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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1268–1280
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Bidirectional scattering distribution function by screen imaging synthesis

Yeh-Wei Yu, Yen-Lin Chen, Wei-Hsin Chen, Hen-Xiang Chen, Xuan-Hao Lee, Che-Chu Lin, and Ching-Cherng Sun  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 1268-1280 (2012)
http://dx.doi.org/10.1364/OE.20.001268


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Abstract

Light-emitting diodes are common light sources in modern lighting. The optical distribution of an LED package and the bidirectional scattering distribution function (BSDF) of diffusing optical components are important factors in lighting design. This paper proposes an innovative method of measuring both the optical distribution of LEDs and BSDF quickly. The proposed method uses a 2-D screen and a camera to capture the illumination on a screen, and acquires the whole-field optical distribution by synthesizing the images on the screen in different angles. This paper presents theoretical calculations and experimental results demonstrating the construction of the BSDF.

© 2012 OSA

1. Introduction

The development of light-emitting diodes (LEDs) has led to a revolution in modern lighting [1

1. Z. Feng, Y. Luo, and Y. Han, “Design of LED freeform optical system for road lighting with high luminance/illuminance ratio,” Opt. Express 18(21), 22020–22031 (2010). [CrossRef] [PubMed]

5

5. C. H. Tsuei, J. W. Pen, and W. S. Sun, “Simulating the illuminance and the efficiency of the LED and fluorescent lights used in indoor lighting design,” Opt. Express 16(23), 18692–18701 (2008). [CrossRef] [PubMed]

]. To design a high quality lamp, both the light distribution and overall appearance of the lamp are important factors. For example, the materials used in an artistic lamp make a huge difference because they affect properties such as the degree of glare. To simulate the properties of a lamp using software, a database of the optical distribution of LED packages and bidirectional scattering distribution functions (BSDFs) of elements is important [6

6. M. A. Greiner, B. D. Duncan, and M. P. Dierking, “Bidirectional scattering distribution functions of maple and cottonwood leaves,” Appl. Opt. 46(25), 6485–6494 (2007). [CrossRef] [PubMed]

9

9. I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008). [CrossRef] [PubMed]

]. The optical distribution and BSDF can generally be measured by the same instrument, a goniometer [10

10. J. S. Kim, P. K. H. Ho, N. C. Greenham, and R. H. Friend, “Electroluminesence emission pattern of organic light-emitting diodes: Implications for device efficiency calculations,” J. Appl. Phys. 88(2), 1073–1081 (2000). [CrossRef]

, 11

11. S. I. Chang, J. B. Yoon, H. Kim, J. J. Kim, B. K. Lee, and D. H. Shin, “Microlens array diffuser for a light-emitting diode backlight system,” Opt. Lett. 31(20), 3016–3018 (2006). [CrossRef] [PubMed]

]. However, there are some differences between the requirements of these two kinds of measurements. To measure the optical distribution of an LED package, the maximum zenith angle typically must exceed 90°. In BSDF measurement, a zenith angle up to 90° is sufficient for bidirectional transmission distribution function (BTDF) or bidirectional reflection distribution function (BRDF). However, the demands of changing incident angles and the critical system noise make BSDF measurement more complicated.

Most BSDF measurement devices are based on a scanning process. A goniometer has the ability to achieve broad angular coverage. It is common to measure the light scattering properties of samples in directions within the plane of incidence because this configuration requires the least amount of hardware and is the easiest to construct. Because of the 4-D nature of the BRDF [12

12. T. F. Schiff, J. C. Stover, D. J. Wilson, B. D. Swimley, M. E. Southwood, and D. R. Bjork, “Design review of a unique outof- plane polarmetric scatterometer,” in Stray Radiation in Optical Systems II, R. P. Breault, ed., Proc. SPIE 1753, 262–268 (1992).

