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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 9 — Apr. 26, 2010
  • pp: 9192–9206
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Resolving range ambiguity in a photon counting depth imager operating at kilometer distances

Nils J. Krichel, Aongus McCarthy, and Gerald S. Buller  »View Author Affiliations


Optics Express, Vol. 18, Issue 9, pp. 9192-9206 (2010)
http://dx.doi.org/10.1364/OE.18.009192


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Abstract

Time-correlated single-photon counting techniques have recently been used in ranging and depth imaging systems that are based on time-of-flight measurements. These systems transmit low average power pulsed laser signals and measure the scattered return photons. The use of periodic laser pulses means that absolute ranges can only be measured unambiguously at low repetition rates (typically <100 kHz for > 1 km) to ensure that only one pulse is in transit at any instant. We demonstrate the application of a pseudo-random pattern matching technique to a scanning rangefinder system using GHz base clock rates, permitting the acquisition of unambiguous, three-dimensional images at average pulse rates equivalent to >10 MHz. Depth images with centimeter distance uncertainty at ranges between 50 m and 4.4 km are presented.

© 2010 OSA

1. Introduction

Improvements in single-photon detection technology and data acquisition electronics have facilitated a number of emerging applications employing the time-correlated single-photon counting (TCSPC) approach [1

1. W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, Berlin, 2005).

]. These applications include quantum key distribution [2

2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

] and linear quantum computing [3

3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]

], as well as expanding the reach of more traditional photon-timing applications, such as time-resolved fluorescence spectroscopy [4

4. A. Cleary, A. Glidle, P. J. R. Laybourn, S. García-Blanco, S. Pellegrini, C. Helfter, G. S. Buller, J. S. Aitchison, and J. M. Cooper, “Integrating optics and microfluidics for time-correlated single-photon counting in lab-on-a-chip devices,” Appl. Phys. Lett. 91(7), 071123 (2007). [CrossRef]

]. The use of photon-timing techniques in time-of-flight ranging has been investigated for a number of years, notably in ranging to retro-reflecting, earth-orbiting satellites [5

5. J. J. Degnan, “Satellite Laser Ranging: Current Status and Future Prospects,” IEEE Trans. Geosci. Rem. Sens. GE-23(4), 398–413 (1985). [CrossRef]

] and, more recently, for altimetry measurements from airborne platforms [6

6. J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002). [CrossRef]

]. Recording individual photon incidence events and correlating them to the trigger signal of the transmit laser yields time-of-flight data of high precision and repeatability, as previously demonstrated with non-cooperative targets at kilometer range with low average transmitted output powers [7

7. G. S. Buller and A. M. Wallace, “Ranging and Three-Dimensional Imaging Using Time-Correlated Single-Photon Counting and Point-by-Point Acquisition,” IEEE J. Sel. Top. Quantum Electron. 13(4), 1006–1015 (2007). [CrossRef]

]. In the demonstrations described in [7

7. G. S. Buller and A. M. Wallace, “Ranging and Three-Dimensional Imaging Using Time-Correlated Single-Photon Counting and Point-by-Point Acquisition,” IEEE J. Sel. Top. Quantum Electron. 13(4), 1006–1015 (2007). [CrossRef]

], high laser pulse repetition rates were used, typically 10’s MHz, to deliver the required optical illumination power to the target resulting in the rapid acquisition of sufficient statistical photon-timing data. The low per-pulse energy and correspondingly low returns per outgoing pulse avoids potential pulse pile-up errors and reduces the effects of dead-time effects [8

8. W. C. Priedhorsky, R. C. Smith, and C. Ho, “Laser ranging and mapping with a photon-counting detector,” Appl. Opt. 35(3), 441–452 (1996). [CrossRef] [PubMed]

]. Furthermore, the use of high repetition rate, low energy optical pulses permits the use of efficient, compact semiconductor laser sources.

The transition from a single-point time-of-flight rangefinder to a three-dimensional imaging system can be achieved by implementing a two-dimensional detector array to provide spatial information for each registered photon event. This approach has been demonstrated both with micro-channel plate (MCP) detectors [9

9. C. Ho, K. L. Albright, A. W. Bird, J. Bradley, D. E. Casperson, M. Hindman, W. C. Priedhorsky, W. R. Scarlett, R. C. Smith, J. Theiler, and S. K. Wilson, “Demonstration of literal three-dimensional imaging,” Appl. Opt. 38(9), 1833–1840 (1999). [CrossRef]

] and arrays of single-photon avalanche diodes (SPADs) [10

10. R. M. Marino and W. R. Davis Jr., “Jigsaw: A Foliage-Penetrating 3D Imaging Laser Radar System,” Lincoln Lab. J. 15, 23–36 (2005).

]. Alternatively, mechanical [11

11. J. Massa, G. Buller, A. Walker, G. Smith, S. Cova, M. Umasuthan, and A. Wallace, “Optical design and evaluation of a three-dimensional imaging and ranging system based on time-correlated single-photon counting,” Appl. Opt. 41(6), 1063–1070 (2002). [CrossRef] [PubMed]

] or optical scanning of a single rangefinder spot allows for time-multiplexing a single detector, and subsequent reconstruction of a complete depth image.

We recently described an advanced, scanning time-of-flight profiler, capable of acquiring data for the creation of three-dimensional images by optically scanning a single, combined receive- and transmit-channel across the scene of interest [12

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]

]. The system was based on a pulsed semiconductor laser at a wavelength of 842 nm operating at average optical power levels of approximately 50 µW. A thick-junction silicon SPAD was used, although the system has since been re-configured for other single-photon detectors, as described below. A pair of galvanometer mirrors were used to scan the receive- and transmit-channel over the scene, and detailed depth images at 100’s of meters target distance were recorded.

