## Abstract

Non-contact surface mapping at a distance is interesting in diverse applications including industrial metrology, manufacturing, forensics, and artifact documentation and preservation. Frequency modulated continuous wave (FMCW) laser detection and ranging (LADAR) is a promising approach since it offers shot-noise limited precision/accuracy, high resolution and high sensitivity. We demonstrate a scanning imaging system based on a frequency-comb calibrated FMCW LADAR and real-time digital signal processing. This system can obtain three-dimensional images of a diffusely scattering surface at stand-off distances up to 10.5 m with sub-micrometer accuracy and with a precision below 10 µm, limited by fundamental speckle noise. Because of its shot-noise limited sensitivity, this comb-calibrated FMCW LADAR has a large dynamic range, which enables precise mapping of scenes with vastly differing reflectivities such as metal, dirt or vegetation. The current system is implemented with fiber-optic components, but the basic system architecture is compatible with future optically integrated, on-chip systems.

© 2014 Optical Society of America

## 1. Introduction

Since its inception in the 1960’s, Laser Ranging and Detection (LADAR) has become a mainstay for providing accurate surface profiling and mapping. Where the simplest LADAR relies on time-of-flight of a laser pulse off of a target, more sophisticated approaches, including those that rely on a frequency-modulated continuous wave laser (FMCW), can provide even higher sensitivity through coherent detection and higher resolution, precision, and accuracy through high optical bandwidths [1]. With the recent advent of high slew rate frequency agile lasers and the continuing advancement of fiber optic components in the telecom band around 1550 nm, FMCW LADARs have achieved range resolutions below 100 µm and range accuracy well below 1 µm [2–4]. Furthermore, the heterodyne nature of FMCW LADAR allows for very sensitive detection of weak signals scattered from rough surfaces at a distance. With this level of performance, developing FMCW LADAR techniques can compete with state-of the art surface profiling and imaging systems.

Here, we demonstrate a scanning imaging FMCW LADAR whose range measurements are referenced directly to the tooth spacing of a free-running frequency comb. In that way, the measured range is directly traceable to the rf standard used to measure the frequency comb tooth spacing, rather than to a physical artifact such as an interferometer or etalon, whose properties can change with environmental conditions. The comb-calibrated FMCW LADAR imaging system is based on the design of Ref. [4], where single point ranging to a target was demonstrated using a fast-swept laser with 1 THz bandwidth. Here, we have implemented the design with all polarization maintaining fiber to reduce sensitivity towards environmental perturbations, incorporated a fast steering mirror (FSM) to scan the beam across a surface, and implemented real-time digital signal processing of the signals to produce real-time range measurements at 2000 points per second limited by the optical sweep rate of the cw laser. The final imaging system combines the high intrinsic sensitivity of FMCW LADAR with the high accuracy associated with direct comb-ranging [5–12], thereby opening up the capability of high-resolution, high-accuracy surface profiling at large standoff distances. The system operates near the fundamental limits imposed by speckle phase noise [13]. For a 10 m standoff, we show that the precision (here defined as the standard deviation) can be below 10 µm and the accuracy well below 1 µm (for a specular reflection). In addition the system operates under ambient lighting conditions and offers a high dynamic range in return power and high sensitivity making it capable of measuring different reflecting surfaces with the same precision (with returns as low as ~110 dB below the launched power).

In this work, we demonstrate three-dimensional surface profiles with megapixel images of multiple objects including machined aluminum, footprints, a shoe tread, a flower, and a cactus. Figure 1 and Fig. 2 show 3D surface profiles that emphasize the application in forensics. In forensic science, casts of impression evidence are still a widely used technique [14–16]. Casts are labor intensive, difficult to cross-reference, and can destroy the evidence especially on soft ground. Figure 1 shows a close-in photo of a footprint in dirt (taken at a few meters) and a 3D image of the same footprint taken at 10.5 meter distance. In this case, the calibrated 3D image reveals more details of the footprint than the photo, along with the structure of the dirt itself. The actual shoe tread was also measured at 10.5 m range, as shown in Fig. 2. The power levels were not adapted between measurements, demonstrating that the FMCW LADAR offers sufficient dynamic range in return power to capture the aluminum tabletop, the impression in dirt and the rubber in a single measurement. The shoe tread shows individual wear marks from a bicycle pedal. Such marks are important to capture since they can link a specific shoe to a crime scene.

