Chapter 1 Introducation
1.5 Organization of this Thesis
The thesis is organized as follows: The principles of backlight systems are presented in Chapter 2. In Chapter 3, the major instruments for characterizing backlight systems are described. The modeling process of the UFL system is described and then the simulation results and the experimental results are verified in Chapter 4. The BFL system model and the experimental results are presented in Chapter 5. Finally, conclusions of this thesis and recommendations for the future work are presented in Chapter 6.
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Chapter 2
Principles of Backlight System
For analyzing and designing backlight systems, some optical principles, radiometry, photometry, bidirectional transmittance and reflectance distribution function (BTDF and BRDF), and colorimetry, are described in this chapter. The ray-tracing method simplified behavior of light propagation. However, the optical characterizations of phosphor films, which included light-scattering mechanism and wavelength-converting mechanism simultaneously, were difficult to be described by ray-tracing only. Accordingly, the BTDF and BRDF based on radiometry and photometry are described and utilized to characterize the scattering characterization of phosphor film. Moreover, basing on colorimetry, the CIEXYZ and CIELUV color spaces, which specify color numerically, are also presented in this chapter.
2.1 Principles of ray-tracing method
Ray-tracing method is based on Snell‟s law, Fresnel‟s equation, and other optical principles. By electromagnetic theory, light is a kind of electromagnetic waves with time varying electric and magnetic fields. The light waves take a spherical form when just radiated from a point source and then behave like plane waves as traveling away the source. The path of a hypothetical point on the wave front of light is called a ray of light. Such a light ray is an extremely convenient fiction. Thus, the ray-tracing provides a simplified solution for discussing the behavior of light and analyzing optical systems. Therefore, some optical software, such as LightToolsTM, OSLOTM, et al., apply the ray-tracing method to build optical module for a simulated environment.
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Snell’s law (Law of refraction)
Snell‟s law, also known as law of refraction, defines the appearance of refraction in the plane of incidence. A light ray making an angle i (the incidence angle) with the surface normal strikes a boundary separating two optical media will induce a refracted ray transmitted through the boundary and makes a new angle t (the refraction angle) with the surface normal.
Snell‟s law says that the ratio of the incidence angle to the refraction angle of light equals to a constant which depends on the opposite ratio of the refractive indices of two optical media
In the plane of incidence, the deviation of optical rays due to reflection is defined as the following equation, which is the so-called law of reflection[18]:
i r
(2-2)
where i (incident angle) and r (reflected angle) are the angles made by the incident and refracted ray with the surface normal, respectively. In other words, the reflected ray makes equal but opposite angle with the incident ray.
Fresnel’s equations
Fresnel‟s equations describe the energy of transmitted and reflected light at an interface between two different optical media. For the P (parallel to the plane of incidence) and S (perpendicular to the plane of incidence) polarization waves, the amplitude reflection and transmission coefficients r and t are respectively given by[19]:
11 the angle of incidence and angle of propagation respectively.
According to irradiance[20], the reflectance and the transmittance for polarized light are transmittances for S and P polarization light, respectively. When a random polarized light (eg.
the nature light) strikes the interface, the reflectance R and transmittance T are defined as the average of the polarized case as following equations:
2
Basing on laws of reflection and refraction, the ray-tracing method could analyze the way light propagated, reflected, and refracted. Besides, by Fresnel‟s equations, the energy of reflected and transmitted light at an interface separating two media could be calculated.
Accordingly, the energy of a particular light on the defined receiver could be obtained.
Therefore, the ray-tracing method adopted optical design software, LightToolsTM, is adequate
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for developing simulation model to design and optimize the optical performances of the backlight systems.
2.2 Radiometric and Photometric quantities
Radiometric quantities
Radiometry is the measurement of optical radiation within wavelengths ranging from 10 nm to 106 nm[21]. Therefore, the optical systems which utilize ultraviolet-, visible-, and infrared-light as a light source could all be discussed by radiometry.
