Extreme Ultra‐Wideband Optoelectronic Frequency‐Modulated Continuous‐Wave Terahertz Radar

A novel photonic terahertz measurement system based on a frequency‐modulated continuous‐wave (FMCW) radar approach is presented. In previous works, fast frequency modulation has been demonstrated in connection with a continuous wave terahertz spectroscopy setup based on the photomixing principle. In this paper, a terahertz radar based on both a photomixing transmitter and a photomixing receiver, in contrast to the rigid spectroscopy approach, is reported. Hereby, frequency modulation bandwidths of more than 1.65 THz in radar operation is achieved. This corresponds to an order of magnitude more than what is previously achieved by terahertz radar systems. At the same time, measurement rates can be achieved that are comparable with radar systems based on Monolithic Microwave Integrated Circuits (MMICs) according to the current state of the art. Within the scope of the work, two operating modes are realized, one with a measurement rate of about 560 Hz at 600 GHz modulation bandwidth and one with 200 Hz at 1.65 THz modulation bandwidth, which can be set within the spectrum from 50 GHz to about 4.5 THz. The possibility to adjust the operating range of the radar without necessary hardware adaptations is another unique feature of the presented system, which allows the operator to choose a suitable frequency band that corresponds best to a certain measurement scheme via software settings. Besides the potential for multi‐layer thickness inspections, the capabilities of this technique for terahertz imaging applications are presented.


Introduction
[7] The latter application benefits considerably from better resolutions and high operating frequencies up to the terahertz range and its associated large signal bandwidths.Millimeter-wave and terahertz integrated circuits can address this only to a very limited extent, which is why terahertz time-domain spectroscopy systems are often used, for example, for the inspection of multi-layer automotive paint coatings. [8]In recent years, these systems have undergone an impressive development and, in addition to large signal bandwidths of several terahertz, also achieved measurement rates of a few kilohertz that are comparable to integrated millimeter wave radar systems thanks to sophisticated system concepts. [9]igure 1.Optoelectronic FMCW radar concept consisting of a sweeping laser and a fixed-frequency laser.The two laser output signals are superimposed using a fiber coupler which is attached to an erbium-doped fiber amplifier (EDFA).A fiber splitter is used to guide the amplified laser beat signal by the EDFA to the transmitter (Tx) and receiver (Rx) in a terahertz measurement setup.A data acquisition unit (DAQ) records trigger signals of the laser tuning events, while synchronously acquiring the received terahertz signals, which are amplified by a transimpedance amplifier (TIA).The THz radiation is collimated or focused using off-axis parabolic mirrors (OAPM) and the transmitted and reflected signals are guided with a beam splitter made of float-zone silicon (FZ-Si) wafer.
However, such systems are comparatively complex and require femtosecond laser systems as well as a sophisticated laser delay unit.In addition to high system costs, this implies limited system scalability, especially with regard to multi-sensor systems.In contrast, tunable continuous-wave terahertz systems based on two-color laser radiation represent a promising, cost-efficient alternative. [10,11]Interesting implementations of frequency-modulated photonic microwave and terahertz radars are shown in Refs.[12] and [13], respectiveley.The latter features a modulation of 300 GHz at a center frequency of 600 GHz with a continuous bandwidth of 167 GHz and a sweep time of 48 ms, offering a much larger bandwidth but a much lower measurement rate compared to Si-Ge based monolithic microwave integrated circuits (MMIC) radar systems.
While the possibility of fast frequency modulation based on the photomixing concept has been shown before in a spectroscopy setup, [14] the here addressed realization of the radar measurement principle is the key for the possible application in the field of non-destructive testing.Hereby the implementation of radar signal processing methods (Section 2) as well as the characterization and linearization of the frequency modulation is a necessity [15][16][17] and a crucial subject of the new contribution (Section 3).
The developed optoelectronic FMCW radar has a modulation bandwidth of 1.65 THz at a measurement rate of 201.6 Hz in a frequency range of 50 GHz to 1.7 THz, which is more than one order of magnitude higher than the bandwidth of today's MMIC radar systems, while the measurement rates are of comparable order.In a second, faster, measurement mode with 604.3 GHz modulation bandwidth at 558.2 Hz measurement rate, the center frequency can be tuned in the characterized range from 350 GHz to 1.4 THz (technically up to 4.2 THz).The outstanding performance of the developed system is ultimately demonstrated in the form of thickness measurements and imaging examples (Section 4).

