshot imaging spectrometers can obtain high spatial resolution, but cannot obtain high spectral resolution and cannot obtain ultra-wide FOV [57–60]. Some snapshot imaging spectrometers can obtain both high spatial resolution and ultra-wide FOV, but cannot obtain high spectral resolution. In short, none of the existing static imaging spectrometers can simultaneously achieve high spatial resolution, high spectral resolution and ultra-wide field of view.
In order to obtain both high spatial resolution and high spectral resolution, to meet both wide-angle search requirements and real-time detection requirements, and to have high stability and compact size, this paper proposes a compact ultra-wide-angle high-spatial-resolution high-spectral-resolution snapshot imaging spectrometer. Section 2 describes the principle and gives a first-order approximations of system performance. Section 3 shows the preliminary numerical simulations of two examples. The first example has a field angle of 120°, an angular resolution of 0.1°, and a spectral resolution of 0.2 cm−1 in the visible region. The second example has a field angle of 120°, an angular resolution of 0.08°, and a spectral resolution of 0.1 cm−1 in the near-infrared region. The last section gives the conclusion.
2. Principle
Figure 1 shows the optical layout of the compact ultra-wide-angle high-spatial-resolution high-spectral-resolution snapshot imaging spectrometer (UWA-2HSR-SIS), which consists of a microlens array (MLA), multiple fiber bundles, a micro-cylindrical-lens array (MCLA), a cylindrical lens, a static grating interferometer (SGI), a band-pass filter, and an area-array detector. The SGI comprises a beam splitter, a fixed reflection grating in Littrow configuration, and a fixed plane mirror. The SGI obtains the one-dimensional spatial distribution of the optical path difference in real time, namely, the SGI obtains the one-dimensional spatial sampling of the interferogram in real time. The MLA is arranged in a circular arc of 120° or more to obtain an ultra-wide field angle in the horizontal plane. The MCLA is arranged in a straight line. The MCLA and the cylindrical lens have a common front focal plane, that is, the front focal plane of the MCLA is coincident with the front focal plane of the cylindrical lens. In order to reduce reflection, the cylindrical lens is coated with anti-reflection coating.
Fig. 1. Optics of the compact ultra-wide-angle high-spatial-resolution high-spectral-resolution snapshot imaging spectrometer (UWA-2HSR-SIS): (a) Equivalent light path diagram in the horizontal plane and (b) Equivalent Sectional view in the vertical plane. BS: beam splitter.
Each fiber bundle containing multiple optical fibers is coupled to a separate microlens of the MLA, enabling the field angle of each microlens of the MLA to be subdivided into multiple smaller field angles to improve angular resolution (spatial resolution). Because the MCLA and the cylindrical lens have a common front focal plane, the other end of each optical fiber is simultaneously coupled to a separate micro-cylindrical lens of the MCLA and the cylindrical lens. That is, the light passing through each optical fiber is first collimated by a separate micro-cylindrical-lens of the MCLA into a separate parallel beam in the horizontal plane (it is a divergent beam in the vertical plane), and then collimated by the cylindrical lens into a separate parallel beam in the vertical plane. Consequently, the light passing through each optical fiber is collimated into a separate parallel beam (both in the horizontal plane and in the vertical plane) that is approximately perpendicular to the SGI and received by a separate part (i.e., a separate column or a separate three-consecutive-columns) of the area-array detector. Therefore, the light passing through each subdivided smaller field angle of each microlens of the MLA is collimated into a separate parallel beam (both in the horizontal plane and in the vertical plane) that is approximately perpendicular to the SGI and received by a separate part (i.e., a separate column or a separate three-consecutive-columns) of the area-array detector. Both the spatial information and spectral information of each subdivided smaller field angle of each microlens of the MLA are recorded in real time on a separate part (i.e., a separate column or a separate three-consecutive-columns) of the area-array detector.
