Master thesis on “Development of GUI application for computation of light distributions in fog due to volume scattering” By

Master thesis on
“Development of GUI application for computation of light distributions in fog due to volume scattering”
By: Mahesh Kumar. Chintapalli
In Cooperation with
Department of Light and Vision Projects (TB-W4)
IAV GmbH, Gifhorn
Thesis Submitted in Partial Fulfillment of the
Requirements for the Degree of:
Master of Science in Scientific Instrumentation
Department of SciTec
Ernst-Abbe Hochschule, Jena
University Supervisor:
Prof. Dr. Christina B. Claß
Department of IT
Ernst-Abbe Hochschule, Jena Company Supervisor:
Dr. Ing. Michael. Marutzky
Department of Light and Vision Projects (TB-W4)
IAV GmbH, Gifhorn

-6223031750 48704517399000

Acknowledgement
Foremost, I would like to extend my thanks to Dr. Ing. Michael Marutzky, who has given me the opportunity to write my Master thesis at IAV GmbH. His immense support, valuable suggestions and facilities he provided throughout my thesis gave me an excellent platform to enhance my practical skills and knowledge on Automotive Lighting. He consistently encouraged me to implement my own ideas into the research and directed me in achieving the results.
I also like to extend my thanks to Prof. Dr. Christina B. Claß at Ernst-Abbe Hochschule, who has shown great interest in this topic right from the beginning and accepted to provide her guidance. She constantly offered her support whenever I had the trouble in research or writing.
I would also like to acknowledge, all the colleagues at IAV GmbH for their support and making me much more comfortable at working. Especially, I thank my colleague Mr. Torsten Uekermann, who was always there to share his knowledge and made my work easier.
Finally, I express my intense gratitude to my parents, friends, and everyone who provided me their unconditional support, continuous encouragement throughout my entire studies. Besides, a special thanks to my uncle who has been always inspiring me professionally in achieving my dreams. This accomplishment would not have been possible without them. Thank you.

Mahesh Kumar. Chintapalli
Table of Contents TOC o “1-3” h z u List of Figures PAGEREF _Toc516578345 h viList of Tables PAGEREF _Toc516578346 h vii1INTRODUCTION PAGEREF _Toc516578347 h 11.1Background and Motivation PAGEREF _Toc516578348 h 11.2Overview of current ray tracing methods PAGEREF _Toc516578349 h 11.3Goal PAGEREF _Toc516578350 h 21.4Research questions PAGEREF _Toc516578351 h 21.5Contents of thesis PAGEREF _Toc516578352 h 22BACKGROUND PHYSICS PAGEREF _Toc516578353 h 42.1Fundamentals of light technology PAGEREF _Toc516578354 h 42.1.1What is light? PAGEREF _Toc516578355 h 42.1.2Photometric quantities PAGEREF _Toc516578356 h 52.1.3Behavior of light PAGEREF _Toc516578357 h 92.2Fundamentals of Automotive Light technology PAGEREF _Toc516578358 h 112.2.1High beam lighting PAGEREF _Toc516578359 h 112.2.2Low beam lighting PAGEREF _Toc516578360 h 122.2.3Glaring PAGEREF _Toc516578361 h 122.2.4ISO-LUX curves PAGEREF _Toc516578362 h 132.2.5Structure of IES file format PAGEREF _Toc516578363 h 132.3Meteorology PAGEREF _Toc516578364 h 152.3.1What is fog? PAGEREF _Toc516578365 h 152.3.2Compressibility factor (Z) PAGEREF _Toc516578366 h 163LITERATURE REVIEW PAGEREF _Toc516578367 h 173.1Diffusion of light in fog PAGEREF _Toc516578368 h 173.2Importance of Gaussian distribution PAGEREF _Toc516578369 h 193.3Calculation of fog density PAGEREF _Toc516578370 h 213.4Calculation of effective radius for water droplet from LWC PAGEREF _Toc516578371 h 243.5Types of ray-tracing PAGEREF _Toc516578372 h 264PREVIOUS WORK PAGEREF _Toc516578373 h 294.1Theory from IAV PAGEREF _Toc516578374 h 294.2Algorithm from IAV PAGEREF _Toc516578375 h 324.3Construction and Working of fog chamber PAGEREF _Toc516578376 h 355DEVELOPMENTS TO PREVIOUS WORK PAGEREF _Toc516578377 h 385.1Algorithm development PAGEREF _Toc516578378 h 385.2Conceptualization for the validation of Algorithm PAGEREF _Toc516578379 h 455.3Graphic User Interface application PAGEREF _Toc516578380 h 476RESULTS & DISCUSSIONS PAGEREF _Toc516578381 h 516.1Light simulations using MatLab PAGEREF _Toc516578382 h 516.2Light simulations in fog chamber PAGEREF _Toc516578383 h 536.3Light simulations using ray-tracing method PAGEREF _Toc516578384 h 547CONCLUSION PAGEREF _Toc516578385 h 578BIBLIOGRAPHY PAGEREF _Toc516578386 h 59

List of Figures TOC h z c “Figure” Figure 21 EM Spectrum 1 PAGEREF _Toc516595787 h 4Figure 22 Radiometric and Photometric chart 2 PAGEREF _Toc516595788 h 5Figure 23 Visual Sensitivity curve PAGEREF _Toc516595789 h 6Figure 24 Luminous flux 36 PAGEREF _Toc516595790 h 6Figure 25 Luminous intensity 33 PAGEREF _Toc516595791 h 7Figure 26 Illuminance illustration 3 PAGEREF _Toc516595792 h 7Figure 27 Luminance illustration PAGEREF _Toc516595793 h 8Figure 28 Illustration of luminous flux in Solid angle 4 PAGEREF _Toc516595794 h 9Figure 29 Types of reflections 37 PAGEREF _Toc516595795 h 9Figure 210 illustration of light refraction PAGEREF _Toc516595796 h 10Figure 211 Illustration of Absorption and Transmission of light in medium PAGEREF _Toc516595797 h 11Figure 212 High beam lighting from vehicle 7 PAGEREF _Toc516595798 h 11Figure 213 Low beam lighting from vehicle 7 PAGEREF _Toc516595799 h 12Figure 214 Iso-lux curve of light distributions from vehicle headlight 10 PAGEREF _Toc516595800 h 13Figure 215 Structure of IES Data file 11 PAGEREF _Toc516595801 h 14Figure 31 volume scattering of light in fog 32 PAGEREF _Toc516595802 h 18Figure 32 Forward ray tracing PAGEREF _Toc516595803 h 26Figure 33 Backward raytracing PAGEREF _Toc516595804 h 27Figure 41 Block diagram illustrates algorithm in Pascal PAGEREF _Toc516595805 h 34Figure 42 Blueprint of fog chamber construction 28 PAGEREF _Toc516595806 h 35Figure 51 Block diagram illustrates algorithm in MatLab PAGEREF _Toc516595807 h 39Figure 52 Illustration of coordinate transformation geometric plane PAGEREF _Toc516595808 h 40Figure 53 Solid angle of Cartesian coordinate system 29 PAGEREF _Toc516595809 h 41Figure 54 Luminance distributions on to the oncoming vehicle PAGEREF _Toc516595810 h 44Figure 55 Sketch of fog chamber concept PAGEREF _Toc516595811 h 46Figure 56 Block diagram of GUI PAGEREF _Toc516595812 h 47Figure 57 Light Computation GUI application PAGEREF _Toc516595813 h 48Figure 61 Results of Light distributions using MatLab PAGEREF _Toc516595814 h 51Figure 62 Light distributions for different assumed fog densities PAGEREF _Toc516595815 h 52Figure 63 Light distributions for assumed dummy values PAGEREF _Toc516595816 h 54Figure 64 Light simulation without fog using Lucid shape (software) PAGEREF _Toc516595817 h 54Figure 65 Light simulations in fog using Lucid shape (Software) PAGEREF _Toc516595818 h 55Figure 66 Input parameters for light simulations in fog using ray tracing method PAGEREF _Toc516595819 h 56
List of Tables TOC h z c “Table” Table 1 Relation between Classification of cloud and LWC 21 PAGEREF _Toc516574066 h 25Table 2 Structure of expected dummy results from Fog chamber PAGEREF _Toc516574067 h 53Table 3 Sensor position (dummy values) in Fog chamber PAGEREF _Toc516574068 h 53
Abbreviations:
ECE: European Commission
SAE: Society of Automotive Engineers
GUI: Graphic User Interface
LWC: Liquid water content
BIPM: International Bureau of Weights and Measures
INTRODUCTIONBackground and Motivation
The automotive lighting technology evolved from gas lamps to laser beams, and since many years the vehicle lighting plays a crucial role in vehicle safety. From past two decades, the idea of optimizing the headlamp beam in response to ambient weather conditions has been developed. Driving in the bad weather conditions, especially in foggy conditions is becoming challenge because the fog has strong potential to significantly reduce the visibility. As the fog contains small water droplets, causes the light to scatter multiple times leading to glare the driver in oncoming vehicle. The changing face of automotive technology needs to address this issue in evaluating the glare in this kind of bad weather conditions. Therefore, faster computation of light distributions is essential to evaluate the glare in real time.
This thesis addresses the required computation part for light distributions in fog due to volume scattering. Conventionally in automotive industry, there are many ray-tracing methods like Mie, Gegenbauer, Henyey Greenstein etc. in hand to compute the light scattering. These methods compute faster when the light interacts with matter at the interface between two mediums. In contrast, when the light interacts with the medium like fog, it tends to multiple scattering in resulting the slower computation. Thus, to overcome this issue, the IAV introduced the new method to achieve the faster computation.
The method from IAV is derived from the physics fundamentals which supposed to be faster than the ray-tracing methods. In the concept of ray-tracing, each ray is traced along the path of its travel in Fog. Whereas the IAV method estimate the path of ray travel using Gaussian distribution, which produces the low computation time to compute the volume scattering. Therefore, this thesis presents the algorithm development to compute the light scattering and proposes some methods for light simulations in fog.Overview of current ray tracing methods
In the field of computer graphics, there are three types of methods available for ray-tracing. These methods work on the basic idea by tracing the light ray exhibiting its properties reflection and refraction by repeatedly following its path as its bounces through an environment. The methods mentioned below are elucidated in the later section REF _Ref514011177
h 3.5:
Forward ray tracing
Backward ray tracing
Hybrid ray tracing
Goal
The aim of this thesis is to develop Graphic User Interface (GUI) application which perform the light simulations with low computation time, from the measurement data representing the light distribution from vehicle headlamp in environmental conditions like fog. Besides, conceptualizing the validation model for algorithm from IAV through experiments, which take place using fog chamber. Furthermore, proposing some new methods to evaluate the accuracy of results of algorithm with standard ray tracing method using software like Lucid shape. Therefore, the algorithm development is executed using MatLab, which is well known for the powerful computation work.
Research questions
Based on the goal of this thesis, a research questions which mentioned below has been formulated and this thesis target to answer in the later section REF _Ref513910609
h 3.1 and REF _Ref514018720
h 3.2:
Does diffusion behave like scattering? as there is no substantial proof to support this argument
How the ray propagation explained using Gaussian distribution?
Contents of thesisForemost, this thesis divided into sections and sub sections to provide the detailed explanation about the following main tasks:
Optimization and Development of available algorithm in Pascal to compute the light distributions from vehicle.

