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Abstract
In this paper, we present a static imaging Fourier transform spectrometer (sIFTS) for the mid-infrared spectral range. The system employs imaging optics, a single-mirror interferometer, and an uncooled broadband microbolometer array. As the hyperspectral data cube is acquired using a windowing method, a comparatively high light throughput in a spectral range from 2600 cm−1 to 800 cm−1, respectively 3.8 µm to 13 µm is achieved. The spectral resolution is 12 cm−1, and the spatial resolution amounts to 16 lp/mm, corresponding to a resolution of 62.5 µm at a design wavelength of 10.6 µm. As the employed spectrometer, in contrast to scanning Fourier transform infrared (FTIR) spectrometers, contains no moving parts, the measurement rate is mainly limited by the detector read-out and is currently 25 Hz. After an evaluation of the spatial resolution by both simulations and experimental results, the spatially resolved transmission spectra of a sample containing different polymer films are recorded and compared to a laboratory FTIR spectrometer. Thereby, the acquired spectra show good agreement. As the system combines both a spectrometer with low internal light loss and a windowing technique allowing high etendue, the presented hyperspectral imager shows significant potential especially for the mid-infrared.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays, hyperspectral imaging plays an important role in various fields of applications such as remote sensing [1,2], medical and pharmaceutical analysis [3–5], food quality control [6–8] or industrial process monitoring [9,10]. In addition, this technique has recently found more and more applications in the analysis of 2D and other nanoscale materials [11,12].
Hyperspectral imagers (HSI) typically consist of imaging optics to obtain the spatial information of the sample and a spectrometer to extract the spectral information for each pixel. The resulting two-dimensional spatial image and the associated spectral data are often referred to as hyperspectral data cube. In the mid-infrared spectral range, where useful information about the composition and quality of numerous materials can be obtained, typically scanning Fourier transform infrared (FTIR) spectrometers are used in combination with a two-dimensional detector array [5,13,14]. Due to their throughput and multiplex advantages, they show excellent performance even at low light intensities. Since the interferogram is recorded over time, however, the measurement speed of these systems is limited by principle and the sample must not be moved during the entire measurement, respectively scanning procedure. In addition, the complexity of a system suitable for industrial application is high due to the employment of moving mirrors and reference lasers. Other approaches include either tunable light sources - typically quantum cascade lasers [15,16] - or tunable detectors, for example using Fabry-Perot filters [17,18]. A very recent development is the use of supercontinuum laser sources offering outstanding imaging quality [19]. While the laser-based systems suffer from a limited spectral range, respectively employ expensive light sources, the filter-based approaches exhibit low signal-to-noise ratios (SNR) and long acquisition times. Here, static Fourier transform spectrometers (sFTS) offer a valuable alternative, especially if the spectral resolution is not the main criterion for the respective application. As these instruments contain no moving parts, but are still based on the Fourier transform principle, they inherit the multiplex and throughput advantages of their scanning counterparts while requiring a reduced mechanical design. Therefore, they show sufficient SNR at high measurement rates. The most commonly used HSI designs based on static Fourier spectrometers include common-path [20–22] and birefringent spectrometers [23] working in pushbroom mode. Although these systems offer a comparatively high stability, at least 50 % of the incident radiation is lost in the spectrometers as a matter of principle and the input aperture must be limited by a slit to ensure sufficient spatial resolution. Recently a new sFTS concept was introduced with the static single-mirror Fourier transform spectrometer [24–27], providing a comparatively high etendue as well as a reduced optical design, which can potentially overcome these drawbacks.
Therefore, in this paper we present an HSI based on a single-mirror interferometer, working in the mid-infrared spectral range from 3.8 µm to 13 µm. First results of this project have already been published in the context of a conference [28]. The spectral resolution amounts to 12 cm−1 and the measurement speed is currently limited to 25 Hz by the employed detector. The maximum spatial resolution is around 16 lp/mm, respectively 62.5 µm. In order to obtain the hyperspectral data cube while maintaining high light throughput, we use a windowing method [29], combining the raw detector images to two-dimensional interferograms for each spatial element of the sample during post-processing, from which the respective spectra can be calculated.