Assuming that the rows of the area-array detector are parallel to the x-axis of the detector plane, the columns of the area-array detector are parallel to the y-axis of the detector plane, b is the pixel size of the area-array detector, ${f_1}$ is the focal length of each microlens of the MLA, ${f_2}$ is the focal length of each micro-cylindrical lens of the MCLA, ${f_3}$ is the focal length of the cylindrical lens, ${d_x}$ is the aperture size in the horizontal plane of each parallel beam obtained by collimating the light passing through each optical fiber, ${D_y}$ is the aperture size in the vertical plane of each parallel beam obtained by collimating the light passing through each optical fiber, ${\theta _o}$ is the angle of the cone of light emitted from each optical fiber, ${R_1}$ is the radius of the circlular arc of the MLA, and $\varphi$ is the field angle (in degree) of each microlens of the MLA.
The number of microlenses of the MLA is given by
The aperture size of each microlens of the MLA can be approximately calculated by
According to the characteristics of the cylindrical lens and the geometry shown in Fig. 1(b), it can be obtained that
and the aperture size in the vertical plane of each micro-cylindrical lens of the MCLA isThe number of pixels in each column of the area-array detector used to record the spectral image is given by
Figure 2 shows the schematic diagram of some components of the UWA-2HSR-SIS. Figure 2(a) shows the cross-sectional view of a single fiber bundle containing nineteen hexagonal optical fibers [64]. Figure 2(b) shows the equivalent schematic diagram of a single fiber bundle coupled with a microlens of the MLA and each optical fiber coupled with a separate micro-cylindrical lens of the MCLA. ${D_F}$ is the cross-sectional size of the core of a single optical fiber, ${D_{FB}}$ is the cross-sectional size of a single fiber bundle, and ${\theta _{in}}$ is the angle of the cone of light entering each optical fiber core.
Fig. 2. Schematic diagram of some components of the UWA-2HSR-SIS: (a) Cross-sectional view of a single fiber bundle containing nineteen hexagonal optical fibers, (b) Equivalent Schematic diagram of a single fiber bundle coupled with a microlens of the MLA and each optical fiber coupled with a separate micro-cylindrical lens of the MCLA, and (c) Equivalent Side view of the static grating interferometer (SGI).
Each fiber bundle contains nineteen (or more) hexagonal optical fibers, and one end of each fiber bundle is the heavily fused hexagonal cores as shown in Fig. 2(a) (the cladding thickness can be reduced to much less than 2.5 μm over the short fuse length [38]), which enables the field angle of each microlens of the MLA to be subdivided into nineteen (or more) smaller field angles to improve angular resolution. The curved fiber bundle as shown in Fig. 2(b) is used to obtain uniformly efficient coupling across the field of view of each microlens of the MLA [36], which makes ${\theta _{in}}$ of each optical fiber almost equal so that ${\theta _o}$ and ${d_x}$ of each optical fiber almost equal.
When each fiber bundle contains nineteen optical fibers as shown in Fig. 2(a), the angular resolution of the UWA-2HSR-SIS can be approximately calculated by
the number of micro-cylindrical lenses of the MCLA is given by the aperture size in the horizontal plane of each micro-cylindrical lens of the MCLA can be given by and the number of pixels in each row of the area-array detector used to record the spatial image can be given byThe value of ${\tau _1}$ should be considered in conjunction with the values of ${f_2}$ and ${\theta _o}$. Usually $1 \le {\tau _1} < 2$. When ${\tau _1} = 1$, we can choose ${\tau _2} = 1,\,{\tau _2} = 2$, or ${\tau _2} = 3$. When $1 < {\tau _1} < 2$, we can choose ${\tau _2} = 2$ or ${\tau _2} = 3$. The values of ${\tau _1}$ and ${\tau _2}$ can also be larger, but this will make the size and weight of the instrument larger.
According to the geometry shown in Fig. 2, the characteristics of the lens and the optical fiber, it can be obtained that
Figure 2(c) shows the equivalent side view of the static grating interferometer (SGI) of the UWA-2HSR-SIS. For the static stepped-mirror interferometer [50–52], the step height of the stepped mirror (staircase mirror) cannot be lower than 50 µm because of assembling constraints and limitations, so the sampling interval cannot be lower than 100 µm and the measurement spectral bandwidth cannot be greater than 50 cm−1 [52]. In order to solve the fabrication issues of the micro stepped mirrors, the SGI uses a fixed reflection grating in Littrow configuration instead of the stepped mirror, so the SGI can achieve an equivalent sampling interval lower than 100 µm. Therefore, the SGI can achieve a measurement spectral bandwidth greater than 50 cm−1.
