1. Ahmed Hassebo 18th
Coherent Laser Radar Conference
CLRC 2016, June 26 – July 1 1
Improve Lidar SNR in Biaxial Systems: Simulation to Examine the
Overlap Function and the Receiver Aperture Alignment
Silvia Tirado (a), Ahmed Hassebo (a), Carl Gordon (a), Abdelrahman Abbas (a), Mohanad Osman
(a), Miar Elaskandarany (b), and Yasser Hassebo (c)
(a) The City College of New York of CUNY
160 Convent Ave, New York, NY 10031
(b) Macaulay Honors College of CUNY; 2900 Bedford Avenue, Brooklyn, NY 11210
(c) LaGuardia Community College of CUNY; MEC Dept. 3110 Thomson Ave, LIC, NY 11101
Lead Author e-mail address: (ahasseb00@citymail.cuny.edu)
Abstract: Lidar daylight measurements are limited by sky background noise (BGN).
Reducing the BGN is essential to improve Lidar signal-to-noise ratio (SNR). The main
objective of this paper is to optimize the signal to noise ratio in a biaxial Lidar system by
improving the geometrical design of Lidar receiver. A series of simulations and modeling
to calculate the overlap area between both the transmitter and the receiver field of view
(FOV) was conducted for a vertically pointing Lidar to determine optimal receiver aperture
shapes within four different lidar ranges. Results show that varying receiver aperture shape,
position, and size, that accommodate all backscattering return signals over a given Lidar
range, while at the same time minimizing detected BGN, will maximize Lidar SNR. This
approach of improving Lidar SNR can be translated to an improvement in Lidar attainable
range for backscatter schemes including Raman Lidar and Differential Absorption Lidar
(DIAL).
Keywords: Biaxial Lidar, FOV, Background noise, SNR, Overlap Factor, Aperture, Simulation, Matlab.
1. Introduction
The impacts of aerosol in the human health with diseases such as lung cancer, bronchitis, and asthma have
been essential motivations to record aerosol properties and transportation. Additionally, many studies
investigate the relationship between the traffic pollution and the damage in human brain and analyze the
effects of traffic pollution on the genome of a newborn, and prematurity and preeclampsia issues [1].Light
Detecting and Ranging (Lidar or Laser Radar) is an active optical remote sensing instrument widely used
for probing the earth’s atmosphere. Lidar system is capable of providing vertical distribution of aerosol and
cloud [2, 3]. Lidar has been applied to study stratospheric aerosols [4], tropospheric aerosols [5], and climate
gases such as stratospheric ozone [6]. Lidar consists of three basic subsystems: the transmitter, receiver,
and electronics subsystems [7]. The typical monostatic configuration of lidar systems can be classified into
two categories, coaxial and biaxial. The main disadvantages in the coaxial configuration, where the coaxial
alignment between transmitted beam and the receiver’s FOVs is maintained, are: (a) the detector saturation
problem due to optical obstacle, and (b) the near field optical distortions for shorter range, where part of
the signal is blocked by the secondary mirror. Biaxial lidar, where the transmitter and receiver are located
adjacent to each other, system is a practical solution to overcome the coaxial configuration problems. On
other hand, the recorded data from the biaxial lidar is negatively affected by the geometrical factor (GF) at
shorter range, as shown in figure 1.This effect makes near field measurements impossible (figure 1, 2). In
this study, we examine the potential of improving SNR for vertically pointing biaxial lidar systems by
optimizing detector aperture geometry and design through a series of simulations and modeling using
Matlab for four different lidar ranges. To realize the effect of GF ’ )(R ’ in the return lidar signal, the lidar
Equation can be written as [8]:








 
R
L
L
LL
o
LL dRRk
c
RR
R
A
PRP
0
2
),(2exp
2
)(),()(),( 


(1)

