Study of reﬂective and polarization properties of objects found in automotive LiDAR applications

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Study of reflective and polarization

properties of objects found in

automotive LiDAR applications

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Study of reflective and polarization properties of objects found in automotive LiDAR applications

Daniel Tonvall c

Daniel Tonvall, 2020

Supervisors: Erik Backström, Veoneer; Joakim Ekspong, Umeå University Examinor: Ove Axner, Umeå University

Master’s Thesis in Engineering Physics Department of Physics

Umeå University

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Acknowledgements

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Abstract

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Chapter 1. Introduction

Each year, the lacking attention of automobile drivers in crucial moments cause numerous life changing accidents [1]. Car-producers have attempted to decrease these accidents by integrating safety-systems designed to assist the driver, such as tracking of pedestrians or driver monitoring systems [2,3]. Another, rather drastic and perhaps controvesial measure, is by introducing autonomous vehicles.

Autonomous vehicles, or self-driving cars, uses different sensors to perceive its environment in order to operate without a human driving. This introduces the opportunity of having the car in absolute attention at all times. However, the technical challenges involved in realizing fully autonomous vehicles are not trivial. For example, the vision of the driver must be replaced by technology that can provide enough detail to determine not only what is an obstacle and what is not, but also be able to determine what the obstacle is. In solving these challenges, a promising technology is Light Detection And Ranging (LiDAR).

LiDAR often works by using a pulsed laser to detect distance, velocity and angle to some object [4]. First, a laser pulse is sent towards an object and is then reflected back towards the source, after which the distance and angle to the object can be measured. When laser pulses are sent in all directions at a high repetition rate, a real-time point cloud of the surroundings can be created. As implied, a condition that must be fulfilled for a LiDAR unit to detect a surface is that a sufficient amount of the light in the laser pulse is reflected back towards the source. In order to predict whether a surface has the reflective properties such that it can be detected by a certain LiDAR unit, the common description of reflectance, which simply describes the ratio of incident and reflected light, is in most cases insufficient. Only in the rare case of a surface displaying ideal diffuse reflection will it prove sufficient. Since surfaces with such properties are rare, the prediction is best made with knowledge of the surface’s Bidirectional Reflectance Distribution Function (BRDF).

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CHAPTER 1. INTRODUCTION

Several gonioreflectometers of different capacity have previously been built to study the BRDF [7,8], where some have also accounted for polarization [9,10]. Quite recently, a study was made on different types of fabric [11], where a go-nioreflectometer similar to the setup presented in this thesis was built to verify a model of the BRDF made for virtual reality and visual simulation technology. Furthermore, additional studies have been made on the polarization properties of automobile paint [12]. However, similar investigations made with automotive LiDAR applications in mind are not very common.

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Chapter 2. Theory

The following sections aims to explain the necessary theory in order to describe radiation from a surface, starting with some basic radiometric concepts followed by theory related to reflection and to the BRDF.

2.1 Radiometric concepts

This theory follows the method described by Frank L. Pedrotti [13]. The irradiance E of a surface is defined as the radiant power Φ emitted per area A of the surface, and is given by

E = dΦ

dA W · m

−2

(2.1) When the power is radiated in a specific direction, it is described by the Radiant intensity I. It is the radiant power Φ per unit solid angle ω and is defined as

I = dΦ

dω W · sr

−1

(2.2) Simply put, the solid angle describes how much an object covers the field of view when viewed from a given position, called the apex. In other words, it describes how large an object appears from a particular position. The solid angle is often expressed in the unit of steradians (sr) and, in spherical coordinates, its differential is given by

dω = sinθdθdφ (2.3)

where θ is the zenith angle, and φ is the azimuth. Integrating equation 2.3 for a circular object (see figure3.1 for an illustration) gives the solid angle

ω = Z 2π 0 dφ Z θ 0 sinθdθ = 2π(1 − cosθ) (2.4)

Considering radiant indensity I per unit projected area dAProj = dA cos θr yields

the radiance L, which is given by

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CHAPTER 2. THEORY

2.2 Lambert’s cosine law

A surface which displays the same radiance independent of viewing angle is called an ideal diffuse reflector, and is said to be Lambertian and obeys Lambert’s cosine law. It states that the radiant intensity from a Lambertian surface is direcly proportional to the cosine of the angle θr between the surface normal and the

viewing angle, and is given by

I(θr) = I(0) cos θr (2.6)