In a periodic illumination range-finder, the maximum distance that can be unambiguously determined, dRep, is simply that range which permits only one optical pulse in transit at one time. For a repetition rate fRep, this corresponds to [Eq. (1)]:
dRep=c2fRep,
(1)
where c is the speed of light in vacuum. In the measurements described in [12

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]

], the highest repetition rate used was 2 MHz, limiting the range which could be determined unambiguously to only 75 meters. In order to increase this unambiguously determined range, the repetition rate in such experiments would have to be further reduced. Clearly, any reduction in repetition rate, without any other changes in system configuration, will increase the required data acquisition time. This is compounded by the expected reduction in collected scatter from the more distant target to incur even further increases in acquisition time. It is clear that for photon-counting techniques to be used for long range, absolute depth measurement with efficient data acquisition times, it is essential to implement approaches for the avoidance of range ambiguity.

The issue of aliasing in periodic range measurements is not just limited to optical methods. A significant amount of work has been performed on microwave radar range resolution employing multiple repetition rates. Approaches such as the Chinese remainder theorem [13

13. W. H. Long, D. H. Mooney, and W. A. Skillman, “Pulse Doppler Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).

] or clustering algorithms [14

14. G. Trunk, and S. Brockett, “Range and velocity ambiguity resolution,” in Proceedings of IEEE National Radar Conference (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 146–149.

] can be applied to extend the system’s unambiguous range beyond that of each of the employed pulse frequencies. Continuous, linear modulation of the output frequency (chirping) can be employed to the same effect and is the most common of a number of pulse compression techniques [15

15. E. C. Farnett, and G. H. Stevens, “Pulse Compression Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).

].

In principle, arbitrarily long unambiguous distances can be achieved using random pattern techniques. Here, one key metric of the emitted signal undergoes a random or pseudo-random modulation. Correlation of the return signal to a time-shifted version of the input modulation yields the target’s distance. In the case of radar systems, bit stream modulation can be implemented by applying π phase shifts to the output wave (phase-coding pulse compression). Implementation of random pattern approaches has also been demonstrated in lidar systems and usually comprises direct on/off-modulation of the outgoing light beam according to a digital random bit stream. Takeuchi et al. investigated this method, using a continuous wave laser with external optical modulator [16

16. N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22(9), 1382–1386 (1983). [CrossRef] [PubMed]

], as well as by directly gain-switching a laser diode source [17

17. N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. 25(1), 63–67 (1986). [CrossRef] [PubMed]

]. Both implementations were used for the characterization of distributed aerosols at depth resolutions of few meters and integration times of several minutes.

Our group previously demonstrated that the random pattern technique is well suited for implementation in a one-dimensional time-of-flight ranging system that uses time-correlated single-photon counting [18

18. P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express 16(18), 13685–13698 (2008). [CrossRef] [PubMed]

]. Bit-to-bit sample rates of up to 1 GHz were applied, and both the complete trigger bit stream and photon detector event timestamps were recorded by TCSPC hardware, allowing for later correlation of the bit stream to incident photons. In the measurements, a pulse ratio of µ = 0.1 was used, where µ is the fraction of randomly distributed 1-bits, i.e. the bits coincident with the laser being triggered. The resolution of two corner-cube retro-reflectors, separated from each other by a few centimeters, was achieved at a range of approximately 330 m.

The duration of a trigger pattern consisting of b bits, sampled with a clock rate fSample, is b/fSample. To allow for unambiguous range resolution, target return photons must complete their target round-trip within this time, resulting in an unambiguous range dNonrep [Eq. (2)]:

dNonrep=cb2fSample.
(2)

This expression indicates that the unambiguous range can be extended simply by increasing b, the length of the repeated pattern, rather than decreasing the average repetition rate of the source, as necessary in the periodic case. Without additional processing, correlations between single target return histogram peaks and every 1-bit throughout the bit stream impose a base correlation level against which an actual, wanted correlation between all target return photon events of an object with a lower return intensity and the bit stream has to stand out. Given the large variation in return intensities of different target materials, typically varying by several orders of magnitude, this effect would severely limit a system's capability to resolve low-return targets in the presence of other high-intensity returns.

In this article, we describe the implementation of this coded ranging approach in our scanning, photon-counting three-dimensional imaging system. This includes evaluation of the system’s performance using different single-photon detection techniques as well as the optimization of analysis routines necessary to process the large amount of high-resolution target pixel return data. Furthermore, a technique is demonstrated which efficiently attenuates the base correlation level imposed by correlations with a wrong relative timing offset.

2. System description

Figure 1
Fig. 1 Schematic diagram showing the key components of the scanning rangefinder system.
shows a schematic of the employed depth imaging system. A pulse pattern generator with a maximum clock rate of 3.35 GHz was used to trigger a PicoHarp 300 TCSPC module with two high-resolution input channels (4 ps timing bin width), as well as a pulsed laser driver. A laser diode emitted transmission pulses with a duration of approximately 100 ps at a wavelength of 842 nm. The output laser beam was deflected in two spatial dimensions using a pair of computer-controlled galvanometer mirrors. This enabled scanning over a maximum optical field of view of 55 mrad when a 200 mm focal length, f/2.8 camera objective was used as the system objective.

The scattered return photons that are collected by the system objective for each pixel pass through the scanning and relay optics that are shared with the transmit channel. The return photons are then separated from the transmit channel using polarization routing optics [12

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]

], and focused into a 5 µm core diameter single-mode optical fiber using a fiber collimation package. The small fiber core diameter provides an efficient means of spatial filtering and defines the receive channel spot size at the target surface, which closely matches that of the illumination spot. The instantaneous field-of-view of the receive channel, i.e. the field-of-view of a single “pixel”, was approximately 45 µrad when using a 5 µm core fiber. This corresponds to a scanning spot diameter of approximately 14 mm at a range of 325 m and 25 mm at a range of 575 m. The single-photon detector is connected to this fiber, and the electrical detector output is connected to the second input channel of the TCSPC module.

Since our recent publication [12

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]

], several modifications have been made to the system including the replacement of the telecentric relay lenses. The new lenses contain fewer optical surfaces that help to reduce both the return signal attenuation and internal back-reflections. New control software uses dual-processor multithreading to make the analysis of periodic illumination range data during ongoing acquisition possible, allowing for quasi real-time display of acquired depth information.