System Setup
A schematic of the fiber-coupled optoelectronic FMCW radar in combination with the optical setup to create a colinear beam path for radar range measurements and imaging applications is shown in Figure 1.The superposed optical signal is fed into an erbium-doped fiber amplifier (EDFA), which drives both a terahertz emitter (Tx) based on a waveguide-integrated PIN diode and a photomixing terahertz detector (Rx).The terahertz signal is emitted and received via silicon lenses as part of the housings of the Tx and Rx modules. [18]The received echo signal is mixed with the laser beat signal and the signal output of the mixing receiver is amplified by a transimpedance amplifier (TIA), which is connected to a data acquisition unit (DAQ).The sweeping laser provides trigger signals indicating the beginning of a frequency sweep, which are recorded simultaneously with the analog measurement data by a sampling rate of 5 MSs -1 .The laser driver provides additional trigger signals according to a preset look-up table presented by the laser manufacturer.In Ref. [14] this feature was used to address the factory default frequency points of the frequency sweep.
For the optoelectronic terahertz FMCW radar the optical signals of two CW diode lasers are superposed via photomixing to generate a beat signal in the terahertz domain equal to the difference frequency of the lasers.In order to establish FMCW operation, a fast sweeping modulated-grating Y-branch laser (COHERENT ® WaveSource TM ) in connection with a fixedfrequency laser (ID Photonics CoBrite DX1) are used.By taking advantage of the Vernier effect the MG-Y laser allows for a very fast frequency tunability of 500 GHzms -1 while both lasers can be tuned throughout the whole C-band (1530 -1565 nm).This way the center frequency of the laser beat signal can be arbitrarily set within a frequency range of around 4.5 THz.
In FMCW radar applications an object is illuminated by a typically linear frequency modulated signal, in order to obtain object information by the received reflected signal portion.The modulated frequency can be described as where  = B∕T is the tuning rate of the frequency modulation, with B the modulation bandwidth and T the modulation time, and f c the carrier frequency.At distance R the reflected echo signal, s R (t), is an attenuated time-shifted replica of the radiated FM signal, s T (t), or s R (t) ∝ s T (t − t).This time delay is related to the object's distance from the radar as t = R∕ n with  n being the group velocity of electromagnetic radiation in the propagation medium.This signal is mixed with a local oscillator's signal, resulting in: in case of a single reflector.This yields a beat frequency (f b ), which is proportional to B∕T and R. The theoretical range resolution of an FMCW radar is where n and c 0 are the refractive index of the propagation medium and speed of light in vacuum, respectively.Using an optical setup, consisting of off-axis parabolic mirrors (OAPM) for collimating and focusing the radiation and a float-zone silicon (FZ-Si) wafer as beam splitter, the colinear transceiver system is realized.After dividing the radiation in two equal parts, one path is used as the measurement signal, while the other part is either absorbed in a beam dump (BD) or reflected in case of a Michelson interferometer setup.The measurement signal path is either used in collimation or in a focused beam path, depending on the application.
As also shown in Ref. [14] measurements with frequencies above 2 THz require a significant integration time of a few seconds up to several minutes.For this reason, we have addressed the lower terahertz regime and established two operation modes for fast terahertz radar operation; one mode provides a FMCW bandwidth of 600 GHz at measurement rates of 560 Hz and another mode provides a bandwidth of 1.65 THz at a rate of 200 Hz.The characterization of these modes and the optimizations for fast linear frequency sweeps are discussed in the following section.