Where I(0) is the observed intensity at an angle θr= 0 to the surface normal. The

radiance L at some angle θr to the surface normal of a surface of area dA is given

by equation 2.5, such that

L(θr) =

dI(θr)

dA cos θr

(2.7) So, for the case of an ideal diffuse reflector of area dA, the radiance will be given by LDiffuse(θr) = dI(θr) dAProj = dI(0) cos θr dA cos θr = dI(0) dA (2.8)

Thus, the radiance is constant and independent of the viewing direction. An illustration of reflection on a Labertian surface is presented in figure 2.1a. Figure

2.1b present an illustration of specular reflection, where all light is reflected with the same angle relative to the surface normal as the incident angle.

(a) (b)

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CHAPTER 2. THEORY

2.3 Bidirectional Reflectance Distribution Function

The reflectance of a surface is commonly described as the ratio between the incident and the reflected radiant energy. This is a dimensionless quantity which only accounts for the total reflected radiant energy, and not its incident or reflected direction. The BRDF describes the reflectance as a function of wavelength and both incident and reflected direction [8]. The following theoretical description follows the method of Anak Bhandari et al [9]. Both the incident ( ˆΩi) and reflected

( ˆΩr) direction of the radiant energy depend on the zenith angle θ and azimuth angle

φ, such that ˆΩi = ˆΩi(θi, φi) and ˆΩr = ˆΩr(θr, φr) and is illustrated in figure2.2.

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CHAPTER 2. THEORY

The BRDF, described with ρ in equations, is defined as the fraction of the reflected radiance L to the incident irradiance E, and is given by

ρ(λ, ˆΩi, ˆΩr) = L(λ, ˆΩi, ˆΩr) E(λ, ˆΩi) = L(λ, ˆΩi, ˆΩr) L(λ, ˆΩi) cos θidωr [sr−1] (2.9) To obtain the reflected radiance, we add contributions to the reflected radiance from all incident angles ˆΩi

L(λ, ˆΩr) =

Z

2π

ρ(λ, ˆΩi, ˆΩr)L(λ, ˆΩi) cos θidωi (2.10)

where the 2π indicate integration over the half-sphere. For a Lambertian reflector, the reflected radiance is independent on incident and reflected direction such that

ρ(λ, ˆΩi, ˆΩr)

Lambert

= ρL(λ) (2.11)

Employing equation 2.11 in equation 2.10 yields

L(λ, ˆΩr) = ρL(λ)

Z

2π

L(λ, ˆΩi) cos θidωi = ρL(λ)E(λ) (2.12)

In the experimental part of this thesis, a collimated beam of incident radiation is used. In the following equations, a superscript s is used to specify referring to the collimated beam of incident radiation. Consider it having a radiance Es normal to the incident direction ˆΩ0. Since the incident radiation is only present when

ˆ

Ωi = ˆΩ0, the reflected radiance is expressed in terms of a Dirac delta function

Ls(λ, ˆΩi) = Es(λ)δ( ˆΩi− ˆΩ0) = Es(λ)δ(cos θi− cos θ0)δ(φi− φ0) (2.13)

Which yields the incident irradiance E(λ, ˆΩ0) =

Z

2π

Ls(λ, ˆΩi) cos θidωi = Es(λ) cos θ0 (2.14)

Combining equations 2.12and 2.14gives the reflected hemspherical radiance for a Lambertian surface with a collimated radiation source

L(λ, ˆΩr) = ρL(λ) cos θ0Es(λ) (2.15)

By using equation 2.15 we can find an expression for the reflected hemispherical irradiance

E(λ, ˆΩ0) =

Z

2π

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CHAPTER 2. THEORY

Using equations 2.3 and 2.15 in equation 2.16 gives the relation

E(λ, ˆΩ0) = ρL(λ) cos θ0Es(λ) Z 2π 0 dφr Z π/2 0 sin θrcos θrdθr = πρL(λ)Es(λ) cos θ0 (2.17)

By rearranging equation 2.17 we can find the irradiance reflectance

ρ(λ, ˆΩ0, 2π) =

E(λ, ˆΩ0)

Es_{(λ) cos θ} 0

= πρL(λ) ≤ 1 (2.18)

where the 2π indicate the radiance reflected onto the halfsphere, which is all re-flected irradiance. Equation2.18implies that for a Lambertian surface the BRDF must only depend on wavelength and obey

ρL(λ) ≤

1

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Chapter 3. Method

This chapter begins with a presentation of the necessary theory related to the setup and the measurements, followed by a description of the experimental setup and its components, and finishes with a description of the alignment procedure of the setup.