Suppose that g is the groove spacing of grating, $\gamma$ is the groove angle of grating, S is the groove depth of grating, $S = g\sin \gamma$, and h is the equivalent step height. Assuming that a total of P grating grooves match a pixel width of the detector as shown in Fig. 2(c), where P is an integer, it can be obtained that
The optical path difference recorded by the $k\textrm{ - th}$ pixel in a column of the detector is given by
where i is the integer, and $i = 1,\textrm{ }\ldots ,\textrm{ }P$.For a single wavenumber $\sigma$ with input spectral intensity $B(\sigma )$, the spectral intensity received by each grating groove is ${{B(\sigma )} / {P{M_Y}}}$, and the recorded intensity on the $k\textrm{ - th}$ pixel in a column of the area-array detector is calculated by
The interferogram of the UWA-2HSR-SIS can be expressed as
The maximum optical path difference of the SGI is calculated by
In practice, the spectral resolution (in wavenumber) across the entire field of view of the UWA-2HSR-SIS can be calculated by
The resolving power of the UWA-2HSR-SIS can be written as
The actual number of sampling points for each interferogram produced by the SGI is given by
The equivalent sampling interval for each interferogram produced by the SGI is given by
According to the Nyquist-Shannon sampling criterion [65,66], for a spectral bandwidth $\Delta \sigma = {\sigma _{\max }} - {\sigma _{\min }}$, the sampling interval should satisfy $\chi \le {1 / {({2\Delta \sigma } )}}$, and so the measurement spectral bandwidth of the UWA-2HSR-SIS is given by
In practice, the field angle (e.g., 0.5°) of each microlens of the MLA is much smaller than the maximum angle of acceptance of each optical fiber, therefore, the influence of the slight deviation of the MLA in the processing of installation on spectral resolution can be ignored. According to the characteristics of the optical fiber and the cylindrical lens, for both spectral resolution and spatial resolution, the influence of the slight deviation in the vertical plane of the micro-cylindrical-lens of the MCLA in the processing of installation can be ignored. Assuming that the deviation angle in the horizontal plane of the micro-cylindrical-lens of the MCLA in the processing of installation is $\beta$, the interferogram of the UWA-2HSR-SIS can be expressed as
In theory, if the deviation angle in the horizontal plane of the micro-cylindrical-lens of the MCLA in the processing of installation is very small, its influence can be ignored by choosing the optical fiber with small numerical aperture and the micro-cylindrical-lens with short focal length.
In order to enable the light passing through each subdivided smaller field angle of each microlens of the MLA to be collimated into a separate parallel beam that does not affect each other, a practical method is that the light passing through each optical fiber is recorded by a separate three-consecutive-columns of the detector and let ${d_x} \le b$ based on Eq. (12). For this method, if $\beta = 0$, the light passing through each subdivided smaller field angle of each microlens of the MLA is only recorded by the middle column of a separate three-consecutive-columns of the detector. The disadvantage of this method is that it will increase the size of the UWA-2HSR-SIS in the horizontal plane.
The UWA-2HSR-SIS has the following features. First, and most importantly, the UWA-2HSR-SIS is the first time to achieve both high spatial resolution and high spectral resolution based on a single sensor. In one aspect, each fiber bundle containing nineteen (or more) optical fibers is coupled to a separate microlens of the MLA, subdividing the field angle of each microlens into nineteen (or more) smaller field angles, which enables the UWA-2HSR-SIS to achieve a high angular resolution of approximately ${\varphi / 5}$ (or more). In another aspect, the use of the SGI enables the UWA-2HSR-SIS to obtain high spectral resolution in the visible and near-infrared region.
Second, the UWA-2HSR-SIS has an ultra-wide field angle in the horizontal plane and can meet wide-angle search requirements, since the MLA is arranged in a circular arc of 120° or more in the horizontal plane.
Third, the UWA-2HSR-SIS can obtain spectral information covering the full spectral range of interest in real time, so the UWA-2HSR-SIS can meet real-time detection requirements.
