Sparse Terahertz Frequency-Domain Sensing with Kilohertz Measurement Rate

Optoelectronic terahertz spectrometers have emerged as a novel tool in the field of spectroscopy, offering broad spectral bandwidth, high dynamic range, and fast measurement rates. Promising industrial applications for terahertz spectroscopy lie in various fields, covering gas sensing, non-destructive testing (NDT), material characterization, and medical applications, as well as security screening and many more [1‐4]. In NDT, broadband terahertz spectroscopy has already been demonstrated as a highly accurate tool for non-contact thickness measurements of multilayer dielectric coatings in the automotive industry [5‐8] and inline wall thickness monitoring for plastic pipe extrusion [9, 10]. For all these applications, fiber-coupled systems are mandatory to facilitate robust and secure handling, making them suitable for use outside of laboratory environments. In an industrial inline application, a terahertz spectrometer must deliver high measurement rates with an extensive dynamic range and maximum spectral bandwidth. In this study, we show that sparsely sampled terahertz spectra can significantly increase the measurement rate without compromising the accuracy of multilayer thickness evaluations.

Time-domain spectroscopy (TDS) systems utilizing mechanical delay lines represent the most widely used technique for fiber-coupled terahertz spectrometers, offering the widest frequency coverage and highest dynamic range. These systems have demonstrated up to 137-dB dynamic range and bandwidths of up to 10 THz [11, 12]. Typically, these systems employ a femtosecond fiber laser and photoconductive antennas to generate and detect the terahertz signals. The mechanical delay lines enable time-domain sampling with measurement rates up to 100 Hz. For industrial applications, faster measurement schemes have been developed by eliminating the mechanical delay line and employing two femtosecond lasers with asynchronous or electrically controlled optical sampling techniques [13‐18]. These methods have been reported in the literature to achieve measurement rates up to 10 kHz, although the dynamic range and terahertz bandwidth at this acquisition rate are not specified [16]. A measurement rate of 1.6 kHz has been shown to yield a single-shot peak dynamic range of 40 dB and a bandwidth exceeding 3 THz [18]. By averaging 1000 traces, it is possible to reach a peak dynamic range of 68 dB and detect signals up to 4.8 THz [17]. The fastest TDS system reported to date operates at a 36-kHz measurement rate using an acousto-optic delay unit, achieving a single-shot signal-to-noise ratio of 27 (equivalent to 14 dB) and a bandwidth of 2 THz (0.8 to 2.8 THz) [19]. However, the acousto-optic delay employed in this system demonstration limits the scan range to only 12.4 ps and, to the best of our knowledge, has never been implemented in a commercial TDS system. Overall, the exceptional signal quality provided by TDS systems comes with the trade-off of substantial system size and considerable costs due to the femtosecond lasers and mechanical delay lines, which restrict their applicability in certain use cases.

In this context, frequency-domain spectroscopy (FDS) is a promising solution to overcome the primary limitations of state-of-the-art TDS systems. FDS signals are generated and detected by photomixing of two continuous wave (cw) lasers. The measurement frequency is defined by the optical beat frequency of the laser superposition, allowing a frequency scan in the terahertz range by detuning one or both laser frequencies. Therefore, this approach allows the use of simple and cost-effective semiconductor diode lasers for the terahertz spectrometer. Additionally, photonic integrated circuits offer the potential for integrating the entire spectrometer onto a single chip, presenting significant opportunities for miniaturization and cost reduction, which are not yet exploited by commercial systems [20]. Advanced FDS systems, composed of discrete fiber-coupled components, have demonstrated a peak dynamic range of 132 dB and a bandwidth of 5.5 THz, closely rivalling the specifications of TDS [21, 22]. Previous research has also shown that, despite the lower bandwidth and dynamic range, FDS provides sufficient measurement accuracy for numerous industrial applications, particularly in the evaluation of layer thickness in single-layer and multi-layer dielectric samples compared to TDS [23].

In recent years, the measurement rate of commercial optoelectronic FDS systems has advanced from merely a few hertz to approximately 100 Hz. The highest rate reported in the literature is 560 Hz over a scan bandwidth of 600 GHz [24‐26]. Commonly, achieving a higher measurement rate in FDS necessitated a reduction in terahertz bandwidth due to the tuning speed limitations of the laser source. This constraint often compels users to compromise on the frequency ranges to be measured, thereby hindering the identification of critical sample features [26]. In many instances, especially during thickness evaluations, it is crucial to incorporate both high and low-frequency components to accurately assess the sample under examination. Our aim is to facilitate the acquisition of a broad range of measurement frequencies at rapid rates by minimizing the total number of measurement steps, thereby enabling highly precise analyses of sample properties.

