THz triangulation and stand-off measurement of the refractive index

We have constructed a pulsed THz imaging system based on the triangulation method. The system is capable of stand-off measurements, especially of retrieving the refractive index in a non-tactile manner even if the thickness of the object is unknown. The distance between emitter and imaged object for the presented measurements was 1.3m. We have measured a variety of samples in order to determine the capabilities and to optimize the optical properties of the instrument. © 2011 Optical Society of America OCIS codes: (040.2235) Far infrared or terahertz; (110.6795) Terahertz imaging; (110.6880) Three-dimensional image acquisition.


Introduction
The development of the photoconductive antenna [1][2][3] has sparked an active and increasingly large field of research trying to make the terahertz (THz) frequency range accessible for academic and industrial applications.While much work in this field still goes into the development of a large variety of elaborate equipment and systems, other activities are approaching or have reached the application stage.Many envisaged applications can be assigned to either of the fields of security or non-destructive testing (NDT).In the security field the aim is the detection and identification of concealed objects, particularly weapons, explosives and drugs.Commercial scanners have been developed for finding objects, they operate in the radar or lower THz range.The frequency range above 1 THz is more demanding but also much more interesting because equipment working in this range may be able not only to detect but also to identify hazardous material since most organic crystals, including explosives and drugs, have spectral fingerprints in this range.Much work in recent years has gone into extracting these fingerprints from transmission and reflection spectra at stand-off distance [4][5][6][7][8][9][10].Molecularly disordered materials such as polymers however typically do not have spectral fingerprints in the THz range.The same can be true for other materials such as semiconductors or ceramics.Yet their identification can be important in NDT applications and also in the security field in those cases where a material does not exhibit clear spectral fingerprints in the relevant frequency range.In this case the identification may be carried out by measuring the refractive index as precisely as possible.Very accurate measurements of the refractive index can be carried out in transmission [11,12] but this assumes that the body of the device under test (DUT) is completely transparent which may often not be the case.Here we focus on the reflection configuration.The refractive index in this case can be measured with variants of THz radar systems [5,13,14].By measuring the pulse travel time, such systems reproduce the product of the refractive index with the thickness of the transmitted material, nd, precisely.So if n is known, d can be calculated, or n can be calculated if d is known but as a matter of principle it is not possible in this way to measure both d and n based on the pulse travel time in a radar configuration.In order to measure both quantities, additional information is needed which can come from the pulse amplitude in relation to a reference amplitude.However to our experience amplitude measurements do not reach a good accuracy due to fluctuations in the laser intensity or the environmental properties (humidity), alignment difficulties with the sample and the THz sensors, and the quality of the surfaces.Alternatively, if the the THz emitter and detector are well separated, it is possible with a THz imaging system to measure the spacial distance between the point where THz radiation is reflected from the DUT's front surface and the point where it leaves the front surface after being reflected at the back surface.This is the principle of THz triangulation which permits the determination of both n and d without a reference measurement and without depending on the THz amplitude.While more and more inventive THz imaging systems are being developed [15] and waveform measurements in triangulation configurations (without imaging) are common [16], refractive index measurement in the way reported here have not beed described before (though parts of the work described here have been published in conference contributions by the authors [17][18][19]).

Triangulation
Triangulation is an established geometric method of distance measurement [20][21][22].An object is illuminated with a collimated or focussed light source from one direction under an angle of incidence ϕ of more than 0 • .The illuminated spot on either a fully or partially reflecting surface of the sample causes a reflection.This reflection is mapped at a different position of a sensor field depending on the geometric 3-D coordinates of the origin of the reflection alone.Since this mapping is well-defined, the origin of the reflection and thus the geometric position of the sample surface can be calculated from the position of its image on the sensor taking into account the beam path of the illuminating light (see Fig. 1(a)).
If THz radiation is used, many dielectric samples are transparent and all surfaces or interfaces with differing refractive indices create signals on the sensor, revealing their geometric positions.

Determination of the refractive index
A simplified classification of samples may be achieved by determining the refractive index n.The refractive index can be calculated if both the optical and geometrical path lengths of the light propagating through the sample are known.The triangulation method enables us to calculate the sample geometry and thus the geometrical path length from the displacement of the detected reflection on the sensor area.At the same time the optical path length is measured based on the pulse delay time.As seen in Fig. 1(b), the geometric path traveled within the sample is x geo,s = 2d/cos θ and the optical path is the same multiplied by the refractive index b a and the optical path difference between the beams is where Δt is the delay time difference, c the velocity of light, and the other quantities are visualized in Fig. 1(b).We insert Eq. ( 1) in Eq. ( 2) and, using the law of Snellius, sin ϕ = n sin θ , obtain Also using Snellius, Eq. ( 2) can be rearranged and then multiplied with Eq. ( 1): With Eqs. ( 3) and ( 4), the sample thickness and refractive index can both be calculated from the measured data.