Conceptualization for validation of algorithm from experiments in cloud chamber
The chapters included in this thesis are:
Chapter 2: This chapter contains about the fundamental definitions of the concepts used in the lighting technology, automotive lighting, and meteorology.

Chapter 3: This chapter provides the literature to answer the research questions occurred during the thesis time and other concepts to characterize fog.

Chapter 4: The method and algorithm developed from IAV to compute the light distributions in fog, and the existing model of cloud chamber and the measurement of light distributions in it are discussed in this chapter.

Chapter 5: The improvements made to the available algorithm, concept for validation of algorithm and developed GUI is explained in this chapter.
The last chapter leaves us the information related to the future work in the way to develop this concept and validate with the results in more accurate way in future.

Chapter 6: This chapter provides the discussion of results obtained from the algorithm and after assumptions for measurement data.
BACKGROUND PHYSICS To understand the lighting distributions, a basic knowledge in light technology is essential. Thus, this chapter provides the lighting fundamentals which related to the work of this thesis.

Fundamentals of light technologyWhat is light?Light is the part of electromagnetic spectrum in the form of radiation energy, travels in wave made up of vibrating electric and magnetic field. The visible light band in EM spectrum lies between the Ultraviolet (UV) and Infrared energy (heat). So, the EM radiation in this range are capable of excite the photoreceptors of human eye in resulting the visual sensation known as Sight. Therefore, to look any object requires the good functioning of eye and visible light

Figure 21 EM Spectrum CITATION Gar18 l 1033 1There are two standards to measure the portion of EM spectrum, which are Radiometry and Photometry. Radiometry is defined as the measurement of any portion (usually limited to UV, visible light, IR) of EM spectrum using optical instruments. Whereas this thesis deals with Photometry, is the science of the measurement of visible light in relevance to the visual response produced by the human eye.

Figure 22 Radiometric and Photometric chartCITATION EFT00 l 1033 2Photometric quantitiesVisual Sensitivity: The sensitivity of the human eye changes with the different colors of light in the visible spectrum, which varies with the wavelength. The sensitivity curve is plotted between the relative visual sensitivity of the eye and the wavelength of visible light. Sometimes, this curve is also referred to as the luminosity curve that divided into two vision regions namely Photopic and Scotopic. In detail, the human eye vision response at higher ambient levels of light is defined as the Photopic vision and at the vision response at lower ambient levels of light is defined as the Scotopic vision. The transition of visual light curve from Photopic vision to Scotopic vision is known as the Purkinje effect. The good visual effect obtained by the eye is at 555 nm (yellow-green) region CITATION AHT96 l 1033 3
Figure 23 Visual Sensitivity curveLuminous Flux (?): The energy of light transferred from the light source is expressed in terms of luminous flux. It is defined as, the amount of light energy (dQ) from the light source travelled in unit time in all directions. The unit of luminous flux is lumen (lm).
One lumen is equal to the luminous flux emitting into the direction of solid angle of one steradian from the point light source having one candela. CITATION AHT96 l 1033 3
?=dQ/dt 2115998135842000
773430296850Figure 24 Luminous fluxCITATION ITC18 l 1033 36Figure 24 Luminous fluxCITATION ITC18 l 1033 36
Luminous Intensity (I): The luminous intensity is the measure of luminous flux emitted by the source in certain direction. As in specifically, the differential luminous flux (d?) emitted in the direction of the differential solid angle (d?). The unit of this quantity is Candela (Cd) CITATION AHT96 l 1033 3I = d?/d? 2214090651253490Figure 25 Luminous intensity CITATION Bas18 l 1033 3300Figure 25 Luminous intensity CITATION Bas18 l 1033 3312782556604000
Illuminance (E): It is defined as the total amount of luminous flux (d?) emitted from the source incident upon the point of a unit surface area (dA). The unit of Illuminance is lux (lx)
E= d?/dA 23Generally, the surface element (dA) can be aligned at any angle (?) towards the direction of the light beam. So, the illuminance upon a surface with random alignment is related to illuminance Enorm upon a surface perpendicular to the light beam by CITATION AHT96 l 1033 3E= Enorm*cos(?) 24897890000

589280266700Figure 26 Illuminance illustration CITATION AHT96 l 1033 30Figure 26 Illuminance illustration CITATION AHT96 l 1033 3
Luminance (L): Luminance is the measure of luminous flux emitting from the surface which have the properties like self-luminous, transmitting, or reflecting in the direction of solid angle. It is defined as the ratio of luminous intensity to the unit projected area in the specific direction. The units of luminance are Candela/square meters (Cdm2)
L= dI/dA 25The relation between luminance and illuminance is given by
L=q.E 26Where q is the reflectance factor, which depends on the surface material
3962401073150
3048001143635Figure 27 Luminance illustrationFigure 27 Luminance illustration
Solid angle (?): A solid angle is subtended by any part of area (dA) on Spherical surface at its center of unit radius (R). In more detail, a solid angle is the plane angle extended into the three-dimensional space, which means the circle turn into the sphere. It is measured in Steradians CITATION Pla18 l 1033 4
?= dA/R2 271838960762000
Figure 28 Illustration of luminous flux in Solid angle CITATION Pla18 l 1033 4Figure 28 Illustration of luminous flux in Solid angle CITATION Pla18 l 1033 4
Behavior of lightLight exhibits different type of behavior when it interacts with the certain medium which like reflection, refraction, diffraction as any wave does. Thus, this section aims to explain in more detail about the light nature.

