1. Introduction
Infrared (IR) spectroscopy is a well-established analytical method for non-destructive chemical characterization of materials in all aggregate states. Since its beginnings, the field of IR spectroscopy has been dominated by instruments based on thermal emitters. Such instrumentation naturally faces limitations imposed by the low brightness of thermal sources. During the last two decades new measurement technologies have been developed to overcome these limitations, facilitated by novel laser technology, such as quantum cascade lasers [
1,
2] and supercontinuum laser sources [
3,
4]. However, these laser sources are rather expensive, which limits their range of application and triggers the development of alternative speed- and sensitivity-enhanced measurement approaches.
Considering the developments in non-laser spectroscopic instrumentation, three conceptual categories of devices can be distinguished: dispersive systems, filter spectrometers (tunable or discrete filters), and the gold-standard technique of Fourier transform spectrometry [
5]. As initially developed, dispersive spectrometers dominated in molecular spectroscopy, being capable of providing high acquisition rates with sufficiently high spectral resolution and a relatively simple design [
6,
7]. State-of-the-art filter-based systems, such as tunable MEMS-based Fabry–Pérot etalons, represent a cost-efficient alternative. However, due to the trade-off between scan speed and spectral resolution, settling times of such filters are usually in the range of tens of milliseconds [
8]. In contrast, Fourier transform IR (FTIR) based spectrometers offer inherently high resolution (reciprocal to the scanning range in interferometric systems), broadband operation (limited by the specific detectors responsivity), and transition of the key spectrum reconstruction procedure to the digital domain [
9]. The methods of Fourier-transform spectrometry comprise primarily low-coherence interferometric FTIR instruments [
10]. Commonly, the approach of FTIR spectrometry holds two inherent advantages over tunable and dispersive systems, namely multiplexing and optical throughput advantages, also known as Fellgett’s and Jacquinot’s advantages, respectively [
9,
11,
12]. The optical throughput—being a function of system geometry—is subject to the optical design (severely limited for slit-based systems), while multiplexing is a property of the detection approach. The multiplex advantage implies that all spectral frequencies of the light source are sampled simultaneously, thus increasing the signal-to-noise ratio (SNR) immensely. Another commonly cited advantage of FTIRs is wavelength accuracy, which is, however, not inherent to FTIR but enabled by the implementation of a reference laser.
In conventional FTIR spectrometers, the autocorrelation function (correlation between the field with its delayed replica, connected with the power spectral density via the Fourier transform) is measured sequentially in time to retrieve IR spectra. Therefore, an intrinsic feature of these instruments is that the measurement time is proportional to the spectral resolution (i.e., the displacement of the scanning mirror; mirror speed can vary for different instruments).
In classical dispersive systems, optical elements such as gratings or prisms are employed to perform the Fourier transform, therefore, eliminating the trade-off between the spectral performance and acquisition speed. This leads to the possibility of fast measurements of spectral regions of interest (SROI), since the spectral resolution is decoupled from the measurement time if array detectors are used. However, since these systems measure only narrow spectral lines per sensing element (spatially or time separated), the multiplex advantage is lost, which causes measured signals to be weak [
13]. Therefore, highly sensitive detectors must be used.
The acquisition speed advantage and multiplexing advantage are inherent either for dispersive or for FTIR spectrometers, respectively, showing that these properties are contradictory. In this work, we address this point by demonstrating a dispersive spectrometer that displays both the multiplex advantage, usually nonspecific for such systems, and the speed advantage by using a spectral coding approach based on the principles of compressive sensing (CS).
The emerging field of CS exploits the fact that a sparse signal can be recovered from far fewer samples than those required by the Nyquist–Shannon–Kotelnikov theorem [
14,
15]. Applications of CS techniques have evolved over the past decade. Besides the employment in the standard vis-imaging scenarios [
16,
17] and new approaches in combination with deep learning [
18], CS has also occupied various specific sectors of applied science such as communication systems, biomedical applications, micro- and nano-electronics, and sound and speech processing [
19,
20]. A recent article about the application of CS in NIR hyperspectral imaging [
21] demonstrated potential advantages over well-established measurement approaches and techniques. For instance, in resonator-based spectroscopy the effective bandwidth can be noticeably broadened by applying CS schemes [
22]. Considering the problem raised, the spectral coding approach—based on amplitude light modulation—can be used in dispersive element-based spectrometer designs to attain the multiplex advantage [
23]; thus, a single detector can be employed to detect several spectral components simultaneously while the spectrum is being computed for distinctive spatial patterns. We applied a compressive measurement approach similar to CS that allows undersampling of spectra to increase acquisition speeds, i.e., less spatial patterns have to be applied to reconstruct encoded spectral information. The main difference from CS is that smoothness of the spectra is used as a regularization instead of the usual exploitation of signal sparsity. Spatial amplitude modulation can be achieved by using fully integrated spatial light modulators. Following this approach, classical moving parts for scanning, such as rotating gratings or mirrors, become unnecessary and highly sensitive single element detectors can be used as opposed to linear arrays. Experimental realization was reported both for Raman and infrared spectroscopy [
24,
25,
26,
27]. This measurement approach enhances sensitivity and speed, which makes applications in the NIR and MIR regime attractive.