Fiber-coupling of the employed single-photon detector permits routine comparisons of different components, including different types of silicon SPADs and superconducting NbN nanowire single photon detectors [19

19. R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005). [CrossRef] [PubMed]

,20

20. R. E. Warburton, A. McCarthy, A. M. Wallace, S. Hernandez-Marin, R. H. Hadfield, S. W. Nam, and G. S. Buller, “Subcentimeter depth resolution using a single-photon counting time-of-flight laser ranging system at 1550 nm wavelength,” Opt. Lett. 32(15), 2266–2268 (2007). [CrossRef] [PubMed]

]. Preliminary tests and parts of the presented results using the coded ranging technique described in this article were performed on a thick-junction silicon SPAD, offering the highest measured quantum efficiency of all investigated devices at the system’s illumination wavelength (42.4% at 842 nm). This high efficiency however is paired with a comparatively large timing jitter of approximately 400 ps FWHM.

Additional measurements were performed using a shallow-junction silicon SPAD with a typical timing jitter of 40 ps FWHM, rendering the temporal pulse width of the illumination laser the dominant contribution to the jitter. This combination yielded an overall instrumental response of approximately 100 ps FWHM. The device has a quantum efficiency of approximately 3.9% at 842 nm, with a maximum continuous count rate of 2 × 107 s−1.

3. Experiment

3.1. Pseudo-random modulation setup

In order to migrate the coded ranging technique to a three-dimensional depth profiler, several optimization steps had to be implemented. Each pixel in a scanning pattern must be analyzed independently for target returns. The continuous recording of unaltered streams of trigger- and return-pulses at timestamp resolutions of few ps is unrealistic both in terms of sustained processing speed and memory size. Improvements on the analysis procedure described by Hiskett et al. [18

18. P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express 16(18), 13685–13698 (2008). [CrossRef] [PubMed]

] furthermore allow for a better signal-to-noise ratio in the correlation domain without increasing the required output power or per-pixel dwell time.

Figure 2
Fig. 2 Cyclic cross-correlation technique for coded range resolution. A pulse pattern generator with clock rate fBase triggers a pulsed laser diode. Based on the known temporal system response and the bit stream, a reference signal for cross-correlation is produced. The cyclic return histogram contains the measured target surface responses, time-shifted by the round-trip duration 2d/c. Not every outbound laser pulse necessarily causes a registered photon event (indicated by dashed returns). The cross-correlation function of the reference and the target response yields a maximum at 2d/c.
depicts the cyclic range-resolution approach. A Mersenne twister pseudo-random number generator was employed to create bit streams for the desired average number of pulses per second at the employed sampling rate. It was also ensured that the minimum temporal separation between two pulses was in excess of the 12.5 ns minimum recovery time of the used pulsed laser driver. This pattern was transferred to a pulse pattern generator. The generator was programmed to continuously send the bit stream to the laser driver, and a single trigger pulse at the beginning of each repetition of the bit stream to the TCSPC hardware. The second input of the TCSPC module was connected to the single-photon detector. An auxiliary input marker channel received a signal every time a computer-controlled D/A-converter applied a new pair of voltages to the system's two galvanometer mirrors, responsible for x/y-deflection of the transmit- and receive channel, thus marking a change of pixel.

The employed TCSPC module did not support synchronization of its internal clock to an external trigger source. The clock of the pulse pattern generator therefore was free-running and not phase-locked to the acquisition hardware, resulting in the potential of a cumulative relative timing drift that would cause the broadening of return histogram pulse shapes towards the end of long (> ms) patterns. However, in the measurements presented, the longest pattern lasted for only 49.2 µs (corresponding to a dNonrep of 7372.8 m) before being re-synchronized by a trigger pulse, and did not cause any noticeable temporal broadening effects. Future experiments may require temporal synchronization of the source and detection hardware.

3.2. Data acquisition and evaluation

In conjunction with the known bit stream pattern, these cyclic histograms contain all information needed to unambiguously resolve surfaces up to dNonrep. Processing software reads in the bit stream and constructs a reference histogram with the selected binning size, replacing each 1-bit with a pre-recorded instrumental temporal response shape dictated by the combined timing jitter of the photon detector and all other system components. Using this prepared histogram as a correlation reference significantly improves the system’s target resolution capability and depth uncertainty for registered target surfaces. Target returns in the recorded histogram will contain a shape of the same temporal characteristics, resulting in a symmetrical correlation shape with reduced relative sideband noise.

The target range resolution process is illustrated in Fig. 3
Fig. 3 Histogram evaluation and base correlation noise suppression for field trial measurements for 16 kbit pattern length at 2 GHz clock rate, trigger pulse ratio µ = 3.48 × 10−3. (a) Excerpt of the photon counting histogram (blue) of a scan containing a target return at 324 m distance. A part of the bit stream reference (red) locks on to three large peaks caused by the internal optical back-reflections. Target return peaks at 92 ns and 192 ns are clearly visible. (b) Cross-correlation between the histogram and the scan’s complete pseudo-random bit stream. The system back-reflections caused a high correlation peak at the beginning of the histogram and an elevated correlation noise level throughout, which obscures the target return in this case. (c) Excerpt of the photon counting histogram after automated removal of back-reflection returns at 17 ns, 38 ns and 215 ns (blue), with a different part of the bit stream now locking on to the target returns (red). (d) Cross-correlation after removal of back-reflection peaks in the time domain. In this example, the correlation background drops by a factor of 36 and now reveals a clear target return at 324 m.
. The number of bins, n, of both the synthesized reference histogram and the target return histograms, at a channel width tBin (typically 16 ps in this setup), is given by Eq. (3):

n=bfSampletBin.
(3)

