We present a terahertz quasi time domain spectroscopy (QTDS) system setup which is improved regarding cost and compactness. The diode laser is mounted directly onto the optical delay line, making the optical setup more compact. The system is operated using a Raspberry Pi and an additional sound card. This combination replaces the desktop/laptop computer, the lock-in-amplifier, the stage controller and the signal generator. We examined not only a commercially available stepper motor driven delay line, but also the repurposed internal mechanics from a DVD drive. We characterize the performance of the new system concept.
© 2015 Optical Society of America
During the last decade numerous practical applications have been demonstrated for THz spectroscopy systems  and the ongoing development regarding the performance of THz time-domain spectroscopy (TDS) systems has opened them the possibility for entering commercial and industrial markets . By using the telecommunication wavelength at 1550 nm and utilizing more compact fiber based fs lasers, the size of THz systems was further reduced; this improves their stability and allows for their usage in industrial environments . Furthermore, fiber coupled InGaAs/InAlAs THz antennas allow for highly flexible THz systems for scientific applications and non-destructive testing [4,5]. Highly accurate THz systems with a signal-to-noise ratio (SNR) of up to 90 dB have been presented recently, involving advanced delay concepts, e.g. voice-coils and motorized delay stage devices .
Alternative delay line concepts utilize the modulation of the femtosecond laser’s repetition rate, e.g. in OSCAT (optical sampling by laser cavity tuning) [6, 7]. ASOPS (asynchronus optical sampling) or ECOPS (electronically controlled optical sampling) driven systems require two synchronized lasers for operation [8–10]. These concepts offer high performance and flexibility in layout and application, but are rather expensive and require fast and specialized electronics for data acquisition and control.
For selected tasks and applications, like process monitoring or water status measurements these high-performance systems are simply oversized and overqualified [11, 12]. Similar information can be obtained with cheaper systems of smaller size, offering an acceptable way to address the needs and tasks.
The quasi time domain spoectroscopy (QTDS) or THz-cross-correlation technology was attested to have the potential for low-cost alternatives to regular THz TDS systems [13, 14]. The technique exploits inexpensive multi-mode laser diodes (MMLD) instead of relying on rather expensive femtosecond (fs) lasers. The resulting signal shape is a pulse train and, hence, similar to that of a TDS system, but with limited and discrete bandwidth. These signals can be treated with the same algorithms that are established in THz TDS to extract frequency dependent material parameters at THz frequencies .
Yet, although the demonstrated THz QTDS systems are much less expensive than THz TDS systems there is still the desire to further reduce cost and footprint.
Here, we present a THz QTDS system, which is improved in three respects. Firstly, we mount the diode laser directly onto the optical delay line. This can lead to a more compact optical setup. Secondly, a Raspberry Pi and an additional sound card operate the entire system. With this cost-effective combination we can replace the desktop/laptop computer, the lock-in-amplifier, the stage controller and the signal generator. We will test the performance of this concept using a commercial mechanical delay line. In another step we replace the commercial mechanical delay with the internal mechanics extracted from a DVD drive. This third improvement results in a further significant cost-reduction. Admittedly, the last step also leads to a moderate performance reduction, which is characterized in this paper.
2. Mounting the laser onto the optical delay line
Let us first recall the well established and classical system scheme used for most THz TDS systems. It is schematically shown in Fig. 1(a). The established setup can be divided into emitter (lE) and detector (lD) paths, starting at the beam splitter and ending at the THz antennas, comprising the THz path (lTHz) in between. The beam from the laser source is split by the beam splitter and directed into both paths. The emitter-path beam is focused onto the photoconductive emitter THz antenna; the detector-path beam is guided over an optical delay line and focused onto the detector antenna. The sample will be positioned in the THz beam path, located in between the THz antennas. THz lenses allow for collimated or focused beams. Typically the THz signal is sampled by moving the position of the optical delay stage in the emitter or detector path of the spectrometer. In the setup shown in Fig. 1(a), the delay line is implemented in the detector path. The path lengths are adjusted to match the condition of coherent detection and follow the equation
Figure 1(b) shows the new concept. Since a multi-mode laser diode (MMLD) is rather small it can be mounted directly onto the mechanical delay stage together with a beam splitter and a mirror. Preferably, both the beam splitter and the mirror are adjustable. Yet, as we want to use the internal mechanics extracted from a DVD drive, weight is an issue. For our demonstration we therefore 3D printed a mount for MMLD, beam splitter and mirror. This is a lightweight solution for which we obtain satisfactory results.
