Time-correlated single-photon counting range profiling and reflectance tomographic imaging

2.1 Hardware description

The basic TCSPC hardware used in all experimental setups was identical. The laser source was a super continuum (SC) fibre laser (SC450, Fianium Ltd., Southampton, UK) with 4 ps pulse duration operating at 40 MHz pulse repetition frequency (PRF). In general, an SC continuum fibre laser may operate at different PRFs affecting the pulse-to-pulse interval and the ambiguity distance in TOF TCSPC applications (see below). The SC fibre laser emits radiation in a continuum, ranging from 450 to 1900 nm, although in this study only a fixed wavelength band in the NIR wavelength region was used.

2.2 Wide FOV transceiver

In the wide FOV setup, the permanently mounted collimator head of the laser output fibre was used to direct the laser beam towards the target. The receiver channel consisted of a short focal length lens focusing the reflected photons into a 62.5 μm core graded index (GRIN) multimode fibre for coupling to the detector module. The transceiver used a bistatic configuration (Figure 1) with the optical axes of transmit and receive channels separated by 70 mm vertically. The system FOV was 6.2 mrad FWHM (full width at half maximum). This bistatic configuration was used in indoor studies of geometrical shapes and for performing reflectance TCSPC tomography.

2.3 Narrow FOV transceiver

To allow outdoor experiments without laser safety restrictions, an acousto-optical (AO) filter operating between 650 and 1100 nm was used to select the wavelength of the laser and reduce the total transmitted power. The output from the AO filter was focussed into a single-mode fibre for transmission to the transceiver and subsequently collimated by a single lens. The receiver channel consisted of a Cassegrain telescope with 500 mm focal length and 125 mm aperture diameter, which focussed the collected photons into the GRIN fibre. The transmit channel was physically isolated from the receiver by a 45° outcoupling mirror, which was attached to the telescope central obscuration providing a monostatic configuration, according to Figure 1. The fibre positions could be adjusted to change the focussing distance from short ranges of below 50 m, useful for acquisition of high-resolution 3D scenes by mechanical scanning of the whole transceiver head, to long ranges of several kilometres for interrogation of retro-reflecting targets. The FOV of the monostatic system was 120 μrad (FWHM) and the beam divergence was adjusted to coincide with the receiver FOV.

Both optical setups (wide and narrow FOVs) were mounted on rotational/goniometer stages for accurate alignment of the system and for scanning azimuth and elevation angles by the computer. In addition, high-resolution 3D datasets could be generated by mechanically scanning the FOV of the TCSPC system [35]. This feature was implemented in a LabView application allowing low speed scanning.

2.4 Detection setup

The collected photons were fed to the detection setup using a GRIN fibre to avoid mode dispersion, which would reduce the range resolution. The detection setup used a SPAD detector (PDM Series, Micro Photon Devices S.r.l., Bolzano, Italy) with 100 μm diameter, <250 dark counts/s, 87 ns detector dead-time and <50 ps timing jitter. The collected photons were collimated onto a band pass filter (λ_c=834 nm, Δλ=3 nm FWHM) and subsequently focussed on the SPAD detector via achromatic lenses. The band pass filter reduced the background count rate and only a small part of the radiation emitted from the SC fibre laser was utilised. The band pass filter was exchangeable allowing for spectral investigations. Aluminium housing enclosed the detection setup to eliminate stray light.

The NIM (Nuclear Instrumentation Module [36]) pulse from the SPAD module was used to trigger the timing acquisition hardware (PicoHarp300, PicoQuant GmbH, Berlin, Germany), measuring the time since the last electrical sync pulses from the SC fibre laser for each collected photon. Data were collected for 100 ms up to 100 s depending on the application and signal level, and typically 4 ps time resolution per bin was used for histograms. Discriminator detection thresholds on both channels were chosen to minimise the system (instrument) response function (IRF). Data acquisition software (PicoQuant GmbH) was utilised to collect histograms, which were subsequently analysed off-line on a PC using in-house developed software written in MATLAB.