Setup and components
We use a reflection scheme THz time-domain spectroscopy (TDS) setup [23][24][25] designed as a stand-off instrument with a total THz path length of 2.6 m.The emitter consists of an in-house produced photoconductive dipole antenna with 60 µm length and a gap width of 5 µm on a LT-GaAs layer on GaAs substrate.Alternatively, we have also operated the system with an InAs surface emitter [26].The laser used in combination with the dipole antenna is a femtosecond fiber laser emitting pulses of 110 fs duration time at a repitition rate of 76 MHz and a center wavelength of 803 nm.The average output power was 120 mW.Operating with the surface emitter, we used a Ti:sapphire laser with a center wavelength of 780 nm, a pulse duration of less than 100 fs, a repetition rate of 80 MHz and an average power of 3 W.Although it would strongly enhance the signal in electro-optic detection, we have not used an amplified laser system because we believe these systems are not yet stable enough to operate reliably in a real industrial environment with fluctuating temperature, dust and vibrations [27].The detector consists of a modified electro-optical sampling (EOS) setup (see Fig. 2) with a zinc-telluride (ZnTe) crystal and a CCD camera [28,29].The camera has 1600 × 1200 quadratic pixels with dimensions 7.4 × 7.4µm 2 .The frame rate is up to 30 fps and the camera is designed for lowlight operations.The detector is operated in crossed-polarizer configuration using a Wollaston prism.The intensity of one polarization orientation is reduced to almost zero and this branch is measured spatially resolved with the CCD camera.(The other branch is not used and not shown in Fig. 2.) Differences in luminance correspond to the THz electric field incident on the corresponding part of the ZnTe crystal.In this way THz waveforms may be retrieved with each sensor pixel.The THz beam path includes a set of planar mirrors which can be rotated and shifted within the optical plane for focusing the THz beam on a desired spot on the sample while keeping the path lengths or the angles constant (see Fig. 2).Mirror movement for moving the THz beam vertically to points off the optical plane have not been implemented in this demonstration setup.Instead, for scanning larger objects in a 2-D manner, a vertical translation stage was mounted in front of the optical table at the sample position for moving the sample up or down (see bottom of Fig. 2).

System characterization and experimential results
For measurements that do not require the imaging capacity of the system, the camera may be substituted by a photodiode [30][31][32] improving the signal-to-noise ratio (SNR) by a factor 10 b a due to a higher chopping frequency and an additional low-pass filter.This setup variant was used during the following test.However, the same results can be achieved by using the camera with a longer integration time and retrieving the waveforms from the luminance values of the respective pixels over time.
For real-world applications, one can not always expect to have a perfectly reflecting sample but diffuse reflection may dominate [33][34][35][36].We simulated these conditions by scattering THz pulses at surfaces with different roughnesses.The result was that for the roughest surface the measurable THz signal decreased significantly by a factor of approximately 18 in total THz electric field amplitude (see Fig. 3(a)) but measurements with the photodiode remained possible.However, since the SNR further decreases when using the camera with the same integration time, objects with rough surfaces are not suitable yet for imaging purposes with the presented instrument and without further improvements.
When measuring with the camera, the instrument resolution is limited by the apparent spot size of the THz beam.According to the Abbe diffraction limit, a point source is imaged by an optical device to a spot of diameter d = 1.22λ /(2NA) where λ is the wavelength and NA is the numerical aperture.In our case with the center frequency between 1 and 1.5 THz, λ ∼ 250 µm, and with a mirror diameter of 50 mm and a sample distance of 1200 mm, the numerical aperture becomes NA = 1/50 so that d ∼ 7.6 mm.So the THz emitter is imaged to a spot of size d at the sample, and each point of the sample is imaged to an apparent size of d in the camera so that the diffraction-limited resolution is expected at 2d ∼ 15 mm.The spot size observed in Fig. 3(b) is close to this value although the slightly oval shape in the figure indicates that there is still room for improvement.
To further demonstrate and evalutate the spatial resolution, a lateral grating pattern consisting of paper stripes attached to a metallic surface is scanned (see Fig. 4(a)).The scanning is achieved by simply moving one of the electrically adjustable mirrors towards the sample while the other one is moved away by the same displacement distance.Thus, the THz beam is moving in plane across the sample.The grating pattern of the sample has a width and a spacing of 1 cm for each stripe.The black line in Fig. 4 amplitude versus lateral displacement of the THz beam verifies that the measured THz signal is genuinely due to the paper stripe pattern on the metal since the removed and added stripe both can be seen (red line in Fig. 4(b)).The lateral resolution was thus confirmed to be better than 2cm.
For a first test of the triangulation capability of the system, we used a metallic screen with a step.This was achieved simply by placing a 12.3 mm thick metallic cuboid ('disk') in front of a metallic wall without any gap in between the two metals.The THz beam was now steered as described above (see Fig. 5 the level of maximum brightness from the line marked 'wall' on the left side to the line marked 'disk' on the right side corresponds to the geometrical arrangement, that is, the thickness of the disk.In (c), the vertical axis holds the pulse delay time, so the shift between the levels marked 'wall' and 'disk' is a difference in pulse arrival times which typically includes information on the refractive index (though in this example n = 1).While the precision of the thickness measurement based on the delay time is generally known to be almost 2 orders of magnitude better than the THz wavelength (300 µm), the precision of the thickness measurement based on the sensor position is an issue within this paper.Assuming the refractive index of air as n = 1, the evaluation of the data displayed in Fig. 5(b) results in a thickness of 12.46 mm (±1%), compared to the actual thickness of 12.3mm.
To verify the system's capability of measuring the refractive index from the time signal and the triangulation displacement of the detected THz spot on the CCD sensor area, we have produced a multilayer sample.The sample consists of a mirror of which the upper part is covered with a 8.30 mm thick semicylindrically shaped piece of polytetrafluoroethylene (PTFE, Teflon®).On top of the piece of PTFE, we fixed a silicon wafer with a thickness of 380 µm to improve the reflectivity of the surface in the THz spectral range.Reflections in this arrangement come from the Si front surface, the Si-PTFE interface and PTFE-mirror interface (red line in Fig. 6).When the sample is moved up with the vertical stage (cf.Fig. 2), the 'sandwich' leaves the THz beam, and there is only a reflection from the mirror (blue line).The shifts of the corresponding spots on the sensor can also be observed in the figure .From the known value for the angle of incidence ϕ = 34.4).If the THz radiation were continuous, the images of the spots on both surfaces would interfere on the detector, and Δb would be given by the spot diameter.Since we are using pulsed THz radiation, we can separate the spots due to their different arrival times, and Δb is given by the uncertainty of reading the position of the spot center which we estimate at 0.5 mm at the sample or 0.05 mm at the ZnTe crystal.So the expected relative accuracy of n and d amounts to 3 % for the air gap or 5 % for the PTFE sample, respectively, in good agreement with the observed deviations.If desired, the accuracy can be improved by more than a factor of 10 by increasing the numerical aperture but this would decrease the lateral scanning range for large objects.
When the sample thickness is large, two effects can compromise the measurement.Firstly, the beam shift b may become so large that the reflected beam fails to hit the instrumentation (mirrors, ZnTe crystal) on the detector side.With the current setup this happens at a thickness of ∼ 5 − 10 cm depending on the refractive index.This value can be strongly increased by using larger mirrors, more complex mirror movement and a smaller angle of incidence ϕ.Secondly, with a large sample thickness, some surfaces will be out of focus resulting in a larger spot size.However due to the small numerical aperture this effect is small in the given setup, it significally reduces the accuracy only at a thickness beyond ∼ 50 cm.