15

15. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999). [CrossRef]

], instruments capable of out-of-plane measurements tend to be complex. In some cases, instruments are simplified by assuming the surfaces are isotropic, making a three-axis instrument sufficient [16

16. J. C. Martínez-Antón and E. Bernabeu, “Automatic three-dimensional spectrogoniometer for determination of optical properties and surface parameters,” Appl. Opt. 33(25), 6059–6061 (1994). [CrossRef] [PubMed]

]. Even so, the intrinsic property of a goniometer leads to time-consuming measurements. Dana presented a fast system that uses a camera to reduce acquisition time, but hundreds of pictures are necessary because of the dimension limit of the CCD [17

17. K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18(1), 1–34 (1999). [CrossRef]

]. Ward presented an elegant system called Image-sphere, which is very fast. It uses a mirrored hemisphere as a projection surface and a fish-eye lens for image capture [18

18. G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26(2), 265–272 (1992). [CrossRef]

, 19

19. H. Kostal, D. Kreysar, and R. Rykowski, “Application of Imaging Sphere for BSDF Measurements of Arbitrary Materials,” OSA Frontiers in Optics Conference, paper FMJ6 (2008).

]. However, this design is limited by optics and hemispherical geometry at near-grazing angles, and cannot measure light distribution with a zenith angle larger than 85° [20

20. Z. E. M. A. X. Radiant, LLC, “Imaging Sphere for Luminous Intensity measurement” (Radiant ZEMAX, LLC, 2011). http://www.radiantimaging.com/index.php?q=system/files/products/specifications/%5BProduct_Sheet%5D_IS-LI_Imaging_Sphere_110328.pdf

].

The current study provides an innovative measuring method that catches the bright distribution on the screen. The screen is rotated to achieve a broad angular coverge. Because only nine pictures are required, the measuring processs is fast. The new scheme is called screen imaging synthesis (SIS). The SIS instrument is small and can easily be set up in an optical table. This study also presents the method of BTDF measurement. Since the maximum zenith angle achieves 117°, this method can also be used to measure the optical distribution of an LED package. The flexible location of the screen makes it suitable for measuring mid-field distribution of the light source, and thus can be applied to construct an LED light model [21

21. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31(14), 2193–2195 (2006). [CrossRef] [PubMed]

, 22

22. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009). [CrossRef] [PubMed]

].

2. Scatterometer design

2.1 Bidirectional scattering distribution function

The BSDF is the most common form of scattered characterization, and can be used to generate scatter specifications. Figure 1
Fig. 1 Photometric and geometric quantities in the polar coordinate system.
defines BSDF as the ratio of the scattering light radiance (Ls) to the incident light irradiance (Ei) [23

23. J. C. Stover, Optical scattering measurement and analysis (Mc Graw-Hill, 1990).

].
BSDF(θi,ϕi,θs,ϕs)=dLs(θs,ϕs)dEi(θi,ϕi),
(1)
where the terms (θi,ϕi), (θs,ϕs) are the incident and scattering direction angles with respect to the surface normal. To easily express the measured data, this study uses cosine corrected BSDF (CCBSDF), which equals the intensity distribution of the diffuser, and can be expressed as

CCBSDF=cosθsBSDF.
(2)

2. 2 Description of SIS

The principle of SIS can be described as follows. Because it is difficult to detect scattering light at large angle using one screen, several pictures should be taken to cover the whole field scattering of the sample. Figure 2
Fig. 2 The equivalent scheme of the imaging setup: (a) The top view of the architecture; (b) The screens put in nine directions to cover broad angle.
illustrates this concept. Screen 1, Screen 2, and Screen 3 rotate −45°, 0°, and 45°, respectively. The camera then captures the irradiance distribution in the screen (Fig. 2(a)). The data collection range can be larger than ±90°. The screen rotates in 2 dimensions to cover the whole scattering light, where Sij indicates the screen facing a different direction (Fig. 2(b)). The whole field optical distribution is obtained by synthesizing irradiance distribution on screen for different angles.

Figure 3
Fig. 3 The setup of the SIS system.
shows the instrument. During the measurement process, an additional black velvet cover is placed over most of the elements to reduce noise. A coaxial rotator rotates two parts of the elements separately along the same axis. The diffuser is fixed on the central rotator. Mirror 2 (M2), Mirror 3 (M3), Mirror 4 (M4), and Mirror 5 (M5) are fixed on the outside rotator. Figures 4
Fig. 4 Side view of the setup when M3 is used as the directional mirror.
-6
Fig. 6 Side view of the setup when M5 is used as the directional mirror.
show side view schemes of the device. The coordinates attached to the diffuser are defined as (x, y, z), and the coordinates attached to the imaging system are defined as (x’, y’, z’). ϕx’ and ϕy’ are defined as the azimuth angle with respect to x’ axis and y’ axis, respectively. The laser beam reflected by Mirror 1 (M1) propagates along the x’ axis. When M2 rotates along ϕx’, the rotational angle of the laser beam reflected by M2 is the same as the rotational angle of M2. Therefore, no matter how the outside rotator rotates, M2 keeps routing the reflected beam to M3, M4, or M5. Thus, M3, M4, and M5 are directional mirrors (DMs). The laser beam reflected from M3, M4, or M5 tilts −45°, 0°, or 45° along ϕy’, respectively. Accordingly, the diffuser tilts the beam −45°, 0°, or 45° along ϕy’.