3.1 System performance

The system performance was characterised in short range indoor experiments. The IRF of the system was determined using a convex Au mirror or a flat Lambertian surface. The experimental IRF could be fitted to the following analytical function (Figure 3) in analogy with Pellegrini et al. [5]:

Figure 3

Instrument response function (IRF) for the TCSPC range profiling system determined by measuring the response from a convex Au metallic mirror at 53 m distance. The graph shows the experimental (stars), the model IRF (solid) and the subtracted signals (dash, experimental model).

(1)y={exp(-(t-t0)22w2), t<t1exp(-(t-t1)22w2)[aexp(-t-t1τ1)+bexp(-t-t1τ2)], t>t1 (1)

with

(2)a+b=1 and τ2=b(t1-t0w2-aτ1) (2)

including the five fitting parameters (t₀, t₁, w, a and t₁). Good agreement between the experimental and model IRF was obtained using a least square fit providing an error <1.5%. The FWHM of the IRF was measured to 53 ps, which corresponds to a range resolution of approximately 8.5 mm.

3.2 Geometrical targets

The studied geometrical shapes included a flat surface (which could be rotated), a variable step between two flat surfaces, cones with different dimensions and spheres having different reflectance ρ. The geometrical objects were placed at 34 m (flat screen) or 82 m distance (cones and spheres) from the TCSPC system and the wide FOV setup was used for the measurements. The flat surface was placed on a rotational stage to study the effect of altering the angle of incidence of the laser radiation with respect to the surface normal. To verify the range resolution of the system, a step between two surfaces was studied in addition to scanning the beam laterally over the step. The painted cones (ρ=0.3) had dimensions (base × height) of 9×40, 20×30 and 30×30 cm, and the diameter of the spheres was 14 cm. One sphere was painted white (ρ=0.3) and the other with metallic colour having a large specular component (ρ>0.9). All objects were carefully aligned towards the TCSPC system.

Figure 4 shows a typical pulse broadening when a plane surface is tilted. In this case, the beam radius is much smaller than the surface area when the angle of incidence θ=0°, that is, the laser beam is parallel with the surface normal. Varying the angle of incidence of the plane surface from 0° to 50° causes a pulse broadening from 0.05 ns (close to the IRF) to 1.9 ns. In addition to the experimental results, the theoretical pulse shape, based on the model IRF above convolved with the impulse response for a plane Lambertian surface, is depicted showing a calculated pulse broadening because of the alteration in geometry [41, 42]. Using this simple model, good agreement with the experimental results was obtained. The deviation at a larger angle of incidence may be attributed to slight inaccuracies in alignment and beam dimension on the surface.

Figure 4

Pulse response from a flat Lambertian surface at varying angles of incidence (0° red dots, 15° black dash, 30° blue solid, 45° black solid, left). Experimental and theoretical pulse width (FWHM) as a function of angle of incidence (right).

The depth resolution was studied measuring the pulse response from the edge of two partially overlapping flat surfaces separated in distance ranging from 30 mm down to 5 mm. The 30 mm distance resulted in two well separated peaks. At 5 mm distance between the plane surfaces a double peak structure was still observable, indicating that there were two surfaces even though they were not fully resolved. This is in agreement with the narrow IRF predicting a resolution of 8 mm from the TOF relation. Similarly, mechanical scanning of the beam across the two surfaces separated by 5 mm in distance results in an evident step considering a two-dimensional (2D) data representation (scan position vs. depth), as is presented in Figure 5.

Figure 5

Pulse response from a cone, base × height, 20×30 cm (A), and sphere, radius 30 cm (B). The red line corresponds to the TCSPC system IRF function. Range profiles as a function of scan position across a step between two flat Lambertian plates separated by 5 mm in distance. The colour scale is proportional to count rate per bin.

In addition to the investigated flat surface, pulse broadening from conical and spherical shaped geometries was also examined. Depending on the conical half angle, a broadening of the pulse shape can be observed, as shown in Figure 5A, for a cone (base × height, 20×30 cm). Here the linewidth increases to 282 ps in comparison to the 53 ps system IRF. The narrowing of the conical shape (9×40 cm) reduces the number of photons reflected towards the system causing a lower signal-to-noise ratio in the signal, as anticipated. With knowledge of the FOV and the target distance, the cone angle can be determined from the increase of the signal with distance [40]. Another example showing the influence of the surface geometry is the case of a Lambertian reflecting sphere with a 14 cm radius (Figure 5B). In this case, the linewidth was 296 ps (FWHM) and the peak shape is determined by the sphere radius relative to the FOV. For a sphere with a specular surface, primarily surfaces perpendicular to the laser beam would be reflecting back towards the system, limiting the possibility to draw conclusions about the shape. A narrow pulse shape (72 ps FWHM) is observed for a specular sphere with the same radius as the presented Lambertian diffusively reflecting surface sphere, which is in agreement with theoretical models [42].

