Chapter 2 Radiometry and Photometry
2.4 Bidirectional Reflection and Transmission Distribution Function
Bidirectional Reflection and Transmission Distribution Function (BRDF and BTDF), which are representations for light distribution, describe how much light is reflected and transmitted when light makes contact with a certain material. As shown in Fig. 12, BRDF taken for example is a function of light incoming direction and outgoing direction of viewer relative to a local orientation at the light interaction point.
BRDF is defined as follows:
Simply speaking, BRDF and BTDF are the distributions in the hemi-spherical space when light is incident on the material with several different incident angles. Fig.
13 indicates BTDF of conventional diffuser passed through by the propagating light with incident angle of 0°, 20°, 40° and 60°. In general, BRDF and BTDF are adopted to describe the scattering phenomenon. BRDF and BTDF are assumed to be position-invariant, which means that whatever positions the propagating light is incident on, BTDFs are the same.
Fig. 12 The definition of BRDF
Fig. 13 BTDF of conventional diffuser
Chapter 3
Beam Shaping Diffuser
3.1 Beam shaping Film with Lens Array
Beam shaping means that the propagating light is redistributed to form a specified shape in the spatial domain, such as the rectangular, circular and square shapes of light distributions. Beam shaping film, which is a transmissive component, designed for some special illumination purposes enable the efficient use of light by controlling light propagation and directing it to form a specified shape in the designated regions of space, as shown in Fig. 14.
Fig. 14 Beam shaping film which controls light propagation and directing it to form a specified shape
Engineered DiffuserTM developed by RPC Photonics is a typical example to shape the spatial distribution [6, 7]. Engineered Diffuser is based on the refractive micro-structures, as shown in Fig. 15. The micro-lens elements are arranged with
100% fill factor. Unlike conventional random diffusers such as bead-coating and micro-structure embossing diffusers, Engineered Diffuser can diffuse the propagating light into any specified shape in the far-field. Fig. 16 shows the beam shaping patterns controlled by Engineered DiffusersTM with different micro-structures. In this chapter, we adopt the characteristics of beam shaping film with lens array resulting in the square beam shaping patterns to apply to the scanning backlight module.
Fig. 15 The micro-structures of Engineered Diffuser
Fig. 16 Examples of LED light control with Engineered Diffusers
3.2 Scanning Backlight Module
Owing to the limitation of response time of liquid crystal, the motion blur is an issue in LCD. When watching the moving object, we can see the residue image behind the object like a tail, as shown in Fig. 17. In order to reduce the phenomenon, a method that a black frame is inserted between two frames can be chosen. Inserting black frame, however, sacrifices a mount of brightness as a result the contrast decreases. Furthermore, the scanning backlight is adopted to solve this problem [8].
As shown in Fig. 18, the backlight contains several rectangular light guides, which illuminate from top to under of the panel sequentially depending on the signal scanning way of the panel. In the ideal situation, each light guide performs high uniformity and efficiency and dose not influence each other. Fig. 19 shows the wedge type tandem light guides for large size panel [9]. Base on the technique of the scanning BLM, the researches, field sequential color LCD and high-dynamic-range (HDR) display, further develop to promote the image quality [10~12].
Fig. 17 Motion blur of a car moving
Fig. 18 The scanning way of the divided light guides
Fig. 19 The divided wedge light guide designed for large size panel
We proposed a film, beam shaping diffuser, whose structure is spherical micro-lens array, to produce the square beam shaping pattern applied to the division areas in the scanning BLM. Fig. 20 illustrates the direct type scanning BLM in the ideal situation, in which the collimated light source illuminates and then the propagating light passes through the beam shaping diffuser to result in the division areas. This direct type BLM only composed of beam shaping diffuser and LED light source reduces some traditional devices such as light guide, BEFs and diffusers. It is expected that the system we proposed can have the uniformity approaching 90% and the tolerance of incident divergent light source.
Fig. 20 Direct type scanning backlight module with beam shaping diffuser
3.3 Simulations
3.3.1 One-sided Lens Array
The shape of the beam shaping pattern primarily depends on the shape of the micro-structures on the film. In Fig. 21, the beam shaping patterns in the far field of the different beam shaping diffusers which the collimated light passes through were demonstrated. The relief structures of the periodic micro-lens array are arranged on the film surfaces, on which each lens surface is spherical and the lenses have different shapes. Fig. 21 shows the examples of (a) square, (b) triangular and (c) hexagonal lens shapes. According to these patterns in the far field, which are the same as those of the lens structures, we know the fact that the shape of the beam shaping pattern is resulted from the shape of each element. The structures of beam shaping diffuser we adopted are the square lens array. The far-field diffraction pattern was simulated by a square lens array subject to different sags.