Reflection: Reflection is when the light bounces off an object. This is classified again into two types depending on the light interaction with the types of surface.
When the light interacting with the smooth and shiny surface like glass, water or polished metal, then the light bounces off at a reflected angle equal to the incident angle. This kind of reflection is called as Specular reflection. In contrast, when the light hits the rough surface, the reflected rays bounces at different angles in all directions leads to Diffuse reflection CITATION Sci12 l 1033 58902705270500
17760951398905Figure 29 Types of reflections CITATION Xia17 l 1033 370Figure 29 Types of reflections CITATION Xia17 l 1033 37
Refraction: The light ray experience refraction, when it travels from fast medium to a slow medium by bending toward the normal to the boundary between two media. Snell’s law describes this phenomenon, which pertained to the refractive indices of two media. In detail, when the light ray travel from high refractive index medium to low refractive index tends to be bent away from the normal and vice versaCITATION The18 l 1033 6
Figure 210 illustration of light refractionTransmission: This explains the amount of light travels through the medium. This is used to define the optical properties of the material. The other properties of light like reflection, refraction, absorption influence the transmission
Absorption: When the light travel through the medium, instead of complete light comes out of the media. Some part of the incident light is absorbed by the medium. In specific, the amount of light attenuated by absorption to the properties of the medium, when the light travelling through it is called Absorption. Many materials absorb some wavelengths while transmitting others, which called as selective absorption CITATION EFT00 l 1033 2
I=I0?-?x STYLEREF 1 s 28Where,
I is the transmitted light through the medium
Io is the incident light entering the medium
? is the absorption coefficient in inverse unit length
x is the thickness of the sample

Figure 211 Illustration of Absorption and Transmission of light in mediumFundamentals of Automotive Light technologyHigh beam lightingA beam used to illuminate the long path distance and when the vehicle not near or following the other vehicle. In detail, High beam headlamps use the center-weighted light distribution without any control over light directed toward any other highway users. They are only suitable for use when no preceding or oncoming vehicles are present. The REF _Ref515211312 h Figure 212 High beam lighting from vehicle CITATION Int18 l 1033 7 shows the unrestricted symmetrical high beam illumination pattern allowed by both the ECE and SAE standards. The photo shows that there is no cutoff in this unrestricted symmetrical high beam illumination pattern CITATION Int18 l 1033 7
Figure 212 High beam lighting from vehicle CITATION Int18 l 1033 7Low beam lighting
In contrast to the working function of high beam, the low beam is used to illuminate the street and its environs ahead of the vehicle near or following another vehicle. In detail, Low beam headlamps must project an asymmetrical pattern that provides sufficient forward and lateral illumination but controls glare by limiting light directed towards preceding or oncoming drivers. International ECE Regulations require a beam with a sharp, asymmetric cutoff creating a defined separation at the top of the pattern compared to the North American SAE beam standard that allows a fuzzier transition at the cutoff in the asymmetrical pattern. The REF _Ref515211352 h Figure 213 Low beam lighting from vehicle CITATION Int18 l 1033 7 shows the right-traffic, asymmetrical low beam pattern required by both the International ECE Regulations and North American SAE regulations. The photo shows the sharp cutoff on the left (in right-traffic countries) required by the ECE Regulation.

Figure 213 Low beam lighting from vehicle CITATION Int18 l 1033 7GlaringGlaring is the serious problem caused when the light beam from headlights giving out, reflecting a strong or dazzling light onto the oncoming vehicle. It leaves the stress and sometimes temporary blindness to the oncoming driver CITATION Car18 l 1033 8. Hundreds of crashes report the glare as one of the contribution an accident to occur. Subsequently, in recent decades there has been a substantial growth in research contributing in evaluating and producing glare-free headlights.

ISO-LUX curvesThese curves represent the number of lines of same illuminance points over the surface. This indicates the total light distributions along the street from the vehicle headlights. Points with the same illuminance on the street are connected to each other by means of curves (Isolux lines). The luminaire is located vertically at the mounting height of the vehicle headlight position which according to the ECE regulations above the coordinate origin in the Y-axis direction. 9
1758950Figure 214 Iso-lux curve of light distributions from vehicle headlight CITATION Val15 l 1033 10Structure of IES file formatFor storing and transferring the data of the luminous intensity distribution in the industry has defined its own standard. In 1986 the Illuminating Engineering Society of North America (IESNA) for the first time awarded the LM-63-86 standard with the title Standard File Format for Electronic Transfer of Photometric Data and Related Information, this describes the IES file format for exchanging photometric data. The document has been revised several times in the past years; the last and fourth version was released in 2002 under the name LM-63-02. The file format with the extension *.ies is a text file that consists of a header and the data. shows the structure of the file. The first line indicates the version of the standard file format such as IESNA: LM-63-1986 or IESNA: LM-63-1995. This is followed by the information about the light source and the location of testing taking place from the line 2 to line 8. Moreover, this information acts like the additional information related to the light source and hence this can be skipped when reading the file CITATION Ing12 l 1033 11
Figure 215 Structure of IES Data file CITATION Ing12 l 1033 11 The line 7 indicates whether the illuminance is dependent on the angle of inclination or tilt of the light source. The information about the angles and the multipliers is displayed in additional lines after line7 when there is influence of TILT on the luminous intensity like (TILT=INCLUDE) or read from an external file (TILT=;filename;). In this work, only light sources are used whose luminous intensity is not affected by the inclination or inclination of the light source tilt angle (TILT=NONE). Line 9 still serves as a separation between the header and the data. In the Lines 10 and 11 contain technical information about the light source (e.g. lumens per lamp). and the measurement (e.g. number of vertical angles, number of horizontal angles). Afterwards all vertical and horizontal angles (lines 12 and 13) and the luminous intensity data (line 14 to 26) are listed. The floating-point values are calculated with a tab character, comma, (several) spaces or a line break. Each line may not be longer than 256 characters CITATION Ing12 l 1033 11.

Meteorology
What is fog?The fog consists of the thick cloud of water droplets in the atmosphere near the earth surface resulting in restricting visibility. Fogs which are composed entirely or mainly of water droplets are commonly classified based on the physical process which produces saturation or near-saturation of the air. The main types of fog are:
Radiation fog
Radiation fog usually occurs in the winter, assisted by clear skies and calm conditions. The air near to the earth surface gets cooler by the thermal radiation from the cooling of land overnight. This reduces the ability of the air to hold moisture, allowing condensation and fog to occur CITATION Met18 l 1033 12Valley fog
Valley fog forms when the cold dense air settles between the lower parts of a valley condensing and forming fog. It is often the result of a heavier air loaded with the condensed water droplets which is surrounded between the warmer and lighter deposits of air CITATION Met18 l 1033 12Advection fog
Advection fog occurs when the moist air passes by the wind over the surface. A common example of this is when a warm air pass over the surface area covered by snow. If the wind blows in the right direction then sea fog can become transported over coastal land areas. CITATION Met18 l 1033 12Upslope fog
Upslope fog or hill fog forms when the winds blow air in the direction upwards on a slope. The air cools as it rises, permitting moisture in it to condense CITATION Met18 l 1033 12Evaporation fog
Evaporation fog is caused by the cool air present over a warm water body. It often causes freezing fog, or sometimes frost. When some of the water molecules present over the surface of warm water evaporates into air layers humidifying the cooler air that has passed over the surface. As a result, the warm and moist air cools as it mixes with the colder air, allowing condensation and fog to occur. CITATION Met18 l 1033 12
Compressibility factor (Z)It is used to describe the deviation of real gas from the ideal gas behavior in a volume. The relation vreal=Zvideal is used to calculate the actual volume vreal, as the product of compressibility factor and the ideal gas volume at the same temperature and pressure. For the ideal gas, the compressibility factor is equal to unity CITATION Lil18 l 1033 13
LITERATURE REVIEW This section aims to answer the questions which originated in the research questions section, beginning of this thesis. Therefore, an explicit explanation presented to attain acquaintance about the topics like the light diffusion in fog, why the light propagation in fog are estimated using gaussian distribution and its importance, how to calculate the fog density from the surrounding ambient parameters, and finally about the different types of ray tracing methods. However, this chapter provide an overview of the concepts, in which a comprehensive knowledge required to understand the later sections of this thesis
Diffusion of light in fog Diffusion and Scattering are two phenomena essential to have a complete knowledge in understanding the light behavior in the fog medium. In brief, when the light beam hits the particle, it underwent change in direction, which called as single scattering. In the same way, the light going through the medium like fog described as the random distribution of water droplets at different concentration in size, whereas the light underwent multiple scatter and every single scatter underwent by the light is disregarded. To some extent, the single scatter becomes qualitative changes from quantitative changes, which described as diffusion.
The outcomes of light diffusion by the small water droplets are classified in two classes, corresponding to the dimensions of the droplet concentration are large or small in comparison with the wavelength of the light. In fog, the linear dimensions of the water droplet be less than thousandth of the inch. In the theory of rainbow, already explained about the light interaction with the spherical water droplet. When the incident light hits the water particle, it got scattered partly by external and internal reflections despite uniformly. Even though the droplet concentration is randomly distributed in the air, only few rays from the source of light receive them directly and other receive them by scattering. CITATION Mal19 l 1033 14 This means, the water droplet acts as an individual source in scattering the light to the other droplet uniformly as it receives in every direction, which seen in REF _Ref514252661 h Figure 31.
Consider a light source in the fog medium and each droplet are perfectly opaque, so that there is no actual loss of light by absorption and consider the illumination at the distance from the source that no direct ray interacts with the particle. Meanwhile the total amount of light penetrating through every spherical droplet of water about the light source is constant, it is explicit that illumination vary with the inverse square law of the distance from the source, and it will be the same as a brightness of a small white plane surface at the equal distance when fully exposed to the direct rays CITATION Mal19 l 1033 14.

