The histograms have 400-ps time bins, short
enough to resolve the 700-ps pulses.
Depth information is recovered by locating
the temporal position of the histogram peak,
dt, which can be achieved with sub–time bin
precision (here, we use Fourier up-sampling by
a factor of 32; see supplementary materials,
section 5 for details). The depth of each pixel,
D, is a function of bothdtand the angular co-
ordinate of the pixel with respect to the optical
axis of the fiber,q
DðÞ¼dt;q1
2cdtcosq ncLcosq 1 sin^2 q
n^2 c ^12
ð 2 ÞThefirsttermontheright-handsideofEq.2
accounts for the different optical path lengths
traveled by pulses in free space, whereas the
latter term accounts for differences accumu-
lated inside the fibers. See supplementary mate-
rials, section 4 for a derivation.
Figure 2 shows snapshots from movies of
several dynamic scenes. Figure 2A shows con-
secutive frames of a swinging pendulum, and
the depth map tracks the 3D motion of both
the pendulum bob and its thread. Figure 2,
B to E, shows scenes with more dynamic
motion—some of the authors moving around
at a progressively increasing distance from the
distal facet, up to 2.5 m away. The full movies
are available in the supplementary materials
(supplementary materials, section 12, and
movies S2 to S4). The depth precision of our
system is largely determined by the level of
return signal from each pixel, rendering it high-
ly dependent on the reflectivity and depth of
objects in the scene. We estimate a typical
depth precision of ~1 cm in the results shown
in Fig. 2.
To more-quantitatively assess the imaging
performance of our prototype, we measure the
depth precision (Fig. 3A) and the signal-to-
noise ratio of the associated reflectivity maps
(Fig. 3B) as a function of scene depth and ra-
dial position within the field of view. In these
measurements, the optimal depth precision
found was ~2.5 mm at a scene distance of 0.4 m,dropping off slightly with distance to ~6 mm
at 2 m.
Because the number of resolvable features
is fixed by the number of spatial modes sup-
ported by the MMF, both the lateral resolution
and the diameter of the field of view grow
linearly in proportion to the distance to the
scene,l. The angular resolutionqris therefore
constant with depth. We experimentally mea-
sure an angular resolution of ~16 mrad, close
to the theoretical valueqr~ 0.61l/a~ 13 mrad.
The spot contrast ratio, defined as the ratio of
power in the spot to the total projected power,
is ~0.4. Both resolution and contrast are rela-
tively constant across the field of view, with
only a slight decrease toward the edges. Sec-
tion 9 in the supplementary materials gives
more details of these measurements.
There are several ways that the image qua-
lity can be enhanced in our current prototype
system if necessary. Althoughtpdoes not di-
rectly limit the depth precision, shorter pulses,
providing they can be properly sampled, will
yield a higher depth precision. Images acquired1396 10 DECEMBER 2021•VOL 374 ISSUE 6573 science.orgSCIENCE
ABCFig. 1. Endoscopic LIDAR.(A) A schematic of the experimental setup. See
supplementary materials, sections 1 to 3, for a detailed description of the TM
acquisition, imaging procedure, and data processing. BS, beamsplitter; PD,
photodiode. (B) A snapshot of the true scene being recorded. (C) Typical depth-
resolved images obtained with our system. Each frame is captured in 200 ms.
The frames show the pieces on a revolving chess board located at a depth of
~30 cm from the distal fiber facet, recorded at a frame rate of 5 Hz (supplementary
materials, section 12, and movie S1). Scene depth is encoded in the color channels,
and scene reflectivity is encoded in the transparency channelÑthus, regions
of the scene with low levels of return signal, and consequently a poorly estimated
depth, are displayed with low brightness. The dark spots in the images are the result
of singularities in the speckle reference used to measure the TM.RESEARCH | REPORTS