Where other techniques may offer good performance in specific cases, FMCW LADAR shows generally high performance and flexibility across differing applications. Interferometry, for example, can potentially offer nm-scale precision while profiling a surface but at a cost of range ambiguity on the order of a wavelength. Multi-wavelength and synthetic wavelength interferometry offer increased range non-ambiguity [17–19], but interferometric methods in general require an artifact (such as a corner cube) in contact with the surface being profiled. FMCW LADAR is in many ways similar to swept source optical coherence tomography (OCT) [20], except it operates at much larger standoff distances. In digital holography [21], light scattered from an object is combined with a reference beam to produce an interference pattern (hologram) on an image array. Where this technique is rapid, it achieves accuracies around 0.7 mm [22]. Structured light is another rapid, camera-based technique but is potentially difficult for use in field locations as it requires specific, calibrated illumination patterns [23].

In contrast, FMCW LADAR, with its combined unique abilities, can successfully produce high-accuracy 3D profiles of a variety of surfaces, including impressions in soil, feature-rich surfaces as encountered in vegetation and biology, and complex fragile mechanical devices at large standoff distances, in ambient light, and in flexible configurations. The synthetic aperture approach [24] to achieve high lateral resolution can also be implemented with FMCW LADAR [25]. Furthermore, FMCW LADAR exploits technologies leveraged from the fiber optic telecommunication industry and can similarly benefit from the increased integration of optical components onto chips. Although the current design is implemented in fiber optics, future FMCW LADAR could easily take advantage of future chip-based frequency combs, swept lasers, and electro-optic scanners [26–29].

The article is organized as follows. Section 2 describes the system and processing in more detail. Section 3 analyzes the various limitations to the range precision for a pixel. The current system operates very close to the fundamental limit set by speckle phase noise, as discussed in Ref [13]. Finally Section 4 provides some additional three-dimensional surface profiles measured with the system.

## 2. System description

#### 2.1 Overview

In its simplest form, FMCW LADAR relies on a perfectly linear frequency swept continuous wave (cw) laser source; the laser is scattered off of a target and the return light compared to the source light. The comparison reveals an optical frequency difference proportional to the range between the source and target. The accuracy and precision rely completely on the system calibration of the ideally perfectly linear frequency sweep. Historically, this linearization is performed by comparison with an artifact such as an interferometer [30–32]. Such systems have shown good performance however their performance is limited by the interferometer, which itself needs calibration to provide absolute system accuracy, and furthermore is subject to environmental effects such as temperature, air pressure, vibration, humidity, and other effects. Here, we instead calibrate a non-linearly swept laser directly against a free-running frequency comb, which has a perfect equidistant tooth spacing; the instantaneous phase between the swept cw laser and comb’s teeth is recorded during the source sweep, and this information (along with a “count” of the comb’s repetition frequency against a rf-standard) is used to linearize the source sweep in the signal processing stage of the range measurement [4,33–35].