Characterization of the Terahertz Frequency Modulation
Wide frequency tunability is accompanied by mode hops corresponding to the free spectral length of the laser cavity.The MG-Y laser is configured in such a way that the modes overlap so that no frequency gaps occur.The non-equidistant mode spacing and complex internal dynamics require sophisticated control and calibration routines to achieve fast and linear tuning.The trigger scheme of the laser driver indicates these mode changes.This allows to derive coarse presets which, as shown in Ref. [14], are a sufficient approximation for the demonstration of spectroscopic terahertz measurements.However, even small discontinuities or nonlinearities in the frequency tuning significantly affect its use in an optoelectronic FMCW terahertz radar.For this reason, we have carefully studied the frequency tuning.This is shown in Figure 2 by two measurements before system optimization for FMCW radar operation (around 400 GHz frequency modulation bandwidth).Figure 2a is the intermediate frequency (IF) signal obtained from a single reflector.Due to the contributions of higher orders in the modulation, it is difficult to distinguish the IF signal without extra processing steps.This could be even more problematic in the case of thickness measurements.Figure 2b, in which we see two reflections from either side of a dielectric slab made of Polytetrafluoroethylene (PTFE) with a thickness of 5.25 mm, depicts the increased difficulty in finding the beat frequencies of the reflected FMCW signal by straightforward algorithms such as peak detection to extract these frequencies.
According to Equation 2, one can calculate the deviation of the measured signal's range due to the altered effective modulation rate and with the beat frequency at 455 kHz in our measurement setting, the -1.37 % deviation of the variable  yields an error in range measurement of 2.05 mm, as observed in Figure 2 For this reason, full characterizations of the modulated laser beat signal and optimizations of the two operating modes for radar operation were carried out as part of the present work.It should be noted that the laser manufacturer of the sweeping laser optimized the trigger scheme based on our studies in the following sections.The optimized laser firmware was used for example in Ref. [19].

Interferometric Setup for FMCW Terahertz Radar Characterization
To determine the frequency modulation characteristics, a Michelson interferometer setup is used.For this setup the configuration shown in Figure 1 is altered, to have a fixed flat mirror in one of the collimated propagation paths, while in the other arm the collimated beam is refelcted by a flat moving mirror.
The terahertz signal from the emitter is collimated using an off-axis parabolic mirror (OAPM) with a reflected focal length of RFL = 50.8mm and an aperture of D = 50.8mm.A float-zone silicon (FZ-Si) wafer with a thickness of ≈ 57 m is used as a beam splitter (BS), dividing the incoming wave into two reflected and transmitted paths with similar signal intensity.The reference interferometer arm has a stationary mirror, and the measurement arm consists of a mirror mounted on a linear translation stage with 1 m motion precision.The incoming waves from both mirrors are focused onto the detector with another OAPM.RFL and aperture are identical to the collimating mirror.
The complex electric field vector of the plane wave of the FMCW emitter, which has a linear polarization, propagates  through the Michelson setup in ẑ direction and is polarized in ŷ direction, Ẽ(z, t) = Ẽ0 e j(kz−(t)t) ŷ (5)   with both temporal and spatial components.k = 2π∕ is the wave number and (t) = 2πf T (t) the angular frequency.As the moving mirror changes position, the received wave from the measurement arm undergoes a phase shift proportional to the displacement of this mirror.For each position of the moving mirror 100 sweeps are measured and the interference pattern of the superposed waves is used to characterize the instantaneous frequency.
If we look at the spatially sampled points along one temporal data point, the phase difference between the reference wave and the measurement wave due to the displacement of the moving mirror (l s ) will be only dependent on the spatial variables of the electric field.Therefore, each sample array detected at any temporal sample point t ′ is the superposition of two monochromatic electromagnetic fields ẼD = Ẽ0r e j(kl r − t ′ t+ 0r ) + Ẽ0r e j(kl m − t ′ t+ 0m ) (6) where the subscripts r and m denote the complex electric field amplitude of the reference and measurement arms, respectively.The intensity sensed by the detector is equal to the time average of the interfered optical signals which yields and assuming that the BS is dividing the power equally and since the optical frequency is the same for both incoming waves we get Using the interference pattern by moving the measurement arm the frequency at each temporal point is obtained.The optical path difference (OPD) causing the interference fringes is related to the displacement of the mirror as d = 2l s = 2(l m − l r ).To conform to the Nyquist sampling frequency and to detect frequencies up to 2 THz, the minimum spatial sampling rate required is so here a spatial sampling of l s = 10 m and a temporal sampling at t s = 8 ns are chosen.
For an initial characterization of the system, we recorded the measurement data outgoing from the starting trigger as well as the trigger signal provided by the laser's controller according to its preset frequency points.In Figure 3 the intensity and frequency of the optoelectronics module is shown for the 600 GHz mode, with the laser's trigger locations depicted in light red.The setting contains eight cavity modes, which can be identified via the discontinuities of the green frequency plot.The frequency modulation according to the laser's triggers, provides an FM signal of 396.38 GHz bandwidth and a modulation duration of 804 s, yielding an overall modulation rate of 493.01 GHzms -1 .
When zoomed in at the trigger locations where the cavity modes change, as shown in the right images of Figure 3, the frequency sweep has discontinuities, which results in a nonlinear behavior of the frequency modulation.Moreover, as seen in the left plot not all the available signal bandwidth is used and only a duty cycle of 44.88 % is addressed by the laser presets (0.804 ms of the total 1.791 ms frequency tuning time for each frequency sweep).
In case of the 1.65 THz mode, we also observe discontinuities after each mode hop and an available duty cycle of 60.85 % (3.018 ms of used data from the 4.959 ms modulation duration).The achieved modulation bandwidth of 1498.596GHz in 3.018 ms, results in a modulation rate of 496.55 GHzms -1 , using 22 cavity modes of the sweeping laser.
These deviations from a linear modulation of the signal's frequency, contribute to errors in the beat signal's phase, which cause errors in the range measurements.In the next section, we show a new optimized sampling for better linearization and more efficient modulations.

