Sensors 2019, 19, 5464 6 of 27
From the wavelength,
λ
laser
, of the laser, one can estimate the number of noise and signal events
per second by dividing Equations (5) and (6) by the energy of the photon at λ
laser
,
N
pixel
=
P_e f f
noise,pixel
hc/λ
laser
, (7)
S
pixel
=
P_e f f
signal,pixel
hc/λ
laser
, (8)
where c is the speed of light (3 × 10
8
ms
−1
) and h, Plancks’s constant (6.626 × 10
−34
Js).
SPADs have a certain dead time between successive detections which limits the theoretically
estimated photon-count statistics. This dead time itself can be paralyzable or non-paralyzable in
nature [
23
]. A non-paralyzable dead time,
t
d
, is assumed for all analyses in the paper. Therefore, the
event rates in Equations (7) and (8) are modified to provide the effective rates.
N_e f f
pixel
=
N
pixel
1 + N
pixel
· t
d
, (9)
S_e f f
pixel
=
S
pixel
1 + S
pixel
· t
d
. (10)
For simplicity, we will continue using the terms,
N
pixel
and
S
pixel
, for the noise and signal event rates
respectively. Based on the established equations, the effective noise and signal events per pixel per
second were simulated for a flat target of
r =
10% reflectivity over varying distances. An average laser
power,
P
avg
, of 20 mW, wavelength,
λ
laser
=
780 nm and a repetition rate of 1 MHz and a pulsewidth
of
≈
500 ps were assumed to be uniformly illuminating the target with FOVs,
θ
H
=
20
◦
and
θ
V
=
20
◦
.
A 780 nm laser wavelength was used for analysis purposes simply because of the practical availability
of such a laser in view of future measurements using that laser. However, a common choice for
LiDAR is working with longer near-IR wavelengths, which would naturally perform better under high
solar exposure compared to a 780 nm laser. A lens with
D
lens
=
11 mm and a f-number of 1.4 (focal
length
≈
15 mm) was assumed to collect light onto a 32
×
32 SPAD sensor (
N =
1024). Additionally,
background light of different levels from 5 klux (
≈
50 W/m
2
) to 100 klux (
≈
1000 W/m
2
) solar exposure
was imposed without changing the laser parameters. A summary of common simulation parameters
used through the paper is mentioned in Table 1.
Table 1. Simulation parameters
Parameter Value
Average laser power, P
avg
20 mW
Laser wavelength, λ
laser
780 nm
Repetition rate , f
laser
1 MHz
Total system FWHM 530 ps
Target reflectivity, r variable, 8–60%
Field-of-view, FOV 15
◦
–40
◦
Background light variable, 5–100 klux
Sensor resolution 32 × 32
SPAD detector PDP 10%
Pixel fill-factor, FF 50%
Diameter of collecting lens, D
lens
11 mm
f-number, f# 1.4
focal length, f 15 mm
Lens efficiency, T
l
0.8
Optical filter passband, ∆
bw
20 nm
Filter efficiency , T
f
0.7
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