In this contribution, we demonstrate an approach that combines the advantages of FTIR instruments with those of dispersive element-based instruments in the NIR spectral region. The developed system is based on a ruled diffraction grating and utilizes spectral coding to achieve spectral multiplexing by means of a MEMS-based digital micromirror device (DMD) [
28]. Such an approach has already been realized in commercial NIR systems based on a concept reported in [
29]. A performance comparison of this concept to other state-of-the-art NIR spectrometer technologies is shown in [
27]. In the present paper we used a laboratory setup with a similar optical approach, however, we focused on harnessing the full potential of the general concept of using spatial light modulators. The programmable DMD makes the systems’ parameters flexible and enables measurements of either the whole spectral band or a dedicated SROI, thus enabling acquisition rates in the millisecond regime while maintaining high spectral resolution. The flexibility of the DMD also makes the implementation of compressive measurements possible, thus, allowing sampling of the whole spectral band or SROI at high resolution with only a fraction of the measurements, resulting in a significant reduction of the acquisition time under the condition that the spectra are smooth.
In the implementation section, the design of the developed system is demonstrated, and its resolution performances and features are investigated by simulations and discussed in detail. In the experimental part, we demonstrate the performance characteristics of our approach in different operational modes (scanning grating spectrometer, spectral coding, and spectral coding combined with a compressive sensing approach). This is then compared to a standard FTIR-spectrometer serving as a gold standard. The theoretical multiplex advantage resulting from the spectral coding principle is experimentally demonstrated by a quantitative analysis of the spectral noise behavior.
3. Results
In order to demonstrate the multiplex sensitivity advantage over a standard mono- or polychromator configuration, zero-absorbance spectra for two modalities of the system (line-scan and spectral coding) were recorded and analyzed. This method is especially suitable for quantification of spectral noise, as shown in
Figure 3, for the line-scan and the spectral coding modality, respectively. It is important to notice the increase of spectral noise towards the edges of the spectral band. This effect occurs due to the geometric mismatch of the DMD and the detector apertures. While the DMD has a rectangular geometry, the detector chip is of circular shape. As further shown in
Figure 3, the mean of the standard deviation (std) of 125 zero absorbance lines, which are calculated from the logarithm of the quotient of two blank spectra (no specimen in the beam path), is bigger than for the line-scan mode by a factor 8.2. The multiplex advantage is quantified by the value
N1/2 [
11,
23], with
N being the number of DMD super-pixels. In this special case of Hadamard multiplexing the multiplex advantage can be calculated by computing [
31,
32]
with
ε denoting the mean square error of a measurement.
σ2 is the rms noise of a single measurement and
H stands for a Hadamard matrix of dimension
N ×
N. In the ideal case, where the 1 and −1 entries of the Hadamard matrix could be measured simultaneously with the same detector, this would result in a multiplex advantage of √128. Due to the fact that we have to split the Hadamard matrix into two matrices and therefore have to perform twice as many measurements, the multiplex advantage should be evaluated for twice as many line scans. This means that the result of Equation (3) has to be multiplied by a factor √(1/2). This gives a theoretical multiplex advantage of 8, which is close to the experimentally found multiplex advantage of 8.2, which was evaluated by computing the standard deviation of 125 zero absorbance lines, calculated from 250 spectral coding measurements and 500 line-scan measurements.
The measurement time for a single spectrum is mainly defined by the illumination time of each modulation pattern and the number of patterns that are used in total. The measurements shown in
Figure 4, except (b), were performed with an illumination time of 55 µs, leading to 14.1 ms pure measurement time per single spectrum when using the spectral coding approach (i.e., 100% of the modulation masks). When introducing compression, the measurement time is given by multiplication of the total measurement time with the fraction of the full set of patterns that is used to sample the spectrum. Thereby, the system becomes even faster at the trade-off of losing spectral resolution.