Fig. 21 The periodic lens array which are (a) square, (b) triangular and (c) hexagonal result in the beam shaping patterns (d), (e) and (f), respectively.
In the following simulations, we chose the spherical lens sculptured into a square shape [Fig. 22(b)] while the square periodic lens is arranged as Fig. 21(a). The pitch p is fixed at 100um. The light source emits collimated light with circular shape with diameter of 0.5mm. Fig. 23 shows the patterns of beam shaping diffusers with different sags, which are observed on the plane located at one focal distance (f) and 100f. The patterns of the sags of 10um and 20um are square at 100f because the shape of the lens is square. However, the distortion of the square patterns is observed obviously while the sag is 30 and 40um. The reason is that spherical aberration occurs.
Fig. 22(a) The spherical surface lens (b) The lens sculptured into square shape
Fig. 23 The bean shaping patterns of the lens array diffusers with different sags observed on the plane located at focal distance of f and 100f
Fig. 24 Spherical aberration
Spherical aberration can be defined as the variation of focus. Fig. 24 is a somewhat exaggerated sketch of a simple lens forming an image of an object at a great distance away. The rays close to the optical axis come to the focus point which is very near the paraxial focus position. As the ray height at the lens increases, the position of the ray intersection with the optical axis moves farther and farther from the paraxial focus. Therefore, the larger the lens is, the more incident light deviates. As a result, the beam shaping patterns are not square and have distortion on the edge of the
aberration. The more obviously spherical aberration is shown, the larger light spot is.
Furthermore, we observe the uniformity and the profiles of the beam shaping patterns as the increase of the numbers of lens, as shown in Fig. 25. The sag of each lens is fixed at 10um, and the pitch is 100um. The light source emits collimated light, and the observed plane is located at 100f. As the numbers of lens increase, the higher uniformity can be obtained, and the hot spot in the center of the beam shaping pattern is more indistinct.
Fig. 25 The uniformities and the profiles of the beam shaping patterns of the diffusers with different numbers of lens
3.3.2 Both-sided Lens Array
Beam shaping diffuser with both-sided lens array shown as Fig. 26(b) is able to increase the tolerance of the imperfect collimated light which is assumed to emit with a divergent angle. The beam shaping diffusers with one-sided lens array mentioned above have low tolerance of the imperfect collimated light, and the beam shaping
pattern is never formed as square shape, as shown in Fig. 27. In order to determine a square shape, square shape ratio is defined as blow:
square shape ratio P
S
A
=
A
, (11)where
A is the area of the beam shaping pattern, in which the boundary is the full
P width at half maximum (FWHM). AndA is the area of the perfect square shape.
S Both of the length,l and
Pl , must be equal.
SFig. 26(a) One-sided lens array (b) both-sided lens array
Fig. 27 Imperfect beam shaping pattern
The beam shaping patterns in Fig. 28 indicate the comparison between the perfect and imperfect collimated light passing through the one-sided square lens array film.
The diameter of the light source is 2mm. The distance between the beam shaping diffuser and the light source is 0mm. The lens size is 100um, and the sag is 20um. The observed plane is located at 100f. In Fig. 28(c), the pattern with square shape ratio of 79% obviously is not controlled by the beam shaping diffuser. Therefore, the one-sided lens array film has low tolerance with incident divergent angle.
Fig. 28 The patterns resulting from the perfect and imperfect collimated light which passes through the one-sided square lens array film
In order to solve this problem, we proposed a method referring to the configuration in projector [13]. The flat plane on the opposite of the film is replaced with lens array in this case. Such two-sided lens array film is able to improve the drawback of low tolerance of one-sided film. The lenses on the two opposite lens array must coincide, and the distance between them is the focal length, f = 355um. Fig.
29 illustrates the lens array pair is able to redirect the incident light with an inclined
angle 10° shown as the red rays. The deviating light can be redirect to the area in which the perfect collimated light (white rays) produces the beam shaping pattern.
The beam shaping patterns in Fig. 30 indicate the comparison between the perfect and imperfect collimated light passing through the two-sided square lens array film. The difference of the square shape ratios is small than 1%. Consequently, the beam shaping diffuser arranged by two-sided lens array has better tolerance with incidence subject to one-sided lens array.