Rapid processing of multiple histograms is facilitated by the periodic nature of signal cross-correlation based on fast, discrete Fourier transform (DFT) algorithms. No padding or shifting of either the reference or the return histogram is necessary to obtain a cyclic target response analysis. Let Cp(i), i{1,2,,n}, be the discrete, cyclic correlation function of an analyzed depth pixel p. Based on the reference histogram R(i) and the target return Hp(i), it is determined by element-wise multiplication of the DFT of R with the complex conjugate of the DFT of Hp, according to the cross-correlation theorem [Eq. (4)]:

Cp=F1[(F(Hp))*F(R)].
(4)

As the repeated bit stream stays the same throughout the measurement, F(R) only needs to be calculated once at the beginning of the analysis routine and can be re-used for each pixel. The algorithm identifies the highest target correlation Cmax,p for every pixel, as shown in Fig. 3(b). The position of this maximum, imax,p, corresponds to the timing offset between reference and return, and therefore denotes the photon round-trip time. Additional target returns at other points in the correlation function now would still have to stand out against an elevated correlation noise level, caused by cross-correlation of the highest returns (in this case caused by optical back-reflections in the sensor) at wrong timing offsets, as illustrated in Fig. 3(b). The lower limit of this noise is Cmax,p/L, where L is the number of laser trigger pulses in each bit stream: this limit is reached when triggers are distributed sparsely enough so that only one pulse contributes to the correlation noise at any given wrong time offset.

To suppress the elevated correlation noise caused by unwanted optical back-reflections, the timing information of the first resolved target return, in conjunction with the known bit stream pattern, is used to delete those parts of the photon return histogram R in the time domain which correspond to expected back-reflections Fig. 3(c). The cross-correlation subsequently is re-calculated, so that both Cmax,p and its correlation noise are removed and additional, smaller returns are revealed Fig. 3(d). This process is repeated until the defined maximum number of target returns per pixel or a minimum correlation threshold is reached. Application of this technique is particularly beneficial for our scanning depth profiler, as the additional relay optics required for spatial steering of the transmit- and receive-channel cause a level of internal optical back-reflection which is far greater than that encountered in previous, less complex, photon counting time-of-flight ranging systems [21

21. G. S. Buller, R. D. Harkins, A. McCarthy, P. A. Hiskett, G. R. MacKinnon, G. R. Smith, R. Sung, A. M. Wallace, R. A. Lamb, K. A. Ridley, and J. G. Rarity, “A multiple wavelength time-of-flight sensor based on time-correlated single-photon counting,” Rev. Sci. Instrum. 76(8), 083112 (2005). [CrossRef]

]. These back-reflections would introduce a correlation noise level that would otherwise render most target returns at extended distances irresolvable. The internal back-reflection inevitably is the closest resolved surface and therefore also serves as a fixed physical calibration point on which the ranges of all other objects are determined. As previously demonstrated in laboratory-scale measurements [22

22. J. S. Massa, A. M. Wallace, G. S. Buller, S. J. Fancey, and A. C. Walker, “Laser depth measurement based on time-correlated single-photon counting,” Opt. Lett. 22(8), 543–545 (1997). [CrossRef] [PubMed]

], this approach is preferable to using the electronic trigger – and hence the beginning of the histogram – as a range reference, since long-term drift of the timing system is seen equally in the target and reference response, resulting in a negligible change in the time difference between reference and target.

4. Modeling predictions

4.1 Numerical simulation

A number of simulations were performed in order to compare the surface resolution capabilities of the technique described here, to that of ambiguous depth scans based on periodic illumination.

As described above, the instrumental response function of the system can serve as a template to reconstruct a reference histogram against which target returns are cross-correlated. This is a valid approach as the target return component of a measurement will converge to this shape over long integration times. This property can also be used to construct a simulated return histogram solely based on information about return photon count rates for the target return, the return from the system’s internal back reflection, and other, non-correlated events such as detector dark counts and solar background contributions.

For any given per-pixel dwell time, the number of photons stemming from each contributor in the return histogram can be calculated based on these count rates. To determine the target return photon positions within the histogram, a time-shifted version of the bit stream, again with 1-bits replaced by normalized reference instrumental responses, was treated as a probability distribution function based on which a random number generator populates the corresponding bins. The internal back reflection was simulated similarly, by employing a bit stream version without time shift and with 1-bits replaced by reference back reflection responses as the distribution function. Afterwards, the uncorrelated noise photons were scattered across the histogram based on an equal distribution.

The resulting histograms were analyzed in the same way as actual depth images. This simulation technique also can be easily extended to periodic illumination ranging by using bit streams containing a single 1-bit. The resolution of the simulated target distance within a defined error margin was rated as a successful ranging attempt. Repeating the simulation many times for each investigated integration period provides success rate estimates as a function of dwell time.

Figure 4
Fig. 4 Modeling of average target resolution success rate against per-pixel dwell time. Numerical simulations were performed based on actual photon count rates recorded at both 325 m and 575 m target distance with a shallow-junction SPAD. Each data point of the coded ranging success curves is based on 2000 independent simulations (two pseudo-random bit streams based on the same input parameters with 1000 simulations each, averaged). Data points of the periodic ranging simulations are based on 1000 independent repetitions each. The horizontal dashed red lines denote 50% success rate.
shows the success rate as a function of per-pixel dwell time at ranges of 325 m and 575 m. By choosing these readily available object ranges, count rate measurements on different target materials could easily be performed. This data directly provided input parameters for the statistical histogram population step without any further atmospheric or beam propagation modeling. Back reflection and solar background count rates are not dependent on target range, and were averaged throughout all taken measurements. The simulations are based on data taken during a bright day on a retro-reflective material with a medium-to-high photon return response, comparable to that of an aluminum sheet at normal beam incidence. A shallow-junction SPAD with a quantum efficiency of approximately 3.9% was used as the detector. The total count rates on which the simulated histograms are based were 5.72 × 104 s−1 at 575 m and 6.10 × 104 s−1 at 325 m for outgoing pulse rates of 7 × 106 s−1. The simulated base clock rate was 2 GHz, with a histogram binning size of 16 ps and pseudo-random bit stream lengths of 16 kbit and 64 kbit (corresponding to 1228.8 m and 4915.2 m maximum unambiguous distance, respectively). Ambiguous, periodic ranging at the same laser pulse rate was simulated with a 286 bit stream containing a single 1-bit. It must be noted that the current iteration of the system would not be able to process periodic illumination ranging information at this rate, as the number of trigger pulses to be processed by the TCSPC hardware would be in excess of its maximum data throughput of 5 × 106 s−1.

