1 Introduction

Terahertz time-domain spectroscopy (THz-TDS) offers a broad range of applications for non-destructive testing, including coating thickness inspection, reconstruction of historical artworks, and material classification [1,2,3]. The latter can be employed to identify pharmaceuticals and explosives, but also more common classes, like polymers and wood products. One feasible application of THz-TDS with high relevance for the future is the sorting of plastic waste for recycling. Recent studies have demonstrated terahertz spectroscopy combined with machine learning for identifying plastics and for distinguishing multilayer from monolayer packaging [4, 5]. While some substances offer unique spectral fingerprints in the terahertz range, enabling more straightforward classification, many common materials lack such features and only present a certain amount of refractive-index dispersion and frequency-dependence of their absorption coefficient [3, 6,7,8].

Nonetheless, the classification of materials typical for indoor environments has been successfully demonstrated in many studies, employing machine learning (ML) algorithms like support vector machines (SVM), linear discriminant analysis (LDA), and convolutional neural networks (CNN) [9, 10]. Some focused on polymers, others include wood and other types of building materials [11, 12]. Commonly, measurements in these studies use THz-TDS setups in transmission geometry, and samples are prepared with smooth, plano-parallel surfaces. This approach mitigates the effects of surface roughness and enables direct material parameter extraction, based on a sample and reference measurement [13, 14].

Enabling THz for mobile applications, like handheld or robotic devices, is a goal of ongoing research. To achieve this, future material classification needs to function reliably under different conditions — in reflective configuration and with no prior knowledge of the surface topology. This will pose serious challenges, as the surface roughness of common objects in our environment can be in the same order of magnitude as the wavelength of the terahertz radiation, for example, raw wood or wallpaper [15,16,17]. Through scattering and diffraction effects, the recorded transients and resulting spectra will be strongly altered, severely affecting ML-based classification. To investigate these challenges in more detail, in this study, we examine the influence of surface roughness on the classification accuracy of a reflection-based THz-TDS system. For this purpose, we produce samples of a total of 11 different materials with well-defined surface roughness parameters. Based on the findings of previous work [18, 19], we employ a reflective goniometer setup to record the reflection from the samples at a range of angles and with different orientations of the samples.

Using the recorded data, we test the performance of two classification algorithms (support vector machines and random forests) to investigate the impact of surface topology. We show that for a classifier that is supposed to recognize materials with unknown surface properties, prior training with rough surfaces is indispensable. Furthermore, we discuss the feature importance of the individual spectral components of the measured spectra.

2 Sample Preparation

To achieve a controlled surface topology, we manufacture specimens of eleven different materials, as listed in Table 1. The set includes four polymers (ABS, PMMA, PC, PVC), two timbers (fir, oak), a wood-composite (MDF), and four castable materials representative of indoor environments: gypsum plaster, concrete, epoxy resin, and paraffin wax. These choices reflect common substrates and finishes of indoor environments, span diverse dielectric properties, and allow reproducible fabrication of flat and rough profiles.

Table 1 List of materials investigated in this study and their method of preparation. CNC-machined samples have been made from sheet material (polymers, MDF) or solid wood. The cast samples have been mixed and cured according to manual (concrete, plaster, epoxy) or molten (parafin wax)
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We consider two important surface parameters for sample preparation, root-mean-square (RMS) roughness \(\sigma \) and the correlation length \(l_c\). RMS roughness is the standard deviation of the surface’s height profile from its mean value. The correlation length, as described in [20], is found by calculating the normalized autocorrelation coefficient of the height profile z(x),

$$\begin{aligned} C(\Delta x) = \frac{\langle z(x) z(x + \Delta x)\rangle }{\langle z(x)^2 \rangle }\text {.} \end{aligned}$$

We define \(l_c\) as the lag where the correlation decays to 1/e, i.e.,

$$\begin{aligned} C(l_c) = e^{-1}. \end{aligned}$$

For surface profiles, \(l_c\) is an indicator of the spacing of roughness features. Shorter values imply sharper variations and steeper slopes.

Fig. 1
Fig. 1
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The plots a and b depict the two different surface profiles used for this work, flat and \(\sigma = 125 \upmu \)m. Rough-surface samples are manufactured based on a CAD model, as shown in a computer rendering in c. From the model, the sample shown in d was fabricated by CNC-milling solid ABS. Three notches were cut to enable repeatable placement in a self-centering mount

For creating surfaces with well-defined roughness, one-dimensional Gaussian height profiles are numerically synthesized by convolving white noise with a Gaussian distribution in MATLAB, using [21]. This way, a profile with \(\sigma = 125~\upmu \)m and \(l_c = 2 \cdot \sigma = 250~\upmu \)m is generated. It is used in this study together with flat samples, and their surface profiles are depicted in Fig. 1a and b. Note that in our study, the profiles are only one-dimensional. This limits scattering to the plane of incidence, in which our goniometric setup (described below) is measuring. The design simplifies manufacturing and, more significantly, increases the power of specular reflection, improving the signal-to-noise ratio (SNR) of our recordings. While, of course, real surfaces generally have two-dimensional roughness, our results are generally valid, as the scattering mechanisms are the same in the third dimension and do not induce qualitatively new aspects.