2. Ahmed Hassebo 18th
Coherent Laser Radar Conference
CLRC 2016, June 26 – July 1 2
X
Z
Rmax
Rmin
f
Telescope
Laser
bo
Lo
t0
Im1
Im2
Figure 1. Biaxial Lidar, overlap between laser and
receiver telescope FOVs [7].
Figure 2. Biaxial Lidar, schematic diagram shows
sounding trace images for lidar objects at heights of
Rmin, and Rmax [7].
Where, ),( RP L is the total scatter laser power received from a distance R, LP represents the average power
in the laser pulse, Ao/R2
describes the solid angle of the receiver optics (Ao is the area of the telescope
primary mirror), )( L denotes the receiver’s spectral transmitter factor, ),( RL is the volume backscatter
coefficient, Lc represents laser pulse length (c is speed of light, L is Laser pulse rectangular duration),
),( Rk L : Atmospheric extinction coefficient. The smaller the value of )(R is the smaller the return signal
and the smaller SNR particularly for low altitudes. GF can be defined as the ratio of the energy transferred
to the photodetector to the energy reaching the telescope primary mirror, Edet /Escat [9]. This reduction in the
detector response to the return signal is caused by a lack of perfect overlap between the receiver telescope’s
FOV and the transmitter laser beam. In the following section, we describe the problem and discuss the
calculations. The overlap effect of the GF including the receiver field stop position and size, and their effect
in lidar SNR improvement will be introduced. Then Lidar simulation results will be introduced.
2. Problem Description and Calculations
The standard configuration for most lidar systems is to place a ‘round’ aperture at the focal point of the
receiver telescope. It is also commonly assumed that once the lidar receiver FOV and transmitted beam are
completely overlapping, the efficiency of collection is unity [8]. However, this analysis does not properly
take into account the shifted position of the collected backscattering signals on the image plane from the
telescope focal point at the receiver. As shown in figure 1 & 2, the image displacement is range dependent
and it is due to the distance ‘bo’ between the laser and telescope optical axis. In our calculations, the
telescope is presented by a lens with diameter ‘to’ and ‘ f’ focal length. The farther the lidar object (z=Rmax),
the smaller the sounding image (Im1). Numerous papers implemented a wedge-like shape aperture design
to overcome this shifted problems [10]. In this paper we analyze the effect of changing the size, shape, and
alignment of a round aperture in the lidar SNR. As shown in Fig. 3, we assume the optical vertical axis z.
the ground level (x-axis), where the location of the telescope primary mirror and the transmitted laser beam,
is at R=0. The range ‘R’ increases, there will be a point ‘R1’ where the first intersection between the left
boundary of the laser beam FOV and the right boundary of the telescope FOV. Then at (z= R2), a complete
overlap is formed. But this is not the effective overlap function. The effective FOV is based on, Do, the
field stop diameter ( fDoeff / the shaded area in this case) [9]. The actual overlap started at (z= R3)
and finally the effective overlap is completed at (z= R4). At short distances (z<R3) the ratio of the
overlapping area ( areaOL ) to the image area ( areaIm ) that formed near to ‘f’ is equal to zero: 0
Im
)( 
area
areaOL
R
, where 0areaOL . This is making near field observations impossible (effective telescope area:
0)()(  RARA oeff  ) [11].

3. Ahmed Hassebo 18th
Coherent Laser Radar Conference
CLRC 2016, June 26 – July 1 3
In the case of a small round aperture (Do = 2 mm diameter) is
placed at the telescope focal point fo, the overlap function
)(R is very small for any object in ranges of (R3<z<R5),
where at R5 there is an arbitrary object which has a large
sounding image and very far from ‘f’ in the imaging plan (see
Fig. 3) [11]. Design of a unique aperture to cover certain
desired ranges becomes feasible. In our calculation, a Matlab
code was created to simulate the biaxial Lidar system
performance using the lidar design parameters in Table 1, and
equations from Table 2 [12]. Then, the size and position of
the sounding image at the telescope were also calculated for
four different ranges. Using the size and position of the
sounding image, apertures were proposed to accommodate
the entire backscattering signal and, at the same time,
eliminate the BGN, then improve the SNR. To visualize this
improvements, the GF was calculated as well.
Lo
Lbo
to
Do
f
R1
R2
R3
R4
fDoeff /
Aperture
FOV
LaserTelescope
X
Z
Aperture
(field stop)
Figure 3. Biaxial Lidar: overlap between
effective FOV of telescope (diameter = to)
and laser beam (initial diameter = Lo) and
aperture (diameter = Do) [11]
Table 1. System Design Parameters Table 2. Equations to Simulate Lidar
Performance
Symbol Value Meaning
to 177.8 x10-3
m telescope effective radius
Lo 5 x10-3
m laser effective radius
bo 200 x10-3
m Distance between laser and
telescope axis
f 3910 x10-3
m Focal length
θ 7x10-4
rad Laser’s half divergence
angle
Symbol Equation Meaning
tT(R) 𝑡 𝑇(𝑅) = 𝑡 𝑜 + 𝜑𝑅 FOV cross-section radius
L(R)
𝐿(𝑅) = √ 𝐿 𝑜
2
+ 𝜃2 𝑅2
Laser beam radius at
range R
W(R)
𝑊(𝑅) = (
(𝐿 𝑜 + 𝜃𝑅)𝑓
𝑅 − 𝑓
)
Radius of the image at
range R
x(R)
𝑥(𝑅) =
𝑏 𝑜 𝑓
𝑅 − 𝑓
Image position
coordinate at range R
z(R)
𝑧(𝑅) =
𝑓2
𝑅 − 𝑓
Image position
coordinate at range R
3. Results and Analysis
(a) (b)
(c) (d)
Figure 4. Images position, proposed aperture size and shape, and the corresponding comparison of the geometric
factor of the new and old aperture in (a) Short Range, (b) Mid-low Range, (c) Mid-Range, and (d) Long Range