To align the data evaluation scheme with these high kilohertz acquisition rates and the sparse frequency resolution, an algorithm tailored to the measurement task is essential. For multi-layer thickness evaluation based on sparsely sampled terahertz spectra, a transfer matrix method evaluation scheme has been demonstrated to achieve runtimes below 1 ms using off-the-shelf computer hardware [27]. This algorithm operates under the assumption of a fixed number of layers and fits the measured reflection coefficients to a model of the sample. Here, two main optimizations are utilized. First, only the low number of selected frequencies are used for the evaluation which drastically cuts down the number of computations required. Second, a function derived from the primary objective function is optimized, effectively narrowing the search space in the final stage and further decreasing computational demands. In [27], the feasibility of this evaluation scheme has been demonstrated and it was shown on a three-layer sample that runtimes below a millisecond with a thickness standard deviation below 5 µm for each layer were achieved.

This work focuses on the implementation of the measurement scheme that allows for sparse terahertz spectroscopy with kilohertz measurement rates. In the applications we envision, the time-consuming full spectral characterization of samples under test should be conducted once to identify the significant spectral features. Subsequently, our fast sparse measurement scheme can be employed in industrial production lines to keep track of these features in real-time monitoring.

The proposed spectrometer consists of a fixed-frequency laser and a tunable laser source that are fed into a wavelength selective phase modulator (WSPM), optical amplifiers, and a pair of cw terahertz antennas as emitter and receiver. Details of the implemented phase modulation scheme can be found in [24, 28, 29]. In an earlier work, this setup was operated at a measurement rate of 24 Hz over a bandwidth of more than 2 THz and a frequency resolution as low as 40 MHz [24]. Here, we reduce the number of measurement frequencies to only eight discrete frequencies by using a fast random-access tuning of the laser. The dwell time for each frequency step is set to 100 µs, resulting in an 800-µs repetition rate for the measurement. A RedPitaya STEMlab 125–14 system on a module with a Xilinx Zynq 7010 FPGA is used to drive the WSPM with a 125-kHz modulation signal and to acquire the laser synchronization trigger together with the amplified receiver signal at 12.5 MSamples/s. An additional operational amplifier is used to provide the necessary voltage range to the phase modulator. The measurement scheme for the sparse spectrometer is depicted in Fig. 1.

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For the evaluation of the spectrometer, we implement the measurement scheme with the static laser set to a frequency of 191.56 THz (1565 nm). The tunable laser is initialized with a frequency list of 50 GHz, 150 GHz, 200 GHz, 600 GHz, 750 GHz, 800 GHz, 1 THz, and 1.5 THz offset relative to the static laser. The flexibility and impact of selecting different frequencies and laser dwell times with the implemented system will be addressed in the discussion at the end of this work.

To extract the layer thickness of a multi-layer sample from the measured reflection coefficient at the selected frequencies and for a given sweep, we employ the transfer matrix method (TMM). Details about the TMM can be found in [30]. Utilizing the TMM, we calculate the expected reflection coefficient depending on the number of layers denoted by n and their respective refractive indices at each frequency. This model was chosen because it accounts for internal reflections, dispersion of the refractive indices, and it can easily be extended to any number of layers. Since the refractive indices of the individual layer materials are determined beforehand through calibration measurements, the only free parameters in the calculation are the n layer thicknesses. Furthermore, we define two objective functions F1 and F2. F1 is the sum of the squared differences of the measured and calculated reflection coefficient depending on the layer thickness at each frequency; consequently, F1 has n free parameters. The second objective function F2 is obtained by simplifying F1 algebraically, so that it only depends on n-1 parameters. F2 is therefore easier to minimize compared to F1 since it has one less input parameter. Further information regarding the procedure and the derivation is presented in [27].

The implemented algorithm exploits this by first optimizing F2 at each point of a 50 µm evenly spaced starting point lattice using the Nelder-Mead [31] optimization algorithm. The most promising n-1 dimensional starting point is then used in the second step for the optimization of F1. In the final step, optimizations are again performed at each point of an evenly spaced n-dimensional starting point lattice but for each starting point, only the nth thickness is varied in steps of 50 µm. The result with the lowest function value obtained through the optimizations of each starting point is then the final set of thicknesses for that sweep. This approach is more efficient compared to the direct optimization of all n thicknesses in the function F1 [27].