#### 2.2 Experimental setup

The experimental setup is shown in Fig.
3(a).. The frequency swept laser is a microelectromechanical systems (MEMS)
based external cavity diode laser centered around
*f _{0}*~192 THz (1560 nm) with a linewidth of around 1.5
MHz corresponding to a coherence length of around 70 m [36]. This laser is swept quasi-sinusoidally over a
bandwidth

*B*= 1 THz at a rate

*f*= 1 kHz, ideally giving an optical frequency of${f}_{laser}(t)~{f}_{0}+B/2\cdot \mathrm{cos}(2\pi {f}_{m}t)$. The sweep rate (chirp) is ${\alpha}_{nom}(t)~d{f}_{laser}/dt=B{f}_{m}\pi \mathrm{sin}(2\pi {f}_{m}t)$, with a maximum measured amplitude ${\alpha}_{\mathrm{max}}$ = 3.4 PHz/s. As discussed later (see also Fig. 4), the frequency sweep is not perfectly sinusoidal and must be directly measured. Light from this source is split into two paths, one serves as a local reference and the other is launched as a free beam through an expander. This beam is scattered off the target, superimposed with local reference light and converted to a voltage with a photodiode.

_{m}#### 2.3 Processing

The swept laser field can be written as$E\left(t\right)=\left|E\right|{e}^{2\pi i\phi (t)}$, and the resulting heterodyne voltage between the local reference and the return signal is then

*α*the swept laser frequency ${f}_{laser}\left(t\right)={f}_{0}+\alpha t$ can be substituted in Eq. (1) and$\Delta {t}_{obj}$ can then be directly extracted from the measured beat frequency of ${V}_{LADAR}\left(t\right)$ (typically through a Fourier transform with respect to time of ${V}_{LADAR}\left(t\right)$).

Here, the frequency sweep is not linear and instead we directly measure${f}_{laser}\left(t\right)$. In this way, the laser can be swept at its maximum rate, allowing for the much higher acquisition rate required to form 3D images. We then regard the measured LADAR signal as a function of ${f}_{laser}$, rather than time and Fourier transform the measured heterodyne signal with respect to ${f}_{laser}$. (Strictly speaking, Eq. (1) ignores higher-order terms of the Taylor expansion in the phase, but they lead to negligible errors [37], provided of course the instantaneous laser frequency is measured simultaneously with the LADAR signal.) The hence obtained range spectrum is:

*c*is the speed of light in air. The resulting spectrum$F(R)$from a surface will have a signal with a width (i.e. range resolution) of$\Delta R=c/(2B)$ centered at the range to the surface (with respect to the local reference delay), see for example, Fig. 3(c).

Ideally${f}_{laser}\left(t\right)$would simply be given by the laser’s sinusoidally varying electrical drive voltage. However, hysteresis and other nonlinearities in the device cause the laser’s output sweep to deviate from the drive voltage. Figure 4 shows the real modulation frequency of the swept laser as measured against the frequency comb, as well as the deviations from the sinusoidal drive voltage. The deviations can lead to strong range-spectrum distortions. For example, Fig. 3(c) compares a broadened range signal where the laser sweep is assumed to follow a perfect sine wave to a bandwidth-limited range signal where the laser is properly calibrated against the frequency comb throughout the sweep.

As shown in Fig. 3(b), this data
processing is carried out in a field-programmable gate array (FPGA), returning
one range measurement every 0.5 ms (for each optical frequency sweep of the
laser, as indicated by the shaded area of Fig.
4). The input digitizer to the FPGA is sampled synchronously with the
comb repetition frequency *f _{r}* ~207 MHz. The Nyquist
condition leads to a range window of $\pm ({f}_{r}/2\cdot c/2{\alpha}_{\mathrm{max}})=\pm 4.5\text{m}$relative to the local reference branch, where

*α*is the amplitude maximum of the optical sweep rate. For our present measurements we coarsely set the reference branch delay to obtain free-space range measurements between ~2 m and ~11 m.

_{max}The processing of the delay time measurement $\Delta {t}_{obj}$is clocked with the free-running comb’s repetition rate. This
repetition rate is also simultaneously counted against a rf –standard (maser).
Since the optical sweep is calibrated against this free-running comb the
accuracy of the rf-standard is transferred to the range measurement$\Delta {t}_{obj}$. The comb offset frequency is not actively monitored, however
it can be shown that the contribution of offset frequency drift to the overall
fractional range uncertainty is negligible or below 2 × 10^{−7} (see Ref
[4].). This contributes ~2 µm to our
overall range uncertainty at 10.5 meters.