Figure 4a shows the reconstructed spectra recorded using the spectral coding approach. An effective pattern repetition time of 55 µs was used and 14 spectra were averaged in total, yielding an overall measurement time of 0.2 s. When compared to the verification measurements (
Figure 4b), it is clearly visible that the spectral resolution of the developed spectral coding spectrometer is comparable to that of the commercial FTIR standard spectrometer, which was set to be 12 cm
−1. The measurement time of the FTIR spectrometer for a single scan at the given resolution is 0.2 s. This result is in a good agreement with those of the optical design and Zemax simulations, which predicted a spectral resolution below 10.5 nm. The two central bands that are 20 nm apart could be resolved as precisely as with the standard instrument, thus suggesting an approximate spectral resolution of 12 cm
−1, which is about 5.5 nm in the given spectral range.
All the spectra recorded using the spectral coding approach that are depicted in
Figure 4 were zero-filled and Blackman–Harris-filtered.
Figure 4d indicates the results when a monochromator approach is used (no multiplexing, equivalent to standard dispersive spectrometers), with an acquisition time for two spectra of 14.1 ms. This measurement was realized by imitating line scans by applying only a single bar pattern per illumination mask on the DMD. In
Figure 4e only 50% of the barcode pattern set was used to sample the spectrum, resulting in 50% compression at an acquisition time of 7 ms. Compressing the measurement by 70% reduces the acquisition time to 4.2 ms (
Figure 4f) but at the same time a severe trade-off to spectral resolution is made.
The high flexibility of the spectral coding spectrometer and the associated speed advantage can be demonstrated by measurements of SROI. For sampling the spectra shown in
Figure 5, modulation patterns of 16 super-pixels were used, as indicated in the inset in
Figure 1, thus, decreasing the measurement time further, by a factor of 1/8. This results in single spectra acquisition of 1.8 ms. Since the size of the super-pixels remained unchanged, the spectral resolution in the ROI is the same as that for a full 128 pixel measurement. On the left side in
Figure 5, the raw, unprocessed 16-point absorbance spectra of PS are shown for different compressions. On the right side we show that the absorption bands of PC and PS can still be resolved when only 50% of the full set of modulation patterns are used to sample the SROI (50% compression), resulting in an acquisition time of 0.88 ms. As mentioned above, the multiplex advantage is extenuated due to the fact that spectral power of only a small sub-band is modulated and measured by the detector.
4. Discussion
In this work we introduced a fast and cost-effective spectral coding-based grating spectrometer for the near-infrared spectral domain (5250–4300 cm−1; 1.9–2.33 µm). The spectrometer combines desirable advantages of dispersive element-based spectrometers with that of FTIR spectrometers. Spectral flexibility of the system is enabled by use of a programmable spectral light modulator, i.e., a DMD, allowing for spectral coding. With the chosen approach the multiplex advantage can be exploited due to the fact that 50% of the spectral components projected onto the DMD are captured by the detector per measurement, thus providing an increase in sensitivity compared to that of classical dispersive approaches. The spectral resolution of the system was characterized using an optical design software (Zemax), suggesting a spectral resolution better than 10.5 nm for the used number of super-pixels. The implementation of the DMD-based detection allowed for single measurements at a rate of 18.2 kHz, thus enabling sampling times of 14.1 ms for full spectra with 128 pixels. Additionally, we introduced a compressive measurement approach that enabled full spectral acquisition in 4.2 ms. Single SROI of 50 nm bandwidth can be measured in 0.9 ms. Test spectra of well-known polymers (polycarbonate and polystyrene) were recorded and compared to those of reference measurements with a standard FTIR spectrometer, confirming satisfying quality of the obtained spectra. Additionally, the spectral coding approach was compared to line-scans that were performed using single-bar illumination masks in order to demonstrate the multiplex advantage. The spectral noise could be reduced by a factor of 8.2 by using the spectral coding approach. The approach presented in this paper could potentially be used in process analytical applications and high-speed applications in general. These could be, for example, screening applications where specific spectral features are monitored with an adapted SROI and, once identified, a full spectrum can be taken for verification; target industries could thus be classical ones (chemical industry, pharmaceuticals, etc.), but also food and recycling industries. Besides the advantages in flexibility and spectroscopic performance, the proposed concept presents an interesting and effective alternative to expensive detector arrays. This aspect is even more relevant at higher wavelengths, such as the mid-infrared spectral region, where sensitive detector arrays are particularly expensive. Therefore, an extension of the presented near-infrared system into the mid-infrared, with the purpose of gas-sensing (CO2), is the subject of our future research.