Radiometric quantities include radiant energy, radiant flux, radiant intensity, irradiance, radiant exitance, and radiance. Table 2-1 shows these fundamental radiometric quantities whose unit is based on energy and SI units[22].
Table 2-1 Radiometric units.
Quantity Symbol Definition Unit
radiant energy Q joule
radiant flux dQ/dt watt
radiant intensity I d/d watt/sr
irradiance E d/dA watt/m2
radiant exitance M d/dA watt/m2
radiance L d2/dA d watt/(m2 sr)
( t: time, : solid angle, A: area )
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Radiant energy Q defines the energy of a collection of photons (as in a laser plus).
Radiant flux is the measure of total power of radiation. The power may be the total emitted from a source or the total landing on a particular surface. Basing on radiant energy Q and radiant flux , the other quantities are derived by various geometric normalizations.
Radiant intensity I is generally used to describe the characteristics of sources whose size is infinitesimal, such as a point source. The definition of I is the radiant flux per unit solid angle of a specified surface which the radiation is incident upon or passing though, as shown in Fig.2-1(a).
Irradiance E describes radiation distribution on a received plane. The definition is the radiant flux per unit area of a specified surface which the propagating radiation is incident on or passing though, as shown in Fig. 2-1(b).
If the radiant flux leaving the plane per unit area is considered, the term radiant exitance M is used instead of irradiance E but is expressed by the same equation. Radiant exitance M
describes radiation distribution on the plane which emits the radiation, as shown in Fig.
2-1(c).
When an extended source, such as a planar source, is considered, radiance L is used to describe its characteristic. The definition is the radiant flux per unit project area and per unit solid angle of a specified surface which the propagating radiation is incident on or passing through, as shown in Fig. 2-1(d). The projected area of the plane element equals to dAcos, where is the angle between the normal of the plane element and the direction of observation.
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Photometric quantities
For human visual system, the responses to the optical radiation with different wavelengths are dissimilar. Photometric quantity is an operationally defined quantity designed to represent the way in which the human visual system evaluates the corresponding radiometric quantity. Accordingly, it is also called a psychophysical quantity. In particular, the optical radiation within the wavelengths range between 380 nm and 780 nm, so-called visible light, are discussed by photometry.
Photometric quantities include luminous energy, luminous flux, luminous intensity, illuminance, luminous exitance, and luminance. In geometric terms, the definitions of these photometric quantities are the same as for the corresponding radiometric quantities. Table.2-2
Solid angle element d
Radiant flux d
(a) Radiant intensity
Radiant flux d
Plane element dA
(b) Irradiance
Radiant flux d
Plane element dA
(c) Radiant exitance
Radiant flux d
Plane element dA
(d) Radiance
Fig. 2-1 Defining geometry of radiometric quantities.
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shows the photometric quantities whose unit is based on lumen (lm)[22]. Lumen is defined as
„luminous flux emitted into a solid angle of one steradian by a point source whose intensity is 1/60 of the intensity of 1 cm2 of a blackbody at the temperature of platinum (2042K) under a pressure of one atmosphere.‟
From the definition of lumen, the maximum value of spectral luminous efficiency could be determined. At the wavelength 555 nm, which corresponds to the maximum spectral efficiency of human eyes, 1 watt is equal to 680 lumens. Therefore, the luminous flux v
emitted by a source with a radiant flux is given by:
680 ( ) ( )
v V d
, (2-13)where is the wavelength and V() is the spectral luminous efficiency function as shown in Fig.2-2.
Table 2-2 Photometric quantities.
Quantity Symbol Definition Unit
luminous energy Qv lm s
luminous flux v dQv/dt lumen (lm)
luminous intensity Iv dv/d lm/sr (cd)
illuminance Ev dv/dA lm/m2 (lux)
luminous exitance Mv dv/dA lm/m2 (lux)
luminance (brightness) Lv d2v/dA d lm/(m2 sr) (nit)
(t: time, : solid angle, A: area)
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Fig. 2-2 Human visual response function.