The processing of the delay time measurement $\Delta {t}_{obj}$is clocked with the free-running comb’s repetition rate. This
repetition rate is also simultaneously counted against a rf –standard (maser).
Since the optical sweep is calibrated against this free-running comb the
accuracy of the rf-standard is transferred to the range measurement$\Delta {t}_{obj}$. The comb offset frequency is not actively monitored, however
it can be shown that the contribution of offset frequency drift to the overall
fractional range uncertainty is negligible or below 2 × 10^{−7} (see Ref
[4].) This contributes ~2 µm to our
overall range uncertainty at 10.5 meters.

The processing related to Eq. (2)
requires that the LADAR signal and instantaneous frequency are processed with
the same time offsets. Otherwise, relative time offsets combined with the
nonlinear sweep will cause range errors and broadening of the spectrum. This
time offset is adjusted in the FPGA code and through cable lengths. We measure a
range error of 80 nm per ns of time delay mismatch at a 10.5 meter range,
corresponding to < 2 μm range error over a ± 15 cm depth range
*R*.

#### 2.4 Two-dimensional scanning and image formation

The FSM allows for a radial mapping of a surface in *R*, with the
FSM angles *ϕ* and *Ө* (see Fig. 3(a)). Figure
5 shows data from a flat cast-iron lapping plate, oriented perpendicularly
to the incident laser beam as measured at a stand-off
*z _{0}* = 10.54 m. The radial range

*R*across the surface is measured in a lateral scanning pattern as the angle

*ϕ*is steered with a triangular voltage (to raster the beam back and forth across in

*x*), and

*Ө*is swept with a slow ramp voltage (slow displacement in

*y*). The selection of the scanning pattern and speed is governed by trade-offs between covered surface, measurement time, lateral resolution and speckle noise (see Section 3.2); all those are further linked to the laser’s spot size on the target. In the case of the cast-iron plate in Fig. 5, the stand-off distance was ~10.5 m and the total covered surface ~200 mm x 100 mm, the measured diffraction-limited radius of the spot size at $1/\sqrt{e}$ is ${\omega}_{0}=\text{175}\text{\mu m}$ (limited by the beam expander’s 50 mm lens diameter). The number of measurement points per

*ϕ*-triangle were 2500 and per

*Ө*sweep were 400, giving a total of 10

^{6}points.

The geometrical factors coming from the radial scanning lead to an apparent
curvature of the flat plate: *R* varies by ~470 µm over ~100 mm
coverage in *x* (or *y*). It is hence necessary to
convert *ϕ, Ө* and *R* to Cartesian coordinates
*x, y* and *z*. Treating *ϕ,
Ө*, *R* as spherical coordinates and applying the usual
transformation to Cartesian coordinates is not sufficient since the FSM angle
drive voltages are not linear with respect to the actual FSM angles
*ϕ*, *Ө*. Therefore, we calibrated
*ϕ* and *Ө* against the pixel position, ${x}_{0}(\varphi ,\theta )$,${y}_{0}(\varphi ,\theta )$, *z _{0}* on a focal plane array IR
camera at known distance

*z*to obtain a 9 × 9 calibration look-up table. The Cartesian coordinates are then obtained as $x={x}_{0}(\varphi ,\theta )R/{r}_{0}$,$y={y}_{0}(\varphi ,\theta )R/{r}_{0}$, $z={z}_{0}(\varphi ,\theta )R/{r}_{0}$, where ${r}_{0}=\sqrt{{z}^{2}{}_{0}+{x}^{2}{}_{0}(\varphi ,\theta )+{y}^{2}{}_{0}(\varphi ,\theta )}$. This look up table can then be applied to any point cloud translating the simultaneously recorded FSM monitor voltages (see Fig. 3(b)) through bilinear interpolation into a calibrated Cartesian (

_{0}*x, y, z*) surface as seen in Fig. 5(d).