3.1 Theory applied to the setup and measurements

3.1.1 Solid angle subtended by the sensor

The sensor used in the setup is placed at some distance r from the center of the half-sphere traced by its rotation. This is presented in figure3.1;

Figure 3.1 – Geometry of the sensor’s relation to the light spot including the double apex angle β, reflection angle θr, and sensor diameter dSensor.

Since the sensor has a flat surface one can find a relation between the sensor diameter dSensor, the radius r of the setup, and the double apex angle β, presented

in figure 3.1. Starting with identifying an isosceles triangle, marked dashed red in figure 3.1, we can use the law of cosines to find

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CHAPTER 3. METHOD

Solving equation 3.1 for β gives

β = acos1 − d 2 Sensor 2r2 (3.2) Including equation 3.2 in equation 2.4, we can also find the solid angle ω of the setup ω = 2π 1 − cosβ 2 (3.3)

3.1.2 Numerical aperture

With an aperture of diameter dAperture placed at a distance s in front of a sensor

of diameter dSensor, the field of view of the sensor will be made smaller and thus

hinder unwanted stray light from reaching the sensor. A schematic of the sensor and the aperture is presented in figure 3.2. The numerical aperture (NA) of the sensor will be given by

NA = nsin(α) = nsin

tan−1dSensor+ dAperture 2s

(3.4)

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CHAPTER 3. METHOD

3.1.3 Case-specific simplifications

Since most materials are symmetric around the surface normal, the azimuthal angles can be replaced by their difference;

φ = φr− φi (3.5)

In addition to this, the reflected radiation is measured in the plane of incidence such that the azimuthal angles are equal (i.e., that φ = 0) and the BRDF reduces to

ρ(λ, θi, θr, 0) = ρ(λ, θi, θr) (3.6)

Also, the wavelength-dependence is removed by using a monochromatic light source so that the BRDF further reduces to [14]

ρ(λ, θi, θr) = ρ(θi, θr) (3.7)

3.1.4 Measuring the Bidirectional Reflectance Distribution

Function

The illuminated area A on the sample will be determined by A = ALaser

cos θi

(3.8) where ALaser is the cross-sectional area of the laser beam, such that the incident

radiance is given by E(θi) = Pi A = Pi ALaser cos θi (3.9)

where Pi is the power measured on the sensor. From the point of view of the

sensor, the projected illuminated area on the sample will be determined by A0 = A cos θr =

cos θr

cos θi

ALaser (3.10)

Thus, the irradiance measured at the sensor will be given by L(θi, θr) = Pr A0_ω s = Pr ALaserωscos θr cos θi (3.11)

where Pr is the reflected power measured by the sensor and ωs is the solid angle

subtended by the sensor. Using equations 3.9 and 3.11 in equation 2.9 yields

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CHAPTER 3. METHOD

3.1.5 Estimating total reflectance

Under the assumption that the samples are symmetric around their surface normal, the total reflection can be estimated from the measurements made with the light source in the surface normal. To start with, using equation 2.1 in equation 2.5

and solving for E gives an expression for irradiance, which for the reflected light is given by

dEr = Lrcos θrdωr (3.13)

The total reflectance r can be estimated by taking the ratio of reflected and incident radiance. Using equation 3.13 yields

dr = dEr Ei

= Lr Ei

cos θrdωr (3.14)

By employing equations 2.3 and 3.12 in equation 3.14, we find

dr = Pr Piωs

sin θrdθr (3.15)

Finally, by integrating equation3.15 we get the total reflectance

r = Z 2π 0 dφr Z π/2 0 Pr Piωs sin θrdθr (3.16)

Which is calculated in accordance with the trapezoidal rule.