To gather reliable success rate statistics, 1000 histograms for each dwell time and each parameter set were simulated. Furthermore, in order to suppress any detrimental or beneficial effect of a specific employed bit stream, coded illumination ranging success data is based on the average of two simulations with different bit streams, created with the same parameters.

An expected increase in minimum required dwell time can be observed both for periodic and coded methods with increasing target distance. The acquisition length also has to be extended to maintain the same success rate with longer bit stream pattern lengths. Both relevant extrema of the system were regarded: to successfully resolve half of the scanned pixels with periodic ranging methods – and therefore with the minimum meaningful bit stream length – dwell times of approximately 140 µs and 400 µs are required at 325 m and 575 m object distance, respectively. The longest actual target distance resolved in this paper is 4415 m, requiring at least a 64 kbit pattern with the selected settings (4915.2 m unambiguous range). The simulations predict an increase in dwell time at these parameters to approximately 570 µs and 1900 µs.

Two factors were not considered in these simulations: dead-time of the system and scintillations due to turbulent atmospheric effects. The use of a single-photon detector with a relatively low quantum efficiency in conjunction with efficient spatial and spectral filtering methods results in an average time of 1.64 µs between two photon events at a simulated object distance of 325 m. The system’s dead-time of less than 100 ns in its current configuration is dominated by the TCSPC module’s contribution and will mainly affect the amplitude of the internal optical back-reflection, as it provides the majority of photon events. Atmospheric turbulence along the beam path is largely dependent on environmental conditions during the scan. Their main impact on laser rangefinder measurements is a decrease in return optical power due to wavefront distortions and defocusing [23

23. W. P. Cole, M. A. Marciniak, and M. B. Haeri, “Atmospheric-turbulence-effects correction factors for the laser range equation,” Opt. Eng. 47(12), 126001 (2008). [CrossRef]

], which is inherently considered in the recorded count rate data. However, they can also cause temporal scintillation effects, resulting in modulation of histogram bin counts at comparatively high frequencies. While approaches such as the application of median or low-pass filters to data with large target return photon numbers can improve overall timing precision, their contribution to histograms in the single-photon regime, such as investigated here, is negligible.

4.2 Atmospheric modeling

SNR=npnp+nb.
(5)

Only one target return peak per resolved surface will be present in periodic illumination imaging. Thus, the capability of an employed peak finder algorithm to reliably resolve a target return can be linked to this quantity. nb for a given acquisition time tAcq is determined based on the average background count rate, rBG, [Eq. (6)]

nb=tAcqrBGfReptBin.
(6)

The maximum peak count was calculated based on the LiDAR range equation for target distances d [Eq. (7)]:

np=tAcqPOutλhceαMod×2d2d2TLensTTransTMatDRC.
(7)

POut is the average output power of the depth profiler at the illumination wavelength λ and h is Planck’s constant. The atmospheric attenuation coefficient αMod was determined with the MODTRAN software package [24

24. A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN 7,” Technical Note GL-TR-89–0122, available from Geophysics Laboratory/OPE, Air Force Systems Command, Hanscom AFB, Mass. (1989).

]. Transmission factors TLens, TTrans and TMat take into account the loss in photons caused by the system objective and the remaining transceiver components in both directions of travel, and the back scattering properties of the target material, respectively. The detector response coefficient DRC converts the number of returned photons into the number of photons in the highest bin of the detector response and is based on the temporal detector output shape and the employed binning width.

The applicability of this model to the presented coded depth profiling method is limited: the overall signal received from the distant target is spread across the time-of-flight histogram, based on the distribution of trigger pulses in the bit stream pattern. Due to a priori-knowledge about the output signal shape, the required SNR of each individual peak is drastically decreased and will vary for each employed bit stream. The application of the peak removal technique described in section 3.2 furthermore alters the return signal shape during the analysis process.

However, this atmospheric modeling approach can serve as a verification of the proposed computational simulation of the ranging process. A prediction of maximum target range as a function of per-pixel dwell time was performed in [12

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]

], based on the SNR required to reliably lock on to the actual target distance in 90% of the cases. By matching the input parameters (target material, solar background and detector properties) of the atmospheric model to the simulated target scenario, it is possible to check the integrity of the results of both approaches. Numerical simulations of periodic ranging were performed to determine the required dwell time that results in the same success rate of 90% at a number of simulated target ranges.

Figure 5
Fig. 5 Plot of maximum resolvable range as a function of pixel dwell time, both according to the SNR-based atmospheric model and numerical simulations. The simulated target scene comprises retro-reflective material in slightly overcast daylight conditions. Simulated fRep = 7 MHz, 89.7 µW average laser power leaving the depth profiler. The maximum range in both cases is defined as the range at which the system achieves a reliable target lock in 90% of cases. Numerical data points based on 1000 simulations each.
shows a plot of maximum resolvable range against pixel dwell time, both according to SNR modeling and the numerical simulation. Good agreement is found between the analytic SNR approach and the numerical approach, indicating the validity of the proposed modeling technique.

5. Results

Coded range profiling techniques offer two distinct advantages compared to time-of-flight measurements based on periodic illumination pulses: the ability to resolve long absolute distances, and the correct relative positioning of segmented target surfaces with significant depth separations. The following two sections describe experimental work which demonstrates these abilities.