Fig. 5 Side view of the setup when M4 is used as the directional mirror.

Figure 7
Fig. 7 Top view for diffuser rotating along ϕx’ (a) −45°, (b) 0°, and (c) 45°, respectively.
shows a top view scheme in which M2, DM, and the diffuser rotate together along φx’. The rotational angle equals 45°, 0°, and −45° in Fig. 7(a), Fig. 7(b), and Fig. 7(c), respectively. Due to the geometry of the setup, the irradiance distribution captured by the camera’s CMOS sensor (Ec) is not equal to the CCBSDF of the sample. To determine the relationship between Ec and CCBSDF, consider Fig. 8
Fig. 8 The geometry of the measurement setup.
. θz’ as the zenith angle with respect to z’.
θz=tan1(x2+y2d1),
(3)
θc is the zenith angle with respect to the normal direction of the camera, and can be expressed as

θc=tan1(x2+y2d2).
(4)

The irradiance distribution on the screen (Es) is

Es(x,y)cos3θzCCBSDF(x,y).
(5)

Consider the scattering light from the screen as Lambertian distribution. For a camera lens with a small f-number, the irradiance distributing on the CMOS sensor of the camera (Ec) is then [24

24. V. N. Mahajan, Optical imaging and aberrations (SPIE PRESS, 1998).

].

Ec(x,y)cos4θcEs(x,y),
(6)

This reveals the relationship between Ec and CCBSDF

CCBSDF(x,y)Ec(x,y)cos4θccos3θz,
(7)

The origin of the coordinate is located at the center of the sample impinged by laser, as Fig. 9
Fig. 9 The geometry of coordinate transformation.
shows. Because each picture is expressed by coordinates (x’, y’, z’) rotating in a particular angle, the coordinate (x’, y’, z’) must be converted to (x, y, z).

When the imaging system rotates ϕx’ and ϕy’, the coordinate transformation is

[xyz]=[cosϕysinϕxsinϕycosϕxsinϕy0cosϕxsinϕxsinϕysinϕxcosϕycosϕxcosϕy][xyz].
(8)

The parameters θx and θy come from the concept of angular spectrum. It is convenient to describe the CCBSDF in 2-D plane by (θx, θy), and it can be transferred from coordinates (x, y, z)

r=x2+y2+z2,
(9)
θx=cos1(xr),
(10)
θy=cos1(yr),
(11)

The coordinate transformation required to describe CCBSDF in spherical coordinate system is

θs=cos1(zr),
(12)
ϕs=tan1(yx).
(13)

3. Measurement

In the measurement, a Verdi cw laser with a wavelength of 532 nm and a beam size of 2.5 mm illuminates the diffuser. The distances of S1 and S2 are equal to 8 cm and 108 cm, respectively, the size of the screen is 25 cm × 45 cm, the camera is a Canon EOS 500d digital camera with a Sigma 17-70 F2.8-4 lens, the focal length of the imaging lens is 57 mm, the F-number of the lens is set as 7.1, the ISO number is set as 100, and the exposure time is 0.5 s. A diffuser, called “Sample A,” serves as the sample. The 25 cm × 45 cm screen produces an angular coverage of ± 117° in the horizontal direction and ± 102° in the vertical direction. However, it is easy to increase the angular coverage in the vertical direction to ± 117° by changing the screen size.