3.1.6 Extinction ratio

The ratio of the optical powers of perpendicular linear polarization is called the Extinction ratio (ER). An example of ER related to this thesis is the ratio of the power Φ of s polarization to p polarization. The ER would then be given by

ER = Φs Φp

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CHAPTER 3. METHOD

3.2 Experimental setup

A picture of the experimental setup is presented in figure 3.3a with a zoom in of the raisable and tiltable stand in figure 3.3b. The dimension and parameters are specified in table 3.1.

(a) (b)

Figure 3.3 – In (a), an overview of the setup built for measuring the BRDF is presented. The raisable stand is presented in (b), where the mechanical stop and the vertical turn knob which raises or lowers the stand is visible.

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CHAPTER 3. METHOD

Figure 3.4 – Schematic of the setup showed in figure3.3a, excluding the sample stand and the motors controlling the arms.

Table 3.1 – Dimensions and parameters of the setup. Parameters

Parameter Value

Sensor NA 0.26

Apex angle 1.28◦

Sensor angle range -80◦ - 80◦ Incident angle range 0◦ - 80◦

Dimensions

Setup center to sensor 252 mm Setup center to aperture 224 mm Sensor to aperture 27 mm

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CHAPTER 3. METHOD

3.3 Aligning the setup

For the setup to produce reliable and reproducible measurements, a specific align-ment procedure was followed. Apart from the rough alignalign-ment of the laser, this procedure was performed before measurements of each sample.

3.3.1 Rough alignment of the laser

The laser should be directed towards the center of the circle created by the zenith rotation of the laser, see figure 2.2. This center will be referred to as the setup center. To achieve this, the laser arm was rotated to a position where it lies in the extended plane of the sample surface. Then, a vertical surface was placed near the setup center, with a horizontal line drawn in the same height as the setup center. When the laser was aligned such the laser beam struck somewhere along the line drawn on the vertical surface, the rough alignment was considered finished. This rough alignment was essential for aligning the vertical position of the sample.

3.3.2 Vertical position of the sample

In order for the sample to be placed in the setup center such that the laser and sensor rotated around the sample at a constant distance to the laser spotsize, its elevation with respect to the table was carefully aligned. After the laser was turned on, the laser arm was moved back and forth from approximately the sample surface normal to the horizontal plane extended from the sample surface. As the laser moved back and forth, the sample was vertically positioned such that the laser spotsize was kept stationary. When this was achieved, the vertical position of the sample was considered aligned and a mechanical stop was set in place to simplify repositioning after performing reference measurements, which are further described in appendix A.3.

3.3.3 Laser - Sensor alignment

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CHAPTER 3. METHOD

3.3.4 Sample surface tilt

For the setup to accurately measure specular reflections, it is required that the sample surface normal is directed right between the sensor position and the laser position. This was achieved by stepping both the sensor and the laser towards the horizontal, adjusting the tilt of the sample stand, presented in figure 3.3b, such that the specular reflection from the laser is fully detected by the sensor at each incident angle.

3.4 Samples

The samples investigated in this thesis are primarily samples from the painted hoods of four cars. The car samples were cut to fit in the setup (approximately 10 cm x 10 cm max), and are presented in figure 3.5. Two diffuse reference samples were also investigated.

(a) Black (b) Gray

(c) Red (d) White

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CHAPTER 3. METHOD

The two reference samples were an uncalibrated Labsphere SRM-99-020 and a calibrated Labsphere SRS-02-010, and are presented in figure 3.6

(a) SRM-99-020 (b) SRS-02-010

Figure 3.6 – Pictures of the reference samples positioned in the setup.

3.5 Setup stability

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Chapter 4. Results

Note that the combinations of incident and reflected polarization are abbreviated for the s- or p-polarization of the incident and analyzed polarization. For example: sp; in which case the incident light is s-polarized and p-polarization of the reflected light is analyzed. Also, the values measured in the angle of specular reflection increase the scale of the vertical axis of the plots such that details are dificult to notice. Therefore, they are removed from the plots in the following sections and are instead presented in appendix C.

4.1 Bidirectional Reflectance Distribution Function

In this section, the measurements of the BRDF are presented. Note that, in figures4.1 -4.6, ss and pp are colored blue to indicate that these combinations of polarizations are described on the left vertical axis. sp and ps are marked red to indicate to indicate that these are described on the right vertical axis.