5.1. Distance determination

Unambiguous distance determination in depth imaging applications can take on two different forms: with no a priori knowledge about the contents of the scene, every depth pixel has to be acquired and analyzed with unambiguous ranging methods. However, if the scanned target scene is known to contain surfaces with an overall distance spread smaller than dRep at typical operating parameters, the image can be acquired based on a periodic pulse pattern, and one or more scanned pixels can be repeated with the proposed coded illumination technique. This approach greatly reduces computation times due to the majority of histograms to be cross-correlated being significantly shorter. A higher frame resolution could be achieved, as each coded illumination pixel histogram requires much more space in the scanning computer’s memory. To ensure small absolute depth uncertainties based on one or few known unambiguous distances, pixels with a high target return would be chosen to be re-scanned with a pseudo-random pulse pattern.

As a proof of concept, the scans shown in this section entirely consist of unambiguous depth pixels.

Figure 6
Fig. 6 22 × 22 pixel scans at a standoff distance of 324 meters, of a three-dimensional 4 × 4 chessboard pattern with an aluminum surface. fSample = 2 GHz, 7 × 106 pulses s−1, 16 ps histogram binning size, pattern length b = 16384 bits. Measurements acquired using a shallow-junction SPAD. (a) Photo of the target. Adjacent squares alternate in depth. (b) Schematic drawing of the three dimensional chess board target. (c) 100 ms per-pixel dwell time. (d) 1000 ms per-pixel dwell time.
shows unambiguous 22 × 22 pixel scans of a 4 × 4 chessboard with an aluminum surface and adjacent squares alternating in depth by 19.2 mm, positioned 324 m away from the depth imager. Per-pixel dwell times of 100 ms and 1000 ms were chosen to illustrate the gain in depth precision due to improving photon statistics: whereas each pixel within the shorter scan was reliably resolved, the pixel-to-pixel depth uncertainty visibly increases compared to the scan with longer dwell times. Figure 7
Fig. 7 20 × 24 pixel scan of a life-size mannequin at 324 m distance. fSample = 2 GHz, 7 × 106 pulses s−1, 16 ps histogram binning size, pattern length b = 16384 bits, 2 s per-pixel dwell time. Measurement acquired using a shallow-junction SPAD. (a) Close-up photograph of the scene. (b) Segmented surface plot of the scan, including several pixels locking onto background objects.
, depicting a life-size mannequin at the same distance, contains materials providing a much lower return intensity than aluminum at the same illumination parameters. Especially at shallow beam incidence angles, much longer per-pixel dwell times are required for successful range resolution.

Due to atmospheric attenuation, there will be an exponential decay in return signal with round-trip target range. The expected Gaussian propagation of the beam will reduce spatial resolution at the target, and the rate of scattered photons detected by the sensor will have the expected d−2 dependency [compare Eq. (7)]. These effects, combined with the increased susceptibility to atmospheric turbulence and other non-homogenous distortion effects in turbid environments pose a challenge to all optical depth profiling systems in terms of both spatial and depth resolution at extended target distances, particularly at kilometer ranges. Figure 8
Fig. 8 9 × 2 pixel scan of a retro-reflective target board. The target board shown schematically in (a) was placed at 4415 m distance from the scanning system. In these measurements: fSample = 2 GHz, 7 × 106 pulses s−1, 16 ps histogram binning size, pattern length b = 98304 bits, 0.5 s per-pixel dwell time. Measurement acquired using a thick-junction SPAD. The measured depth profile of the top half of the target is shown in (b). A pixel-to-pixel depth uncertainty estimate of 25.1 mm is based on treatment of the two front surfaces as planes.
shows a scan of the upper half of a target board covered with retro-reflective material at a distance of 4.4 km. A thick-junction SPAD was used to measure target returns based on a 96 kbit pattern at a base clock rate of 2 GHz (dNonrep = 7372.8 m). The chosen angle between adjacent depth pixels of approximately 37.8 µrad horizontally and 138.2 µrad vertically correspond to spatial translations at the target of 166.8 mm and 610.0 mm, respectively. Scans were performed with per-pixel dwell times of 0.5 s and 1 s, and a depth uncertainty estimate was calculated based on the matrix norm of the depth residuals of a plane fitted to the range information of the two front surfaces of the target. Pixel-to-pixel depth errors of 25.1 mm (0.5 s dwell time) and 15.1 mm (1 s dwell time) were determined with this method.

5.2. Segmented target separation

To demonstrate this feature of the presented technique, overlapping target objects at very different ranges were placed within in the depth profiler’s field of view. In this layout, most range pixels contained only one target return, whereas those where the scanning beam clips at the edge of the closer surface provide multiple returns within the same correlation histogram. The objects were placed at 46 m, 326 m and 584 m, and angled to achieve non-normal incidence of the beam in order to demonstrate the system’s pixel-to-pixel depth resolving capabilities across the individual surfaces.

Results of these scans are illustrated in Fig. 9
Fig. 9 Segmented 20 × 20 pixel scan of overlapping surfaces at ranges of approximately 46 m, 326 m and 584 m. In these measurements, fSample = 2 GHz, 2.5 × 107 pulses s−1, 16 ps histogram binning size, pattern length b = 16384 bits. Measurement acquired using a thick-junction SPAD. (a) Depth plot of scanned field angle (0.89 mrad horizontal, 0.82 mrad vertical). Color mapping corresponds to relative range within each tilted surface (blue nearest, red furthest away). (b) Detailed depth plot of surface 1. (c) Excerpt of a correlation plot for a pixel where the beam clips at the outer edge of surface 1 (46 m), and there is a partial return from surface 3 (584 m). Note that the noise level decreases by more than an order of magnitude after removal of the internal reflection returns and subsequent re-correlation.
. The employed pattern length of 16384 bits with a base clock rate of 2 GHz results in a dNonrep of 1228.8 m. Scans of the same scene with pattern lengths of 64 kbit (dNonrep = 4915.2 m) were also successfully acquired, but required reduction of the TCSPC timing resolution from 16 ps to 128 ps bin width to maintain the same total number of pixels, due to memory restrictions. The applied 20 × 20 pixel pattern within a scanned field angle of 0.82 × 0.89 mrad corresponds to a horizontal pixel-to-pixel stepping of 41 µrad or 23.9 mm at the furthest target distance.