Optimization for FMCW Radar Operation
Due to the spread of the IF signal's energy to other frequencies caused by nonlinear contributions in the frequency modulation, the range resolution worsens. [17]As mentioned before, the sweeping laser achieves a high modulation bandwidth by switching its operating cavity mode several times.To improve its linearity and bandwidth, first the nonlinear transient parts of the mode jumps are eliminated and then the overlapping frequency parts are compensated for, so that the new stitched frequency modulation is as linear as possible.Applying linear regression on the data set, the resulting FM optical signal is characterized.With the optical FMCW interferometry information, we find the correct temporal sampling points to achieve a single broadband linearly modulated signal for each operation mode.
To inspect the effect of the new optimized and improved resampling scheme, measurements are done with the 600 GHz mode on a single metal reflector and two dielectric slabs made of PTFE (n g ≈ 1.43).The thicknesses of the dielectric slabs are measured physically using a caliper of 0.05 m precision to be 5.25 and 17.25 mm.The range spectra of the calibrated signals are shown in Figure 4.The range axis is divided by the group refractive index of the PTFE material to show the real thickness of the slabs.In Figure 4a the effect of nonlinearities in the frequency modulation before optimization is shown in red.The nonlinearity effect is even more dominant farther away from the calibration position, meaning a broadening of the main lobe and higher order phase error contributions in the signal due to the higher time delay.Comparing Figure 4b,c one observes that the information of second reflection when the time delay is bigger is almost lost, if we only take the laser's triggers into account, which in turn means that the system cannot properly be used as an FMCW radar, and is only useful for very thin sample characterizations in the calibration plane.With the improved frequency modulation the sidelobes are better suppressed and the signal-to-noise ratio is significantly improved.
The optimized broadband frequency modulations are composed of smaller hop-free modulations between 54 and 92 GHz of width.The modulation rate  = B∕T is 500 GHzms -1 for both modes, and the linear regression for both modes yields coefficients of determination R 2 > 0.99999.Using the obtained information and by adjusting the fixed-frequency laser's frequency to an appropriate frequency, a flexible tunable optoelectronic FMCW radar is realized.Figure 5 shows the intensity curve of the detected frequency spectrum, where losses due to water vapor absorption in air and etalon resonances confirm the system's performance.The etalon or Fabry-Pérot (FP) resonances are present in the colinear FMCW radar setup due to the silicon beam splitter and the standing waves oscillating inside the optical cavity.The FZ-Si wafer we have used as beam splitter in this experiment has a group refractive index of n ≈ 3.416.By using the wafer at a 45 • angle, the available free spectral range (FSR) is ≈786.9GHz.The Fabry-Pérot and atmospheric effects on the signal have a negligible influence on the FMCW radar's performance in total, considering the high bandwidth of the signal compared to the small portion of the signal lost due to the aforementioned destructive effects.Moreover, it has been shown in Ref. [20] in more detail that if the gap in the frequency modulation of the chirp signal is negligible compared to the total sweep bandwidth, we still have enough information on the sample under test and can achieve a range resolution equal to a continuous uninterrupted modulation.