Conclusion
A THz reflection system for triangulation, radar and stand-off retrieval of the refractive index as well as imaging has been demonstrated.A lateral sample resolution of 1.5 cm, close to the diffraction limit, was observed based on the spot size on the detector.A resolution better than 2 cm was also demonstrated from a THz image of a grating.The refractive indices and thicknesses of two samples were retrieved with deviations of 3 % and lower from the known values.The measurement currently works with well reflecting samples only.For measuring diffusely reflecting samples, it is necessary to increase the signal-to-noise ratio, for example, by measuring with a faster camera or increasing the THz-pulse electric field.

Fig. 3 .
Fig. 3. (a) THz signal reflected from a smooth metallic mirror (black arrow) and two differently rough surfaces (blue and red arrows).The main-pulse delay time differs since the positions of the front surfaces change from measurement to measurement due to slightly different holders.(b) Spatially resolved measurement of a THz point source on the sample mirror.The diameter of the measured THz spot correspinds to a possible resolution of approximately 1.5 cm at sample position.

Fig. 4 .
Fig. 4. (a) Sample designed to verify the resolution of the system.One stripe from the center was removed and reattached on the right-hand side.(b) Black line: THz amplitude with a uniform grating pattern.Red line: THz amplitude with a discontinuous grating pattern as described before.The dislocation can be clearly seen in the THz signal.

Fig. 5 .
Fig. 5. (a) Step-shaped object to verify the triangulation capabilities.The incident and reflected THz paths are indicated as well as a scale.(b) THz triangulation signal (brightness) along the sensor (vertical axis) for various sample positions (horizontal axis) at the time of the respective THz pulse maximum.The vertical shift of maximum brightness from the left to the right side corresponds to the thickness of the step.(c) THz waveforms for various sample positions (horizontal axis), the THz electric field is encoded as brightness along the delay time (vertical axis).The sensor position here was chosen to generate a maximum waveform amplitude.The shift of maximum brightness from the left to the right side corresponds to the change in pulse arrival time caused by the step.
5 • , the measured displacement of b = 9.21 mm and the optical path difference cΔt = 14.34 mm, we can calculate the total thickness d of the 'sandwich' as 8.41 mm and the refractive index n of the layer of air to be 1.02.These values come close to the known values of d = 8.7 mm and n = 1.00.On the PTFE side the measured values are b = 6.09mm and cΔt = 21.66 mm resulting in d = 8.40 mm compared to a known value of d = 8.30 mm and n = 1.41 compared to a literature value of n = 1.43.The precision of these values is limited by the presision of reading the beam shift b: Δn/n = Δb/2b and Δd/d = Δb/2b which derive easily from Eqs. (3) and (

Fig. 6 .
Fig. 6.THz time traces of the radar part of the system as well as THz spot displacement on sensor area due to the applied triangulation method.