Since the laser diode itself is positioned on the delay line, a variation of the motor stage’s position induces a change of length in both spectrometer arms at the same time. Varying the position of the motor stage by Δx induces the following change:Eq. (1). The new approach allows for a more compact design, further improving the system’s costs factor by potentially reducing the material cost of the system.
3. System control and data acquisition by a Raspberry Pi
For low cost and highest flexibility, the main control unit is realized with a compact and inexpensive Raspberry Pi single board computer, operated by a Linux system and custom built software (see Fig. 2). The Raspberry Pi was upgraded by an additional Wolfson (now Cirrus Logic) Audio Card for high-quality audio generation and recording. The sound card enables the implementation of a digital software lock-in-amplifier via 24 bit audio recording for detection of the THz signal UTHz and a 16 bit output signal UE for feeding the emitter antenna with the reference signal. To adjust the electric levels, one amplifier boosts the reference signal to ±20 V and another one converts the THz signal from a current to a voltage and amplifies it by 107 V/A. The system uses two identical 200 μm LT-GaAs dipole antennas.
The sound card features an on-board stereo amplifier, which was used for precise and smooth stepper motor control via phase shifted sine signals. All signal streams were processed with sample clock-level synchronicity over the main audio chip with a sample rate of 192 kHz. What would otherwise have required advanced timing to synchronize many devices and functions is now implicitly being done in lock-step by using the same chip and software for controlling the entire setup.
The software is able to filter the signal with different filter orders and time constants, precisely control the stage’s position and movement and thus reliably record the THz signal. Normally, one trusts in the control unit and the manufacturer’s specifications for positioning and accuracy of the used linear stage. Since we are testing a new control method, it is necessary to first check these parameters and functionality.
Below, we investigate the reproducibility of the measurements and the working scheme of the Raspberry Pi controlled system. To verify the stability and functionality, a long term measurement over 500 traces for both directions, forward and backward, was obtained utilizing a Thorlabs (LNR50S/M) stage. A photo of this setup can be seen in Fig. 3. The time window was set to 160 ps, recorded with a speed of 2 ps/s and a time constant of tc = 80 ms. The results are shown in Fig. 4 and emphasize the stability and repeatability for the measurement in both directions. A detailed characterization of the delay line accuracy is given later in this work. The decreasing amplitude of the periodic THz QTDS pulses during a single scan is mainly caused by the signal dephasing of the correlation signals and optical misalignment.
In THz TDS systems the accuracy and linearity can be checked with reference to the position of the water absorption lines in the spectrum. In QTDS systems this is not possible, only discrete frequencies are present.
Since the longitudinal modes of the MMLD operate jointly with equidistant spacing, they can be used for emitting THz frequencies via difference frequency generation at the emitter antenna . The detected QTDS signal shows a periodic pulse shape with constant spacing of T = 1/ΔfM, which is directly proportional to the cavity size of the multi-mode laser diode. By knowing the difference frequency ΔfM of the laser modes, the distance of the QTDS pulses can be used to exactly reconstruct the linear time axis of the THz signal.
In a simple approach, identification and processing of peak or side peak positions provide the necessary supporting points for reconstruction. A more sophisticated approach is to use the auto-correlation of the QTDS signal, which will take all available data into account (see Fig. 5). To check the steadiness we applied the autocorrelation to a measurement over 80 ps, including two QTDS peaks, resulting in the auto-correlation signal in Fig. 5 with three pulses. The main peak spacing in the so transformed data equals the period T and can thus be used to re-create or validate the THz time axis.
The extracted peak distance fits perfectly to the expected value and proves the functionality of the delay scheme. Both, the signal processing and the measurement procedure work flawlessly. The long term recording shows excellent reproducibility for both measurement directions. Thanks to the interconnectability of the device, the measurement setup can be adapted to various configurations and needs.