From the surface profiles, three-dimensional models of the samples are generated for manufacturing. They are used to program a CNC router that cuts samples from the wood and polymer materials. The machine is equipped with a 250 µm-radius tapered ball-nose end mill and applies the height profile with a 50 µm lateral stepover to guarantee faithful reproduction of the designed topology.

To expand the scope of materials to solidifying substances, silicone casting molds have been made from the ABS samples. These molds were then used to cast concrete, plaster, epoxy, and paraffin wax samples.

The finished specimens are circular with 100 mm in diameter and an approximate thickness of 10 mm. They feature notches to allow repeatable use with a self-centering mount. As an example, a specimen made from ABS is shown in Fig. 1d.

Every specimen is machined or cast from the same batch of material to minimize variation of optical parameters inherent to the medium. This can be reliably achieved for polymers cut from the same board, while the inhomogeneity of, for example, wood grain cannot be completely mitigated. Despite this, the surface topology dominates over natural structures in the investigated sample pieces, as we found through surface measurements described below.

Finished surfaces were verified with an achromatic confocal sensor (Micro-Epsilon IFS2405-3; 80 nm dynamic resolution) mounted on a motorized XY-stage. Across all materials, the measured RMS height and coherence length deviated by less than \(10\%\) from the computer model, confirming that the 125 µm profile was faithfully replicated.

Fig. 2
Fig. 2
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Goniometer setup used for the reflective THz-TDS measurements presented here. Two motorized rotation stages, mounting the sample and the transmitter respectively, set the angle of incidence and reflection (\(\alpha \), \(\beta \)) independently. The inset (top right) shows the sample mount, fixed to a third rotation stage, which adjusts the orientation of the sample

3 Experimental Setup

Reflection measurements were carried out using a standard fiber-laser–based THz-TDS system with a physical delay line and photoconductive antennas as transmitter and receiver. The antennas and sample are positioned in a goniometric setup, as depicted in Fig. 2. An aspheric TPX lens with 50 mm focal length and 1.5 inch diameter collimates the beam emitted from the Tx antenna. The full width at half maximum is about 1 cm. The reflection is focused back onto the Rx antenna with the same type of lens.

The angle of incidence and reflection can be set independently by adjusting the two motorized rotation stages. One rotates the sample as indicated in the figure, and the other mounts the transmitting antenna and turns around the same pivot point at the sample’s front surface. Centering the front surface to the pivot point of the stage is achieved by using an industrial laser triangulation distance sensor and a linear stage that shifts the sample.

For this experiment, we measure the specular reflection. For each specimen we record at \(\alpha =\beta \in \{20^{\circ },\,20.5^{\circ },\,\ldots ,\,69.5^{\circ },\,70^{\circ }\}\), i.e., 101 different angles. The minimum angle is set by the proximity of Tx and Rx antenna and the maximum by the THz spot size on the sample.

A third rotation stage is used to turn the sample around its own axis. Because the imposed surface topology is unidirectional (a one-dimensional height profile extruded across the disc), only two in-plane orientations are set: \(0^{\circ }\) and \(180^{\circ }\).

An orientation of the sample at \(90^{\circ }\) was not measured, but it is expected that the scattering and diffraction would mostly be directed outwards of the plane of incidence. This would result in a specular reflection similar to that of a flat surface, dominantly influenced by the Fresnel coefficients. However, the received power would be reduced due to the redistribution of signal power outside the plane of incidence.

Fig. 3
Fig. 3
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Flowchart representing the preprocessing of measurement data. The HDF5 file containing the raw recording data is loaded, then the program iterates through all material groups and measurement subgroups, which each contain a measurement of a certain sample and a certain sample orientation. The THz transients are bandpass-filtered and windowed. For subsequent FFT calculation, zero-padding is applied. The filtered transients, spectra, and unwrapped phase are stored to a new database with the same structure

The described measurement scheme gives us 202 measurement configurations for each sample. For each, 20 scanning repetitions (10 forward and backward movements of the stage) are recorded.

4 Data Processing

The recorded data is stored in a single-file database in the HDF5 format, to allow for fast and modular data access and processing of the raw measurements.

Before a classifier is trained with the data, preprocessing steps are applied, visualized in a flowchart in Fig. 3. Inside the database, measurements are organized in groups, which have similar properties to folders in a regular file system. The groups are separated by the 11 material classes that we investigate. For each material, subgroups are created with individual measurements. A measurement is a single sequential recording, taken for one single sample (i.e., one material and roughness) and one orientation (0\(^{\circ }\) or 1800\(^{\circ }\)). Through this definition, training and test data can be selected by parameters like roughness for evaluating the classification, as explained in the next section (Fig. 4).