Fourth, the lack of any moving parts makes the UWA-2HSR-SIS very stable against a variety of disturbances.
Fifth, the UWA-2HSR-SIS can obtain high-resolution two-dimensional spatial information in real time: the first-dimensional spatial information has an ultra-wide field angle of 120° or more in the horizontal plane, the other-dimensional spatial information has a small field angle of $\varphi$ (e.g., 0.5° or 0.4°) in the vertical plane, and the angular resolution across the entire field of view of the UWA-2HSR-SIS is approximately ${\varphi / 5}$ (e.g., 0.1° or 0.08°) or more.
Sixth, the unique design of the optics makes the UWA-2HSR-SIS capable of achieving nearly uniform spectral resolution across the entire field of view.
Some limitations and shortcomings of the UWA-2HSR-SIS are described as following. First, the use of a large number of microlenses, fiber bundles and micro-cylindrical-lenses will increase the complexity of the system, the difficulty of manufacturability, system integration and calibration. Reliable and repeatable manufacturability of the curved fiber bundles (see Fig. 2(b)) with axes of the fibers perpendicular to image surface of the forward looking optical system constitutes major difficulty. Nevertheless, because the field angle (e.g., 0.5°) of each microlens of the MLA is much smaller than the maximum angle of acceptance of each optical fiber, in practice we can use the straight fiber bundle instead of the curved fiber bundle as shown in Fig. 2(b). The cost of the UWA-2HSR-SIS will be higher as compared to existing snapshot imaging spectrometers. With the development of ultra-precision manufacturing and assembly technologies, the difficulty of manufacturing and assembly of the UWA-2HSR-SIS will continue to decrease in the future, and the cost will continue to reduce in the future.
Second, because the cladding of the optical fiber has a certain thickness, the field of view is not completely continuous. However, the cladding thickness can be reduced to much less than 2.5 μm over the short fuse length [38], and the field angle of each microlens of the MLA is usually small and subdivided into multiple smaller field angles, so the field of view coverage is still enough to obtain high spatial resolution. If each fiber bundle contains nineteen optical fibers as shown in Fig. 2(a), the field of view coverage can be approximately calculated by ${{\left[ {{f_1}\tan \left( {\frac{\varphi }{2}} \right) - 2{r_C}} \right]} / {\left[ {{f_1}\tan \left( {\frac{\varphi }{2}} \right)} \right]}} = 1 - {{2{r_C}} / {\left[ {{f_1}\tan \left( {\frac{\varphi }{2}} \right)} \right]}}$ or $\frac{{5{D_F}}}{{{D_{FB}}}} = \frac{{5{D_F}}}{{5{D_F} + 4{r_C}}}$.
Third, the spectral range of the UWA-2HSR-SIS is still narrow. According to Eq. (24), the smaller the groove angle of grating, the larger the spectral bandwidth of the UWA-2HSR-SIS; the smaller the pixel size of the detector, the larger the spectral bandwidth of the UWA-2HSR-SIS.
Compared with all existing ultra-wide-angle optical systems (e.g., the systems mentioned in the second paragraph of the introduction in this paper), for remote sensing electro-optical reconnaissance sensors, the UWA-2HSR-SIS can obtain both high spatial resolution and high spectral resolution for the first time.
Compared with all existing high-spectral-resolution imaging spectrometers that use either a scanning Michelson-type interferometer, a scanning Fabry-Perot interferometer, or both, for remote sensing electro-optical reconnaissance sensors, the UWA-2HSR-SIS will have the following advantages: (1) the UWA-2HSR-SIS can simultaneously obtain high spatial resolution, high spectral resolution and ultra-wide field angle of 120° or more in the horizontal plane; (2) the UWA-2HSR-SIS can obtain spectral information covering the full spectral range of interest in real time; (3) the UWA-2HSR-SIS has no moving parts and is very stable against a variety of disturbances.
Compared with all existing snapshot imaging spectrometers used as remote sensing electro-optical reconnaissance sensors, the most important advantage of the UWA-2HSR-SIS is that the UWA-2HSR-SIS can simultaneously obtain high spatial resolution, high spectral resolution and ultra-wide field angle (e.g., 120° or more) in the horizontal plane.
