Measurements were taken in bright daylight over distances of ~ 2.8 km (Haymarket chimney) and ~ 4.2 km (Napier University). The solar background counts fluctuated between 500 cps – 3000 cps, depending on the weather conditions. During the experiments the SPAD detector operated in a “low noise” mode, enabling lower achievable DCR of 30 kcps at an expense of detection efficiency (~ 30 %) operating with 3 V excess bias, 20 µs hold-off time, 125 kHz external trigger and temperature of 265 K. The gate width applied to the detector varied between 100 ns and 500 ns which corresponded to an image depth of 15 m and 75 m respectively.
4.13.1
Haymarket Chimney
Over a range of ~ 2.8 km an industrial chimney of unknown dimensions was scanned; a visible-band photograph of the target is shown in Figure 4.20. A delay between the external SPAD gate on trigger and the laser pulse trigger was generated by the PPG and was equal to 3275 ns. This ensured that photon returns were located in the centre of a 500 ns gate.
152 Figure 4.20. A visible-band, wide FoV photograph of the Haymarket
Chimney located ~ 2.8 km from the laboratory.
The data was acquired over 32 × 32 pixels with a scan step representing 7.8 cm and 1 s acquisition time per pixel giving the total acquisition time of 17.1 min. Raw plotted depth data of different viewpoints of the target is shown in Figure 4.21(a), (b) and (c). Figure 4.21(a) is an intensity scatterplot where a pixel colour represents at a peak of a histogram at each scan point. Figure 4.21(c) shows the target from a top view on which its curvature can be observed.
Both the radius of curvature of the chimney and the taper angle visible in Figure 4.21(b) were calculated. To calculate the radius of curvature, r, an arc of known width, W, and height, x, were considered as shown in Figure 4.22.
From Pythagoras theorem
where
Thus the radius of curvature, r, is given by
2 2 2
2
m
r
W
Eq. 4.11 x r m Eq. 4.12x
W
x
r
8
2
2
Eq. 4.13153
Figure 4.21. Depth profile measurements of an industrial chimney acquired over a distance of ~ 2.8 km with 32 × 32 scan steps with a scan step resolution of 7.84 cm and 1 s acquisition time per pixel. Images (a), (b) and (c) are scatterplots of raw data where in (a) pixel colour represents the number of counts registered at a peak of a histogram at each scan point, and in (b) and (c) pixel colour represents range
154 Figure 4.22. A circle of a radius of curvature, r, with an arc of width
W/2 and height, x.
From the analysis of data x = 0.1 m and W varies from Wmin ≈ 0.87 m (top of the image)
and Wmax ≈ 1 m (bottom of the image). From Eq. 4.13, the radius of curvature of the
chimney at the top of the image, rmin ≈ 0.9 m and the radius of curvature of the chimney
at the bottom of the image rmax ≈ 1.0 m. The difference between the radii of curvature at
the top and the bottom of the image rmax - rmin ≈ 0.2 m and the chimney height and the
chimney height within the image was measured to be k ≈ 1.285 m (see Figure 4.23).
Figure 4.23. Side view layout of the chimney. Thus, the taper angle, α is given by
From Eq. 4.14 the taper angle of the chimney α = 8.8 °.
)
arctan(
max mink
r
r
155 As shown in Figure 4.21(a), the distribution in the number of photon counts across the x axis of the image resembles a Gaussian intensity distribution.
4.13.1.1
Depth Profile Retrieval
During a depth measurement, the detected photon returns were time-tagged by the TCSPC module and transferred to the control computer where software generated a histogram of photon returns for each scanned pixel. The histograms, produced with 50 ps wide bins, were analysed using a peak finder method. The peak finder finds a peak in the histogram based on least-squares curve fitting. The method yields good results in analysing data which can be judged by a number of well-defined criteria and is relatively simple and easy to implement. [13].
Least-squares curve fitting minimises the square of the error between the experimental data points and the values of the fitting function. In this case the quantity res2 expressed by [13]
is minimised, where f(xi) is the i-th element of the array of y values of the fitted model
and yi is the i-th element of the data set (xi, yi). In this equation Wi is the weighting
factor for the i-th data point and n is the total number of data points [13]. Typically, a quadratic polynomial is fitted into a set of data by the means allowing locations of peaks to be identified with a precision determined by a user-defined number of consecutive data points used in the fitting process [13].
The analysis of the experimental data was conducted in LabVIEW using an in-bulit Peak Detector function [14] which is based on an algorithm that performs least-squares fit described by Eq. 4.15 to a sequential group of data points. Number of data points used in the fit was specified by the user. The weight, Wi, was set to 1 for all data points.
For each peak, the least-squares fit was tested against a user defined threshold (typically above the background level), thus, peaks lower than the threshold were ignored [14] [15].
The algorithm calculated the time-of-flight, t, corresponding to the identified peak. This value was then used to calculate the range, R, to the target. Since there are multiple pulses in transit, establishing the absolute range was not possible without the prior
2 1 2
)]
)
(
[
i n i i if
x
y
W
res
Eq. 4.15156 information about the approximate location of a target. In this case this information was extracted from Google Maps. The absolute range was calculated from
where m is the number of a gates prior to the gate in which the signal is expected to be detected (e.g. if the target is located at an approximate range of 2.8 km and an 8 µs gate period - corresponding to 1.2 km distance is applied - then m = 2) and p is the gate period which is equal to 8 µs. The estimated absolute range to the chimney was 2893.9 m.