For preprocessing, individual measurements are loaded in sequence. All individual THz transients are bandpass-filtered to remove noise and variation of optical power through the delay line cycle (4\(^{th}\)-order Bessel filter, 7.5 GHz–4 THz). Before calculating the spectrum, the transient is truncated to 150 ps. A Tukey window (\(\alpha = 0.1\)) and zero-padding (twice the length of the next power of two) are applied, for a slight interpolation in the frequency range. The transformed transient is separated into absolute values of the FFT and the unwrapped phase.

All processing results, including the filtered transients and metadata, are stored in a new dataset that is used for classification.

Fig. 4
Fig. 4
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Bandpass filtered THz-transients and spectra for two different samples, both recorded at \(70 ^\circ \) angle of incidence and reflection: a the reflection from a mirror-like aluminium surface, c the resulting spectrum. b and d The same plots for an ABS sample with rough-surface (RMS = 125 \(\upmu \)m). The reduced amplitude of the signal and the loss in bandwidth in the spectrum are clearly visible. They can partly be attributed to the refractive index of ABS, more significantly to the scattering of the surface

5 Evaluation of Classification

Based on the recorded and preprocessed data, a material classification system is implemented and evaluated. As mentioned in the introduction, various algorithms have proven to be well-suited for this task, including linear discriminant analysis, SVMs, and various types of neural networks. The amount of data we have collected is significant, but limited to a total of 202 measurements per sample. Thus, we are not using neural networks, but rely on two classic ML methods: SVMs and random forests (RF). We are using the previously calculated spectra as training data, and additionally include the unwrapped phase in the process of optimizing our classification, as described below. Each measurement consists of 10 forward and 10 backward scans, as mentioned above. The scans are treated as individual training instances.

First, we assess the effect of surface roughness on an SVM classifier by using only the FFT magnitude spectrum. We deliberately exclude the unwrapped phase to avoid leakage of sample-position information. We train and evaluate in three regimes — flat-only, rough-only, and the combined set (flat+rough). Because these subsets are drawn from the same pool of measurements, naive random splits can yield overlapping train and test samples. To approach this problem with a flexible solution, we first define “parameter keys” consisting of material, measurement number, and angle.

Our script finds all parameter keys that match the conditions we defined. It finds any overlap between the group keys for training and testing and assigns them to either set through a random shuffle split. Through this process, a train and a test dataset are created for any arbitrary parameter selection.

We repeat the training and evaluation of the SVM classifier for all materials, an angle range of \(2 0 ^{\circ }\) to \(70 ^{\circ }\), both orientations (\(0^\circ \), \(180^\circ \)), and all possible combinations of rough and flat surfaces for testing and training data. In Table 2, the resulting classification performance (weighted recall) is listed. We find that training and testing with only flat samples result in a good classification performance. This indicates that our classifier is able to discern the material classes based on their spectra, while it is not yet disturbed by the effects of roughness. When using only rough surfaces, the performance is slightly reduced, yet the classifier remains functional. Most significantly, the classification becomes dysfunctional if the test samples have a previously unseen surface morphology, exemplary by only \(12.2\%\) accuracy when training with flat and testing with rough surfaces.

Table 2 Classification performance (weighted recall) for SVM classifier, trained with spectral data (absolute FFT). Combined training and/or testing indicates that spectra of samples with both flat and rough topologies were passed to the algorithm
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The last row of the table indicates that combined training with both morphologies mitigates this problem. When training with both surface types, the classification remains consistently good, independent of the test data morphology.

An alternative to SVMs is the random forest classifier, an ensemble of decision tree classifiers that is widely used in supervised classification [22,23,24]. It gives us the ability to directly assign an importance value to each feature passed to it. As we do not apply dimensionality reduction to our data, each frequency point is an own feature. Thus, we can observe the relevance of each spectral component for the classification process.

To evaluate the RF classifier, we train it with the same parameters as the SVM classifier. The results are shown in Table 3. Classification is improved in all cases, exemplary by \(91.6 \%\) recall for combined training and test, compared to \(73.8 \%\) with the SVM classifier.

The fundamental influence of surface topology on classification robustness remains unchanged.