Nine exposures are required to obtain the CCBTDF of a particular incident angle (θi, φi). This study illustrates 3 pictures when M4 is used as the DM and θi is 0°. The captured pictures correspond to S21, S22, and S23 in Fig. 2(b), as shown in Fig. 10(a)
Fig. 10 Pictures taken by camera forϕx equaling to 0°, andϕy equaling to (a)-45°, (b)0°, and (c) 45°.
, 10(b), and 10(c), respectively. The irradiance distributions (Ec) of the pictures are then obtained from the gray level of the pictures using the following equation:
EcClog(255255G),
(14)
where G is the gray level of the picture and C is a constant. Figures 11(a)
Fig. 11 CCBTDF of sample A before coordinate transform.
, 11(b), and 11(c) present the calculation results of CCBTDF(x’, y’) based on Eq. (14) and Eq. (7). These results correspond to Figs. 10(a), 10(b), and 10(c), respectively. Because the angular coverage of each picture overlaps the next, only the central region in each picture is used. As a result, vignetting and distortion aberration are minimized. The red frame in each picture defines the range we are going to use. Figures 12(a)
Fig. 12 CCBTDF of sample A by SIS system.
-12(c) shows the pictures inside the red frame after coordinate transform from (x’, y’) to (θx, θy). Combining these three pictures produces the CCBTDF for θy between −40° and 40° (Fig. 13
Fig. 13 CCBTDF of sample A by SIS system.
). Following the same steps, we take the other six pictures for M3 or M5 used as DM, and finally obtain the whole field CCBTDF (Fig. 14
Fig. 14 CCBTDF of sample A by SIS system.
). In this figure, the spots caused by speckle effect have been removed by low pass filter of the Fourier spectrum.

Based on the isotropic property of the diffuser, it is only necessary to change the incident angle in the zenith direction (θi), and not the azimuth direction (ϕi). This is achieved by setting the difference of rotational angle between central rotator and outside rotator equal to θi. Figure 15
Fig. 15 CCBTDF of sample A by the SIS system for different incident angle: (a) θi = 0°; (b) θi = 10°; (c) θi = 20°; (d) θi = 30°; (e) θi = 40°; (f) θi = 50°; (g) θi = 60°; (h) θi = 70°.
shows the measured CCBSDF for different θi values, indicating that the peak of the scattering light deviates as θi changes.

This study compares the 1-D measurement of a goniometer with the synthetic screen measurement results (Fig. 16
Fig. 16 1-D Comparison of sample A between measurement by uni-planar goniometer and the SIS system: (a) θi = 0°; (b) θi = 10°; (c) θi = 20°; (d) θi = 30°; (e) θi = 40°; (f) θi = 50°; (g) θi = 60°; (h) θi = 70°.
) to confirm the accuracy of the proposed method. The black curve represents the goniometer measurement, and the red curve represents the SIS system measurement. The curves of these two measuring methods are similar.

4. Simulation with the measured BSDF

To demonstrate the usability of the SIS system, this study uses the measured BSDF to simulate the appearance when staring at the lamp. The simulations in this study use ASAP, which is a ray-tracing analysis program. Figure 17
Fig. 17 The setup used to simulate looking into the lamp through the covering diffusing media.
shows the setup used to simulate this condition. Four Cree XP-E LEDs were placed in front of the diffuser, and a lens with F-number 4.5 was used to image the lamp on the CMOS sensor. Figure 18
Fig. 18 Three diffuser samples for (a) Sample A, (b) Sample B, and (c) Sample C.
shows three samples placed over words, indicating that the contrast of the words decreases as the diffusion of the sample increases. These samples are labeled as Sample A, Sample B, and Sample C. The BSDF of these samples measured by the SIS system were also simulated using ASAP. Figure 19
Fig. 19 The simulation results of ASAP based on the SIS system for (a) Sample A, (b) Sample B, and (c) Sample C.
shows the simulation results. Comparing these images with the experimental results in Fig. 20
Fig. 20 The experimental results for (a) Sample A, (b) Sample B, and (c) Sample C.
shows that the SIS system can successfully predict optical performance.

5. Conclusion

This paper proposes a new architecture, called the SIS system, to measure the light pattern or BSDF of a light source or scattering object. Unlike a traditional scatterometer, this approach synthesizes the images of the screen in different rotational angles. The proposed SIS system requires only 9 pictures to achieve broad angular coverage, speeding up the acquisition process. The maximum zenith angle is up to 117°, which enables the SIS system to measure both the BSDF of elements and the light distribution of the LED package. This study describes the proposed synthesis method step-by-step, and confirms the accuracy of the SIS system by comparing it with a goniometer. The 1-D measurement results are quite similar. Finally, based on the Monte Carlo software ASAP, the simulations in this study present a real case with the diffusers equipped with measured BSDF. Compared with experimental measurements, the simulation results are good enough for an engineer to determine the illumination conditions with the BSDF by the SIS system.