2.3 Bidirectional transmission and reflection distribution function
Basing on radiometry and photometry, the bidirectional transmittance and reflectance distribution functions (BTDF and BRDF) are developed to describe scattered light distributions[23]. The BTDF describes the transmissive characteristic of a sample, while the BRDF indicate the reflective characteristic of a sample. In this thesis, the wavelength corresponded BTDF and BRDF were adopted to describe the phosphor film‟s light-scattering characteristics which combine diffusing process with wavelength-converting mechanism.
The defining geometry of BTDF and BRDF is shown in Fig. 2-3, where the subscripts i, t, and r are denoted for incident, reflected and transmitted quantities, respectively. The
notation
is the azimuthal angle between light direction and the normal direction of sample surface, and is the polar angle on the sample surface. If a incident light with luminous fluxv,i and wavelength i illuminating on the sample with area A is considered, the transmitted and reflected light scattered from the sample could be described by BTDF and BRDF which are defined as follows:
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where t and r are the wavelengths of transmitted and reflected light, Ev,i is the illuminance on the sample plane due to incident light, and Lv,t and Lv,r are the luminance of transmitted and reflected light at the particular received angles, respectively.
incident light
Fig. 2-3 Schematic diagram of BTDF and BRDF.
BTDF and BRDF describe the luminance distributions of transmitted and reflected light scattered from a sample. Besides, the terms dv t,(t) /v i,(i)and dv r, (r) /v i,(i) in BTDF and BRDF mean the transmittance and reflectance of the transmitted and reflected light in (t , t) and (r , r) direction, which could be obtained by measuring illuminance of incident light and luminance of the transmitted and reflected light. Moreover, the terms t and
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r indicate the wavelengths corresponded relation of incident light and the scattered light.
Therefore, the BTDF and BRDF provide a convenient solution to describe the way in which the light is reflected and refracted by a sample even propagating in different wavelengths with the incident light. Accordingly, the scattering specification of conventional diffuser films and phosphor films could be generated, and then be utilized by optical designers, manufacturers, and users to communicate and check requirements.
In this thesis, the BTDF and BRDF of phosphor films are measured by our designed BTDF measurement systems and a conoscopic system operating under trasnmissive and reflective mode. The measured BTDF and BRDF data were then imported to out optical design software, LightToolsTM, to develop the simulation models that could describe the light-scattering characteristics of phosphor films. Thus, we could start our design and optimization of UFL and BFL backlight systems.
2.4 Colorimetry
Colorimetry is the science relating color comparison and matching. As mentioned earlier, for visible light, the optical radiations within wavelengths ranging from 380 nm to 780 nm, the photometric quantities have provided measures to describe the amount of energy.
However, in human visual system, the optical radiations arouse not only intensity response (brightness) but also chromatic response (chromaticity). Therefore, in this thesis, colorimetry is imported to specify the chromatic performance of backlight units. The CIEXYZ and CIELUV color spaces, which have been developed for denoting colors numerically, are described in the following paragraphs.
CIEXYZ color space
The CIE XYZ system, created by the International Commission on Illuminance (CIE) in 1931, is one of the first mathematically defined color systems that specify colors
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numerically[ 24]. The human eye has receptors for short (S), middle (M), and long (L) wavelengths. Thus in principle, three parameters describe a color sensation. The tristimulus values of a color are the amounts of three primary colors in a three-component additive color model needed to match that test color[25]. In the CIE XYZ system, the tristimulus values are called X, Y, and Z. The tristimulus values for a color with a stimulus ( ) can be derived from the color matching functions, the numerical description of the chromatic response of standard observer[26] (see Fig. 2-4), according to the following equations:
( ) ( )
vis
X k
x d (2-16)( ) ( )
vis
Yk
y d (2-17)( ) ( )
vis
Z k
z d (2-18)where k is a constant and the integral is taken in the visible light wavelength. The y( ) is set so that is identical to the spectral luminous efficiency function V() mentioned earlier. Thus the tristimulus value Y directly expresses a photometric quantity.