Measurement Results
To demonstrate the outstanding properties of the optoelectronic FMCW terahertz radar, typical non-destructive testing applications are exemplary addressed.The first example highlights the inherent range resolution and thickness measurement capabilities given by the two operation modes of the terahertz radar.The representation of the results refers to A-scans in the field of non-destructive testing.Unlike established terahertz timedomain systems, the underlying concept offers a cost-efficient solution with potentially comparable bandwidth without the need for sophisticated delay lines while being easily scalable to multiple measurement units.Further measurements are performed by extending the setup with focusing optics to demonstrate the performance of the system concept for inspections by terahertz imaging.The results are presented as C-scans and in a 3D representation.

Thickness Measurements
An adaptation of the setup shown in Figure 1 is used for each specific application, such as thickness measurement and imaging.Thereby, the fixed reflecting mirror is replaced by a beam dump (BD) and the moving mirror is removed to establish a radar signal propagation path in free space.This whole unit is then considered an optoelectronic FMCW transceiver, accomplishing a monostatic setup.
To demonstrate the range resolution of the broadband optoelectronic FMCW radar, we use plastic foils with different welldefined thicknesses.The samples are illuminated with the collimated beam, and after calibrating the data [21] a peak detection algorithm is implemented to determine the optical path difference between the front and back surface reflections of the sample.The group index of refraction for each sample is calculated from the Fresnel coefficient of reflection from the first reflection amplitudes.Figure 6 shows the range spectra of these samples referenced to the calibration position.Following Equation (3) the resolution limit for 600 GHz modulation bandwidth is 249.4 m, which corresponds to a sample (n g ≈ 1.8) thickness of around 138 m in the given case.as can be observed, the front and the back surface can nicely be separated in the range spectra down to a nominal sample thickness of 186 m.
However, due to interfering side lobes of the reflection peaks within the Fourier spectrum of the IF signal, we observe deviations of calculated thicknesses and the nominal thicknesses of the samples.While a window function can be applied to the data to suppress the side lobes, it is shown in Ref. [21] that with and without suppression, each reflecting surface can affect the main lobes' location, if peak detection algorithms are used to locate the sample interfaces.
Further investigations using the 1.65 THz mode (Figure 6b) show much smaller deviations between the achieved results and the nominal values down to sample thicknesses of 73.5 m, due to improved peak separation provided by the higher frequency modulation bandwidth providing a resolution of 90.6 m, which corresponds to a sample thickness of around 53 m.The higher standard deviation for this operation mode is due to the lower signal power at higher frequencies, which is closer to the noise floor.An increase in the integration time could improve the standard deviation of the measurements further.
For both measurement modes the two sample interfaces can be separated close to the theoretical resolution limit.More comprehensive investigations in this context, which include material dependencies and different sample thicknesses as well  as the use of signal models as in Ref. [21], are currently the subject of further studies.

B-and C-Scans for 3D Imaging
Building on the studies in Section 4.1, an OAPM was added to the setup to focus the radiation.Furthermore, for imaging purposes we apply a lateral raster scan of the sample.The merging of the A-scans along a scan direction allows the display of corresponding depth section images, B-scans.Finally, the merging of the B-scans, corresponding to the scan area, allows the display of lateral information, C-scans, of a selected depth plane or a 3D representation of the acquired volume.
The lateral resolution and depth of focus for imaging applications can be estimated by the Gaussian beam approximation. [22]ince the measurement signal has a broad bandwidth where the wavelength changes from 5.9 mm to 176 m, the focused beam's radius and the depth of focus are subject to significant changes throughout the spectrum.That is why for our imaging setup two different OAPMs with focal lengths of RFL 1 = 50.8mm and RFL 2 = 76.2 mm are used.Depending on the application, it requires careful consideration, which optics must be used and which frequency ranges have to be selected for the evaluation of the measurement data.