Acknowledgment

References and links

1.

Z. Feng, Y. Luo, and Y. Han, “Design of LED freeform optical system for road lighting with high luminance/illuminance ratio,” Opt. Express 18(21), 22020–22031 (2010). [CrossRef] [PubMed]

2.

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18, 20960–20983 (2010). [PubMed]

3.

S. Wang, K. Wang, F. Chen, and S. Liu, “Design of primary optics for LED chip array in road lighting application,” Opt. Express 19(S4Suppl 4), A716–A724 (2011). [CrossRef] [PubMed]

4.

Z. M. Zhu, X. H. Qu, G. X. Jia, and J. F. Ouyang, “Uniform illumination design by configuration of LED array and diffuse reflection surface for color vision application,” J. Disp. Technol. 7(2), 84–89 (2011). [CrossRef]

5.

C. H. Tsuei, J. W. Pen, and W. S. Sun, “Simulating the illuminance and the efficiency of the LED and fluorescent lights used in indoor lighting design,” Opt. Express 16(23), 18692–18701 (2008). [CrossRef] [PubMed]

6.

M. A. Greiner, B. D. Duncan, and M. P. Dierking, “Bidirectional scattering distribution functions of maple and cottonwood leaves,” Appl. Opt. 46(25), 6485–6494 (2007). [CrossRef] [PubMed]

7.

J. F. Murray-Coleman and A. M. Smith, “The automated measurement of BRDFs and their application to luminaire modelling,” J. Illum. Eng. Soc. (1990).

8.

W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express 15(12), 7572–7577 (2007). [CrossRef] [PubMed]

9.

I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16(3), 1808–1819 (2008). [CrossRef] [PubMed]

10.

J. S. Kim, P. K. H. Ho, N. C. Greenham, and R. H. Friend, “Electroluminesence emission pattern of organic light-emitting diodes: Implications for device efficiency calculations,” J. Appl. Phys. 88(2), 1073–1081 (2000). [CrossRef]

11.

S. I. Chang, J. B. Yoon, H. Kim, J. J. Kim, B. K. Lee, and D. H. Shin, “Microlens array diffuser for a light-emitting diode backlight system,” Opt. Lett. 31(20), 3016–3018 (2006). [CrossRef] [PubMed]

12.

T. F. Schiff, J. C. Stover, D. J. Wilson, B. D. Swimley, M. E. Southwood, and D. R. Bjork, “Design review of a unique outof- plane polarmetric scatterometer,” in Stray Radiation in Optical Systems II, R. P. Breault, ed., Proc. SPIE 1753, 262–268 (1992).

13.

M. T. Beecroft, J. T. Neu, and J. Jafolla, “Bidirectional reflectance data to support paint development and signature calculations,” in Stray Radiation in Optical Systems II, R. P. Breault, ed., Proc. SPIE 1753, 304–316 (1992).

14.

D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37(16), 3450–3454 (1998). [CrossRef] [PubMed]

15.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999). [CrossRef]

16.

J. C. Martínez-Antón and E. Bernabeu, “Automatic three-dimensional spectrogoniometer for determination of optical properties and surface parameters,” Appl. Opt. 33(25), 6059–6061 (1994). [CrossRef] [PubMed]

17.

K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18(1), 1–34 (1999). [CrossRef]

18.

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26(2), 265–272 (1992). [CrossRef]

19.

H. Kostal, D. Kreysar, and R. Rykowski, “Application of Imaging Sphere for BSDF Measurements of Arbitrary Materials,” OSA Frontiers in Optics Conference, paper FMJ6 (2008).

20.

Z. E. M. A. X. Radiant, LLC, “Imaging Sphere for Luminous Intensity measurement” (Radiant ZEMAX, LLC, 2011). http://www.radiantimaging.com/index.php?q=system/files/products/specifications/%5BProduct_Sheet%5D_IS-LI_Imaging_Sphere_110328.pdf

21.

C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31(14), 2193–2195 (2006). [CrossRef] [PubMed]

22.