Fig. 2-4 Color matching functions x( ) , y( ) , and z( ) in the CIE XYZ color system.
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Basing on CIE XYZ system, a color could be specified by utilizing the tristimulus values X, Y, and Z in a three-dimensional color space, called CIEXYZ color space. Besides, for
convenient descriptions of colors, a color space specified by x, y, and Y, known as CIExyY color space, was derived[27]. The x and y are defined as following equations:
x X
X Y Z
(2-19)
y Y
X Y Z
(2-20)
Z 1
z x y
X Y Z
(2-21)
The z coordinate could be omitted by providing Y parameters which is a measure of the luminance of a color. Accordingly, the chromaticity description of a color could be expressed more conveniently in a two-dimensional plane, which is called CIE xy chromaticity diagram and be widely used in practice (see Fig.2-5).
Fig. 2-5 xy chromaticity diagram of CIE XYZ color system.
However, the xy chromaticity diagram is highly non-uniform and has been found to be a serious problem in practice[ 28 ]. The color difference between two colors could not be calculated by using CIEXYZ color space or xy chromaticity diagram. Therefore, a uniform
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color space, the CIELUV color space, is proposed to replace the non-uniform CIEXYZ color space.
CIELUV color space
The CIELUV color space adopted by CIE in 1976 is an attempt to define an encoding with uniformity in the perceptibility of color difference[29]. Such a uniform color space is based on a simple-to-compute transformation of the 1931 CIEXYZ color space[30,31]. For the non-linear relations from CIEXYZ color space to CIELUV color space, the three-dimensinal orthogonal coordinates adopted in CIELUV color space are defined as follows[32]:
* 116( / n)1/3 16 chromaticity coordinates u’ and v’ of reference white, respectively.
' 4
Basing on the uniform CIELUV color space, the color difference of two colors could be calculated. The color difference u’v’ between two colors (u1’,v1’) and (u2’,v2’) at the u’v’
chromaticity diagram is defined as[33]:
2 2 2 2
1 2 1 2
' ' ( ') ( ') ( ' ') ( ' ')
u v u v u u v v
(2-26)
In this thesis, Equation 2-26 is imported to judge the chromatic performance of the backlight units.
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Fig. 2-6 u’v’ chromaticity diagram of the CIELUV color system.
2.5 Summary
Table.2-3 summarizes the principles mentioned earlier in this chapter. In this thesis, ray-tracing method was used to design backlight system in this thesis. By Snell‟s law, law of reflection, and Fresnel‟ equations, the propagation trajectory and the carried energy of light could be calculated. Besides, basing on radiometry and photometry, the wavelength-corresponded BTDF and BRDF provided a convenient solution to describe the scattering characteristics of phosphor films. Therefore, the ray-tracing based optical design software, LightTools, was utilized to simulate a backlight system. And then the measured BTDF and BRDF data were imported to LightTools for development of simulation model for design and optimization of the UFL system and the BFL system. Accordingly, the CIELUV color space and the color difference u’v’ were utilized to judge the optical performances of the backlight units. The wavelength corresponded BTDF and BRDF of phosphor films are the most important part for developing simulation models of UFL system and BFL system.
Therefore, the measurement instruments will be discussed in the following chapter.
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Table 2-3 Function of applied principles.
Method Principle Function
Ray tracing
Snell‟ law
Calculating propagation trajectory and carried energy of light.
Law of reflection Fresnel‟s equations Radiometry
&
Photometry
BTDF Characterizing light scattering properties of phosphor films.
BRDF
Colorimetry
CIELUV color space Specifying chromaticity performance of backlight output distribution.