-68580000Figure 31 volume scattering of light in fogCITATION Car181 l 1033 32Figure 31 volume scattering of light in fogCITATION Car181 l 1033 32
As the illuminance inversely proportional to the distance, the water droplets spread over the distance or assume n drops placed next to each other of diameter c are contained in the volume a3. Then, the incident light entered the volume would stop by all the water droplets, if n = a2c2 but in the reality, they underwent diffusive reflection through a3. In this case, the water droplets screen others, leaving the question how much light reaches to the other far side of the volume a3 and it answered from the probability theory. This problem considered as similar in finding the number of empty spaces probably left on the area a2, when divided into n equal squares, when n things thrown on it at random. The n things can be made into parcels in numerous ways, and these may fall on any combination of the n areas taken 1,2,3, etc., at a time CITATION Mal19 l 1033 14
Generally, the water droplet concentration over the unit area of surface can be possibly determined by dividing into enough number of drops to cover the unit area depending on the how much small the water quantity per unit volume. Nevertheless, in this case, the acceptable water amount is limited by the condition that the diameter of the water droplet not less than ten wave-lengths. Accordingly, at the normal temperature in atmosphere contains about one part in 100,000 of water vapor and when it condensed in the form of spheres 1/5000 inch in diameter it would require a column of air 20 inches long to contain enough drops to stop the incident light, when placed side by side or stop half the light distributed at random in the same volume. CITATION Mal19 l 1033 14
The diffusion of light closely related to the same laws as the diffusion of heat in near conducting body, and with the constraint concerning conductivity the equal degrees apply to both as far as steady flow is concerned, but in the case of light the proportion of conduction is same as the velocity of light, the difference of flow in relations of time has no practical importance in this connection. which means in the law of heat conduction stated by the Fourier, recognizes the two coefficients of conduction are penetrability which relates to the radiant heat and the permeability relates to the ordinary conduction of the substance. Whereas in the diffusion of light, both the terms are identical. In conclusion, the opacity of the direct rays depends only on the size and concentration CITATION Mal19 l 1033 14
Importance of Gaussian distribution
The very essential thing to know, how the light propagates in fog medium. In general, in many lighting applications the spreading of light rays can be approximated by predicating the Gaussian intensity profile. In physics, the most attractive deduction is “Central limit theorem” which states that given a distribution with mean ? and variance ?2, the sampling distribution of the mean approaches to the normal distribution as the sample size increases with mean ? and variance ?2n, where n is the number of samples. There exists a close relationship between central limit theorem and the law of large numbers. From that, the law of large numbers states that carrying out the same test several times result in an average result approaching an expected value. However, the central limit theorem states a similar concept for distributions, in which the sampling distribution of the mean will tend to a normal distribution, even if the distribution is non-normal. CITATION Che18 l 1033 15 Thus, this theorem is used to approximates the diffusion of light propagation in fog as the each water droplet acts as the individual source to scatter the light to other from the theory discussed in the earlier section REF _Ref513910724
h 3.1. When there is no possibility to describe every scatter carried out by the source, then each individual scatter together is a diffusion which act as a Gaussian distribution.
From quantum mechanics, gaussians are the most certain wave functions which explained from the “Heisenberg uncertainty principle”. This states that for any wave function ?X?P?h2, where ?X is the uncertainty in position and ?P is the uncertainty in momentum. Thus, the gaussian is ?X?P=h2, the absolute minimum total uncertainty CITATION Ask18 l 1033 16. The Gaussian is a radially proportioned distribution, the variation in electric field is given by the following equation:
Es=E0?-r2?02 STYLEREF 1 s 31r is defined as the distance from the center of the beam, and ?o is the radius at which the amplitude is 1/e of its value on the axis. CITATION Gau18 l 1033 17. The Fourier Transform of the Gaussian distribution (See equation REF _Ref515106679 h 31) is also a Gaussian distribution. Thus, it is noticed that at every point along the propagation of light path in the Gaussian source distribution remains Gaussian. However, the light intensity after the repeated scattering by the water droplets present at any point in the optical system is well explained using the Gaussian distribution. The intensity is also Gaussian which denoted with the below equation: CITATION Gau18 l 1033 17 Is=?EsEs*=?EsE0*?-2r2?02 32Calculation of fog density From the previous sections, it is clear how the interaction takes place between light and fog, and the influence of fog on the light propagation. Additionally, it is also important to know about the process to calculate the fog density from the ambient weather parameters like temperature, pressure, and relative humidity. In the early chapters, the constituents and formation of fog are explained (See section REF _Ref515108197
h 2.3.1).
When the relative humidity of the air exceeds saturation by a fraction of one percent. The condensation of water in the natural air produces the fog. The relative humidity of the air can be increased by three processes:
cooling of the air by adiabatic expansion;
mixing two humid airstreams having different temperatures; and
direct cooling of the air by radiation CITATION Enc18 l 1033 18
On a simple note, fog is the moisture content present in the dry air. So, the dry air is defined as the air without water content according to the definition from meteorology. Furthermore, the dry air composed of gases in the atmosphere but there is no certain composition explanation about the abundance of each major gas present within dry air. Since water vapor is a variable gas (ranging from a trace to around 4%), the amount of water vapor in the air depends on the dewpoint of the air. When water vapor is ignored, the other traces is a fixed percentage of the percent by volume or percent by mass of Oxygen, Nitrogen and Argon. However, air in the atmosphere will not be perfectly dry since even in very cold air there will still be a trace of water vapor CITATION Jef18 l 1033 19 . Therefore, the fog density can be calculated from the following equations:
Firstly, the below equation describes the formula to calculate the density of moist air and then calculate the required terms to obtain the desired result
?a=pMaZRT1-xv1-MvMa STYLEREF 1 s 33Where the quantities in the equation and its units are
p= Pressure in Pa;
t = air temperature in °C;
T = thermodynamic temperature in K (= 273.15 + t);
xv= mole fraction of water vapor;
Ma = molar mass of dry air in gmol-1;
MV = molar mass of water in gmol-1;
Z = compressibility factor;
R = molar gas constant in jmol-1K-1To calculate the equation 1, requires the values of Ma, MV, Z, xv, and R CITATION APi18 l 1033 20All the parameters are considered according to the CIPM-2007, the recommended value for R by CODATA 2006 is R= 8.314 472 jmol-1K-1
The molar mass of dry air is Ma = 28.965 46 × 10^?3 kgmol-1, which obtained from the equation
Ma=?xiMi?xi STYLEREF 1 s 34Where xi and Mi are the mole fraction and molar masses of the gasses constituent in the dry air CITATION APi18 l 1033 20.
The molar mass of moist air MV consists the amount fraction of water vapor xv and making all other proportions reduces and the sum still equals to one from the equation below;
1-Mv?Ma=0.3780 STYLEREF 1 s 35 Where value of MV = 18.015× 10^?3 kgmol-1
The quantity xv is not measured directly but is determined either from the relative humidity h or from the temperature td of the dewpoint, the compressibility factor of water Z is determined from an additional interpolating equation. The following equations give the relation to determine xv from the relative humidity or the dew-point temperature of air. Determination of the vapor pressure at saturation Psv, and the supposed enhancement factor are primary steps. Thus, Vapor pressure at saturation CITATION APi18 l 1033 20 Psv= 1Pa × exp(AT 2 + BT + C + D/T ) STYLEREF 1 s 36 Where the values of coefficients in the equation are;
A = 1.237 884 7 × 10-5 K-2,
B = ?1.912 131 6 × 10-2K-1,
C = 33.937 110 47,
D = ?6.343 164 5 × 103 K
Enhancement factor f:
f = ? + ?p + ? t2,
with values
? = 1.000 62,
? = 3.14 × 10-8Pa-1,
? = 5.6 × 10-7K-2 where t is the temperature in ?C.

Using these values,
xv=hfP,t?psvtp STYLEREF 1 s 37where h is the relative humidity and the value of psv is obtained from above equation (See equation REF _Ref514275623 h 36). Therefore, h is measured to determine xv. The parameter h has the range between 0 and 1. For instance, the reading of relative humidity ‘53%’ from the instrument is expressed as h = 0.53.