After an introduction to single-mirror Fourier transform spectrometers and the windowing method, we describe the design of our experimental transmission measurement setup in detail. After examining the spatial resolution of the instrument, measurement results of a sample consisting of different polymer films are presented. Eventually, the acquired spectra are compared to an FTIR laboratory device to validate the functionality of the hyperspectral imager.
2. Fundamentals
Before describing the static imaging Fourier transform spectrometer (sIFTS) as well as the obtained experimental results in detail, relevant theoretical aspects are discussed in this section. Besides the operation principle of static single-mirror Fourier transform spectrometers, the windowing method used to generate the hyperspectral data cube is introduced.
2.1 Single-mirror Fourier transform spectrometer
The basic design of a single-mirror Fourier transform spectrometer [24–27] is shown in Fig. 1. By using a Fourier lens, extended light sources can be analyzed with this device, leading to a comparatively high etendue. In addition, in principle no internal light losses occur and the entire incident radiation is directed to the detector, in this case a microbolometer array. The core element thereby is a zinc selenide beam splitter with thickness $T_{bs}$ and refractive index $n_{bs}$, which ensures that the optical path lengths of the two interferometer arms can be matched, allowing the mid-peak of the interferogram to be placed on the detector. One interferometer arm, as indicated in red, consists of the transmitted part of the radiation, the other one, as highlighted with dashed lines, is generated by reflections at both the beam splitter and the plane mirror. The vertical distance of the two central rays $d_s$ can then be calculated using Eq. (1) depending on the beam splitter angle $\alpha$ and the distance between beam splitter and plane mirror $d_{\mathrm {bs-pm}}$ with $n_{bs}$ being greater than the refractive index of the surrounding medium $n_{\mathrm {air}}$.
Eventually, a Fourier lens with focal length $f_F$ brings the light to interference on the detector, which is positioned exactly in the focal plane. Thereby, the two-dimensional interference pattern $I(x,y)$ can be expressed using Eq. (2) [27].
The achievable spectral resolution $\Delta \tilde {\nu }$ is determined by the maximum optical path difference OPD$_{\textrm{max}}$ according to Eq. (4) [27].
Therefore, the spectral resolution can be increased either by using a detector with more pixels $N_x$ in x-direction or by reducing the bandwidth, respectively the maximum resolvable wavenumber $\tilde {\nu }_{\mathrm {max}}$.2.2 Windowing method
For acquiring the hyperspectral data cube, we use a windowing method as introduced in [29]. This approach offers certain advantages over common pushbroom techniques, where the field of view of the spectrometer has to be restricted by a slit and an additional cylindrical optic is required for mapping one column of the sample to the full width of the detector array. A more detailed comparison of these two approaches can be found in [28].
As can be derived from Eq. (3), a single-mirror interferometer creates a two-dimensional fringe pattern, respectively interferogram. Thereby, the main OPD modulation occurs along the x-axis with minor non-linear deviations along the y-axis, resulting in slightly curved interference fringes. In order to calculate a spectrum for a specific spatial element of the sample, this element must travel across the entire optical path difference range, respectively the entire detector x-axis. This is typically achieved by moving the sample stepwise or continuously in x-direction. Thus, if $N$ spatial elements of the sample are to be analyzed independently in this dimension, at least $2N-1$ images must be acquired. Figure 2 shows a simple example for $N=3$, which corresponds to the sample that was measured in the course of this paper. In this case, the field of view (FOV) of the sIFTS is adapted to the dimension of the sample and is also divided into $3 \times 3$ subareas. In the first step only the right column of the sample is in the FOV of the sIFTS. The sample is then moved column by column until each subsection of the sample has passed through each column of the FOV.
Fig. 2. Basic windowing principle to capture a hyperspectral data cube for a scene containing 3 x 3 spatial elements. The two-dimensional interferograms are stitched during post-processing.