As exemplified in the experimental results, the reflective properties, geometry and size relative to the illuminating beam of the studied objects have a large influence on the measured range profile. For a more detailed discussion on this issue, we refer to results presented in a previous study [40].

3.3 Long range reflector characterisation

Long range outdoor experiments were demonstrated by studying the range profile from an optical rifle scope and a road sign. In this case, the range was 750 m and measurements were performed with the monostatic narrow FOV transceiver in full daylight conditions. The background signal was reduced by spectral and spatial filtering (narrow FOV). In addition, turbulence studies using TCSPC range profiling have been carried out using a horizontal propagation path close to ground [43].

The rationale for these experiments was to investigate if high-resolution range profiling using acceptable integration times were achievable at a kilometre range. The objects studied here included reference objects (corner cube retro-reflector, plastic reflex), road signs and optical assemblies such as rifle scopes, focussing on the issue whether TCSPC range profiles can be used to classify an interrogated object using optical augmentation in a security application. Critical issues in long distance range profiling in daylight concern high background count rates, required integration times, distortion and broadening of the IRF because of high count rates and influence from turbulence effects.

The signal was registered from a corner cube retro-reflector (12.5 mm aperture) at 1.3 km distance using integration times varying between 100 ms and 10 s. A slight broadening of the histogram (61 ps FWHM) was observed compared with indoor measurements (53 ps FWHM). Several effects may contribute to this broadening. Both the position and the width of the IRF depend on the count rate, although with the thin junction SPAD detector used in this study this effect is less pronounced than with older thick junction SPAD detectors [44]. Thus, changes in average count rate and count rate fluctuations generated by turbulence-induced scintillations cause temporal broadening of the measured signal. Another source of temporal broadening is atmospheric scattering [45]. Typically, the contribution from the background was 20 to 100 kcps (kilo counts/s) without causing any limitation in retrieving histograms from different objects at a 750 m range. The signal-to-background ratio was of the order 28 to 30 dB. Pulse broadening because of slant surfaces was investigated by comparing the linewidth from two road signs, one directed with the surface perpendicular to the TCSPC system and one rotated 45°. Rotating the road sign caused an increase in the linewidth from 57 ps to 110 ps in agreement with the indoor results presented above for a flat surface.

In Figure 6, the observed TCSPC range profile from a road sign and a commercial rifle scope is shown, clearly indicating the different pulse shapes. The road sign exhibits a single peak close to the system IRF, whereas the rifle scope gives a range profile consisting of several peaks originating from the front optical group, a reticle in a focal plane and the lens group from the ocular. It should be stressed that the detailed optical schematics was not known in this example, limiting the information that can be extracted from the TCSPC data. However, if information about the optics is available modelling can be used to predict the TCSPC response [34].

Figure 6

Time-correlated single-photon counting signals from a road sign (black) and a rifle scope (blue) at 750 m range in daylight conditions. The road sign was rotated 45° relative to normal incidence and the rifle scope was aimed at the TCSPC system.

Previously long range outdoor experiments were performed using a TCSPC laser radar system having a slightly lower range resolution focussing on the influence from turbulence effects on the single photon signal [38, 43]. Signal statistics, turbulence effects and influence from the background were analysed studying retro-reflecting objects at a 1080 m range, suggesting that integration times <100 ms were obtainable. Moreover, a novel method based on the co-variance of the signal which can be used in situations with low count rates and high temporal resolution for determining the scintillation index using TCSPC data was proposed [46]. In addition, this scheme was compared with a traditional approach based on fitting theoretical probability density functions to the intensity fluctuations capable of including detector dead-time effects and to be used at higher count rates.