Fig. 29 The opposite lens correcting the red light with an inclined angle
Fig. 30 The patterns resulting from the perfect and imperfect collimated light which
3.3.3 Applying to the Backlight Module
Both-sided beam shaping diffuser is able to be adopted for the divided areas in the scanning BLM. The material of the film is PMMA, and the substrate thickness is 125um. We designed that the lens pitch is 100um and the sag is 24um. Then, two films are put together as a result the thickness of the film is the focal length of 250um, as shown in Fig. 31. The tolerance of light divergent angle of the diffuser we designed can be approaching 15°. Fig. 32 illustrates the direct type BLM within both-sided beam shaping diffuser. The distance between the detector and the both-sided micro-lens array diffuser is 120f, which is 30 mm. The light source close to the film illuminates imperfect collimated light with divergent angle 15° and the beam size is 10mm. One light source whose beam size is 10mm can produce a square beam shaping pattern whose length is 24mm. when combining 9 light sources, the length of the pattern is 54mm, as shown in Fig. 32(b), and we can get the uniformity achieved to 86%.
Fig. 31 Two one-sided lens array films put together
Fig. 32(a) The profile of the direct type BLM (b) the beam shaping pattern (c) 9 LED light sources
Chapter 4
High Gain Diffuser Film
4.1 Light Diffusion and Collection
Optical films are usually employed to promote light uniformity and collimation in the conventional backlight module (BLM). As shown in Fig. 33(a), after emitting from the light guide, light propagates through diffuser and is scattered into all directions of the hemi spherical space. Then the scattered light is redirected by two orthogonally arranged brightness enhancement films (BEFs) and collected to the normal direction. In order to reduce the production cost of the BLM, many novel devices were developed to reduce the usage of optical films or combine their functions [14~16]. In this chapter, a novel optical layout, high gain diffuser film with surface relief of lens array, performing dual functions of light collection and diffusion was proposed to combine BEFs and diffusers, as shown in Fig. 33(b).
Fig. 33(a) The conventional backlight module (b) lens array film replacing BEFs and diffuser in the BLM
4.2 Film Structures
On the lens array film, the lens surfaces can be divided into five types, oblate ellipsoid, sphere, ellipsoid, paraboloid and hyperboloid, respectively. Any form of the aspheric or spherical surface can be described by aspheric equation, which is expressed as blow:
where c is the conic constant and r is the vertex radius of curvature. The surface type depends on the conic constants, as shown in the Table 2 and Fig. 34.
Table 2 Conic constants and surface types
c (conic constant) Surface type
(a) c > 0
Oblate ellipsoid(b) c = 0
Sphere(c) -1 < c < 0
Ellipsoid(d) c = -1
Paraboloid(e) c < -1
HyperboloidFig. 34 Surface types depending on conic constants in Table 1
Fig. 35 exhibits the hyperboloidal, paraboloidal and spherical surfaces, in which the length l is fixed and the vertex radius of curvature r decreases, where aspect ratio (AR) is defined as below:
AR h
=
l
. (13)Fig. 35 indicates that AR increases as r decreases. The prismatic structure of BEF can be regarded as a hyperboloidal surface shown as Fig. 35(a)(iii), where c = -2 and r is infinitesimal. In the other words, the feature shape is the asymptotes with slope angle of 45°. Therefore, the maximum AR of the hyperboloidal surface with c = -2 is 0.5. In Fig. 35(c), the spherical surface with c of 0 also has the maximum AR of 0.5, which is a hemi-spherical surface (r = l/2). However, the paraboloidal surface does not have the limit of AR because of its parallel asymptotes.
Fig. 35 Examples of spherical and aspheric surfaces as r decreases
The lens shown as Fig. 36(a) is an aspheric lens model, where l is the length on the x-y plane and h is the height along the z axis. Aspect ratio (AR) was defined as the ratio of h to l. The lens surface is sculptured into a square shape to make 100%
fill-factor on the substrate, as shown in Fig. 36(b), where p is the pitch of the square
lens.
Fig. 37(a) is the schematic illustration of a lens array film periodically arranged with square shape. In order to reduce Moiré effect caused by the interference between its periodic structures and TFT array, the lens pitches are randomized as a result the lenses are not square as the periodic arranged one, as shown in Fig. 37(b).
Fig. 36(a) An aspheric surface lens (b) an aspheric surface lens sculptured into square shape
Fig. 37(a) The lens array film arranged by periodic square lens array (b) the lens array film subject to random lens pitches
4.3 Simulations
4.3.1 Periodic Arrangement
The optical function of a periodically-arranged lens array is primarily provided for light collection. The increase of the on-axis intensity along the normal direction is able to explain the light-collecting ability of a film. In general, BEF containing prismatic features is regarded as the best light-collecting component which enhances on-axis intensity achieved to 152%. And conventional diffuser not only scatters light into all directions but also offers about 123% on-axis intensity enhancement, as shown in Fig. 4.
To compare the functions of the lens array film with BEF and diffuser, a backlight was modeled by the optical software, in which the light guide plate was assumed to emit light with Lambertian distribution. In the following angular intensity distribution figures, the x-axis is the viewing angle and the y-axis is the relative radiant intensity.
