Abstract

Frequency-modulated continuous-wave laser detection and ranging (FMCW LADAR) measures the range to a surface through coherent detection of the backscattered light from a frequency-swept laser source. The ultimate limit to the range precision of FMCW LADAR, or any coherent LADAR, to a diffusely scattering surface will be determined by the unavoidable speckle phase noise. Here, we demonstrate the two main manifestations of this limit. First, frequency-dependent speckle phase noise leads to a non-Gaussian range distribution having outliers that approach the system range resolution, regardless of the signal-to-noise ratio. These outliers are reduced only through improved range resolution (i.e., higher optical bandwidths). Second, if the range is measured during a continuous lateral scan across a surface, the spatial pattern of speckle phase is converted to frequency noise, which leads to additional excess range uncertainty. We explore these two effects and show that laboratory results agree with analytical expressions and numerical simulations. We also show that at 1 THz optical bandwidth, range precisions below 10 μm are achievable regardless of these effects.

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2013 (2)

2012 (1)

2010 (2)

2009 (1)

2004 (1)

2003 (1)

2001 (1)

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

1998 (1)

M. V. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

1989 (1)

1983 (1)

1981 (1)

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Amann, M.-C.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

Babbitt, W. R.

Barber, Z. W.

Baumann, E.

E. Baumann, F. R. Giorgetta, I. Coddington, L. C. Sinclair, K. Knabe, W. C. Swann, and N. R. Newbury, Opt. Lett. 38, 2026 (2013).
[CrossRef]

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Belmonte, A.

Berg, T.

Berry, M. V.

M. V. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Bosch, T.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

Capron, B. A.

Coddington, I.

E. Baumann, F. R. Giorgetta, I. Coddington, L. C. Sinclair, K. Knabe, W. C. Swann, and N. R. Newbury, Opt. Lett. 38, 2026 (2013).
[CrossRef]

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Dahl, J. R.

Dainty, J. C.

J. C. Dainty, The Statistics of Speckle Patterns, Progress in Optics Series (North-Holland, 1976).

Erkmen, B. I.

Fricke-Begemann, T.

Gao, S.

Giorgetta, F. R.

E. Baumann, F. R. Giorgetta, I. Coddington, L. C. Sinclair, K. Knabe, W. C. Swann, and N. R. Newbury, Opt. Lett. 38, 2026 (2013).
[CrossRef]

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Goodman, J. W.

E. Ochoa and J. W. Goodman, J. Opt. Soc. Am. 73, 943 (1983).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, 1985).

Harney, R. C.

Hinsch, K. D.

Hui, R.

Kaylor, B.

Knabe, K.

E. Baumann, F. R. Giorgetta, I. Coddington, L. C. Sinclair, K. Knabe, W. C. Swann, and N. R. Newbury, Opt. Lett. 38, 2026 (2013).
[CrossRef]

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Lescure, M.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

Letalick, D.

Myllyla, R.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

Newbury, N. R.

E. Baumann, F. R. Giorgetta, I. Coddington, L. C. Sinclair, K. Knabe, W. C. Swann, and N. R. Newbury, Opt. Lett. 38, 2026 (2013).
[CrossRef]

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Ochoa, E.

Pavlicek, P.

Reibel, R. R.

Renhorn, I.

Rioux, M.

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

Roos, P. A.

Shapiro, J. H.

Sharpe, T. L.

Sinclair, L.

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Sinclair, L. C.

Soubusta, J.

Steinvall, O.

Swann, W. C.

E. Baumann, F. R. Giorgetta, I. Coddington, L. C. Sinclair, K. Knabe, W. C. Swann, and N. R. Newbury, Opt. Lett. 38, 2026 (2013).
[CrossRef]

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

M.-C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, Opt. Eng. 40, 10 (2001).
[CrossRef]

Opt. Lett. (3)

Proc. R. Soc. A (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Proc. SPIE (1)

M. V. Berry, Proc. SPIE 3487, 1 (1998).
[CrossRef]

Other (3)

E. Baumann, F. R. Giorgetta, I. Coddington, K. Knabe, L. Sinclair, W. C. Swann, and N. R. Newbury, “3D precision imaging with a terahertz-bandwidth, comb-calibrated swept laser,” in Europhoton, Stockholm, Sweden, 2012.

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. C. Dainty, The Statistics of Speckle Patterns, Progress in Optics Series (North-Holland, 1976).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Coherent FMCW LADAR measures the range z to a diffusely scattering surface. The laser beam is focused to a roughly diffraction-limited spot with 1/e radius, w0=200μm at a range of z0=10.5m, and laterally scanned across the surface via a fast steering mirror. The frequency linearization (against a frequency comb) is carried out in a field-programmable gate array (FPGA). LO: swept laser local reference. The Fourier transform, S(f), of the linearized return yields a range spectrum, whose center is the measured range. (b) Example measured range spectra. The gray shaded region are typical spectra, with bandwidth-limited resolution of 150 μm. Very occasionally, range spectra exhibit a strong phase modulation due to destructive interference in the speckle field (colored traces). (c) Measured range z minus mean range z0 to a flat metal piece for ΔR150μm [B=1THz] (red) and ΔR1.5mm [B=0.1THz] (blue). The range precision (standard deviation) is 6.5 μm (B=1THz). Here, geometric variations are removed. The apparent outliers are a result of strong speckle phase modulation [colored traces in (b)]. (d) Measured range at a slow (Vscan=0.0026, gray) and fast (Vscan=1.05, green) normalized lateral scan speed, offset for clarity. The increase in the central spread with lateral scan speed is due to conversion of the speckle phase spatial variation to time-dependent frequency noise.

Fig. 2.
Fig. 2.

(a) Distribution of 200,000 measured ranges to a machined metal surface at z0=10.5m for ΔR150μm [B=1THz] (red line). The data fit well to PT(δz), with σz=4.8μm (black line). The measured range precision (standard deviation) is 7.9 μm. (b) Range distributions for three different resolutions (bandwidths) to a metal surface located at z0=3.5m (offset for clarity). Truncation occurs at ±ΔR/2 as expected. Simulations (σz=3μm) at ΔR150μm (orange line) and ΔR500μm (light green line) agree with the data. (c) Measured and simulated range distributions to a rougher metal surface at z0=10.5m for ΔR380μm (data: green, simulation at σz=15μm: light green) and ΔR150μm (data: red, simulation at σz=15μm: orange), offset for clarity. A simulation at ΔR50μm and σz=15μm (black) illustrates the convergence toward a Gaussian distribution for a partially range-resolved surface.

Fig. 3.
Fig. 3.

Range uncertainty (standard deviation) versus normalized lateral scan speed for a smooth (σz3μm, red circles) and rough surface (σz15μm, black diamonds), along with simulations (dashed line, scaled by 1.17) for ΔR150μm.

Equations (3)

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S(t)Σiexp[((xix)2+(yiy)2)/(2w02)]×exp[j4πc1zi(f0+αt)];τ/2<t<τ/2,
P(I,δz)=IπI3/2σzexp[II]exp[II(δzσz)2]
P(δz)=σz22(σz2+δz2)3/2.

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