To validate the sparse frequency measurement scheme, we examine the optical laser spectra and the time-resolved terahertz-receiver signal. The obtained time signals are analyzed for the terahertz amplitude and phase as well as the dynamic range in dependence on the integration time. In the final phase of our study, we investigate a multilayer sample using reflection geometry and employ the proposed algorithm to calculate layer thicknesses, comparing these results with measurements obtained from a continuously swept spectrometer.

The optical signal of the superimposed laser beating is captured using a WaveAnalyzer 1500s optical spectrum analyzer (OSA) with a spectral sampling resolution of 20 MHz. Given the rapid switching speed of the tunable laser, we integrate multiple consecutive OSA measurements to capture all eight frequencies. Figure 2 shows the recorded optical spectra with annotations indicating the observed peak frequencies. All targeted laser frequencies are distinctly evident in the optical spectra. Additional spectral artifacts occurring at optical powers below − 40 dBm are attributed to the transitions of the tunable laser between the different frequencies.

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In the subsequent step, the two optical beatings at the phase modulator output are individually amplified to 30 mW optical power by erbium-doped fiber amplifiers (EDFAs) and directed onto the terahertz emitter and receiver, respectively. The terahertz antennas are positioned in front of two off-axis parabolic mirrors, and the resulting receiver current is amplified with a FEMTO DHPCA-100 transimpedance amplifier (TIA) at a gain of 10⁶ V/A. The FPGA captures the laser synchronization trigger as well as the amplified receiver signal at a sampling rate of 12.5 MSamples/s. Figure 3 illustrates the acquired signals over a measurement period of 1.7 ms. The envelope of the amplified receiver signal displays a step function, consistent with the expected discrete frequency steps of the tunable laser. The signal modulation follows the intended 125-kHz phase modulation; however, the beginning of each frequency step experiences distortion due to the frequency transitions of the tunable laser. The stable segments of the signal, following the laser transitions, are highlighted in a different color and contain seven full modulation periods (56 µs) for each frequency step.

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We utilize the stable and synchronized receiver signal from each measurement step to conduct an offline lock-in evaluation, allowing us to extract terahertz amplitude and phase information. Figure 4 presents the obtained amplitude values in comparison to a reference measurement obtained from a continuously swept spectrometer. The results demonstrate very good agreement between the measured amplitudes obtained through the sparse frequency measurement scheme and those from the continuously swept reference.

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To validate the phase information obtained from the measurements, we examine a 30-mm-thick high-density polyethylene (HDPE) sample in transmission, varying the incident angle of the terahertz signal. As a reference, the expected phase shift is calculated based on the change in the optical path length using Snell’s law, assuming a refractive index of 1.54 for the HDPE sample. The results presented in Fig. 5 demonstrate a strong agreement between theoretical predictions and experimental measurements for each frequency, with minor deviations attributed to the manual rotation and non-uniform properties of the sample. This represents a preliminary example of a straightforward single-layer thickness measurement utilizing the discrete frequency set, achieved at a measurement rate of 1.25 kHz. It is important to note that the frequency of 750 GHz is in close vicinity to a water vapor absorption line (753 GHz), which may introduce additional shifts in amplitude and phase under varying ambient air conditions. However, the data presented in Fig. 5 show no additional influence on the phase at this particular frequency over a total measurement time of approximately 30 min. Consequently, the controlled environment of our laboratory allows us to obtain accurate amplitude and phase information at this frequency, facilitating further signal analysis.