Multi-Layer Thickness Measurement
By obtaining the B-scans of multi-layered materials the thickness deviations of each layer and hidden features and defects can be detected.To test the optoelectronic FMCW radar's performance, the sample shown in Figure 7a, which is a section of a threelayer sewer pipe is used.Its thickness changes from 12.3 mm to 13 mm, the outer layers are made from polyvinyl chloride (PVC) and the inner material is foamed recyclate.On one side, steps with a height of about ≈ 100 m were milled into the sample surface.The flat side of the sample is facing the focusing mirror, which has a focal distance of 76.2 mm for a higher depth of focus required by the thick sample.Due to the sample's thickness, the 600 GHz mode was used for inspection.100 measurements are recorded for each pixel at 0.1 mm intervals, to inspect an area of 19×46 mm 2 of the sample.
For this measurement, the lasers are set to address a frequency modulation from 55 to 656 GHz.By considering the signal attenuation and the depth of focus of the sweep's higher frequency portion, only the measurement data in the range 55-430 GHz is used, providing a theoretical depth resolution in free space of R = 0.39 mm.The results are in good agreement with our previous results using an all-electronic FMCW radar. [21]In contrast to the previous work, the features of the sample can be resolved without additional signal processing methods due to the high bandwidth of the optoelectronic radar.
The 3D representation of the processed measurement data in Figure 7b shows the outer and inner boundary interfaces of the tube wall.For each boundary interface a separate color map is selected for better visualization.As can be seen, the second interface has significant deviations from an ideal flat layer.

Frequency-Selective 3D Imaging
To demonstrate the performance and potential of frequency selectivity for imaging inspections, studies were conducted on an AVR microcontroller chip in a dual in-line package (DIP) mounted on a breadboard, as shown in Figure 8a.The measurement is performed using the 1.65 THz FMCW mode to inspect its smaller inner structure.In contrast to the previous setup a 200 m thick FZ-Si wafer is used as beam splitter, providing an FSR of ≈ 224.3 GHz.An OAPM of 50.8 mm diameter and back focal length to focus the measurement signal into the sample, since the sample is thinner compared to the sewer pipe section and the lateral features are smaller.The spatial sampling is done at 0.2 mm intervals and for each interval 250 sweeps are measured for a better signal-to-noise ratio (SNR) at higher frequencies.
Figure 8 shows C-scan cross-sections of the FMCW volumetric data using the whole measurement spectrum at five different depths.While many details inside the microcontroller package can be seen, finer structures, such as the strip lines connecting the chip to the terminal pins (z = 6.71 mm and z = 6.83 mm), appear blurred due to the low-frequency components of the measurement signal.
As can be seen in Figure 5, the SNR in the lower part of the signal spectrum is more than 40 dB higher of that at higher signal frequencies.For this reason, the contribution of the lower frequency information is more dominant and stronger in the Cscan cross-sections.For further investigations, the measurement range has been divided to four different frequency bands with the same bandwidth and the respective C-scans plotted for comparison in Figure 9.As can be seen, not only can the finer details of the strip lines be seen with much greater contrast in the images of the higher frequency ranges, but also details that only have signal components in the lower terahertz frequency spectrum.