Calculation of the compressibility factor Z (see section REF _Ref515125028
h 2.3.2 for definition) is given by:
Z=1-pTa0+a1t+a2t2+b0+b1txv+c0+c1txv2+p2T2??+exv2 STYLEREF 1 s 3 SEQ Equation * ARABIC s 1 8a0 = 1.581 23 × 10-6KPa-1,
a1 = ?2.9331 × 10-8Pa-1,
a2 = 1.1043 × 10-10 K-1 Pa-1,
b0 = 5.707 × 10-6 KPa-1,
b1 = ?2.051 × 10-8Pa-1,
c0 = 1.9898 × 10-4KPa-1,
c1 = ?2.376 × 10-6Pa-1,
d = 1.83 × 10-11 K2 Pa-2,
e = ?0.765 × 10-8 K2 Pa-2. CITATION APi18 l 1033 20In conclusion, from the values obtained from the equation REF _Ref515114279 h 34, REF _Ref514189195 h 35, REF _Ref515114290 h 37, and REF _Ref515114292 h * MERGEFORMAT 38 by inputting in to the equation REF _Ref514189090 h 33, produces the value of moisture air density. CITATION APi18 l 1033 20Calculation of effective radius for water droplet from LWC LWC is the short form of Liquid Water Content, which is another important element in characterizing the fog. The effective radius of fog particle is useful in determining the width of the fog distribution. It is typically the measure of mass of cloud present in the amount of given dry air. This variable is essential to find the parameters such as effective droplet radius, number of droplet concentration, and droplet size distributions. Here the cloud type depends on different LWC range, which is measured in (g/m3).
Cloud Type LWC (g/m3)
Cirrus .03
Fog .05
Stratus .25 to .30
Cumulus .25 to .30
Stratocumulus .45
Cumulonimbus 1.0 to 3.0
Table 1 Relation between Classification of cloud and LWC CITATION Liq06 l 1033 21The value of LWC from the cloud chamber is simply calculated from the equation
LWC=mw/Vc STYLEREF 1 s 39Where mw is the mass of water content in the cloud chamber and Vc is the volume of the cloud chamber and the value of mass of water content is found by the equation involving the latent heat of condensation. CITATION Liq06 l 1033 21mw=-ma.cp.?TaLc(T) 310Where Lc(T) is the latent heat of condensation of water at temperature T. ma is the mass of air in the cloud chamber, cp is the specific heat of dry air at constant pressure and ?Ta is the change in the temperature of the air due to latent heat CITATION Liq06 l 1033 21. So, the final LWC is calculated from the inputting the result of equation REF _Ref515120602 h 315 in the equation REF _Ref515120606 h 314.

However, the relation between the droplet effective radius, liquid water content (LWC) and droplet concentration can be obtained from the above results. The effective radius is given by the equation CITATION Jef99 l 1033 22reff=0infr3.n(r)dr0infr2.n(r)dr
311Where nr denotes the concentration number of droplets with radius r. The effective radius rewrite into the terms of LWC and number concentration N. Therefore, for the mono dispersed distribution of droplet of radius r is given by CITATION Jef99 l 1033 22r=100.3(3 LWC/4?N) 312This equation REF _Ref515122643 h 317 is also applied to the poly dispersed distribution of droplet radius by replacing the r with droplet radius of average volume (rv) which equal to the effective radius (reff) given by: CITATION Jef99 l 1033 22reff=100.3(3 LWC/4?N) 313Where the value of LWC is known from the measurements and calculated by the equation REF _Ref516093158 h 39.

Types of ray-tracing The objects are visible to the human eye, when they are illuminated by beams of light. In the way around, following the path of light beams backwards from the eye to the objects that light interacts with. This process is called ray tracing CITATION Wha18 l 1033 23. The different types of ray tracing are explained below
Forward ray tracing
Forward ray tracing is the process of following the light particles (photons) from the light source to the object. it is highly inefficient, even though the forward ray tracing method can accurately determine the coloring of each object. This is because many rays travel from the light source never go through the view plane and into the eye. This kind of tracing of each ray from the light source down leave many rays to waste because they never contribute to the final image as seen from the eye. Forward ray tracing is also known as light ray tracing and photon tracing CITATION Cha18 l 1033 24
Figure 32 Forward ray tracingBackward ray tracing
Backward tracing is the most efficient method introduced to trace the light ray in a method opposite to the forward ray tracing. In backward ray tracing, the ray from the eye is created and traced down the view plane and on into the world. Backward ray tracing is also known as eye ray tracing. The most drawback of this method is that it assumes only the light rays that come through the view plane and on into the eye contribute to the final image of the scene. CITATION Cha18 l 1033 24Figure 33 Backward raytracingFigure 33 Backward raytracing
Hybrid ray tracing
To overcome the drawbacks in both forward ray tracing and backward ray tracing. The new research tries to develop new method which gives hybrid solutions that will compromise speed and accuracy. Only certain levels of forward ray tracing are performed using these hybrid solutions. The algorithm records the data, then goes on to perform backward ray tracing. The final coloring of the scene takes both the backward ray tracing and the forward ray tracing calculations into account.CITATION Cha18 l 1033 24Ray-Sphere interaction:
Normally to compute the light interaction with fog medium using the ray-tracing methods, the light ray interacting with sphere is considered since fog consists the spherical water droplet. It is explained theoretically by the equation:
The water droplet is denoted by the mathematical spherical equation
x2+y2+z2=r2 314The light ray equation is denoted by the following:
x=px+tdxy=py+tdyz=pz+tdz
STYLEREF 1 s 315After substituting the equation REF _Ref515120602 h 315 in the equation in REF _Ref515120606 h 314
(px+tdx)2+(py+tdy)2+(pz+tdz)2=r2 316The variable t is solved by the quadratic function
At2+Bt+C=0 STYLEREF 1 s 317Where
A= dx2+dy2+dz2=1 (unit vector)
B=2(pxdx+pydy+pzdz)C=px2+py2+pz2-r2
STYLEREF 1 s 318Quadratic formula gives the two roots,
t=(-B-+sqrt(B2-4C) )/2 STYLEREF 1 s 319From the result obtained from the equation REF _Ref515122643 h 317 by using the values from the equation REF _Ref515122611 h 318 and REF _Ref515122666 h 319 gives the information related to the light ray interaction with the sphere, which correspond to the two intersection points.

The positive root denotes the ray touching the sphere and negative root denote the ray missing the sphere. From these results, the overall light scattering in the fog is estimated. However, using this method, the computation time is high in considering volume scattering CITATION Car00 l 1033 25.
PREVIOUS WORK FROM IAV
This section aims to explain the previous work developed from the IAV, in which presented the work about evaluation methods in measurement and simulation, with focus on the glare evaluation from vehicle headlights. This work essential to optimize the headlights in the very early stage of development phase, and to maximize the photometric performance of headlights by minimizing the glare on oncoming vehicles or persons. Hence this method plays pivot role in improving the traffic safety. There exists a development tool which called as CAGE (Computer Aided Glare Evaluation) to evaluate glare from vehicle headlights. Nevertheless, is restricted to only consider the wet pavement during bad weather conditions. Now, the idea is to extend this as a potential tool to evaluate glare in also weather conditions such as rain, fog etc.
Theory from IAV Before delving into this method, some fundamentals are to be considered to understand this theory better. So, begin with the relation of complex refractive index and light CITATION Mic l 1033 26
n?=n?-i?? STYLEREF 1 s 41The above equation defines the optical properties of a specific material which called as complex refractive index with n as refraction index, ? is the wavelength of light, i is the complex identity, and ? is absorption index CITATION Mic l 1033 26cm?= cn? STYLEREF 1 s 42This equation states the relation between velocity of light in vacuum c and refractive index of the material n CITATION Mic l 1033 26sd, absorb?= s0? e-K?d STYLEREF 1 s 43The above equation states the Beer’s law, which describes the decay of light intensity when it passes through the medium of distance d. The concept is explained from the equation REF _Ref514190881 h * MERGEFORMAT 28 in the previous chapter REF _Ref514190929
h * MERGEFORMAT 2.1.3
K?=4? n??? 44This gives the relation between absorption coefficient and the absorption index, which taken from the textbooks on optics like CITATION EWo06 l 1033 27ss, absorb?= s0? e-4???ct STYLEREF 1 s 45The above equation is modified from the equation ( REF _Ref514193610 h 43) by inserting the equations ( REF _Ref514193531 h 42) and REF _Ref514193601 h 44), and the propagation time d= cmt CITATION Mic l 1033 26.

Normally, the tracing of rays is widespread in real space when volume scattering takes place. Primarily, we calculate light distribution in the momentum space, in which all the photons with a wavelength ? propagate in the direction of angles (?,?) at time t =0, are found at the point p?,?,?= ?k?,?,?. With the time, photons happen to scatter out of the initial position p?,?,? and due to the elastic scattering according to the Lorentz dispersion theory, the photons will tend to change their path direction and have their absolute momentum constant with respect to their wavelength k? = 2?? . This describes the movement of photons on the sphere with radius k in momentum space. From the diffusion equation, which based on scattering process, we describe the intensity distribution in momentum space with the following equation: CITATION Mic l 1033 26sscatter?mom, t,?= s0 14?a?te-?mom24a?t e-4???ct STYLEREF 1 s 46In short, this equation explains the light distribution in fog medium. Here, the ?mom is the angle between a specific point on the sphere and (?,?). sscatter?mom, t,? is the number of photons with wavelength ? per solid angle at ?mom, t. a? is mathematically the full width at half maximum of a Gaussian and relates to the density of the fog. When there is no absorption, the factor e-4???ct which abstracted from the Beer’s law, equations ( REF _Ref514193610 h 43) and ( REF _Ref514199022 h 45) can be neglected to the value ‘one’ CITATION Mic l 1033 26. As mentioned above, this process is first calculated in momentum space but our main area of interest is in the real space. Apparently, there is need to deduce the relation between basis in real and momentum spaces as k?,?e?,?=2? , which obtained from the Fourier transformation.

