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.

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    [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).
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2009

2008

2007

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]

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]

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]

2005

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]

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

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]

2002

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

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]

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

2001

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]

1999

1997

1996

1986

1985

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

1983

Aitchison, J. S.

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]

Albright, K. L.

Baba, H.

Bird, A. W.

Bradley, J.

Buller, G.

Buller, G. S.

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]

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]

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]

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]

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]

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]

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]

Casperson, D. E.

Cleary, A.

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]

Cole, W. P.

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]

Collins, R. J.

Cooper, J. M.

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]

Cova, S.

Davis, W. R.

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

Degnan, J. J.

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

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

Fancey, S. J.

Fernández, V.

García-Blanco, S.

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]

Gisin, N.

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

Glidle, A.

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]

Gruber, S. S.

Hadfield, R. H.

Haeri, M. B.

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]

Harkins, R. D.

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]

Helfter, C.

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]

Hernandez-Marin, S.

Hindman, M.

Hiskett, P. A.

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]

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]

Ho, C.

Knill, E.

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]

Krichel, N. J.

Laflamme, R.

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]

Lamb, R. A.

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]

Laybourn, P. J. R.

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]

MacKinnon, G. R.

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]

Marciniak, M. A.

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]

Marino, R. M.

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

Massa, J.

Massa, J. S.

McCarthy, A.

Milburn, G. J.

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]

Miller, A. J.

Mirin, R. P.

Nam, S. W.

Parry, C. S.

Pellegrini, S.

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]

Priedhorsky, W. C.

Rarity, J. G.

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]

Ribordy, G.

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

Ridley, K. A.

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]

Sakurai, K.

Scarlett, W. R.

Schwall, R. E.

Smith, G.

Smith, G. R.

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]

Smith, R. C.

Stevens, M. J.

Sugimoto, N.

Sung, R.

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]

Takeuchi, N.

Theiler, J.

Tittel, W.

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

Ueno, T.

Umasuthan, M.

Walker, A.

Walker, A. C.

Wallace, A.

Wallace, A. M.

Warburton, R. E.

Wilson, S. K.

Zbinden, H.

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

Appl. Opt.

Appl. Phys. Lett.

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]

IEEE J. Sel. Top. Quantum Electron.

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]

IEEE Trans. Geosci. Rem. Sens.

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

J. Geodyn.

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

Lincoln Lab. J.

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

Nature

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]

Opt. Eng.

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]

Opt. Express

Opt. Lett.

Rev. Mod. Phys.

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

Rev. Sci. Instrum.

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]

Other

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).

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

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).

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.

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

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram showing the key components of the scanning rangefinder system.

Fig. 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.

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.

Fig. 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.

Fig. 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.

Fig. 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.

Fig. 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.

Fig. 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.

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.

Equations (7)

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d R e p = c 2 f R e p ,
d N o n r e p = c b 2 f S a m p l e .
n = b f S a m p l e t B i n .
C p = F 1 [ ( F ( H p ) ) * F ( R ) ] .
S N R = n p n p + n b .
n b = t A c q r B G f R e p t B i n .
n p = t A c q P O u t λ h c e α M o d × 2 d 2 d 2 T L e n s T T r a n s T M a t DRC .

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