4.1.1 Diffuse reference samples

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CHAPTER 4. RESULTS

Figure 4.1 – Measured BRDF at diffuse reflections on the SRM-99-020 reference sample.

Figure4.2 shows the BRDF of the SRS-02-010 reference sample. When comparing to SRM-99-020 in figure 4.1, we can see similarities for ss and pp polarizations, with some deviations. We can also see that sp and ps present an increasing BRDF at higher observation angles. At times, the power of the reflections measured on the SRS-02-010 sample was below the specified resolution of the sensor, which is a possible reason for the deviating behaviour compared to the SRM-99-020.

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CHAPTER 4. RESULTS

4.1.2 Car samples

The overall behaviour of the car samples is quite similar to each other, as can be seen in figures 4.3-4.6. In all samples, there is a clear peak around the angle of specular reflection, with a decreasing BRDF further away.

Figure 4.3 – Measured BRDF at diffuse reflections on the black car sample.

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CHAPTER 4. RESULTS

For the red and white car sample there are some deviations that will be discussed here. The red car sample, presented in figure 4.5, presents a deviating behaviour with an increasing BRDF further away from the angle of specular reflection. This is most notable at incident angles 0◦ and -20◦, in which cases the BRDF reaches values in range of that very close to the specular angle. This is an unexpected and quite interesting result, giving the impression of the occurance of internal reflection, reminding of waveguiding, within the red car sample.

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CHAPTER 4. RESULTS

In the white car sample, presented in figure 4.6, an almost constant BRDF is displayed for sp and ps. This means that for sp and ps, the white car sample is almost Lambertian, and could thus be detected by a LiDAR at a high range of angles.

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CHAPTER 4. RESULTS

4.2 Extinction ratio

Similarly as in section4.1, the data in the following plots are marked blue (dotted and circled) or red (solid and dashed) to refer to the left or right vertical axis, respectively.

4.2.1 Diffuse reference samples

What is common for the diffuse reference samples, presented in figures 4.7 and

4.8, is a very high reduction in the ER. Any incident linear polarization is almost completely extinguished as it reflects on these samples. The reason for this is that these samples are made of porous material, so the incident light is reflected several times within the surface of the material before it escapes the surface quite diffusely and reaches the sensor. This is also the likely cause for the quite constant reflected ER at incident angles 0◦ and -20◦.

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CHAPTER 4. RESULTS

Figure 4.8 – Measured ER at diffuse reflections on the SRS-02-010 reference sample.

4.2.2 Car samples

The ER measured on the car samples are presented in figures4.9 -4.12. Common for all car samples is a clear increase in the reflected ER closer to the angle of specular reflection, and that diffuse reflection seem to result in a lower reflected ER.

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CHAPTER 4. RESULTS

Figure 4.9 – Measured ER at diffuse reflections on the black car sample.

Figure 4.10 – Measured ER at diffuse reflections on the gray car sample.

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CHAPTER 4. RESULTS

Figure 4.11 – Measured ER at diffuse reflections on the red car sample.

Figure 4.12 – Measured ER at diffuse reflections on the white car sample.

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CHAPTER 4. RESULTS

4.3 Total reflectance

Figure 4.13 shows the results of the estimation of the total reflectance, which is based on the results in section 4.1. As one could expect, there seem to be a correlation with the total reflectance and how dark a sample appears. Also, the polarization combination pairs ss, pp and sp, ps seem to display a similar behaviour in all samples apart from the red hood sample, for which ss and pp are quite different. This implies a higher degree of absorption for pp compared to ss in the red sample.

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Chapter 5. Conclusions

With the goal of measuring the BRDF of selected objects commonly found in automotive LiDAR applications, an experimental setup was successfully built. The measurement software was integrated with the hardware and a user interface was created for simple controlling of the setup. The setup was successfully used to measure the BRDF and polarization properties of the selected samples.

The SRM-99-020, SRS-02-010 and sp and ps polarization for the white car sample displayed closest to Lambertian reflection. None of the other car samples displayed much similarities to a Lambertian surface, with the black and gray being the least Lambertian.

The red car sample displayed an overall unexpected behaviour in total reflec-tion, BRDF for pp polarization at diffuse reflecreflec-tion, and in the ER. A similar behaviour in the ER was also noticed for sp and ps of the black car sample.