## 3. Ranging precision

The following sub-sections discuss and define different precision limitations found in the presented FMCW-LADAR system.

#### 3.1 Precision limits from SNR

The ranging precision in a FMCW LADAR has a statistical limit of
*ΔR/(SNR _{rms})*, where $\Delta R=c/(2B)$is the range resolution and

*SNR*is the electrical root-mean-square signal to noise ratio. As a coherent LADAR,

_{rms}*SNR*can be close to shot noise limited (and thus proportional to the square root of the optical return power). Figure 6 shows the experimentally achieved precision as a function of return power (for an eye-safe output power level of 9 mW) while ranging to a single point on a brushed metal plate placed at

_{rms}*z*= 10.5 m. A precision below 10 µm is maintained down to return powers as low as ~75 fW, which corresponds to a signal attenuation of ~110 dB relative to the launched optical power of 9 mW. However, the precision does not follow the expected dependence of

_{0}*ΔR/(SNR*but rather reaches a floor of ~3 µm. This floor is higher than for the static system of Ref. [4] and is due to the introduction of the FSM that, even at a fixed position, will have small variations leading to small Doppler piston-like motion and additional speckle induced phase noise.

_{rms})#### 3.2 Precision limits from speckle-induced phase noise

Any diffusely scattering surface with roughness *σ _{z}*
illuminated with coherent light with wavelength $\lambda <{\sigma}_{z}$ will exhibit speckle. Speckle is the far-field intensity
pattern produced by the mutual interference of a set of random wave fronts
[38]. Thus, any coherent laser
ranging system mapping a diffusely scattering surface is subject to speckle. The
speckle-induced intensity in ranging was studied before, see eg Refs. [39–41]. Speckle-related errors in self-mixing interferometry are
discussed in Refs. [42,43]. However, the limiting factor in our
system is speckle-induced phase noise. Intensity noise is suppressed by the
large supported intensity dynamic range and an automatic-gain-control in the
processing. Speckle causes an additional phase noise in the return signal that
effectively appears in the argument of the cosine in Eq. (1). As discussed in [13], this additional speckle phase noise
can lead to large apparent outliers in the range distribution for an otherwise
nominally flat surface. In fact, the resulting distribution of measured range
values does not follow a Gaussian distribution as one might expect but rather
follow the distribution [13,44]

*z*is the one-standard deviation surface roughness (which is assumed to be Gaussian), and

_{0}, σ_{z}*k*is a normalization factor. The speckle-induced precision limit is the standard deviation of this distribution [13],

*B*= 1 THz, corresponding to an excess variance of

*2σ*.

_{z}^{2}The predictions of Eq. (3) are
compared to measurements in Fig. 5(e).
There is a good agreement, with the expected truncation at ~150 μm. For a single
lateral scan, the corresponding surface roughness was
*σ _{z}* = 5 µm. Note that this $\u3008\delta {z}_{}^{2}\u3009$ is a property of the surface and the extracted surface
roughness

*σ*agrees with surface roughness measurements derived by other means; it is not an intrinsic error of the FMCW LADAR system. The histogram for the full surface shows a broader central peak due to a ~7 µm imperfection in the

_{z}*xyz*calibration (see Section 3.4).

#### 3.3 Precision limits from speckle-induced frequency noise

For the scanning system, there is an additional contribution to the overall
precision that results from the time-dependence of the speckle phase as the beam
is scanned across the surface. The derivative of this time-dependent speckle
phase contributes additional “pseudo-doppler” noise to the measured frequency of
the heterodyne signal, and therefore to the range. For slow scan speeds this
effect is negligible but becomes significant for higher scan speeds. Previously,
we analyzed this effect in terms of the normalized scan speed, which is defined
as ${V}_{scan}={v}_{x}/\left({w}_{0}/{f}_{m}\right)$, *i.e.* the lateral scan speed
*v _{x}* in m/s normalized to one beam diameter
per frequency sweep of the swept laser. Here, the sweep in x gives ${V}_{scan}=$0.23, which gives no additional contribution to the precision
limit set by the speckle induced phase noise, based on Fig. 3 of Ref. [13].