In this way, the intensity values for every available optical path difference are collected for each spatial element of the sample. After rearranging the resultant data to two-dimensional interferograms for all elements, the corresponding spectra can be calculated, allowing a distinction between different materials. The interferogram stitching is shown schematically for two different spatial elements in Fig. 2.
It should be noted that the sample in this case could in principle be resolved much finer in y-direction, as a spectrum can be obtained from every single detector line. Therefore, the resolution in y-direction is not limited by the number of captured images but only by the spatial resolution of the imaging optics and the number of pixels in this dimension.
3. Experimental setup
To validate the proposed sIFTS concept, a transmission setup as shown schematically in Fig. 3 was used both for simulations and measurements. A broadband thermal light source (Hawkeye Technologies - IR-Si207) at a temperature of 1375 °C is magnified onto an adjustable aperture (Thorlabs - D25SZ) with diameter $d_a$ by two germanium plano convex lenses with focal lengths $f_C$ of 40 mm and $f_1$ of 75 mm, respectively. Since the light source has a diameter of 4.4 mm, it cannot be collimated ideally with L$_C$. Another lens L$_2$ with a focal length $f_2$ of 75 mm ensures that the sample is illuminated roughly collimated. In order to ensure proper imaging despite relatively large angles $\Omega$, the sample is placed in the front focal plane of the spectrometer input lens L$_3$. To use the proposed windowing technique, the sample can be moved along the x-axis with a motorized linear stage providing a maximum speed of 30 mm s−1 (Thorlabs - NRT150/M).
Fig. 3. Schematic overview of the experimental setup including a light source, a moveable sample and a single-mirror Fourier transform spectrometer.
Subsequently, the single-mirror interferometer is passed, resulting in a two-dimensional image of the sample on the detector as well as varying optical path differences and thus a superimposed interference pattern. The image forming for a scattering point on the sample is as well indicated in Fig. 3. The scattered light is collimated by L$_3$ and then refocused onto the microbolometer by the Fourier lens. Note that only scattered rays within the acceptance angle of the spectrometer, which is 1.1°, are imaged onto the detector. The zinc selenide beam splitter (Spectral Systems) has a diameter of 25.4 mm and a thickness of 3.1 mm, the plane mirror is gold-coated and has a diameter of 12.7 mm. As both the imaging lens L$_3$ and the Fourier lens have a focal length of 75 mm, the magnification $M$ of the sample is $1$ in this configuration. All lenses were purchased from Edmund Optics and are coated for a spectral range from 3 µm to 12 µm. As detector we use a 800 px $\times$ 600 px microbolometer array by GUIDE Infrared (CUBE Series), having a pixel pitch of 17 µm. Therefore, the detector size is 13.6 mm $\times$ 10.2 mm and the angular field of view (AFOV) amounts to $ {10.36}^\circ \times {7.78}^\circ $. The detector is read out with a camera link interface provided by GUIDE. The maximum etendue, i.e. the product of the focal point diameter and the corresponding accepted solid angle of the spectrometer, is 0.26 sr mm2. The etendue is mainly determined by the detector size and the focal length of the Fourier lens. The fringe spacing on the detector for a wavelength of 10 µm is around 125 µm.
The achievable spatial resolution essentially depends on the divergence angle $\Omega$ of the beam illuminating the sample. This angle, as indicated in Fig. 3, can be controlled by the adjustable aperture. The smaller the aperture diameter $d_a$ and the larger the focal length $f_2$, the smaller the divergence angle given by Eq. (5) and the higher the spatial resolution of the hyperspectral imager.
In practice, a trade-off between throughput and spatial resolution will obviously be necessary, since the aperture limits the light throughput of the system considerably and diffraction effects might come into play.4. Results and discussion
In order to illustrate the aforementioned operating principle of the sIFTS, the logo of the Technical University of Munich (TUM), laser printed on a polyester foil with a thickness of 0.1 mm, was imaged with the experimental setup. The result is given in Fig. 4.