4. Ahmed Hassebo 18th
Coherent Laser Radar Conference
CLRC 2016, June 26 – July 1 4
The simulation of the Lidar system shows that the telescope and laser beam overlap starting after 40 meters
of altitude. We examined the GF for four different ranges: Short Range: from 0.05km up to 3km, Mid-low
Range: from 3km to 15km, Mid-Range: from 15km to 30km, and Long Range: from 30km to 50km (the
maximum altitude of the Lidar). Figure 4 is the graphical representation of the results summarized in Table
3 (the size and position of the sounding image) for four cases. The black circumference represents an initial
proposed aperture of radius 1mm at the focal point of the telescope, while the red figure represents the new
proposed aperture. The comparison of GF between the traditional aperture and the GF obtained with the
new aperture shows a significant improvement. Table 3 summarized the proposed apertures position
(center), size, shape, area, and the GF for each of the four cases.
Table 3. Results for Aperture Size and GF
4. Conclusions
In the effort of improving the SNR in biaxial Lidar system by optimizing the geometrical factor of the Lidar
receiver, we propose a change in the receiver aperture shape, positions and size for different ranges (that
accommodate all backscattering return signals over a given Lidar range, while at the same time minimizing
detected BGN). Using this proposed design, a series of simulations and modeling to calculate the GF of a
vertically pointing Lidar shows significant improvements in GF, hence improves lidar SNR, in mid and
high ranges compared to less improvement in short and mid- low ranges. In this study, the GF in biaxial
Lidar system was analyzed as a parameter to improve the SNR. Our results have shown vast improvements
at different ranges. In the low range, 0.05-3km, GF was increased by using a trapezoidal aperture when it
was nearly impossible to attain a good signal at that altitude. Yet the size and position of the aperture are
too big, therefore it is impossible to be implemented at the low range. In the Mid-low range, 3-15 km a
complex aperture is proposed to better fit all the images at this range. An overlap factor of 43.7% was
achieved within this range. For Mid (15-30km) and High (30-50km) ranges elliptical shaped apertures have
been tested and showing changes in the GF (81.6% and 91.1%, repetitively).
5. References
[1] R. C. D. R. C. J. W. M. R. B. Wu J, "Association between Local Traffic-Generated Air Pollution and
Preeclampsia and Preterm Delivery in the South Coast Air Basin of California. Environ Health Perspect," vol.
117, p. 1773–1779, 2009.
[2] E. J. S. J. D. C. J. R. B. T. A. B. D. S. D. O. Welton, "Measurements of the Vertical Structure of Aerosols and
Clouds Over the Ocean Using Micro-Pulse LIDAR Systems," SIMBIOS Project Annual Report, a NASA
Technical Memorandum, 2001.
[3] C. W. H. W. F. I. M. M. L. W. M. d. G. M. M. L. S. A. A. P. A. V. R. G. R. V. M. R. M. R. K. a. E. K. B.
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types," J. Geophys. Res., vol. 104, no. D19, p. 23983–23993, 1999.
[4] V. B. a. A. E. Zuev V., " Ten Years (1986-1995) of lidar observations of temporal and vertical structure of
stratospheric aerosol over Siberia,," J. Aerosol Sci., vol. 29, no. 10, pp. 1179-1187, 1998.
[5] a. G. G. Barnaba F, " Lidar estimation of tropospheric aerosol extinction, surface area and volume: Maritime
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[6] M. S. S. K. a. E. B. Douglass L. R., "A composite view of ozone evolution in the 1995-1996 northern winter
polar vortex developed from airborne lidar and satellite observations," J. Geophys Res., vol. 106, no. D9, pp.
9879-9895, 2000.
Range
(km)
Image 𝑹 𝒎𝒂𝒙
Radius (mm)
Image 𝑹 𝒎𝒊𝒏
Radius (mm)
Aperture
Center
Aperture
Shape
Aperture
Area (𝒎𝒎 𝟐
)
Geometric
Factor
0.05 - 3 1.3735 1.6967 (-8.85, -172.4) Trapezoid 930.71 5.1 x 10−3
3 - 15 1.3695 1.3735 (-0.15, -3.061) Complex 11.535 0.437
15 - 30 1.3690 1.3695 (0, -0.75) Ellipse 7.213 0.816
30 - 50 1.3688 1.3690 (0, 0.408) Ellipse 6.456 0.911

5. Ahmed Hassebo 18th
Coherent Laser Radar Conference
CLRC 2016, June 26 – July 1 5
[7] Y. Y. Hassebo, Lidar signal-to-noise ratio improvements: Considerations and techniques, Vols. 68-10, New
York, NY: ProQuest Dissertations; Thesis (Ph.D.)--City University of New York, 2007, 177 p.
[8] M. R.M, Laser Remote Sensing:Fundamentals and Applications, New York: Wiley , 1984.
[9] B. B. R. C. L. F. a. N. S. R. Velotta, "Analysis of the receiver response in lidar measurements," Appl. Opt.,
vol. 37, p. 6999–7007, 1998.
[10] R. R. a. A. C. Agishev, "Spatial filtering efficiency of monostatic biaxial lidar: analysis and applications,"
App. Opt. , vol. 41, pp. 7516-7521, 2002.
[11] K. E. Yasser Hassebo, "The Impact of Receiver Aperture Design and Telescope Properties on LIDAR Signal‐
to‐Noise Ratio Improvements," in American Institute of Physics Conf. Proc. , 2007.
[12] R. R. A. a. A. Comeron, "Spatial Filtering Efficiency of Monostatic Biaxial LIDAR: Analysis and
Applications," Applied Optics, vol. 41, no. 36, pp. 7516-7521, 2002.