4.1 Theory

In reflectance, TCSPC tomography 2D images are reconstructed from range profiles registered for different view angles of a studied opaque object. The principle is depicted in Figure 7. Based on the scheme for filtered back-projection (FBP) using the inverse Radon transform, the tomographic image can be reconstructed. Mathematically, the 2D object can be expressed as [47]:

Figure 7

Schematic showing the principle of reflectance TCSPC tomography with projections and range profiles for each angle of incidence θ_i, and the corresponding tomogram after the filtered back projection (FBP) transform.

(3)g(x,y)=∑i=1mq(zcosθi+xsinθi)Δθ (3)

where

(4)q(r,θ)=ℱ-1(fℱ{p(r,θi)}) (4)

and ℱ, ℱ−1 denotes the forward and inverse Fourier transform, respectively, r is the distance along the measurement direction with zero at the rotation centre of the studied object (not a polar coordinate), p(r,θ_i) is the range profile for each rotation angle θ_i and f is a filter function. Here it was assumed that the rotation axis is parallel to the y-axis.

The filter function, f, was chosen to be a generalised ramp function according to:

(5)f(ω)=|ω|⋅e-ξ|ω|a           0≤|ω|≤π (5)

and ξ=|1ωc|a with ω_c defining the cut-off frequency and a an adjustable parameter. Typical values used in this work to reduce the high frequency components were a = 3.4 and ω_c = π/4. The values need to be optimised based on the IRF of the measurement system. Further improvement of the tomographic images was obtained by removing artefacts from strongly reflecting features of the studied opaque object that cause linear features stretching through the reconstructed image. The influence from these artefacts can be partly removed by using the ‘convex hull’ method where the first response (opaque surface) at each angle from the object is used to create an image mask outside which the response is known to be zero. Subsequently the tomographic image can be multiplied with the created mask to remove linear features stretching past the borders of the object. It should be stressed that in the scheme described above only opaque objects have been considered, although the tomographic method is applicable to partial reflecting surfaces within the TCSPC range profile. Critical issues regarding the quality of the reconstructed tomogram include defining the centre of rotation, applied angular resolution and the used angular projection sector.

4.2 Experimental measurements

In the TCSPC tomography experiments, objects were placed at 53 m distances on a rotational stage allowing azimuth angles from -170° to +170° using a typical step size of 1°–5°. A step and stare mode was used to register range profiles (histograms) for each angle step controlled by a LabView application. Histograms were stored on a computer for off-line data processing and tomographic image reconstruction. TCSPC tomography was exemplified by studying an object possessing several flat surfaces, a metallic optical rail (girder) and a model boat.

In Figure 8, the result from TCSPC tomography of a metal girder placed on the rotational stage is shown. The TCSPC range profiles are arranged in a 2D matrix with a column corresponding to a specific angular projection θ_i. In this case, the angular resolution was 1° and the angular sector ±170°. An example of an individual range profile corresponding to θ_i = 10° projection angle is depicted. After performing the inverse Radon transform of the range/projection matrix, the reflectance tomogram is obtained (Figure 8B).

Figure 8

Time-correlated single-photon counting tomography of a metal girder (A, B). An example showing the angular range profile (C) and all angular projections (D) are depicted in the lower figures. The grey scale is proportional to the normalised number of photon counts.

A more complicated studied object is a boat model (44 × 23 × 35 cm, length × width × height) viewed from the side. The strongest range profile signals from the boat model were obtained in projections with the long side of the model directed towards the TCSPC system with strong contributions from the hull, the cabin wall and sails. The corresponding tomogram obtained after FBP is depicted in Figure 9A. As observed, there are still some artefacts present in the tomogram because of strong specular signals in the range/projection matrix and 3D reflecting features. Moreover, limitations in the angular resolution and the covered angular sector may also generate artefacts.

Figure 9

Reconstructed tomographic TCSPC image of a model boat (A) and after applying a mask based on the convex hull, that is, the first return surface in the range profiles (B). Photograph showing the model boat (upper right).

In Figure 9B, the tomographic image of the model boat is enhanced by applying the ‘convex hull’ method. Here the first return in the range profiles is used to create a mask, which is subsequently multiplied with the tomogram. Other examples such as limited angular section and background contribution have to be taken into account to reconstruct the tomographic image, and have previously been presented [47]. In particular, the case with a TCSPC sensor on a moving airborne platform studying an object on the ground was considered and found to be difficult.