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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 Optical Society of America
1. Introduction
The development of light-emitting diodes (LEDs) has led to a revolution in modern lighting [1–5]. 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 [6–9]. The optical distribution and BSDF can generally be measured by the same instrument, a goniometer [10, 11]. 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 [12–15], 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]. 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]. 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, 19]. 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].
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, 22].
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 defines BSDF as the ratio of the scattering light radiance (Ls) to the incident light irradiance (Ei) [23].
where the terms (), () 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 as2. 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 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.
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.
Figure 3 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 -6 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’). x’ and y’ 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 x’, 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 y’, respectively. Accordingly, the diffuser tilts the beam −45°, 0°, or 45° along y’.
Figure 7 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 . θz’ as the zenith angle with respect to z’.
θc is the zenith angle with respect to the normal direction of the camera, and can be expressed asThe irradiance distribution on the screen (Es) is
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].
This reveals the relationship between Ec and CCBSDF
The origin of the coordinate is located at the center of the sample impinged by laser, as Fig. 9 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 x’ and y’, the coordinate transformation is
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)
The coordinate transformation required to describe CCBSDF in spherical coordinate system is
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) , 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:
where G is the gray level of the picture and C is a constant. Figures 11(a) , 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) -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 ). 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 ). 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 (i). This is achieved by setting the difference of rotational angle between central rotator and outside rotator equal to θi. Figure 15 shows the measured CCBSDF for different θi values, indicating that the peak of the scattering light deviates as θi changes.
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°.
This study compares the 1-D measurement of a goniometer with the synthetic screen measurement results (Fig. 16 ) 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.
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°.
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 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 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 shows the simulation results. Comparing these images with the experimental results in Fig. 20 shows that the SIS system can successfully predict optical performance.
Fig. 19 The simulation results of ASAP based on the SIS system for (a) Sample A, (b) Sample B, and (c) Sample C.
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
This study was sponsored by the National Science Council of the Republic of China under contracts 97-2221-E-008-025-MY3, 99-2623-E-008-002-ET, 99-2221-E-008-047, and NSC100-3113-E-008-001.
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