The system’s focus was optimized for a balanced return from the three surfaces, resulting in a defocused beam at the closest target surface and best focusing at 326 m. The depth uncertainty on each planar surface was determined by separately analyzing each horizontal line of scanned pixels: the first order polynomials were subtracted from these lines, and a mean of their residual standard deviations was taken. An average pixel-to-pixel depth uncertainty of 1.53 mm at a range of 46 meters, 1.01 mm at 326 meters, and 1.50 mm at 584 meters was determined. The smallest depth uncertainty at an intermediate target distance was achieved due to the increase in return signal strength with optimized focus.

6. Conclusions

We have demonstrated the first application of a bit pattern-matching time-of-flight ranging method to a scanning depth imaging system based on time-correlated single-photon counting, in order to extend its unambiguous range. These measurements include the first photon-counting depth imaging of non-cooperative targets using this coded ranging approach. Detailed scans of objects at target distances between 46 meters and 584 meters exhibit mm depth uncertainty and the technique’s ability to reliably analyze segmented targets with 100’s of meters of surface separation at average laser pulse rates equivalent to 25 MHz. Using this approach, we unambiguously resolved a depth image of a cooperative target object positioned 4.4 km from the scanning system with a depth uncertainty of 15 mm and 25 mm at 1 s and 0.5 s per-pixel dwell time, respectively.

Numerical simulations were carried out to compare the technique’s performance to ranging methods based on periodic illumination. Use of the bit stream matching method with an increase in per-pixel dwell time by less than a factor of ten was found to increase the maximum achievable unambiguous ranging distance by more than two orders of magnitude while maintaining the system’s target return sensitivity. This numerical approach was demonstrated as being highly consistent with a known SNR-based atmospheric modeling approach.

These investigations showed that the bit pattern-matching depth imaging method is an efficient solution to range aliasing issues in photon-counting time-of-flight applications. Further work to integrate this approach into an autonomous high-speed depth profiler device may comprise the application of the coded ranging method to a small fraction of the acquired depth pixels, in order to provide absolute distance offset information for all remaining pixels. A higher level of integration of the involved acquisition hardware is desired, including phase-locking of the clocks on which the production of the bit stream and the creation of time-of-flight histograms are based. Novel, low timing-jitter single-photon detectors with high quantum efficiencies at illumination wavelengths of interest are currently under investigation, which could further improve the system’s performance.

Acknowledgments

The work reported in this paper was partly funded by the Electro-Magnetic Remote Sensing (EMRS) Defence Technology Centre, established by the UK Ministry of Defence and run by a consortium of SELEX Galileo, Thales Defence, Roke Manor Research and Filtronic (EMRS/DTC/4/98). The authors also acknowledge the support of the UK Engineering and Physical Sciences Research Council (EP/F048041/1). The authors thank their colleagues and collaborators for their valuable contributions and discussions: Cat Fitzpatrick (National Physical Laboratory), Robert Collins (Heriot-Watt University), and Michael Wahl (PicoQuant).

References and links

1.

W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, Berlin, 2005).

2.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]

3.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]

4.

A. Cleary, A. Glidle, P. J. R. Laybourn, S. García-Blanco, S. Pellegrini, C. Helfter, G. S. Buller, J. S. Aitchison, and J. M. Cooper, “Integrating optics and microfluidics for time-correlated single-photon counting in lab-on-a-chip devices,” Appl. Phys. Lett. 91(7), 071123 (2007). [CrossRef]

5.

J. J. Degnan, “Satellite Laser Ranging: Current Status and Future Prospects,” IEEE Trans. Geosci. Rem. Sens. GE-23(4), 398–413 (1985). [CrossRef]

6.

J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002). [CrossRef]

7.

G. S. Buller and A. M. Wallace, “Ranging and Three-Dimensional Imaging Using Time-Correlated Single-Photon Counting and Point-by-Point Acquisition,” IEEE J. Sel. Top. Quantum Electron. 13(4), 1006–1015 (2007). [CrossRef]

8.

W. C. Priedhorsky, R. C. Smith, and C. Ho, “Laser ranging and mapping with a photon-counting detector,” Appl. Opt. 35(3), 441–452 (1996). [CrossRef] [PubMed]

9.

C. Ho, K. L. Albright, A. W. Bird, J. Bradley, D. E. Casperson, M. Hindman, W. C. Priedhorsky, W. R. Scarlett, R. C. Smith, J. Theiler, and S. K. Wilson, “Demonstration of literal three-dimensional imaging,” Appl. Opt. 38(9), 1833–1840 (1999). [CrossRef]

10.

R. M. Marino and W. R. Davis Jr., “Jigsaw: A Foliage-Penetrating 3D Imaging Laser Radar System,” Lincoln Lab. J. 15, 23–36 (2005).

11.

J. Massa, G. Buller, A. Walker, G. Smith, S. Cova, M. Umasuthan, and A. Wallace, “Optical design and evaluation of a three-dimensional imaging and ranging system based on time-correlated single-photon counting,” Appl. Opt. 41(6), 1063–1070 (2002). [CrossRef] [PubMed]

12.

A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]

13.

W. H. Long, D. H. Mooney, and W. A. Skillman, “Pulse Doppler Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).

14.

G. Trunk, and S. Brockett, “Range and velocity ambiguity resolution,” in Proceedings of IEEE National Radar Conference (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 146–149.

15.

E. C. Farnett, and G. H. Stevens, “Pulse Compression Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).

16.

N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22(9), 1382–1386 (1983). [CrossRef] [PubMed]

17.

N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. 25(1), 63–67 (1986). [CrossRef] [PubMed]

18.

P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express 16(18), 13685–13698 (2008). [CrossRef] [PubMed]

19.

R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005). [CrossRef] [PubMed]

20.

R. E. Warburton, A. McCarthy, A. M. Wallace, S. Hernandez-Marin, R. H. Hadfield, S. W. Nam, and G. S. Buller, “Subcentimeter depth resolution using a single-photon counting time-of-flight laser ranging system at 1550 nm wavelength,” Opt. Lett. 32(15), 2266–2268 (2007). [CrossRef] [PubMed]

21.