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To further verify the signal obtained, we analyze the dynamic range from the lock-in evaluation in comparison to the continuously swept spectrometer. Figure 6 presents the detected normalized power from both, a signal trace, and a background trace, where the terahertz signal is blocked, for the two measurement schemes in the transmission setup. Utilizing the sparse frequency set, we extract a peak dynamic range of 60 dB at 150 GHz from a single-shot measurement with 56-µs integration time (comprising seven full modulation periods of 8 µs each). The dynamic range of the spectrometer is expected to increase by 10 dB per decade in integration time [25]. This increase is illustrated by the colored lines representing the noise floor of the discrete frequency spectrometer in Fig. 6 for each frequency. Notably, a vertical spacing of the averaged noise levels exceeding 10 dB is attributed to fluctuations in the noise floor, resulting from the limited number of values available for calculating the average noise level. With 1000 averages (totaling 800 ms of measurement time), the sparse frequency spectrometer achieves a peak dynamic range exceeding 90 dB at 150 GHz, aligning with the noise floor of the continuous reference. The continuous reference is evaluated with a 500-µs integration time per frequency step, which corresponds to approximately 10 averages in the discrete frequency measurement scheme. Consequently, the sparse frequency spectrometer exhibits an approximate 20-dB reduction in dynamic range compared to the continuous spectrometer when employing the same integration time.

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As a next step, we test the ability of the sparse spectrometer to resolve the layer thickness of a multi-layer sample. This challenges both the signal quality of the spectrometer and the quality and speed of the algorithm necessary to extract the thickness values. The sample under test is a ceramic coated with slightly different paint layers on the front and back. A schematic of the sample is shown in Fig. 7a. The evaluation carried out follows the evaluation in [27]. The sample is measured in a reflection geometry with the state-of-the-art continuous spectrometer regarding the measurement speed [25] and the sparse spectrometer; each time, we record 5000 sweeps for evaluation with the algorithm. For the continuous spectrometer, we employ a 1.5-THz scan range with 1-GHz resolution at a 200-Hz measurement rate and 2-µs integration time per frequency step. Please note that due to the distinct hardware of the two spectrometers, we have to conduct the measurement series with the two systems consecutively. Each measurement series includes multiple measurements—typically comprising at least a short measurement, a background measurement, and the sample measurement. Consequently, this required the manual repositioning of the sample under test for each configuration, resulting in slightly different measurement positions. However, the position of the sample remained unchanged during the acquisition of the 5000 sweeps.

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Figure 7b shows the extracted values of the layer thickness in comparison. Here, all three layers of the sample are clearly recognized and we obtain similar thickness values with both measurement schemes.

For further evaluation, the fluctuation in individual layer thicknesses is visualized as histograms, accompanied by fitted Gaussian distributions indicating the mean values and single-shot standard deviations of the 5000 measurements, as shown in Fig. 7c, d, and e. For all three layers and both measurement schemes, a strong agreement between the histograms and Gaussian fits is observed, indicating the absence of systematic noise sources. The data demonstrates an excellent single-shot standard deviation of less than 1 µm across all layers when utilizing the continuous spectrometer. In contrast, the sparse frequency measurement scheme exhibits a standard deviation that is approximately doubled yet remains at 2 µm or less for each layer. It is important to note that this evaluation is based on a fixed dataset of 5000 measurements obtained under varying measurement times. Consequently, the data indicates that an increase in measurement speed by a factor of 6.25 results in only a factor of 2 increase in single-shot standard deviation.

The primary discrepancies in absolute thickness values shown in Fig. 7c, d, and e can be attributed to the selection of measurement frequencies used with the sparse spectrometer, as well as variations in measurement positions and the non-uniform properties of the sample. Based on the extraction of sparse frequency variations from the full spectral data (not shown), we estimate that the differences in measurement positions contribute deviations of − 4 µm, + 1.7 µm, and + 3.9 µm in the mean thickness from layer 1 to layer 3, while the selection of measurement frequencies accounts for + 0.7 µm, − 3.1 µm, and − 0.5 µm deviations, respectively. This results in a remaining static offset of 3.9 µm in the mean thickness of layer 3 between the two measurement schemes. Here, potential other sources of error include the angle of incidence of the measurement signal, limitations of the algorithm due to the material properties (e.g., identical refractive indices for the paint layers), and inaccuracies in refractive index estimations. Finding the cause of the static offset will require further evaluation of the employed algorithm. However, we emphasize that such systematic errors can be effectively controlled and assessed through ground truth measurements obtained via destructive testing methods in industrial contexts.