Table 3 Classification performance (weighted recall) for RF classifier, trained with spectral data (absolute FFT). Combined training and/or testing indicates that spectra of samples with both flat and rough topologies were passed to the algorithm
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Fig. 5
Fig. 5
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Confusion matrix, depicting the performance of the support vector machine classifier. Predicted labels are on the x-axis, true labels on the y-axis. In a, the classifier was only provided with absolute spectral data. In b, the unwrapped phase was added to both test and training set, resulting in a significant improvement of classification

Fig. 6
Fig. 6
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Confusion matrix, depicting the performance of the random forest classifier. Predicted labels are on the x-axis, true labels on the y-axis. In a, the classifier was only provided with absolute spectral data. In b, the addition of unwrapped phase improved the weighted recall significantly, as also shown for the SVM classifier

Fig. 7
Fig. 7
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Feature importance for the random forest classifier, binned in 50 GHz intervals. a Training with flat surfaces. Here, the importance is relatively higher for higher frequencies. For rough surfaces as shown in b, the importance shifts towards lower frequencies. For combined training c, the distribution represents a mix of the two previous cases. In all cases, the importance is distributed across the entire spectrum

One potential way to improve classification accuracy is to add the phase to the data used for classification. To assess this, the classifiers are trained with two different scenarios. One scenario is combined training and testing only with spectral data (absolute FFT), as in all evaluations discussed before. In the second, the unwrapped phase data is added to the training data, along with the absolute spectra, in the form of \(\text {cos}(\phi )\) and \(\text {sin}(\phi )\). The transformation removes the linear increase in the phase that would otherwise bias feature scaling.

The effect on the classification of the SVM can be observed in Fig. 5, where a) shows the training previously used and b) the inclusion of phase data. A significant improvement of classification accuracy can be observed, from 73.8 to 82.4%.

The RF classifier also shows significant improvement, as shown in Fig. 6, with an increase of the weighted recall from 91.6 to 97%. This shows that the phase contains relevant information for distinguishing material classes, for both classifiers evaluated here.

As previously stated, we can observe the feature importance for an RF classifier. In Fig. 7, the spectral importance is plotted for all combinations of morphologies. Generally, the importance is distributed over the whole area of the spectrum. This indicates that all frequencies contribute to the classification. For training with flat surfaces (Fig. 7a), higher frequencies up to 1.6 THz seem most relevant. In contrast, for rough topology, the importance shifts to lower frequencies, with increased values between 0.1 and 0.35 THz. This shift can likely be attributed to reduced scattering effects at lower frequencies, leaving more meaningful information in the lower range. It also agrees with the observed reflection spectrum depicted in Fig. 4. The combined training results in a more equal distribution over the frequency range.

For the linear SVM classifier used in this study, the learned decision weights (feature coefficients) can be interpreted as feature importance values. We normalized these values for comparability with the RF classifier and show them Fig. 8. All frequencies contribute to the decision boundary, but with a more even distribution over the spectrum than for the RF. The combined and flat-surface trainings exhibit an increased importance between approximately 0.25 THz and 1 THz, whereas the rough-surface training shows a comparably constant and slight decrease over frequency.

Peaks can be observed in the feature importance of the RF classifier, at about 1 THz and 1.25 THz. These frequencies are in proximity to water-vapor-absorption lines; however, we consider a direct connection unlikely. More prominent lines at approximately 556.9 GHz and 752 GHz do not show a comparable increase in importance, and the SVM feature importance does not exhibit a corresponding peak at 1.25 THz despite being trained on the same data.

Overall, the feature importance obtained from the RF and SVM classifiers seems to be in good agreement with the actual information content of the spectra, as it is distributed over the whole spectral range with sufficient SNR.

Fig. 8
Fig. 8
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Feature importance for the SVM classifier, binned in 50 GHz intervals. a Training with flat surfaces, b with rough surfaces, and c combined training. Compared to the random forest classifier, the importance is distributed more evenly

6 Conclusion

We systematically investigated ML-based material classification in reflective THz-TDS with controlled surface morphologies. Using eleven representative materials with either flat or rough \(\sigma = 125\,\mu m\), one-dimensional profiles and a goniometric setup, we curated an HDF5 dataset of amplitude and unwrapped-phase spectra for training and evaluation.

Our results show that surface morphology is a dominant factor for generalization: an SVM trained on flat samples fails when tested on unseen rough surfaces (15.3% accuracy), whereas training on the combined set (flat + rough) restores robust performance across morphologies. Random forests outperform SVMs on combined data (91.6% vs. 73.8% weighted recall), and adding phase information boosts RF accuracy to 97%. Feature-importance analysis further clarifies the role of surface structure: for flat data, higher frequencies contribute most, while for rough data the importance shifts towards lower frequencies with a peak around \(\sim 0.3\,\textrm{THz}\), consistent with the observed reduction in signal amplitude and spectral bandwidth caused by rough-surface scattering.

Our findings suggest that practical, reflection-based THz classifiers should include a variety of realistic rough surfaces during training, leverage phase information, and design features that account for frequency-dependent scattering and bandwidth loss on rough surfaces. Future work could extend to non-specular reflection for performance improvement [18], the employment of neural networks, and further expanding the range of materials.