G. S. Buller, R. D. Harkins, A. McCarthy, P. A. Hiskett, G. R. MacKinnon, G. R. Smith, R. Sung, A. M. Wallace, R. A. Lamb, K. A. Ridley, and J. G. Rarity, “A multiple wavelength time-of-flight sensor based on time-correlated single-photon counting,” Rev. Sci. Instrum. 76(8), 083112 (2005). [CrossRef]

22.

J. S. Massa, A. M. Wallace, G. S. Buller, S. J. Fancey, and A. C. Walker, “Laser depth measurement based on time-correlated single-photon counting,” Opt. Lett. 22(8), 543–545 (1997). [CrossRef] [PubMed]

23.

W. P. Cole, M. A. Marciniak, and M. B. Haeri, “Atmospheric-turbulence-effects correction factors for the laser range equation,” Opt. Eng. 47(12), 126001 (2008). [CrossRef]

24.

A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN 7,” Technical Note GL-TR-89–0122, available from Geophysics Laboratory/OPE, Air Force Systems Command, Hanscom AFB, Mass. (1989).

OCIS Codes
(030.5260) Coherence and statistical optics : Photon counting
(030.5290) Coherence and statistical optics : Photon statistics
(040.3780) Detectors : Low light level
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(280.3400) Remote sensing and sensors : Laser range finder

ToC Category:
Imaging Systems

History
Original Manuscript: February 23, 2010
Revised Manuscript: April 8, 2010
Manuscript Accepted: April 12, 2010
Published: April 16, 2010

Citation
Nils J. Krichel, Aongus McCarthy, and Gerald S. Buller, "Resolving range ambiguity in a photon counting depth imager operating at kilometer distances," Opt. Express 18, 9192-9206 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9192


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References

  1. W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, Berlin, 2005).
  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
  3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]
  4. A. Cleary, A. Glidle, P. J. R. Laybourn, S. García-Blanco, S. Pellegrini, C. Helfter, G. S. Buller, J. S. Aitchison, and J. M. Cooper, “Integrating optics and microfluidics for time-correlated single-photon counting in lab-on-a-chip devices,” Appl. Phys. Lett. 91(7), 071123 (2007). [CrossRef]
  5. J. J. Degnan, “Satellite Laser Ranging: Current Status and Future Prospects,” IEEE Trans. Geosci. Rem. Sens. GE-23(4), 398–413 (1985). [CrossRef]
  6. J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002). [CrossRef]
  7. G. S. Buller and A. M. Wallace, “Ranging and Three-Dimensional Imaging Using Time-Correlated Single-Photon Counting and Point-by-Point Acquisition,” IEEE J. Sel. Top. Quantum Electron. 13(4), 1006–1015 (2007). [CrossRef]
  8. W. C. Priedhorsky, R. C. Smith, and C. Ho, “Laser ranging and mapping with a photon-counting detector,” Appl. Opt. 35(3), 441–452 (1996). [CrossRef] [PubMed]
  9. C. Ho, K. L. Albright, A. W. Bird, J. Bradley, D. E. Casperson, M. Hindman, W. C. Priedhorsky, W. R. Scarlett, R. C. Smith, J. Theiler, and S. K. Wilson, “Demonstration of literal three-dimensional imaging,” Appl. Opt. 38(9), 1833–1840 (1999). [CrossRef]
  10. R. M. Marino and W. R. Davis., “Jigsaw: A Foliage-Penetrating 3D Imaging Laser Radar System,” Lincoln Lab. J. 15, 23–36 (2005).
  11. J. Massa, G. Buller, A. Walker, G. Smith, S. Cova, M. Umasuthan, and A. Wallace, “Optical design and evaluation of a three-dimensional imaging and ranging system based on time-correlated single-photon counting,” Appl. Opt. 41(6), 1063–1070 (2002). [CrossRef] [PubMed]
  12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]
  13. W. H. Long, D. H. Mooney, and W. A. Skillman, “Pulse Doppler Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).
  14. G. Trunk, and S. Brockett, “Range and velocity ambiguity resolution,” in Proceedings of IEEE National Radar Conference (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 146–149.
  15. E. C. Farnett, and G. H. Stevens, “Pulse Compression Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).
  16. N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22(9), 1382–1386 (1983). [CrossRef] [PubMed]
  17. N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. 25(1), 63–67 (1986). [CrossRef] [PubMed]
  18. P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express 16(18), 13685–13698 (2008). [CrossRef] [PubMed]
  19. R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005). [CrossRef] [PubMed]
  20. R. E. Warburton, A. McCarthy, A. M. Wallace, S. Hernandez-Marin, R. H. Hadfield, S. W. Nam, and G. S. Buller, “Subcentimeter depth resolution using a single-photon counting time-of-flight laser ranging system at 1550 nm wavelength,” Opt. Lett. 32(15), 2266–2268 (2007). [CrossRef] [PubMed]
  21. G. S. Buller, R. D. Harkins, A. McCarthy, P. A. Hiskett, G. R. MacKinnon, G. R. Smith, R. Sung, A. M. Wallace, R. A. Lamb, K. A. Ridley, and J. G. Rarity, “A multiple wavelength time-of-flight sensor based on time-correlated single-photon counting,” Rev. Sci. Instrum. 76(8), 083112 (2005). [CrossRef]
  22. J. S. Massa, A. M. Wallace, G. S. Buller, S. J. Fancey, and A. C. Walker, “Laser depth measurement based on time-correlated single-photon counting,” Opt. Lett. 22(8), 543–545 (1997). [CrossRef] [PubMed]
  23. W. P. Cole, M. A. Marciniak, and M. B. Haeri, “Atmospheric-turbulence-effects correction factors for the laser range equation,” Opt. Eng. 47(12), 126001 (2008). [CrossRef]
  24. A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN 7,” Technical Note GL-TR-89–0122, available from Geophysics Laboratory/OPE, Air Force Systems Command, Hanscom AFB, Mass. (1989).

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