k?= ksin?mom, k?= kcos?mom with k= 2?? 47The relation between ?mom and ?pos are the angle in momentum space and real space
respectively. The angle between these can be the angle between e? and e? which are related with tan?pos= e?e?. By inserting this deduction, we obtain the transformation results to
?pos=arctancot?mom STYLEREF 1 s 48Whereas in the momentum space, will only move on the k-sphere, and the light propagate in the real space:
r=cm? t STYLEREF 1 s 49Finally, the intensity for every point in the real space r, ?pos can be obtained from the equations ( REF _Ref514200198 h 46), ( REF _Ref514200200 h 48), and ( REF _Ref514200202 h 49). A counter argument against the proceeding is that not all rays propagate in the fastest and shortest path as assumed in the equation ( REF _Ref514200202 h 49) due to scattering phenomena. Therefore, only some rays take this path and is the sum of Gaussians according to the central limit theorem, which tells the sum of gaussian will be the gaussian as consideration in the equation ( REF _Ref514200198 h 46). CITATION Mic l 1033 26To sum up, the equation modified to the real-time application to calculate the light distributions in fog medium using the photometric values. As already explained in the previous chapter REF _Ref514201671
h 3.3 about the fog, is the mixture of air and water droplets in the visible range of optical radiation. Therefore, we neglect the wavelength absorptive factor in equation ( REF _Ref514200198 h 46). Then it is integrated with ? and weighted with V (?) to st, ?pos . As stated before, the sum of Gaussian is a Gaussian and the integral will be like the equation REF _Ref514200198 h 46 without depending on wavelength. The light intensity distribution is defined by the photometric table LID (Light Intensity Distribution) in I (?,?) CITATION Mic l 1033 26Without scattering the Illuminance at point in the real space coordinate (rP, ?P, ?P) given by:
EonrP, ?P, ?P= I?P, ?PrP2 STYLEREF 1 s 410When scattering takes place, all elements I (?,?) contribute to the ErP, ?P, ?P:
EmnrP, ?P, ?P= ?, ?I?, ?rP2 st, d?P, ?P, ?,? d?d? 411Where d?P, ?P, ?,? is the angle distance between ?P, ?P and ?,? , which means the euclidean distance between two points in euclidean space.CITATION Mic l 1033 26Algorithm from IAVThis algorithm is implemented in the PASCAL programming language, which process the computation of light distributions with and without fog. In detail, it is explained in three steps below
STEP 1:
This step illustrates about the inputs to the algorithm, the LID file which generated from the goniophotometer, contains the information of light intensity with respect to the azimuthal and polar angle. From which the coordinate points on the X-Y plane are calculated easily using the Spherical to Cartesian coordinate transformation formulae. This transformation is also depending on the other input, height of the head light position which typically 0.63 meters and the height of the driver position on oncoming vehicle which is 1.05 meters from the ground level, according to the ECE regulations. These inputs are responsible for the generation of the light distribution and the other input, fog density a(?) results in generation of fog.

STEP 2:
This step explains process of various functions in the algorithm. After reading the LID file, the values are passed to the light distribution function, which calculate the coordinates (X, Y, R) for every light distribution angle I (?,?). These points are the transformation of Spherical to Cartesian coordinate system.
R=ztan? X=Rcos? Y=R sin?(?) 412Where Z = height of the headlamp.

After the transformation, there is no complexity to calculate the illuminance values with (Emn) and without fog (Eon) using formula values from the equations REF _Ref514459156 h 410 and REF _Ref514460673 h 411. However, the calculations of fog distributions from the diffusion function (see equation REF _Ref514200198 h 46) and transformation of distribution angle (see equation REF _Ref514200200 h 48) are calculated beforehand. According to the theory, light distribution angle is simply the distance between the angles, which obtained by the equation:
?mom=(?p-?)2+(?p-?)2 STYLEREF 1 s 413Finally, the reflections from different road surface can be found using the Luminance and Illuminance relation
L=q.E
Where q is the reflectance, is assigned as the quadratic function from the regression methods for different road surface types. At this point, the luminance in fog is calculated by the multiplying the extinction coefficient i.e.

L=E.q.e-4a(?)R_d STYLEREF 1 s 414Where R_d is the distance from reflection point to the eye of the driver in oncoming vehicle (See equation REF _Ref516107146 h * MERGEFORMAT 512 ).
STEP 3:
This step explains the end results acquired from the algorithm. However, the values of Illuminance and Luminance, with and without fog are computed as elucidated in the above steps by using the equations. Finally, the complete results are written to text file for further evaluation, which include plotting of the data to estimate the light distributions using UniPlot software. As mentioned in the beginning of the explanation, this program was developed in Pascal, the algorithm consists several functions and syntax to present here in structure of coding. So, the process in algorithm is explained in the block diagram to avoid vagueness.

Figure 41 Block diagram illustrates algorithm in Pascal
Construction and Working of fog chamber933450471170000 Since the fog chamber is to validate the algorithm presented in section REF _Ref514558922 h Algorithm from IAV REF _Ref514558940
h 4.2, it is sufficient to show that the measured values determined in the cloud chamber correspond to the simulated illuminances with acceptable accuracy. This is the minimum requirement for the artificially generated fog. Ideally, an infinite number of different fog situations can be realized. The most important requirement from the fog chamber is producing the homogenous fog, because the theory in section REF _Ref514560955
h 4.1 was developed for the uniform distribution of fog parameter, which represent the half-width of two-dimensional gaussian distribution. The parameter is equal everywhere regardless with the location. Consequently, the homogenous fog distribution is desirable and characterizes be the optimal condition. However, it is meaningful to presume that a height-dependent droplet diameter distribution within a reference volume is formed in a compact cloud chamber. Therefore, the minimum requirement for homogeneity is a homogenous fog at an altitude. To assess the homogeneity, the assessment of the meteorological visibility at several measuring points is useful CITATION Joh18 l 1033 28.

Figure 42 Blueprint of fog chamber construction CITATION Joh18 l 1033 28Figure 42 Blueprint of fog chamber construction CITATION Joh18 l 1033 28
The positioning of the sensors like illuminance, temperature, pressure and humidity are very helpful in characterizing the fog, and the ultrasonic fog generator during the test are shown in REF _Ref516601447 h Figure 42. In this non-scaled sketch, the base area represents the bottom of the housing with a volume of 760 mm x 450 mm x 480 mm. The moisture emission surface is the water level of the liquid container. Throughout the ultrasonic fog generation, the water droplets detach from it. The light exit surface represents the interface between the lens body of the LED and the fog. Similarly, the light entry surface represents the interface between the translucent glass ahead of the illuminance sensor and the fog CITATION Joh18 l 1033 28.

Measurement procedure:
At the beginning, the data acquisition of the sensors was started with the tool Brick Viewer. In advance, the frequency with which the data were recorded was set to 1 Hz. Furthermore, the measuring range of the illuminance sensors was set to a range of 0.01 to 64000 lx. Afterwards, the housing cover was removed and the housing of the LEDs and the acrylic glass panes in front of the illuminance sensors of the visual range sensors were coated with a thin layer of detergent using a microfiber cloth. To eliminate the influence of ambient light, the housing of the fog chamber was then closed and covered on all sides with Molton material. To check whether the sensors displayed measured values different from 0.01 lx was tested. As soon as this was the case, the LEDs of the visual range sensors were switched on. The LEDs were lighted on over a period of 50 minutes. This procedure was used to bring the LEDs and the measurement technology up to operating temperature. Lighted on led to a constant variation in the measured illuminance over time without any noteworthy drift. The pump was then started to fill the liquid container with water. As soon as the container overflow was audible, the ultrasonic nebulizer was operated for 10 minutes at full power and then switched off together with the pump. It waited for a period of one hour until the fog in the chamber had evaporated and a water film had formed on the interfaces due to the hydrophilic layer. The pump was then switched on again. After the liquid container was filled, the ultrasonic nebulizer was put back into operation at full capacity. The applied control voltage was measured with a multimeter. As soon as the control voltage of the ultrasonic nebulizer had been lowered to 0 V, the submersible water pump was also switched off. The measurement was finished 30 minutes later CITATION Joh18 l 1033 28.

DEVELOPMENTS TO PREVIOUS WORK This section contains the work related to the motivation and goal of this thesis. In this work, the further developments made to the previous work in algorithm development and conceptualization for the validation of this algorithm. Developing the existing algorithm in Pascal into user-friendly Graphic User Interface (GUI) application, for the computation of light distributions along with the consideration of computation time is main part of this thesis. Furthermore, the conceptualization for the validation of this algorithm also proposed in the progression of the concept and this application into the potential software.

Algorithm developmentBased on the main criteria for computation time and user-friendly application, MatLab is used in this work. MatLab is renowned for its numerical computing environment and come with the package of many inbuilt functions to ease the plotting of data, implementation of algorithms and creation of user interfaces. The GUI application in this thesis is developed using the GUIDE, which is known as Graphic User Interface Development Environment. Eventually, the algorithm scripted in MatLab explained below clearly in steps, which involve in process of computing the light simulations with and without fog, and the modifications made to the provided algorithm in Pascal.
Explanation of Algorithm
Step1: This algorithm starts with reading the IES file, the luminous intensity distribution measurements stored in the ASCII format. The luminous intensity distribution values are very essential to compute the light distributions. The intensity of light values and their respective horizontal and vertical angles are obtained from the IES file. The REF _Ref516105730 h Figure 215) describes the structure of IES file and very useful in understanding the method of sorting out the angles and their luminous intensity values.