All the samples displayed a substantial decrease in the extinction ratio in all measurements of diffuse reflection. This means that very little of the incident polarization is conserved as it reflects diffusely on the samples.

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Chapter 6. Discussion

6.1 Experimental procedure

In the analysis of the results, the assumption was made that the diffraction in-troduced by the 1 mm aperture placed in front of the laser is so small that the laser can still be considered collimated. This assumption is considered fair since the angle to the first diffraction minima caused by the aperture was calculated to arcsin635nm_1mm ∼0.04◦_{, which is very small.}

There is some uncertainty regarding whether the distance from the spotsize to the sensor is kept constant. During the measurements, the sample stage is lowered to allow for reference measurements. However, the mechanical stop installed to ensure that the sample is subsequently raised to the original position is not com-pletely rigid as it flexes a little bit. This means that the sample could be returned to a position slightly higher or lower compared to before, possibly resulting in a different part of the sample being illuminated. Even though the samples are assumed to have a low amount of irregularities in the sample surface, this does introduce an uncertainty.

Another possible source of uncertainty is instability in the laser used during measurements. The setup stability measurements showed no indication of prob-lems related to this, but nevertheless, some measures are taken to account for instability in the laser. Before starting measurements, the laser is kept turned on for approximately one hour to allow it to stabilize. Also, a reference measurement is performed on three occations during a measurement series, which allow for the user to notice any substantial instabilities. With these measures in mind, the instability in the laser over the time period of a measurement series is assumed negligible.

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CHAPTER 6. DISCUSSION

6.2 Future work

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Bibliography

[1] NHTSA’s National Center for Statistics and Analysis 2018 Fatal Motor Vehicle Crashes: Overview [2] Takashi Ogawa, Hiroshi Sakai, Yasuhiro Suzuki (2011)

Pedestrian Detection and Tracking using in-vehicle Lidar for Auto-motive Application

[3] A E Lörincz et al 2018 IOP Conf. Ser.: Mater. Sci. Eng. 294 012046 Driver monitoring system for automotive safety

[4] https://www.veoneer.com/index.php/en/lidar

Collected on 2020-05-12

[5] David A. Haner, Brendan T. McGuckin, Robert T. Menzies, Carol J. Bruegge, and Valerie Duval (1998)

Directional–hemispherical reflectance for Spectralon by integration of its bidirectional reflectance

[6] Andreas W. Winkler and Bernhard G. Zagar (2015)

Building a gonioreflectometer - a geometrical evaluation [7] Réjean Baribeau , William S. Neil and Éric Côté (2009)

Development of a robot-based gonioreflectometer for spectral BRDF measurement

[8] Hongyuan Wang, Wei Zhang, Aotuo Dong (2013)

Measurement and modeling of Bidirectional Reflectance Distribu-tion FuncDistribu-tion (BRDF) on material surface

[9] Anak Bhandari, Børge Hamre, Øvynd Frette, Lu Zhao, Jakob J. Stamnes, and Morten Kildemo (2011).

Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherend unpolarized and plane-polarized light

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BIBLIOGRAPHY

[11] Qingzhi Lai, Bing Liu, Junming Zhao, Ziwei Zhao, Jianyu Tan (2020)

BRDF characteristics of different textured fabrics in visible and near-infrared band

[12] Dennis H. Goldstein (2008)

Polarization measurements of automobile paints [13] Frank L. Pedrotti, S.J; Leno M. Pedrotti; Leno S. Pedrotti,

Introduction to Optics, Third edition

[14] V.T. Prokopenko, S.A. Alekseev, N.V. Matveev, and I.V. Popov (2013) Simulation of the Polarimetric Bidirectional Reflectance Distribu-tion FuncDistribu-tion

[15] https://www.edmundoptics.com/knowledge-center/ application-notes/optics/polarizer-selection-guide/

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Appendix A. The program

When the sample is in place and the setup has been covered to block unwanted stray light, the program is ready to run. Before and during measurements, the user must interact with the program to some extent.