3. Preliminary numerical simulation with two examples
3.1. First example in the visible region
Suppose that a source spectra has a central wavenumber 20000 cm−1 (wavelength 500 nm) and a spectral bandwidth $\Delta \sigma = 120\textrm{ c}{\textrm{m}^{ - 1}}$, i.e., a wavenumber range from 19940 cm−1 to 20060 cm−1, the desired field angle is 120°, the desired angular resolution is 0.1°, and the desired spectral resolution is 0.2 cm−1.
According to Eq. (24), the equivalent sampling interval for each interferogram produced by the SGI should be $\chi \le {1 / {({2 \times 120\textrm{c}{\textrm{m}^{ - 1}}} )}} \approx 41.6\mu m$. Based on Eq. (23), the equivalent step height should be $h \le {{41.6\mu m} / 2} = 20.8\mu m$. Let the pixel size of the detector be $b = 2\textrm{0 }\mathrm{\mu}\textrm{m}$, and let the groove angle of grating be $\gamma = 45^\circ$, from Eq. (15), the equivalent step height is $h = 20\mu m \times \tan 45^\circ{=} 20\mu m$. Let a total of $P = 3$ grating grooves match a pixel width of the detector, from Eq. (14), the groove spacing of grating is $g = {b / {({P\cos \gamma } )}} = {{20\mu m} / {({3 \times \cos 45^\circ } )}} \approx 9.4281\mu m$. Thus, we can choose a reflection grating with 106 grooves/mm. Based on Eq. (20), the maximum optical path difference of the SGI is ${x_{\max }} = {1 / {({0.2\textrm{c}{\textrm{m}^{ - 1}}} )}} = 5\textrm{ cm}$, and the number of pixels in each column of the detector used to record the spectral image is ${M_Y} = {1 / {({2 \times 20\mu m \times 0.2c{m^{ - 1}}} )}} = 1250$. Based on Eq. (22), the actual number of sampling points for each interferogram produced by the SGI is $K = 1250$. According to Eq. (5), the focal length of the cylindrical lens is ${f_3} = {{{M_Y} \times b} / {({2 \times \tan ({{{{\theta_o}} / 2}} )} )}} = {{1250 \times 2\textrm{0}\mathrm{\mu}\textrm{m}} / {({2 \times 0.1} )}} = 125\textrm{ mm}$.
Assuming that the field angle of each microlens of the MLA is $\varphi = 0.5^\circ$, the radius of the semicircle of the MLA is ${R_1} = 35\textrm{ mm}$, and each fiber bundle contains nineteen hexagonal optical fibers. The number of microlenses of the MLA is $Q = {{120^\circ } / {0.5^\circ }} = 240$. From Eq. (2), the aperture size of each microlens of the MLA can be ${D_1} = \textrm{300 }\mathrm{\mu}\textrm{m}$. From Eq. (7), the number of micro-cylindrical lenses of the MCLA is ${Q_2} = 240 \times 19 = 4560$. From Eq. (6), the angular resolution of the UWA-2HSR-SIS is $\delta {\phi _{UWA - 2HSR - SIS}} = {{0.5^\circ } / 5} = 0.1^\circ$. Considering that the UWA-2HSR-SIS has no moving parts, the light passing through each optical fiber can be received by a separate column of the detector. The aperture size in the horizontal plane of each micro-cylindrical lens of the MCLA can be ${D_{2X}} = b = 2\textrm{0 }\mathrm{\mu}\textrm{m}$. From Eq. (9), the number of pixels in each row of the detector used to record the spatial image can be ${M_X} = 4560$.
When the numerical aperture of the optical fiber is $NA = 0.1$ and ${n_0} = 1$, from Eq. (13), $\tan ({{{{\theta_o}} / 2}} )= 0.1$. From Eq. (12), the focal length of each micro-cylindrical lens of the MCLA can be ${f_2} = 0.1\textrm{ mm}$. From Eq. (4), the aperture size in the vertical plane of each micro-cylindrical lens of the MCLA can be ${D_{2Y}} = 25\textrm{ }\mathrm{\mu}\textrm{m}$. From Eq. (10), if the focal length of each microlens of the MLA is ${f_1} = 8\textrm{ mm}$ and the cladding thickness of each optical fiber in each fiber bundle is ${r_C} = 3\textrm{ }\mathrm{\mu}\textrm{m}$, we can choose ${D_F} = 12\textrm{ }\mathrm{\mu}\textrm{m}$ and ${D_{FB}} = 5 \times 12\mu m + 4 \times 3\mu m = 72\textrm{ }\mathrm{\mu}\textrm{m}$. Some parameters of the UWA-2HSR-SIS for the first example are shown in Table 1.