The dotted line represents the Lambertian distribution light extracting from the light guide plate, in which the maximum intensity is normalized to be 1. In the following simulations, the lenses were classified by conic constants, and the parameter is aspect ratio (AR).
A hyperboloidal lens model whose profiles shown as Fig. 38(a) is formed when conic constant c = -2, in which p = 100um and l = 100 2um. Furthermore, the maximum AR is 0.5. Fig. 38(b) indicates the simulation results of hyperboloidal lens array films (HLAF) with c = -2. The “square symbol” represented by HLAF with AR of 0.5 has the highest relative intensity of 1.41 at viewing angle 0°. As the decrease of AR, the radiant intensity is lower.
Fig. 38(a) The profiles of hyperboloidal surfaces (b) The angular intensity distributions of HLAF with different ARs
Fig. 39(a) The profiles of paraboloidal surfaces (b) The angular intensity distributions of PLAF with different ARs
A paraboloidal surface is formed when c = -1. Fig. 39(b) indicates the simulated performance of angular intensity distribution of paraboloidal lens array films (PLAF) with AR of 0.4, 0.6 and 0.8, whose profiles are shown in Fig. 39(a). The paraboloidal surface does not have the maximum value of AR. As the AR increases to exceed 0.6, the on-axis intensity does not increase. The “square symbol” represented by PLAF with AR of 0.6 has the highest relative intensity of 1.55 at viewing angle 0°.
A spherical surface is formed when c = 0, whose profiles are shown in Fig. 40(a).
The maximum value of AR is 0.5. Fig. 40(b) indicates the simulated performance of angular intensity distribution of spherical lens array films (SLAF). The “square symbol” represented by SLAF with AR of 0.5 has the highest relative intensity of 1.22 at viewing angle 0°. As the decrease of AR, the radiant intensity is lower.
Fig. 40(a) The profiles of spherical surfaces (b) The angular intensity distributions of SLAF with different ARs
Fig. 41 The enhancements in the range of conic constants of -2.5~0.5 and the corresponding ARs
The conic constants of the examples mentioned above are -2, -1 and 0. Then, we will show the simulation results in the range of -2.5~0.5. In Fig. 41, the y-axis is the maximum enhancement of on-axis intensity and the corresponding AR. The x-axis is the conic constants. When conic constants are in the range of -1.4~-0.6 within AR of 0.5~0.7, these lens array films perform the high enhancement of about 1.55. Moreover, the paraboloidal surface located in the range is the applicable lens structure for light collection. Consequently, paraboloidal lens array film with periodic arrangement, which has better on-axis enhancement than conventional diffuser and single sheet of BEF, as shown in Fig. 42, is able to be regarded as a light-collecting component.
Fig. 42 The angular intensity distributions of PLAF compared with conventional diffuser and BEF
4.3.2 Random Arrangement
Moiré effect in the conventional BLM is due to the interaction of the periodic structures of BEFs and the LCD pixels. In order to reduce Moiré effect, randomization of micro-features can alleviate such undesired characteristics [4].
Therefore, PLAF with periodic lens array is reformed as the random arrangement of the lens pitches. PLAF subject to random lens pitches was proposed as the high gain diffuser which diffuses and collimates light simultaneously.
Considering the fabrication of PLAF, the vertex radius of curvature was fixed at 20um. According to the equation (1) and (2), the pitch of PLAF with AR of 0.6 is 68um. The smallest pitch of fabrication is 5um. The randomizing pitches are in the range of 5~68um within uniform distribution. Fig. 11 indicates light-collecting effects among conventional diffuser and PLAFs by the angular intensity distribution.
periodically-arranged PLAF but 9% increase compared with conventional diffuser.
The random arrangement sacrifices the decrease of on-axis enhancement for the reduction of Moiré effect. Furthermore, the random range was not optimized.
Fig. 43 The angular intensity distributions of PLAFs and conventional diffuser
The diffusing ability can be explained by full width at half maximum (FWHM) of light diffusion in bidirectional transmittance distribution function (BTDF). Fig. 44 shows the BTDF of conventional bead-coating diffuser and PLAF subject to random lens pitches. At incident angle 0° shown by the “black solid lines”, FWHM of diffuser is 24° and randomly-arranged PLAF is 36°. In accordance with the comparison, the random arrangement has better diffusing ability than conventional diffuser.
The diffusing ability can be explained by full width at half maximum (FWHM) of light diffusion in bidirectional transmittance distribution function (BTDF). Fig. 44 shows the BTDF of conventional bead-coating diffuser and PLAF subject to random lens pitches. At incident angle 0° shown by the “black solid lines”, FWHM of diffuser is 24° and randomly-arranged PLAF is 36°. In accordance with the comparison, the random arrangement has better diffusing ability than conventional diffuser.