Color difference (u’v’)
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Chapter 3
BTDF and BRDF Measurement Instruments
A phosphor film simulation model was essential for designing and optimizing the UFL and BFL systems. In order to specify the light scattering characteristics of phosphor films and develop phosphor film models, BTDFs and BRDFs were first measured. The BTDFs and BRDFs were measured using a conoscopic system and a customized BTDF measurement system. Then, the measured BTDF and BRDF data were imported into the optical design software, LightTools, to start modeling. The principle of conoscopic system and the specially designed BTDF measurement system will be presented in this chapter.
3.1 Conoscopic system
Transmissive mode
A conoscopic system was utilized to measure the angular light distributions of samples. The optical radiations within wavelength ranges between 380 nm to 780 nm, known as visible light, were measured by this system. The measuring mode of this system could be classified into transmissive and reflective modes. In transmissive mode (as shown in Fig. 3-1), a Fourier transform lens was adopted to transform the received light into a two-dimensional pattern. Each light beam emitted from the test area at incident angle, θ, could be focused on the focal plane at the same azimuth and at a position x=F(θ). Then, a relay system was utilized to project this transform pattern onto a CCD-array detector. In this transform pattern, each area corresponded to one specific light propagation direction. Thus, when this pattern was projected on the CCD-array detector, the light intensity and chromaticity versus dissimilar viewing directions were obtained simply and quickly, without mechanical movement. Then, after combining a BTDF
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measurement system which will be described later in this chapter, the BTDFs of phosphor films and the optical performance of backlight systems were measured using the conoscopic system in the transmissive mode directly.
Fig. 3-1 Schematic of the conoscopic system in transmissive mode.
Reflective mode
Besides the transmissive mode, a reflective mode in the conoscopic system is available to measure the angular distributions of light reflected from samples. In the reflective mode (as shown in Fig. 3-2), a light source is implemented at the Fourier transform plane to illuminate samples from inside the conoscopic system. A collimated light struck the sample surface with a tiny illuminated area was reflected back into the conoscopic system. Therefore, the angular distribution of these reflected lights were obtained with the CCD-array detector. The illuminating angle, θ, of the built-in source was easily varied by controlling the position of the light source on Fourier transform plane. Therefore, the BRDFs of a sample were measured. In this experiment, the BRDFs of phosphor films and reflectors were obtained by measuring the angular distributions of reflected light under the reflective mode of conoscopic system.
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Fig. 3-2 Schematic of the conoscopic system in reflective mode.
3.2 BTDF measurement system
To measure the BTDFs of phosphor films, a device which could provide a collimated light in different illuminating angles was required. The BTDF measurement system was designed and fabricated for this purposes, as shown in Fig. 3-3.
In the BTDF measurement system, an LED stage was connected to a slippery track located on the side plane of the system. The rail of the slippery track was an arc and the LED stage slid along this rail. Besides, an aperture with small diameter is placed on the exit plane of the LED and a circular hole with a tiny surface area was bored on the top plate of system.
In this structure, the sample placed on the top plate of this measurement system was illuminated using a collimated light whose illuminating angle could be varied from 0 to 70 degrees.
When measuring BTDFs of phosphor films, the BTDF measurement device was placed under the conoscopic system to serve as a light source. The optical properties in each viewing direction were measured using the conoscopic system in transmissive mode. A photograph of the experimental setting is shown in Fig. 3-4.
27 Slippery track
(a) Front view (b) Side view
Fig. 3-4 Diagram of BTDF measurement.
Conoscopic system
Measured sample (e.g. phosphor film) Our designed light
source device
LED stage Aperture
Fig. 3-3 Schematic of designed device for BTDF measurement.
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3.3 Summary
To develop a phosphor film simulation model and design the UFL and BFL systems, the
To develop a phosphor film simulation model and design the UFL and BFL systems, the