Table 1. Some parameters of the UWA-2HSR-SIS for the first example
According to Eq. (18), the interferogram produced by the UWA-2HSR-SIS with a spectral resolution of 0.2 cm−1 is shown in Fig. 3, which includes only wavenumber 19999.6 cm−1, 19999.8 cm−1, 20000 cm−1, 20000.2 cm−1 and 20000.4 cm−1. Figure 4 shows the spectrum obtained from the Fourier transform of the interferogram shown in Fig. 3. Spectral peaks of the five wavenumbers 19999.6 cm−1, 19999.8 cm−1, 20000 cm−1, 20000.2 cm−1 and 20000.4 cm−1 are clearly distinguished.
Fig. 3. Interferogram produced by the UWA-2HSR-SIS with a spectral resolution of 0.2 cm−1 for the wavenumber range from 19940 cm−1 to 20060 cm−1.
According to Eq. (21), the resolving power of the UWA-2HSR-SIS for the spectral range from 400 nm to 2500 nm for the first design example is shown in Fig. 5.
Fig. 5. Resolving power of the UWA-2HSR-SIS for the spectral range from 400 nm to 2500 nm for the first design example.
3.2. Second example in the near-infrared region
For the second design example, a source spectra has a central wavenumber 5000 cm−1 (wavelength 2 µm) and a spectral bandwidth $\Delta \sigma = 120\textrm{ c}{\textrm{m}^{ - 1}}$, i.e., a wavenumber range from 4940 cm−1 to 5060 cm−1, the desired field angle is 120°, the desired angular resolution is 0.08°, and the desired spectral resolution is 0.1 cm−1.
When the pixel size of the detector is $b = 2\textrm{0 }\mathrm{\mu}\textrm{m}$ and the groove angle of grating is $\gamma = 45^\circ$, the equivalent step height is $h = 20\mu m$. Let $P = 3$, we can also choose a reflection grating with 106 grooves/mm. According to Eq. (20), the maximum optical path difference of the SGI is ${x_{\max }} = {1 / {({0.1\textrm{c}{\textrm{m}^{ - 1}}} )}} = 10\textrm{ cm}$, and the number of pixels in each column of the detector used to record the spectral image is ${M_Y} = {1 / {({2 \times 20\mu m \times 0.1c{m^{ - 1}}} )}} = 2500$. The actual number of sampling points for each interferogram produced by the SGI is $K = 2500$. The focal length of the cylindrical lens is ${f_3} = {{2500 \times 2\textrm{0}\mathrm{\mu}\textrm{m}} / {({2 \times 0.1} )}} = 250\textrm{ mm}$.
Assuming that the field angle of each microlens of the MLA is $\varphi = 0.4^\circ$, the radius of the semicircle of the MLA is ${R_1} = 45\textrm{ mm}$, and each fiber bundle contains nineteen hexagonal optical fibers. The number of microlenses of the MLA is $Q = {{120^\circ } / {0.4^\circ }} = 300$. The aperture size of each microlens of the MLA can be ${D_1} = \textrm{310 }\mathrm{\mu}\textrm{m}$. The number of micro-cylindrical lenses of the MCLA is ${Q_2} = 300 \times 19 = 5700$. The number of pixels in each row of the detector used to record the spatial image is ${M_X} = 5700$. The angular resolution of the UWA-2HSR-SIS is $\delta {\phi _{UWA - 2HSR - SIS}} = {{0.4^\circ } / 5} = 0.08^\circ$. Some parameters of the UWA-2HSR-SIS for the second example are shown in Table 2.