Fig. 4. Detector image acquired by the sIFTS, showing the TUM logo as well as superimposed interference fringes.
As expected, a clear two-dimensional image of the logo and superimposed, slightly curved interference fringes can be observed. Note that the mid-peak of the interferogram is slightly shifted to the left side of the detector in order to capture larger optical path differences and thus ensure an increased spectral resolution. This is achieved by slightly increasing the distance $d_{\mathrm {bs-pm}}$ between beam splitter and plane mirror in the interferometer.
The dependence between spatial resolution and divergence angle $\Omega$ can be evaluated by simulating the modulation transfer function (MTF) using a ray tracing approach in Zemax OpticStudio. The simulations were carried out for the design wavelength of the spectrometer, which amounts to 10.6 µm. Thereby, $\Omega$ was varied to simulate different light source sizes, respectively aperture diameters. As can be seen in the results in Fig. 5, the achievable resolution increases with smaller $\Omega$. While at a divergence angle of 1°, which corresponds to the maximum accepted light source size of the spectrometer, a resolution of about 10 lp/mm, respectively 100 µm can be achieved, resolutions of up to 20 lp/mm, respectively 50 µm are obtained by reducing the aperture diameter. The variable $dw$ denotes the corresponding line spacings. As a resolution limit, the Rayleigh criterion was used, which corresponds to a necessary Michelson contrast of at least $0.15$ for distinguishing two adjacent lines [31].
Fig. 5. Ray tracing simulation of the modulation transfer function with varying divergence angles $\Omega$ at a wavelength of 10.6 µm.
In order to validate the simulation results, a USAF 1951 test target was measured with the experimental setup. Relevant dimensions of the target are given in Table 1. The aperture was adjusted manually to achieve both, sufficient spatial resolution and light intensity, on the detector. Thereby, $d_a$ is about 1.3 mm, which corresponds to a divergence angle of 0.5°.
Table 1. Relevant dimensions of the USAF 1951 test target used for evaluating the spatial resolution of the sIFTS.
As shown in Fig. 6, all elements from group 3 as well as the first element of group 4 are clearly visible. This leads to a spatial resolution of 16 lp/mm, respectively 62.5 µm in this configuration, matching the simulation quite well. Also note the interference fringes that can be identified across group 2. The spatial resolution is mainly limited by spherical abberations in this configuration. In the future, the sIFTS imaging optics will be optimized and evaluated for different wavelenghts.
The background spectrum of the sIFTS when averaging over the entire y-dimension of the detector is given in Fig. 7. The upper end of the wavenumber range is defined by a longpass filter, which cuts in at a wavenumber of about 2770 cm−1, respectively at a wavelength of 3.6 µm. Towards smaller wavenumbers, the spectral bandwidth is limited by the coating of the lenses and the beam splitter. The loss of intensity in the center of the spectral range is due to the transfer function of the employed microbolometer array. Furthermore, the characteristic absorption bands of water (H$_2$O) and carbon dioxide (CO$_2$) are evident. A more detailed description of a similiar background spectrum shape can be found in [27].
The windowing method as well as the spectral accuracy of the system are evaluated using a sample consisting of a $3 \times 3$ arrangement of different polymer films. For this purpose three parts of each polyvinyl chloride (PVC), polyester (PP) and polycarbonate (PC) were used. The sample dimensions amount to 15 mm x 10 mm.
Consequently, in order to calculate a spectrum for each part of the sample, at least five detector images must be recorded, as shown in Fig. 8. The sample was moved once through the FOV of the sIFTS from left to right (compare Fig. 2) with a linear stage at a speed of 5 mm s−1, whereby the five images shown here were taken. In Step 3, all spatial elements are displayed on the detector as indicated. Note that here each component of the sample is slightly wider than a third of the detector width and in total 12 images were taken into account to facilitate the later two-dimensional interferogram generation. Therefore, we chose the apropriate three images manually for each material to facilitate the later comparison to the reference FTIR spectra.