A.1 Measurement type

First, the user chooses the type of measurement to perform. There are three choices:

• Diffuse measurement • Specular measurement • Backscatter measurement

A.2 Measurement parameters

When the user has made a choice, the user is asked to enter the following param-eters:

• Sample to measure • Laser to use

• Desired resolution (step size) – HIGH (2 degree steps) – MID (5 degree steps) – LOW (10 degree steps) • Incident polarization

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APPENDIX A. THE PROGRAM

These entries then form the basis for a part of the file name, which is presented to the user. The user then starts the measurements by pressing the enter-key. An image of the user interface in these steps is presented in figure A.1.

Figure A.1 – Screen-shot of the user interface during the initation of the mea-surements.

Depending on the choice of measurement, the resolution is defined differently. In the case of Diffuse measurements, the resolution is applied to the stepsize of the sensor. The stepsize of the laser is then set to 20 degrees. For Specular measurements and Backscatter measurements, the resolution is applied to the stepsize of both the sensor and the laser.

A.3 Reference measurements

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APPENDIX A. THE PROGRAM

A.4 Information to the user

As the program runs, the user is continuously informed of what is being done. As either the sensor or the laser is being moved, the user is informed of which one is moving and where it is moving to. When a measurement is to be done, the user is informed of this, and is then informed when it is finished. An image of the user interface during measurements is presented in figure A.2.

(a) At the start. (b) During measurement.

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Appendix B. Stability measurements

FiguresB.1-B.3present the setup stability measurements made on three samples. In all measurements of the setup stability, the 95% confidence interval is smaller than the specified measurement uncertainty of the Thorlabs S130C sensor. This implies that the uncertainty in the setup is too small to be detected with this sensor. One interesting thing to note is that the specified resolution of the sensor is 100 pW, but the setup has consistently measured smaller variations. This is most notable in figure B.2.

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APPENDIX B. STABILITY MEASUREMENTS

Figure B.2 – Mean and 95% confidence interval presented during stability mea-surements on the SRS-02-010 reference sample. The dashed red lines present the ±3% uncertainty in the S130C sensor.

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Appendix C. Specular measurements

C.1 Bidirectional Reflectance Distribution

Func-tion

C.1.1 Diffuse reference samples

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APPENDIX C. SPECULAR MEASUREMENTS

Figure C.2 – Measured BRDF at specular reflection on the SRS-02-010 reference sample.

C.1.2 Car samples

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Figure C.4 – Measured BRDF at specular reflection on the gray car sample.

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Figure C.6 – Measured BRDF at specular reflection on the white car sample.

C.2 Extinction ratio

C.2.1 Diffuse reference samples

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Figure C.8 – Measured ER at specular reflections on the SRS-02-010 reference sample.

C.2.2 Car samples

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Figure C.10 – Measured ER at specular reflections on the gray car sample.

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Study of reﬂective and polarization properties of objects found in automotive LiDAR applications

Study of reflective and polarization

properties of objects found in

automotive LiDAR applications

Acknowledgements

Abstract

Contents

Chapter 1. Introduction

Chapter 2. Theory

2.1

Radiometric concepts

2.2

Lambert’s cosine law

2.3

Bidirectional Reflectance Distribution Function

Chapter 3. Method

3.1

Theory applied to the setup and measurements

3.1.1

Solid angle subtended by the sensor

3.1.2

Numerical aperture

3.1.3

Case-specific simplifications

3.1.4

Measuring the Bidirectional Reflectance Distribution

Function

3.1.5

Estimating total reflectance

3.1.6

Extinction ratio

3.2

Experimental setup

3.3

Aligning the setup

3.3.1

Rough alignment of the laser

3.3.2

Vertical position of the sample

3.3.3

Laser - Sensor alignment

3.3.4

Sample surface tilt

3.4

Samples

3.5

Setup stability

Chapter 4. Results

4.1

Bidirectional Reflectance Distribution Function

4.1.1

Diffuse reference samples

4.1.2

Car samples

4.2

Extinction ratio

4.2.1

Diffuse reference samples

4.2.2

Car samples

4.3

Total reflectance

Chapter 5. Conclusions

Chapter 6. Discussion

6.1

Experimental procedure

6.2

Future work

Bibliography

Appendix A. The program

A.1

Measurement type

A.2

Measurement parameters

A.3

Reference measurements

A.4

Information to the user

Appendix B. Stability measurements

Appendix C. Specular measurements