Table 2. Some parameters of the UWA-2HSR-SIS for the second example
Based on Eq. (18), the interferogram produced by the UWA-2HSR-SIS with a spectral resolution of 0.1 cm−1 is shown in Fig. 6, which contains only wavenumber 4999.8 cm−1, 4999.9 cm−1, 5000 cm−1, 5000.1 cm−1 and 5000.2 cm−1. Figure 7 shows the spectrum obtained from the Fourier transform of the interferogram shown in Fig. 6. Spectral peaks of the five wavenumbers 4999.8 cm−1, 4999.9 cm−1, 5000 cm−1, 5000.1 cm−1 and 5000.2 cm−1 are clearly distinguished.
Fig. 6. Interferogram produced by the UWA-2HSR-SIS with a spectral resolution of 0.1 cm−1 for the wavenumber range from 4940 cm−1 to 5060 cm−1.
From Eq. (21), the resolving power of the UWA-2HSR-SIS for the spectral range from 400 nm to 2500 nm for the second design example is shown in Fig. 8.
Fig. 8. Resolving power of the UWA-2HSR-SIS for the spectral range from 400 nm to 2500 nm for the second design example.
4. Conclusion
The principle of the UWA-2HSR-SIS is described, the first-order approximations of system performance are given, and the preliminary numerical simulations of two examples are shown. The UWA-2HSR-SIS has six advantages. First and foremost, the UWA-2HSR-SIS can obtain both high spatial resolution (e.g., an angular resolution of 0.08° or more) and high spectral resolution (e.g., 0.1 cm−1 or more in the visible and near-infrared region) for the first time. Second, the UWA-2HSR-SIS has an ultra-wide field angle (e.g., 120° or more) in the horizontal plane and can meet wide-angle search requirements. Third, the UWA-2HSR-SIS can obtain spectral information covering the full spectral range of interest in real time and can meet real-time detection requirements. Fourth, the UWA-2HSR-SIS has no moving parts and is very stable against various disturbances. Fifth, the UWA-2HSR-SIS can obtain high-resolution two-dimensional spatial information in real time: one dimension with an ultra-wide field angle of 120° or more in the horizontal plane, the other with a small field angle of $\varphi$ (e.g., 0.5° or 0.4°) in the vertical plane, and both dimensions with an angular resolution of ${\varphi / 5}$ (e.g., 0.1° or 0.08°) or more. Sixth, the UWA-2HSR-SIS can achieve nearly uniform spectral resolution across the entire field of view. Compared with all existing ultra-wide-angle optical systems used as remote sensing electro-optical reconnaissance sensors, the UWA-2HSR-SIS has the first advantage mentioned above. Compared with all existing snapshot imaging spectrometers used as remote sensing electro-optical reconnaissance sensors, the UWA-2HSR-SIS has the first two advantages mentioned above. Compared with all existing high-spectral-resolution imaging spectrometers with at least one scanning component, for remote sensing electro-optical reconnaissance sensors, the UWA-2HSR-SIS has the first four advantages mentioned above. However, the UWA-2HSR-SIS also has three main limitations. First, the use of a large number of microlenses, fiber bundles and micro-cylindrical-lenses will increase the complexity of the system, the difficulty of manufacturability, system integration and calibration. Second, since the cladding of the optical fiber has a certain thickness, the field of view of the UWA-2HSR-SIS is not completely continuous. However, the cladding thickness can be reduced to much less than 2.5 μm over the short fuse length [38], and the field angle of each microlens of the MLA is usually small and subdivided into multiple smaller field angles, so the field of view coverage is still enough to obtain high spatial resolution. Third, the spectral range of the UWA-2HSR-SIS is still narrow. In summary, the UWA-2HSR-SIS provides a new concept that not only obtains both high spatial resolution and high spectral resolution based on a single sensor for the first time, but also has an ultra-wide field angle (e.g., 120° or more) in the horizontal plane, the ability to obtain spectral information covering the full spectral range of interest in real time, and very high stability against various disturbances. In the future, the UWA-2HSR-SIS will be very suitable for remote sensing electro-optical reconnaissance sensors (e.g., for unmanned aerial vehicles, manned reconnaissance aircraft) in the visible and near-infrared region.
Funding
National Natural Science Foundation of China (61605151).
Disclosures
The authors declare no conflicts of interest.
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