#### 3.4 Systematic error from spherical to Cartesian coordinate transformation

From Fig. 5(e), the spread in ranges is increased from 5 µm to 8 µm when going from a 1D lateral scan to a full 2D lateral scan covering a surface; we attribute the additional uncertainty to an error of roughly 6 µm in the radial to Cartesian coordinate calibration, although there could also be slight variations in the surface flatness. In addition, over the entire surface of ~210 mm × 100 mm we measure a slight, ± 7 µm twist. Assuming the plate to be flat, we therefore attribute a maximum ~7 µm systematic uncertainty to the imperfect transformation from spherical to Cartesian coordinates (due to small variations in the FSM motion not captured in our calibration process).

#### 3.5 Uncertainty due to time-dependent variations in the overall air path

The overall 10 m air-path distance and the fiber optic path of the local reference branch vary due to refractive index changes during an image acquisition and these variations will be incorrectly assigned to the measured surface. The long term uncertainty (Allan variance) as measured at 10.5 m in our laboratory is shown in Fig. 7, while ranging to a single point on a brushed metal surface. This uncertainty reaches ~1 µm at 500 seconds (8.3 minutes), which is the time it takes to generate typical surface scans as presented in this paper. This uncertainty is attributed to temperature-driven optical path variation in air and fiber. However, these effects could be corrected for with knowledge of the local temperatures.

#### 3.6 Overall uncertainty (precision)

Table 1 summarizes and quantifies the different error sources affecting the achievable precision per point at 10 m standoff. The dominant fundamental uncertainty is given by speckle noise, which is a fundamental limit to any coherent laser ranging system mapping a diffusely scattering target. True Doppler motions will cause range error, but these are suppressed for our high optical sweep rates (3.4 PHz/s) and can be alleviated through different techniques such as specialized processing [45], averaging up and down sweeps (as was done with opposite chirped pulses [8]), or with a vibrometer [46] co-aligned with the FMCW-LADAR light.

Taking all the above mentioned effects into account an overall uncertainty (summed in quadrature) of 9.5 µm is achievable at 10 m stand-off with a comb-calibrated FMCW LADAR applied to 3D imaging. The achieved accuracy while ranging to a specular target is below 1 µm as shown in Ref [4], and is effectively limited by knowledge of the speed-of-light in the ambient air conditions.

## 4. High precision 3D images at a stand-off

We acquired multiple high-resolution three-dimensional surface profiles of various different objects. Typically, the system acquired 1 million pixel images, which takes ~8.3 minutes at the current 2000 point/second measurement rate. Figure 1 and Fig. 2 showed example images of both a shoe tread and a footprint. In this section we give additional examples of 3D surface profiles.

Figure 8 shows images of a machined Aluminum step block measured at a stand-off of 4.75 m. The block has a flat surface with the NIST logo as an ‘imprint’ followed by 7 staircase steps of varying step-heights, ranging from ~30 µm to 10 mm. Figure 8(c) compares a cross-section extracted from the 3D image to a measurement carried out with a coordinate measuring machine (CMM). These CMM truth data were obtained with a contact probe for 44 measurement points on the flat part of the step block and 36 points on each step, whereas the comb-calibrated non-contact FMCW LADAR provides a calibrated profile, containing ~1 million points. The standard deviation of the difference (red crosses) between the averaged LADAR measurements and CMM measurements is ~2 µm, the difference does not depend on the step height. The first 3 steps, (inset, Fig. 8(c)) were measured to have step heights of 110 µm, 30 µm and 100 µm. In other words, the LADAR is capable of measuring a step of 30 µm and a step of 10 mm with the same precision.