4. Using the internal mechanics extracted from a DVD drive as the optical delay line
With the ambition to realize a low-cost QTDS system with a small footprint, the cost and size of each system component is crucial. The internal mechanics from DVD drives show potential for usage as the optical delay line in QTDS systems.
To verify the concept, we realized the setup with two different types of delay lines, described in Table 1. The first delay line (TL) was the previously mentioned, commercially available stage from Thorlabs (LNR50S/M), driven by a standard stepper motor. The second delay line (LC) consisted of the sled obtained from an optical drive and customized for use as a delay line, from here on called ”low-cost delay line“.
To find out whether the presented motor control system can achieve an acceptable accuracy, this section will first explore the reproducibility of position of the two different stages. To ensure comparability, all measurements were done with the same delay line velocity of approximately v = 1 ps/s and a time constant of the lock-in amplifier tc = 80 ms. The room in which the setup was located was not air conditioned. This should, however, only affect the amplitude of the THz signal and not its phase.
As a first step, the motor stages’ assumed leadscrew pitch was checked by employing the self-referencing scheme explained above (cf. Fig. 5). The difference frequency ΔfM = 24.30 GHz of the used MMLD was known from previous measurements, leading to an expected pulse spacing of Tref = 1/ΔfM = 41.15 ps. A reference measurement was done with each stage. From their auto-correlation signals, pulse spacings of T(TL) = 41.15 ps and T(LC) = 41.29 ps were obtained. So with the assumed parameters, the (TL) stage could already reproduce the reference pulse spacing. On the other hand, the (LC) stage’s assumed leadscrew pitch needed to be adjusted by 0.34% to yield the expected pulse spacing.
4.1. Measurement reproducibility of delay lines
For investigating the reproducibility of the system, multiple reference measurements for both stages were performed over a time window of 48 ps. This time window was chosen such that one QTDS pulse is included, shown in Figs. 6(a) and 6(b). To rule out stage tolerances and backlash when switching movement directions, only measurements in one direction were considered for the evaluation of reproducibility.
Figures 6(a) and 6(b) show 25 normalized reference measurements for stages (TL) and (LC), respectively. While the amplitude for stage (LC) is less stable than that for stage (TL), the pulse features appear at the same temporal positions for both and are stable over all 25 measurements. To further quantify the reproducibility, the cross-correlations of the first measurement with the respective 24 ones following it were calculated. The standard deviation of the delays taken from the cross-correlations are then used as a measure of reproducibility: the stages yield σ(TL) = 6 fs and σ(LC) = 14 fs. A variation of the amplitude of 4 % for stage (TL) and 6 % for stage (LC) could be registered, mainly induced by the environmental conditions. It is again noteworthy that the system concept does not include any external position sensors or reference switches, but still manages to achieve a reproducibility in the very low femtosecond regime.
4.2. Characterization of delay line linearity
To put the system concept to the test, the two refractive indices of a birefringent sample were to be determined. It should be noted that one can only obtain average refractive indices over all involved frequencies, since the evaluation happens in the time domain only. A birefringent liquid crystal polymer sample (LCP) with 30 vol% glass fiber and a thickness of 2.94 mm was measured under two angles α = 0° and α = 90° and compared to a reference measurement. The measurement data is shown in Fig. 7(a) for stage (TL) and Fig. 7(b) for stage (LC) and agrees with previous measurements of the same sample [15, 16].
The resulting refractive indices for the two orientations are shown in Table 2. Within the margin of error (estimated based on the reproducibility of the respective stage), we are unable to obtain the same refractive indices with both stage types. Assuming that the (TL) stage yields the more accurate results, a systematic error in our (LC) setup has thus been ascertained which has not yet been characterized and taken into account.
As can be seen, the refractive index difference ΔnLCP differs for the (LC) measurements depending on the how it is calculated: extracting it directly from the time delay between the two orientations or calculating it indirectly as . This fact is indicative of pronounced non-linear movement of the (LC) stage.