Fig. 8. Shift of the sample along the x-direction of the detector array. Images taken at five consecutive instants of time. The sample contains three different materials arranged in a 3 x 3 pattern.
Finally, Fig. 9 shows the spectra of selected sample parts reconstructed from the corresponding data. Thereby, the spatial elements were intentionally selected from different vertical detector ranges. Figure 9(a) shows the reconstructed two-dimensional interferograms. The one-dimensional interferograms of the samples are displayed in Fig. 9(b). These are obtained from the respective two-dimensional interferograms by averaging along the y-axis, respectively along the lines of equal optical path differences [24]. A high-pass filter with cut-on wavenumber 500 cm−1 was applied and a triangular window was used for apodization. The maximum optical path difference amounts to 0.78 mm yielding a spectral resolution of around 12 cm−1.
Fig. 9. (a) Two-dimensional interferograms of selected samples; (b) Corresponding one-dimensional interferograms obtained by averaging along the lines of equal OPD; (c) Transmission spectra compared to a laboratory FTIR spectrometer.
The transmission spectra are given in Fig. 9(c). The sample spectra were calculated from the interferograms in Fig. 9(b) using a non-uniform Fourier transform and then related to the background spectrum from Fig. 7. A conventional laboratory FTIR spectrometer with a spectral resolution of 8 cm−1 (Thermo Nicolet Avatar 330) was used as a reference. Since the reference spectrometer thus features a slightly higher spectral resolution, the absorption peaks recorded with the sIFTS are less prominent. This can be primarily observed in the PVC1 sample spectrum. Due to low signal strength outside this range, the wavenumber band was limited to 800 cm−1 to 2600 cm−1.
Here a commercially available microbolometer detector with implemented correction algorithms was used. This led to some problems due to overcorrection of fluctuating intensity values between consecutive detector images caused by the movement of the sample through the field of view. This resulted in some additional signal peaks when combining the two-dimensional interferograms, as indicated here in the interferogram as well as the spectrum of sample PC2. While significant absorption peaks are still clearly recognizable, a disturbance is superimposed on the signal. These effects can be eliminated in the future by both improving and automating signal processing and using a customized detector.
5. Conclusion and outlook
In this paper we have presented a novel mid-infrared hyperspectral imager using a static single-mirror Fourier transform spectrometer to acquire spectral data, working in a spectral range from about 2600 cm−1 to 800 cm−1, respectively 3.8 µm to 13 µm. The spectral resolution in the current configuration amounts to about 12 cm−1. Since the system exhibits a high etendue and the hyperspectral data cube is recorded using a windowing method, a high light throughput can be achieved, which offers potential advantages over existing pushbroom methods and comparable sIFTS approaches. As no moving parts are used in the spectrometer, the measurement speed is limited mainly by the frame rate of the camera, which is an advantage over scanning FTIR or filter-based systems. The spatial resolution is about 16 lp/mm, respectively 62.5 µm, which has been verified both by simulations and measurements. The spectra of different polymers recorded in transmission mode showed good agreement with results obtained by a laboratory FTIR spectrometer.
In the future, the system will be designed for reflection and transflectance measurements, as this would certainly open up more applications. In addition, the spatial resolution can be improved by customized optics and signal processing should be optimized and automated. A last major part of future research is the further development of the static Fourier transform spectrometer. Here the aim is to increase the spectral bandwidth and resolution. With the current development of microbolometer arrays towards higher resolutions and smaller pixels, the spectral resolution of the sIFTS can be increased significantly in the future. Also we are working on various concepts for improving the overall spectrometer performance.
Funding
Bundesministerium für Wirtschaft und Energie (ZF4304602RR6).
Acknowledgments
The authors gratefully acknowledge the funding by the Federal Ministry for Economic Affairs and Energy of Germany and the contributions from our project partner Comline Elektronik Elektrotechnik GmbH. This work was supported by the German Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open Access Publishing Program.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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