Figure 9 shows a 1 Megapixel image of a piston head measured at a stand-off of 10.5 m.
After subtracting a piecewise polynomial fit to remove the overall shape (as no
truth data was available), the residuals (green trace in Fig. 9(c)) show a clear dependence on the object slope. This
noise level is due to the range-depth covered by the beam spot on a slanted surface.
In other words, the range distribution of Eq.
(3) assumed the illuminated surface range depth was below the system
range resolution Δ*R*. However, if the surface is significantly
slanted, then the illuminated range depth within the laser spot is larger, given
roughly by $\Delta {R}_{surface}={D}_{spot}\mathrm{tan}\beta $, where *β* is the slant angle and
*D _{spot}* = 700 µm is the measured 1/e

^{2}spot diameter at 10.5 m stand-off. When Δ

*R*exceeds Δ

_{surface}*R*, the FMCW LADAR will return a single range value with a standard deviation on the order of 0.1-0.2 Δ

*R*. For this system, the uncertainty increases at a rate of about ~1.7 µm/degree of slant. In the cases of the flat cast iron lapping plate (Fig. 5) and the Al-step block (Fig. 8) the maximum surface slant is less than 0.6 degree, resulting in a negligible uncertainty increase due to the slant.

_{surface}Figure 10 shows the top of the same piston head as in Fig. 9, measured at closer stand-off distance of 4 m. (Note that this
closer distance was not chosen based on SNR considerations, but solely to decrease
the diffraction limited spot size to 1/e^{2} spot diameter of 300 µm for
higher lateral resolution.) The image clearly reveals an imprinted serial number,
with an imprint depth of ~100 µm.

In Fig. 11(a), the false colored, calibrated 3D surface profile of the flat granite plate
from Fig. 5(a) is shown. Even though the
granite is mechanically polished to a flat surface, the LADAR signal penetrates the
surface occasionally picking up different reflection from underlying grain
boundaries within the bulk of the granite. (Granite is a conglomerate of quartz and
other minerals.) The histogram in Fig. 11(b)
shows a sharp peak given by the polished surface, which follows the analytical model
of the range distribution given in Eq.
(3) for *σ _{z} =* 12 µm, and a tail extending into
the granite. This tail is fit with a double exponential having a first exponential
constant of 0.8 mm and a second of 40 µm. This penetration is also seen in Fig. 11(a) as spikes penetrating the
surface.

The large dynamic range in return power of the comb-calibrated LADAR is emphasized in
Fig. 12. The scene consisting of a cactus, a ceramic plate and the optical table is
mapped in one measurement. The scene covers a ~(120 mm)^{3} cube in
*x,y* and *z*. In Fig. 12(c), one branch of the cactus is shown acquired at a closer
stand-off of 4 m to allow for sufficient lateral resolution to clearly image
individual cactus spikes, which have a diameter of ~75 µm.

## 5. Conclusions

We presented a comb-calibrated FMCW LADAR that can be applied to 3D mapping of diffusely scattering surfaces at over 10 meters of stand-off. The system linearization is based on a free running comb, which is used as a frequency ruler. The processing is carried out in real time in an FPGA. The overall achieved uncertainty is at the ppm level and there is no need for continued calibration since the accuracy can be tracked back to the continuously monitored repetition frequency of a free-running comb, and hence to an rf standard. The system offers a high sensitivity (low return powers of 75 fW), has a high dynamic range in return power achieving the same precision with 70 dB variation in return power. We provided some example calibrated 3D images that reveal fine details captured in ambient lighting at 10 meter-scale stand-offs. This basic system is potentially useful for different applications, such as precision machining, precision assembly of components or forensics.

## Acknowledgments

We acknowledge helpful comments from P. Williams and C. Cromer and funding from DARPA EPHI and NIST. We also acknowledge ACT Denver for technical assistance.

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