To investigate the influence of the measurement rates employed, we evaluate the standard deviation in relation to the time required for the frequency scans. By averaging multiple single-shot measurements, we can decrease the standard deviation of the layer thickness obtained; however, this concurrently reduces the update rate of our measurements by the number of averages used. Figure 8a, b, and c illustrate the decreasing standard deviation for each of the three layers as a function of measurement time when averages are applied. The standard deviation is obtained from 500 different datasets for each number of averages ranging from 1 to 1000. For both measurement schemes, we can observe an improvement of approx. 0.52 decades in standard deviation per decade in measurement time. In Fig. 8a, the standard deviation of layer 1 aligns closely between the two measurement schemes when applying the same measurement time, underscoring the effectiveness of the sparse sensing approach. For layers 2 and 3 (Fig. 8b and c), a contrasting offset in standard deviation relative to the measurement time is noted between the two schemes. The increased standard deviation in one layer corresponds to a decreased standard deviation in the other, indicating a consistent improvement in the standard deviation for the combined optical thickness of all layers. This behavior suggests that further optimization may be achievable through fine-tuning of the algorithm. Overall, compared to the continuous scan, our proposed sparse sensing measurement scheme reduces the minimum measurement time by nearly a decade, from 5 ms to 800 µs, while the achieved standard deviation of layer thickness remains largely unchanged with respect to the measurement time.

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Our measurements demonstrate consistent results in the optical domain, along with reliable processing of terahertz amplitude and phase data. Additionally, the assessment of multi-layer thicknesses, facilitated by the algorithm from [27], yields reliable outcomes with excellent standard deviations suitable for industrial applications. This section discusses constraints and potential improvements of the implemented measurement scheme related to (i) the observed reduction in dynamic range when applying the same integration time compared to a state-of-the-art continuous spectrometer, (ii) the selection of measurement frequencies for the sparse sensing, and (iii) the maximum achievable measurement speed. We will also highlight ongoing investigations and outline future directions for this research.

We observe an approximately 20 dB reduced dynamic range with the sparse frequency spectrometer when applying the same integration time per frequency step. Here, the main difference between the sparse and the full measurement systems is the necessity for a higher bandwidth when acquiring and processing electronic signals in the faster sparse measurement scheme, which leads to an increased bandwidth of the associated noise spectra. Furthermore, the continuous spectrometer employs a data acquisition resolution of 16 bits, whereas the faster analog-to-digital converters utilized in the FPGA are limited to 14 bits for the signal acquisition. This nominal difference in bit depth accounts for a 12-dB reduction in dynamic range. However, when considering factors such as the signal to noise and distortion ratio specified for the data acquisition, amplitude matching of the measurement signal with the data acquisition input span, and the difference in the employed sampling rates, the overall difference in the effective number of bits (ENOB) accounts for a 26-dB difference in dynamic range. Consequently, we anticipate that most of the reduction in dynamic range can be attributed to the electronic signal acquisition and data processing. Here, we expect a 12-dB improvement by adjusting the levels of our measurement signal and data acquisition, a change that is within easy reach. Other possible reasons for a difference in dynamic range are the frequency accuracy and stability of the “jumping” laser scheme. The voltage trace in Fig. 3 illustrates a predominantly stable signal following each laser transition. However, fluctuations in the amplitude envelope—particularly evident for the 50-GHz and the 150-GHz frequency steps shown in Fig. 3—suggest that the laser stability is not entirely optimal. Future investigations will focus on the frequency and amplitude stability of the “jumping” laser through interferometric measurement capable of resolving these rapid fluctuations. Overall, the observed increase in dynamic range of 10 dB per decade of integration time indicates a good system stability in our sparse measurements.

As shown, we implement the measurement scheme utilizing a set of eight frequencies ranging from 50 GHz to 1.5 THz. The main criteria for frequency selection were a non-equidistant spacing throughout the frequency range in which we expect a single-shot dynamic range that is sufficient to investigate multi-layer samples and at the same time avoid absorption from water. The non-equidistant frequency spacing is employed to mitigate challenges in thickness determination that arise due to the periodicity of Fabry–Perot resonances associated with layer thicknesses. While avoiding equidistant frequency spacing and multiples of other frequency differences is not a strict requirement, doing so can enhance the accuracy of the results. The selection of frequencies is further connected with the total number of measurement frequencies used for the sparse sensing. Theoretically, only one measurement frequency per unknown property of the sample is necessary. However, a greater number of measurement frequencies enhances the accuracy of the extracted sample properties but will also increase the evaluation time of the algorithm [27]. In this work, we concentrate on the implementation and validation of the sparse sensing terahertz setup. During the implementation of the measurement scheme, we determined that a total of eight measurement frequencies provide functional measurements with good results for the layer thickness evaluation. It is important to note that the terahertz frequencies utilized were not specifically optimized for the sample under test. The selection of measurement frequencies and the total number of measurement steps represent an optimization challenge that necessitates further intensive investigation, including imaging scans to validate thickness accuracy and standard deviation across a broader range of samples and materials.

