A Study on Ranged-Gated Lidar System with Linear Plus
YU Lin-yao,WEI Qun,JIANG Hu-hai,ZHANG Tian-yi,WANG Chao,ZHU Rui-feiθJIANG Zhen-hai
Changchun Institute of Optics, Fine Mechanics and Physics,CAS
Changchun,Chinese
Abstract—According to the study of super-resolution range-gated system, we proposed an improved system with linear plus
detects. And a range function is derived by considering the shot effect noise and dark current noise. The simulation shows that the
improved system has a good range accuracy capability.
Keywords—lidar㸹range-gated㸹linear plus㸹range accuracy
1. Introduction
Non-scanning imaging lidar is among the most popular
development laser radar systems. The range-gated technology
and device in the system have been very mature[1]. In the
study of laser radar , range accuracy is an important indicator
of appraising a laser radar system, so how to improve the
range accuracy has become a very important issue that all
researchers chasing for[2]. There are two range-gated laser
radar systems which can achieve high range accuracy. The
first one is centroid algorithm that 3D images can be derived
from an sequence of 2D images[3]. Hower it costs a lot of
time to calculate which slows down the 3D imaging speed. In
2007, French scientist Martin et al, presented a super-
resolution range-gated technique that only two 2D images are
needed to create a 3D image which speeds up the calculation
with a higher range accuracy[4]. Based on the super-
resolution system this paper presented an improved system
which replace the constant plus of the receiver with linear
plus ,and results show that it has a better SNR and range
accuracy capability[5].
2. Range function of range-gated system
with linear plus
Figure 1. Sequence diagram of laser pulse and gate during falling ramp
Figure 2. Sequence diagram of laser pulse and gate during rising ramp
Assuming the power and width of the laser pulse is0
P,
p
t
.
So the function of laser pulse can be written:
 
0
rect
pp
PtP ttt
㸦1㸧
The initiated linear plus of the range-gated receiver is
b
,
the slope is
k
. Assuming the width of range gate and laser
pulse is equal as
p
t
. Then the linear plus function can be
written:
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  
1rect p
Gtkt btt 
㸦2㸧
There are two intensities of images to calculate. Firstly,
we derive the intensity when only the front part of the pulse
received by the range gate, the Sequence diagram of laser
pulse and gate during falling ramp is shown in figure 1. The
distance between the target and the detector isz, and the time
that the laser pulse travels is2tzc . The delay time between
the pulse starting transmitting and the range gate getting open
is D
W
. The width of the pulse which received by range gate
when it is open can be written:
2
Dp Dp
z
tt c WW WW '   㸦3㸧
The intensity of the image is:
 
11
p
p
t
tt
IR dtPtGt
'
³ 㸦4㸧
We can get another intensity function in the same way, the
delay time is
'
DDp
WWW 
. The Sequence diagram of the pulse
and gate during falling ramp is shown in figure 2.
The width of the pulse which received by range gate is:
''
2
pD D
z
tttc WW '   㸦5㸧
The intensity function can be written:
 
'
21
0
t
IRdtPtGt
'
³
㸦6㸧
From equation (1)~(7),we can get the range function:
 

22
2
2
21
pp p
p
Dp
Mkt bt kt b
kt b
c
zt
kkM
k
W
§·



¨¸

¨¸

¨¸
©¹
㸦7㸧
While M is:


22
2
1
22
2
2
2
2
22
p
D
p pp
D
kt bzb
ck k
I
MIkt b
kt btzb
kck k
W
W
ªº
§·
«»

¨¸
«»
©¹
¬¼
ªº
 §·
§·
«»

¨¸ ¨¸
¨¸
«»
©¹
©¹
¬¼
㸦8㸧
3. SNR and range accuracy
The differential coefficient of equation (9) can be written:
12
12
p
dI dI
dzAABdtCdk Ddb
II

㸦9㸧
Then the range accuracy of the system is:

 
2
222
22
12
22
22
11
2
p
AABt
cSNR SNR
z
Ck Db
G
G
GG


㸦10㸧
We only consider the first and second term approximately
as the affection of other terms is small. Then the range
accuracy of the linear plus system can be written:
 


2
22
2
22 2
12
2
42
1
11
1
pp
pp p
kt bt
c
z
Mkt bt kt b
kkM
k
M
SNR SNR
M
G

u
 


㸦11㸧
If the shot effect noise and dark current noise are
independent, then the total noise of the system can be
presented as:
222
2
alliccd sd
di
iccd
FG
It
FNG
e
VVV 

㸦12㸧
While
iccd
F
is noise factor (usually is
2
),
N
is the
number of photoelectrons,
G
is the plus of the system,
d
I
is
the dark current of ICCD,i
tis the integral time of ICCD,
e
is
the charge of an electronic.
Then the SNR of the system can be written:


2
2
out
all di
iccd
pc
r
t
pc di
iccd r
t
NN
SNR
GIt
FN e
Gptdt
w
GIt
FG ptdt
we
V
K
K


³
³
㸦13㸧
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The SNR of the two images with linear plus are
respectively:
22
10
2
12
22
10
2
4
4
pc g
p
di
pc g
p
wDt
pt
tz
SNR
GIt wDt
FGp t
tz e
UKW
K
UKW
K
§·
'
¨¸
¨¸
©¹
§·
'
¨¸
¨¸
©¹
㸦14㸧
22
20
2
22
22
20
2
4
4
pc g
p
di
pc g
p
wDt
pt
tz
SNR
GIt wDt
FGp t
tz e
UKW
K
UKW
K
§·
'
¨¸
¨¸
©¹
§·
'
¨¸
¨¸
©¹
㸦15㸧
While

r
pt
is the power irradiating at the detector,
pc
K
is the quanta efficiency,
w
is energy of single photonics,
U
is the reflection of target,
K
is the efficiency of the optics
system,
W
is the transmission of atmosphere,
D
is the
diameter of the receiver optics system.
t'
is the width of
pulse received by the range gate.
Then the range accuracy of system can be rewritten as :
 


2
22
2
22 2
12
2
42
1
11
1
pp
lin
pp p
out out
kt bt
c
z
Mkt bt kt b
kkM
k
M
SNR SNR
M
G

u




(16)
Figure 3. Curve of SNR with linear plus
The curve of SNR with linear plus are shown in fig 3. The
SNR of two images are quite different: grown and fallen as
distance increased respectively. Because when the distance
between the target and detector is increased, the width of the
pulse that received by the detector is augmented and reduced
respectively. This results their intensities quite different which
make their SNR curves have different shapes.
Figure 4. Curve of range accuracy with linear plus vs distance
Fig.4 shows the curve of range accuracy with linear plus
vs distance. During the distance when the pulse can be
received by range gate, firstly the range accuracy is increased
when the target gets away from the detector, and it decreases
as the distance continues growing.
4. Conclusion
This article presented a new type of range gated laser radar
system which uses linear plus ICCD receiver instead of
constant plus. Further more we derived the range function
from the intensity of two images by changing the time-delay.
Then the range accuracy expressed by SNR is derived from
the range function. The dark current and shot noise is
considered. At last the curves of SNR and accuracy is given to
show the performance of the improved system.
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