Figure 51 Block diagram illustrates algorithm in MatLabStep 2: After required values (angles and luminous intensity) obtained as described in the process from the file in the step 1, then the algorithm directed to compute the Cartesian coordinate points from the angles (?,?), and using the other input namely the position of headlight from the ground level.
1377952610485Figure 52 Illustration of coordinate transformation geometric plane00Figure 52 Illustration of coordinate transformation geometric plane13716063500
In the REF _Ref514715557 h Figure (52), (?,?) denotes the horizontal and vertical angle of the light ray R from the light source located on the Z axis which equal to the height (Z=h) of the headlamp position from the ground level. Therefore, by applying the Pythagoras theorem, the Cartesian coordinate points from the Spherical coordinate system is simplified.

35763206985000337820698500
From the right-angle triangle, simplified from the REF _Ref514715557 h Figure (52), the following relations are obtained:
r=Zcot(?)X=Z*cot? cos(?)Y=Z*cot? sin(?) STYLEREF 1 s 51Step 3: After successful processing of the Cartesian coordinate transformation, the algorithm narrows down to compute the solid angle of a Cartesian surface element. Normally, solid angle is calculated for the section of sphere by its center of unit radius (See Section REF _Ref514719188 h Photometric quantities REF _Ref514719199
h 2.1.2). On the other hand, there exists methods also to calculate on different surface areas and are equally valid CITATION Ron98 l 1033 29. It is to recognize that solid angle subtended by a differential area (from a given point) is equal to the projection of the area (i.e., the area as seen from the point) divided by the square of the distance from the point to the differential area CITATION Ron98 l 1033 29.
1183088508012712702785110Figure 53 Solid angle of Cartesian coordinate system CITATION Ron98 l 1033 29Figure 53 Solid angle of Cartesian coordinate system CITATION Ron98 l 1033 29
the distance is given from point P to the differential area given by R and the projected area of dA from the point P is:
dAp=dA.cos?=dA.zR 52From the above equation, the solid angle is defined as follows:
d?=?ApR2=z dAR3=z dx dy(x2+y2+z2)3 STYLEREF 1 s 53This consideration could be the most promising modification to the equation ( REF _Ref514720944 h 413) from the algorithm in previous work. This suggests that there is no essential to convert the distribution angle from the Spherical momentum space to Cartesian coordinate space. Because, this method could calculate the distribution angle in real space straightaway. In addition, considering solid angle would produce productive results since this thesis main interest is to compute the illuminance distributions on surface of the street and this simply ignore the light scatter into the outer space. The contribution of solid angle yields better results than calculating angle distance between the two points on the surface (See equation REF _Ref514720944 h 413 )
Step 4: The next most important step in the process, estimating the fog concentration using the diffusion equation as follows
C?,t,?=1(4?a(?)t)n2exp(-?24a(?)t) 54Where n is the dimension of fog distribution in solid angle. According to the International Bureau of Weights and Measures (BIPM), the solid angle is dimensionless and called as dimension of unit one CITATION Org06 l 1033 30. Therefore, the two-dimensional light distribution in fog (See equation REF _Ref514200198 h 46) from previous algorithm is modified to the dimension of unit one as shown below
Iscatter?,t,?=Io1(4?a?t)12exp(-?24a?t).e-4???ct 55The illuminance values without fog and with fog could be easily computed by modifying the equation ( REF _Ref514460673 h * MERGEFORMAT 411) with equation ( REF _Ref514767875 h 55), this returns the illuminance distributions in fog. As mentioned earlier, this thesis focus is to compute the illuminance distributions on the street. So, the illuminance values spread over the surface of the street in fog medium are given importance depending on their location. The weighted average is introduced to compute the distribution of illuminance values along the solid angle and is given by the following formula:
Weighted average = ?wixi?wi 56here wi is the relative weight of distribution of points along the solid angle and xi is the illuminance value. To make the statistical comparison, the weighted average data should normalization with the illuminance data without fog which denoted as ‘X’ in the following equation
Zi=xi-min?(x)maxx-min?(x) 57From the observations of data, the illuminance values over the surface are not spread out uniformly and missing some values at some coordinate points. To obtain the light distributions on entire surface of the street, the missing values at the missing coordinate points are to be find out with the mathematical methods such as interpolation and extrapolation of gridded data. This gives the entire surface light distributions by approximating the values between two points
Fxuk,yuk=1-a1-bFx,y+a1-bFx+?x,y+b1-aFx,y+?y+ab F(x+?x,y+?y) STYLEREF 1 s 58Where the xuk,yuk are unknown values in the X-Y Plane (?x,?y) and variable a and b can be calculated by the CITATION DMG98 l 1033 31a=xuk-x?x and b= yuk-y?y STYLEREF 1 s 59Interpolating the data in this case is calculated to concrete the results accuracy. By observation, the missing coordinates and the values concerned to it are mostly far away from the light source and this does not have major impact on the results obtained without interpolation.

Step 5: This step illustrates the luminance distribution from the street to the driver in oncoming vehicle to evaluate the glare. Generally, the luminance computation (See equation REF _Ref514789038 h 414 ) is very complex quantity to measure. From the REF _Ref516593320 h Figure (54) below, Vehicle ‘A’ and ‘B’ are set to be in the stationary position in X-Y plane. The illuminance distributions computed as discussed from the above steps using solid angle in the equation ( REF _Ref516594621 h 53). The oncoming vehicle ‘B’ position is assumed at the distance of 6 meters away from the origin stationary in the direction opposite to X.
76205064125Figure 54 Luminance distributions on to the oncoming vehicle0Figure 54 Luminance distributions on to the oncoming vehicle762011303000
The four black points are representing the illuminance values formed at the coordinate points according to the equation REF _Ref514924156 h 51). From these points, the light distributed with the reflection factor ‘q’ and is depend on the surface of the street. This factor was supported by the quadratic function whose variables a,b,c are different for different street type materials in the equation below;
q=a?ref2+b?ref+c 510Where ?refis the reflected angle from the surface and is computed by the atan function which given as
?ref=atan(x-xd)2+(y-yd)2(z-zd)
511With the above equation, the rays are tracked down to the oncoming vehicle ‘B’ driver position, which defined by the point (xd,yd,zd). Consequently, the reflections of light from the points on street surface calculated on to the driver in oncoming vehicle by
Rd=(x-xd)2+(y-yd)2+(z-zd)2 STYLEREF 1 s 512 However, the luminance distribution is calculated to evaluate glaring from the earlier equation ( REF _Ref514789038 h * MERGEFORMAT 414).
Conceptualization for the validation of Algorithm This section proposes the method of light distributions measurement and originate the fog parameters needed to validate the algorithm. The two types of fog parameter are important, which namely fog density and the other being radius of the droplet particle. The fog particle radius is very interesting factor, since there exists many accurate and possibilities to compare the light distribution results from the experiments with standard software. In contrary, this is all very hard to obtain this parameter and expensive as it particle measurement instrument. However, an interesting concept is presented to calculate the radius of the particle from the value of liquid water content in the cloud chamber. When this related with the fog density gives the effective radius in the chamber.
Validation of algorithm is very important criteria to prove the concept and to recommend further improvements if required. Nonetheless, from the previous section of this thesis already discussed the method to calculate the fog density and the construction of cloud chamber (See sections REF _Ref514201671
h 3.3 and REF _Ref514791553
h 4.3)
light distributions measurement in fog chamber
The most important is to construct the fog chamber which emulate the real-time scenario. For instance, it should replicate the shape of room (See REF _Ref516593382 h Figure 55) in which the light source stands at one face of the room from the ground level and then the illuminance sensors placed horizontally to measure horizontal illuminance and opposite to the light source, to calculate the vertical illuminance.

44453748405Figure 55 Sketch of fog chamber concept0Figure 55 Sketch of fog chamber concept36639516764000
After arranging the illuminance sensors on the measuring plane at given coordinate points, the values at coordinate points are acquired and the unknown values of illuminance over the entire surface plane could be calculated by the mathematical method of gridded interpolation of data (See equations REF _Ref514977564 h * MERGEFORMAT 58 and REF _Ref514977566 h * MERGEFORMAT 59).

Moreover, the sensors like temperature, humidity, pressure are used to calculate the fog density present in the cloud chamber. Additionally, the LWC value is calculated in the cloud chamber to obtain the effective radius of the fog particle as discussed in the section REF _Ref516155913
h 3.4. To achieve good accuracy in results, the number of sensors play the key role. So, more number of illuminance sensors are recommended over the surface of fog chamber. Furthermore, to compare the results with the algorithm four steps are proposed:
First step is to do measurements to record the illuminance values with fog to obtain the fog density parameter.
Repeat the measurements to get the illuminance value without fog
Input the illuminance values measured without fog, and the coordinate points of sensor position, fog density parameter obtained from the first step, and other inputs such as height of the lamp or distance to the other face of the cube depending on the measurement plane selected to the algorithm.