The maximum achievable measurement rate is currently constrained by the performance of the tunable laser. The voltage trace presented in Fig. 3 reveals that the tunable laser requires approximately 30 µs to stabilize the signal after transitioning between two frequencies. Notably, this stabilization time decreases when transitioning between closely spaced frequencies, such as from f₂ = 150 GHz to f₃ = 200 GHz and f₅ = 750 GHz to f₆ = 800 GHz, suggesting that these frequencies lie within the same optical mode of the tunable laser. If we were to reduce the dwell time to 50 µs, we could allocate 20 µs for the evaluation of the terahertz amplitude and phase, potentially doubling our measurement rate. However, this adjustment revealed that only certain selected frequencies would yield functional measurements, again indicating that these frequencies must be within the same or an adjacent optical mode of the tunable laser. This introduces an additional layer of complexity to the ongoing optimization of measurement frequency selection. In this study, the implementation of a 100 µs laser dwell time provides a robust measurement scheme, ensuring that no limitations arise from the selection of measurement frequencies.

Alongside the ongoing optimization through selection of measurement frequencies and frequency counts, the most headroom for improvement of the sparse measurement scheme is identified at the tunable laser source hardware. Here, the frequency stability and the transition between different frequencies offer potential to increase the dynamic range and facilitate higher measurement rates. To address the limitations posed by the currently employed tunable laser, we plan to implement the measurement scheme using a tunable laser that is directly driven by the same FPGA that is already employed for signal acquisition. This approach will eliminate the need for synchronization between the “jumping” tunable laser and the applied phase modulation. Furthermore, with comprehensive knowledge of the optical modes of the tunable laser and full control over the tuning signals, we can optimize the transitions between different frequencies. Notably, widely tunable C-band lasers have already demonstrated nanosecond switching capabilities between different lasing modes [32]. Once we have integrated the tunable laser with direct FPGA control, the primary bottleneck will shift to the data transmission from the FPGA. Currently, we are constrained by a continuous data stream of 12.5 MSamples/s per acquired signal used in this work. To enhance the performance, we plan to implement the lock-in evaluation directly on the FPGA, allowing us to reduce the transmitted data to a single complex value for each measurement frequency while increasing the sampling rates to 125 MSamples/s, as supported by the FPGA. With this implementation, we anticipate that the measurement scheme will facilitate frequency switching times on the order of 10 µs, yielding an expected tenfold improvement in measurement rate compared to the implementation in this work.

In conclusion, we introduce a terahertz frequency-domain sparse sensing scheme that enhances measurement speed compared to existing full spectra FDS systems by a factor of ~ 6. By employing only eight discrete measurement frequencies between 50 GHz and 1.5 THz, we achieve an unprecedented measurement rate of 1.25 kHz. This represents, to our knowledge, the first demonstration of a terahertz FDS system attaining a kilohertz rate covering a spectral bandwidth exceeding 1.2 THz. Through signal averaging, we achieve a peak dynamic range surpassing 90 dB within a total measurement time of 800 ms.

Our approach facilitates accurate multi-layer thickness evaluation based on a sparse sensing model. This is evidenced by a single-shot standard deviation of 2 µm across three dielectric layers. Notably, the sparse sensing approach offers a precision in layer thickness measurements which is comparable to that of a continuously swept spectrometer over the same bandwidth and measurement duration. Additionally, by opting for a reduced averaging time, a measurement rate of up to 1.25 kHz can be achieved, compared to 200 Hz for the fastest existing terahertz FDS system covering the same frequency range.

The presented sparse terahertz sensing approach marks a significant advancement in expanding the industrial applicability of FDS terahertz systems. Our implementation enables efficient data acquisition and analysis, with the same hardware capable of performing comprehensive spectral scans as well as rapid sparse frequency scans. This enhances both the reusability and cost-effectiveness of the system. Furthermore, the sparse frequency scan can be tailored to focus on the specific spectral characteristics of different samples, paving the way for novel applications of terahertz sensing. Importantly, the sparse spectrometer is ideally suited for photonic integration and is within realistic reach of becoming a fully handheld spectrometer, further broadening its potential impact in various fields.