C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009). [CrossRef] [PubMed]

23.

J. C. Stover, Optical scattering measurement and analysis (Mc Graw-Hill, 1990).

24.

V. N. Mahajan, Optical imaging and aberrations (SPIE PRESS, 1998).

OCIS Codes
(000.2700) General : General science
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation

ToC Category:
Optical Devices

History
Original Manuscript: November 7, 2011
Revised Manuscript: December 20, 2011
Manuscript Accepted: December 20, 2011
Published: January 5, 2012

Citation
Yeh-Wei Yu, Yen-Lin Chen, Wei-Hsin Chen, Hen-Xiang Chen, Xuan-Hao Lee, Che-Chu Lin, and Ching-Cherng Sun, "Bidirectional scattering distribution function by screen imaging synthesis," Opt. Express 20, 1268-1280 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1268


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References

  1. Z. Feng, Y. Luo, and Y. Han, “Design of LED freeform optical system for road lighting with high luminance/illuminance ratio,” Opt. Express18(21), 22020–22031 (2010). [CrossRef] [PubMed]
  2. F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express18, 20960–20983 (2010). [PubMed]
  3. S. Wang, K. Wang, F. Chen, and S. Liu, “Design of primary optics for LED chip array in road lighting application,” Opt. Express19(S4Suppl 4), A716–A724 (2011). [CrossRef] [PubMed]
  4. Z. M. Zhu, X. H. Qu, G. X. Jia, and J. F. Ouyang, “Uniform illumination design by configuration of LED array and diffuse reflection surface for color vision application,” J. Disp. Technol.7(2), 84–89 (2011). [CrossRef]
  5. C. H. Tsuei, J. W. Pen, and W. S. Sun, “Simulating the illuminance and the efficiency of the LED and fluorescent lights used in indoor lighting design,” Opt. Express16(23), 18692–18701 (2008). [CrossRef] [PubMed]
  6. M. A. Greiner, B. D. Duncan, and M. P. Dierking, “Bidirectional scattering distribution functions of maple and cottonwood leaves,” Appl. Opt.46(25), 6485–6494 (2007). [CrossRef] [PubMed]
  7. J. F. Murray-Coleman and A. M. Smith, “The automated measurement of BRDFs and their application to luminaire modelling,” J. Illum. Eng. Soc. (1990).
  8. W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express15(12), 7572–7577 (2007). [CrossRef] [PubMed]
  9. I. Moreno and C. C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express16(3), 1808–1819 (2008). [CrossRef] [PubMed]
  10. J. S. Kim, P. K. H. Ho, N. C. Greenham, and R. H. Friend, “Electroluminesence emission pattern of organic light-emitting diodes: Implications for device efficiency calculations,” J. Appl. Phys.88(2), 1073–1081 (2000). [CrossRef]
  11. S. I. Chang, J. B. Yoon, H. Kim, J. J. Kim, B. K. Lee, and D. H. Shin, “Microlens array diffuser for a light-emitting diode backlight system,” Opt. Lett.31(20), 3016–3018 (2006). [CrossRef] [PubMed]
  12. T. F. Schiff, J. C. Stover, D. J. Wilson, B. D. Swimley, M. E. Southwood, and D. R. Bjork, “Design review of a unique outof- plane polarmetric scatterometer,” in Stray Radiation in Optical Systems II, R. P. Breault, ed., Proc. SPIE 1753, 262–268 (1992).
  13. M. T. Beecroft, J. T. Neu, and J. Jafolla, “Bidirectional reflectance data to support paint development and signature calculations,” in Stray Radiation in Optical Systems II, R. P. Breault, ed., Proc. SPIE 1753, 304–316 (1992).
  14. D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt.37(16), 3450–3454 (1998). [CrossRef] [PubMed]
  15. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum.70(9), 3688–3695 (1999). [CrossRef]
  16. J. C. Martínez-Antón and E. Bernabeu, “Automatic three-dimensional spectrogoniometer for determination of optical properties and surface parameters,” Appl. Opt.33(25), 6059–6061 (1994). [CrossRef] [PubMed]
  17. K. J. Dana, B. van Ginneken, S. K. Nayar, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph.18(1), 1–34 (1999). [CrossRef]
  18. G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph.26(2), 265–272 (1992). [CrossRef]
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