Using a Michelson interferometer, the linearity of the time-axis was examined for both translation units (TL) and (LC). The setup utilized a single mode laser operating at a wavelength of λ = 633 nm in combination with a photodiode connected to the main unit. This allowed for synchronized recording of the interference signal together with the stepper motor driving signal. The measurement was performed with vchar. = 1 ps/s over a time window of Tchar. = 80 ps. Knowing the wavelength of the laser, the fringes of the interference pattern allow precise reconstruction of the linear time axis. Fig. 8 shows the actual THz time position against measurement time together with the ideal linear time axis (clipped to a 1.5 s time window for better visibility). In contrast to the appearingly near perfect linear movement of the (TL) stage, the (LC) stage exhibits strong non-linearities.
4.3. Analysis and improvements of the linearity
For a more thorough analysis, the actual difference to linear movement is plotted in Fig. 9, overlaid with the motor driver signal. In the case of stage (TL), the deviation of the time axis follows a Gaussian distribution with standard deviation σ(TL) = 3 fs and no correlation with the motor driver signal is apparent. However, as the LCP measurements have already indicated, the deviation of stage (LC) from linear movement is significant. In contrast to (TL), it does not follow a Gaussian distribution. Instead, the fluctuation appears very periodic and correlates with the driver signal. In the worst-case scenario, two data points can be Δtnonlin = 350 fs farther apart than a linear time axis would have one expect.
The correlation of the motor driving signal and the THz time difference indicate a dependence on the mechanical and electrical properties of the optical drive. Four dominant influences affecting the linear movement were identified: A two-fold influence from the electric field distribution inside the stepper motor, the coarse-pitch leadscrew as well as the spring-affixed sled connector.
Since the deviation is periodic in nature, a sum of sines lends itself as a model function. Based on above-mentioned influences, a model function F(t) of four sines was chosen:
This model function is now fitted onto the data set obtained at a measurement speed of vchar. = v1 = 1 ps/s. Subtracting the fitted function from the difference data lowers the deviation from linearity considerably. While still retaining some periodic parts, the deviation now mainly follows a gaussian distribution. To validate the model function, the same interference measurements have been done for measurement speeds of v2 = 2 ps/s and v4 = 4 ps/s. These were then corrected with the previously generated fit (cf. Fig. 10 and Table 3).
The results exhibit the same characteristics as the original low-speed measurement. The worst-case point-to-point time difference can be reduced significantly by a factor of 3 to 3.5 in comparison to the uncorrected time axis. This, together with the remaining periodic parts in the corrected signal, shows the potential for further mitigating the influence of non-linearities in the stage movement.
To summarize, the new concept in combination with the signal processing unit and the characterization of delay line linearity bears the potential for precise QTDS measurements. Especially the highly-integrated signal processing, data acquisition and device control scheme enable the high reproducibility utilizing commercial low-cost hardware and electronics. Moreover, the concept still has room for further mediating the non-linearity of the translation stage and other systematic imperfections. Due to the non-linearities in the delay line, environmental conditions in the lab and internal reflections in the optical paths, the amplitude of the signal is subject to expected variations: As Kuwashima et al. presented, optical reflections being fed back into the MMLD affect the amplitude and spectrum of the THz signal . Furthermore, optimizations of the mechanical parts are expected to improve the overall system performance. Solving the latter problems will be part of future work.
A new system concept for THz spectroscopy systems has been proposed. Utilizing inexpensive and commercially available components for system assembly, e.g. a MMLD, a stepper motor delay line and consumer audio based data acquisition, allows to address the lower price segment. The sophisticated delay line control with signal self-referencing enables the reliable reconstruction of the time axis - assuming a linear delay line. In the case of non-linear movement, a simple method for correcting the deviations has been presented. The system thus allows for realization of QTDS setups with competing performance compared to standard laboratory equipment based systems.
In conclusion, the cunning system approach reveals the potential of QTDS technology and paves the way for affordable THz systems capable of real world applications in the low price segment. For future usage, more development has to be done, mainly to improve stability, performance and footprint of the setup. Using ultra low-cost delay lines may be an option in the future, however requiring sophisticated improvements to signal post-processing algorithms and active system stabilization. Direct usage of the mechanical unit from optical drives together with the new concept would be an opportunity to realize QTDS systems at the lower end of the price segment. Industrial applications would especially benefit from such a development.
The authors would like to thank the TEM Messtechnik GmbH, especially Mr. Lübbecke, for providing the amplifier and booster modules.
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