Conclusion
In this paper, we showed that an ultra wide-band FMCW system in the terahertz range can be realized with compact optoelectronic components incorporating a fast sweeping laser and a fixed frequency laser.Large modulation bandwidths and fast measurement rates can be achieved by stitching smaller FM signals produced from different cavity modes of the sweeping laser.Careful investigations of the laser behavior and selection of the laser settings maintain a linear frequency sweep.Since both lasers can be operated throughout the whole C-band, different terahertz frequency bands and center frequencies can be addressed within a frequency range of more than 4.5 THz without the need for hardware changes.The measuring rate for a given frequency bandwidth is primarily defined by the speed of the laser tuning.It is shown that this prototype allows for state-of-the-art layer thickness determination and can provide full 3D terahertz images.The use of radar systems with comparable modulation rates for industrial imaging applications [23][24][25] demonstrates the great application potential of the new technology in this field.In addition to the unprecedented bandwidth of a terahertz FMCW radar to the best of our knowledge, the optoelectronic continuous wave concept offers a simple possibility to distribute terahertz modulated signals by means of optical fibers and thus to address several transmitter and receiver units simultaneously , e.g., as an imaging radar array. [26]The scalability is primarily limited by the laser power and can therefore be extended by using additional laser amplifiers.Furthermore, there is the potential to synchronize the laser beat signal with high-frequency electronics, [27] which allows to benefit from their high stability and established radar system concepts in connection with the flexibility of optoelectronic signal distribution.
The use of terahertz technology in the field of non-destructive testing is still dominated by comparatively narrowband electronic radar systems in the lower range of the terahertz spectrum and very broadband time-domain terahertz systems based on femtosecond lasers.We are highly confident that the underlying photonic terahertz radar system will in future be positioned between these two technologies and will push the application spectrum of the previous terahertz technologies further out due to the mentioned features and the easy scalability of the presented system concept.
Currently, the system is being adapted for inline thickness measurement on highly absorbent coatings, such as battery electrodes for the automotive industry.Due to the possibility of precisely adapting the frequency range of the measurement system to the application and high measurement rates, as well as the high scalability of CW terahertz sensors compared to pulsed terahertz systems, this offers enormous application potential.

Figure 2 .
Figure 2. Measurement results achieved with the optoelectronic FMCW radar in connection with the laser's trigger scheme for a) a single metal reflector plate and b) a dielectric slab made of PTFE and a thickness of 5.25 mm, corresponding to an optical path difference of ≈ 7.5 mm between the reflections from each PTFE-air boundary interface.A difference of the IF frequency and as a result in reflection positions, is due to the different modulation rate of each sampling scheme.

Figure 3 .
Figure 3. Data obtained with Fourier transform interferometry for the 600 GHz sweep; a) shows eight mode hop-free cavity modes and their corresponding frequency (green) and intensity (black).The light red lines represent the triggers for the preset frequency points of the laser driver with rising edges spaced 2 s apart.b) shows three boundary points between trigger sequences.

Figure 4 .
Figure 4. Comparison between sampling with triggers and new optimized resampling of a single FMCW chirp signal for a) the FMCW signal reflected of a metal reflector, b) range spectrum of a dielectric slab of 5.25 mm, and c) range spectrum of a dielectric slab of 17.25 mm.The data is calibrated to a reference measurement.

Figure 5 .
Figure 5. Intensity distribution of the detected signal from a metallic mirror (green) in comparison to the system background noise using the 1.65 THz mode.

Figure 6 .
Figure 6.Range spectra of standard calibration dielectric foils, measured with the a) 600 GHz mode and b) 1.65 THz mode.The values in black are the nominal thicknesses of the samples and the numbers in red are the measured thicknesses of each sample with 10k measurements.The group refractive indices are calculated using the Fresnel's reflection coefficient for each sample.

Figure 7 .
Figure 7. a) A section of a sewer pipe with three layers (PVC-foam-PVC) and a customized stepped pattern on one side of the sample.b) 3D Representation of the sewer pipe section.R 1,2,3,4 are individual color maps showing the profile of the different boundary layers.The steps on the back of the sample and the layer interfaces are well resolved.

Figure 8 .
Figure 8. a) AVR microcontroller chip in its dual in-line package (DIP) fixed on a breadboard and b) C-scans of the volumetric data of the DIP microchip at five different depths considering all the modulation bandwidth of 1.65 THz mode.

Figure 9 .
Figure 9. C-scans of the AVR chip by the FMCW radar in different depths at selected frequency bands.The finer structures inside the DIP are better resolved at higher frequencies, whereas some other components are detected in the lower part of the measurement frequency spectrum.