Now, compare the illuminance results under influence of fog obtained from the algorithm with the illuminance results obtained from the fog chamber measured during the presence of fog
Graphic User Interface applicationThis section describes the light computation GUI developed using MatLab. This is divided into three units to show the light simulations in three different areas as follows:
38989063500
9664701520825Figure 56 Block diagram of GUI0Figure 56 Block diagram of GUI
With this GUI, light simulations in different areas are carried out namely on street, in the light laboratory, and in the fog chamber along with data acquisition of sensors and validation of algorithm. The REF _Ref516593429 h Figure (57) below depicts the GUI application.

Figure 57 Light Computation GUI applicationThe process of units 1 and 2 are run as described in the section REF _Ref516186363
h 5.1. But the coordinate points (X, Y, R) calculated from the horizontal (?) and vertical angle (?) for unit 2 is different compared to unit 1 coordinate points (X, Y, R) (see equation REF _Ref516187235 h 51 ) calculation because, here the vertical illuminance is computed, i.e. on the wall which is explained as follows:
X=h.tan? Y=h.tan?, R=X2+Y2+h2
513 Where h = height of the headlight position from the ground.

Coming to the unit 3, the process of computation in fog chamber is different in comparison with the units 1 and 2. Here, the experimental setup is organized with sensors as discussed in section REF _Ref516187586
h 5.2.
45339000
The above flow chart illustrates the steps to follow for the validation of algorithm model for fog chamber with the experimental results. This GUI is scripted with some restrictions to validate the data. It is mandatory to do the illuminance measurements in fog prior to the measurements without fog when interested to validate the algorithm. Since the algorithm require the fog parameter a(?), which is only possible to obtain from the experimental results.
RESULTS ; DISCUSSIONSIn the section, the findings from the investigations during this thesis are provided and described. At first, the results obtained from the GUI application and then following the results from fog chamber which based on supposition and finally, the results obtained from ray tracing methods, using the Lucid shape are presented.
Light simulations using MatLabAs explained in the previous chapter in the section REF _Ref516443282
h * MERGEFORMAT 5.1 about the inputs and working of algorithm, the REF _Ref516444365 h Figure (61) depicts the results of light distributions with and without fog.

Figure 61 Results of Light distributions using MatLabThe input parameters considered here are as follows:
Height of the headlight position from ground: 0.65 meters
Height of the driver position in oncoming vehicle: 1.15 meters
The road surface type is: Concrete
The assumed fog density is: 450
These results are from low beam distribution measurements and the high beam distributions produces the different results (See section: REF _Ref516443983
h 2.2.1). From the REF _Ref516444365 h Figure (61), the involvement of fog parameter a(?) decreases the illuminance distribution over the distance. This is due to the light attenuation when interacts with the water droplets suspended in air (See section REF _Ref513910609 h Diffusion of light in fog). Thus, when the value of fog parameter increases the illuminance distribution attenuated strongly and there is need to deduce this parameter from the experiments.

Figure 62 Light distributions for different assumed fog densities Light simulations in fog chamberIn this thesis, only the conceptualization for the validation of algorithm from experiments is answered. So, the experimental results are not obtained due to the unavailability of completely constructed fog chamber. However, some dummy results are taken to explain the results from validation.
Light Light Light Light Light Light Light Light Light Density Temperature Humidity Pressure
14.41 46.95 50.45 61.25 67.11 74.23 80.55 88.45 94.55 0.456861 28.62 72.7 99178.6
14.67 47.04 51.55 61.55 68.77 75.33 82.22 89.55 95.65 0.456763 28.62 72.6 99156
15.49 47.81 51.63 62.22 69.99 75.55 83.44 90.23 96.77 0.456747 28.62 72.6 99152.6
15.58 49.32 54.65 64.66 72.23 76.45 84.55 91.22 98.44 0.456758 28.62 72.4 99152.1
15.71 49.17 56.55 64.23 72.89 77.56 84.98 91.33 98.33 0.456756 28.62 72.4 99151.7
15.71 49.29 57.23 65.35 73.56 77.65 85.55 91.23 98.66 0.456727 28.62 72.8 99151.4
16.17 49.78 59.68 65.45 74.55 78.45 85.88 91.55 99.89 0.456763 28.62 72.3 99151.6
16.22 50.38 59.89 66.54 74.98 79.98 87.32 92.33 102.45 0.456763 28.62 72.3 99151.6
Table 2 Structure of expected dummy results from Fog chamberX-position of sensors Y-position of sensors
1 0
1 2.5
1 -2.5
3 0
3 2.5
3 -2.5
4.5 0
4.5 2.5
5.5 0
Table 3 Sensor position (dummy values) in Fog chamberThe REF _Ref516453126 h Table 2 indicates the structure of data from the fog chamber after experiments, here random values taken to predict the light distributions in fog chamber. Whereas REF _Ref516453151 h Table (3) represents the sensor positions in the fog chamber. Here, only illuminance sensor positions are considered and the other sensors like temperature, humidity and pressure are neglected due to the non-usage of this position for the validation purpose. Eventually, after following the procedure explained in the sections REF _Ref516451676
h 5.2 and REF _Ref516451663
h 5.3, the validation results could be obtain as shown below:

Figure 63 Light distributions for assumed dummy valuesLight simulations using ray-tracing methodRay tracing method is carried out using Lucid shape software which is the most common tool used for computation of light distributions in automotive industry. Thus, in this thesis the results obtained through “Mie theory” computed by this software is presented.

Figure 64 Light simulation without fog using Lucid shape (software)The light distributions obtained using MatLab (See REF _Ref516444365 h Figure 61 ) and using Lucid shape (See REF _Ref516522580 h Figure 64), produces the almost similar values of illuminance values on the street without fog with maximum being around 131lux and 128 lux. From the observation of ISO plots, both produces the low-beam distributions but having different cut off regions at approximately 38 meters and 47 meters in the x-direction of axes convention in automotive. Although the cut off regions are different, the shape of light distributions for low-beam are accurate. However, this clearly shows the light distributions in presence of fog would produce some interesting results. As this thesis also proposed to find the effective radius parameter (See section REF _Ref516525777
h 3.4) to produce the more precise result for validation of algorithm through the results not only from experiments, but also from the standard software for ray tracing. As a trial of concept in this thesis, the light distributions in fog using ray tracing method also computed which can be observed in following REF _Ref516526297 h Figure (65).

Figure 65 Light simulations in fog using Lucid shape (Software)Comparison between the REF _Ref516522580 h * MERGEFORMAT Figure (64) and REF _Ref516526297 h * MERGEFORMAT Figure (65) brings to the conclusion about the light scattering in fog. Apparently, the cutoff region of illuminance distributions on street diffused over to some extent around 60 meters from its original position 48 meters (without fog). Some rough approximations of parameters were proposed to make this illuminance distributions which are presented in the below REF _Ref516593724 h Figure (66).

Figure 66 Input parameters for light simulations in fog using ray tracing methodCONCLUSIONThe aim of this thesis was to develop the available algorithm in high level program language to compute the light distributions originated from the vehicle headlight, which represented by the IES file. Furthermore, the steps must be taken into consideration in making the algorithm more user-friendly to use, like creating a Graphic User Interface (GUI). The focus of the algorithm development was to do computation faster and produce the light simulation results in ISO-LUX plots, in comparison with the conventional methods like ray tracing used for computing light distributions in automotive industry. Therefore, as a result in this thesis, it is evident that the method developed from IAV using MatLab was substantially enough faster to compute the light distributions on street and on to the oncoming vehicle in contrast to the ray tracing method using Lucid shape. The results obtained in less than five minutes using MatLab, whereas Lucid shape taking more than one day to compute the light distributions due to volume scattering in environment condition like fog. In contrast, when executing the light distributions without fog on both the software consumed similar amount of time.
On the other hand, another important factor for algorithm was proof of concept. Due to the reason of unlikely functioning of fog chamber, the presumed results were considered in this thesis to explain the process for validation model. Therefore, this proposes the future work to carry out the experiments using fog chamber and obtain the measurement results to produce the more accurate output for validation of the algorithm model.
During the time of thesis, after studying some research papers which focus on similar goal, some interesting parameters were introduced in this thesis like calculation of moisture air density, calculation of effective radius of water droplet, solid angle on cartesian surface element. Nevertheless, this thesis proposes to take thorough research in direction of meteorology for deriving the effective radius of droplet parameters. Furthermore, recommends a stable data-acquisition unit to avoid the complexity and unstable sensors connection to the micro controller while doing experiments. However, good results were attained in favor of computation time and this thesis anticipates the proposals given would help to yield some productive results focusing on validation of algorithm. Based on the obtained results then, the necessary improvements for the algorithm with focus on light distribution equation in presence of fog could be modified.
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