Modified point spread function for efficient high dynamic range LED backlight capable of high uniformity, high contrast, and smooth gradients Jakob Emmel and Lorne A. Whitehead* Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada *Corresponding author: [email protected] Received 11 September 2013; revised 18 October 2013; accepted 25 October 2013; posted 28 October 2013 (Doc. ID 197349); published 25 November 2013

We investigate the effect of new point spread functions (PSFs) on the uniformity and contrast of high dynamic range displays that use local dimming of LEDs to yield a large dynamic range. A PSF shaped like a quadratic B-spline was hypothesized to create a uniform brightness backlight, as well as producing linear and quadratic gradients, while maintaining a very high contrast. We have found a practical optical structure to produce such a PSF, yielding a nonuniformity of only 0.8%, while enabling a contrast ratio of 5∶1 and 33∶1 over distances of one and two unit cell spacings, respectively. © 2013 Optical Society of America OCIS codes: (230.3670) Light-emitting diodes; (120.2040) Displays; (080.2720) Mathematical methods (general); (150.2950) Illumination. http://dx.doi.org/10.1364/AO.52.008239

1. Introduction

In typical liquid crystal displays (LCDs), roughly 90% of the consumed power is used in backlighting [1]. Existing methods to improve backlighting efficiency include global backlight dimming [1], whereby the whole backlight becomes dimmer for darker scenes, and local dimming of an array of lightemitting diodes (LEDs), whereby individual LEDs can be dimmed in localized dark image areas [2–5]. The latter method has the additional benefit that images with enhanced contrast can be shown on the screen. Displays using this individual LED dimming approach are one method of making so called “high dynamic range” (HDR) displays (completely different methods might use emissive displays with a 16 bit driving scheme). 1559-128X/13/348239-06$15.00/0 © 2013 Optical Society of America

However, to achieve this high contrast, the uniformity of the backlight luminance created by the LEDs may be sacrificed. We have developed a solution to the problem by modifying the point spread function (PSF), which is the luminance pattern on the screen created by one LED. This intrinsic PSF falls off very slowly over distance, limiting the local contrast. The shape of the PSF also makes a uniform backlight impossible. This means that, when displaying an image with spatially uniform luminance levels, a pattern caused by periodic placement of the LEDs, or by shadows of separation walls, is perceptible within the image. In an LED array, this new PSF can theoretically yield a constant luminance value across the screen. At the same time, the PSF decreases rapidly to zero over a short distance, which improves the contrast of the display. This new PSF solves the intrinsic tradeoff between uniformity and contrast found in stateof-the-art HDR displays, and can also produce 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS

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smooth linear and quadratic luminance gradients. It is desirable to produce such uniform lighting features without requiring inefficient diffusion or large spacings between the LEDs and the diffuser [6,7]. 2. Background

In an HDR display, the backlight LEDs are located behind the LCDs. Displays with such an array of LEDs can yield contrasts of 250; 000∶1 [3], about two orders of magnitude greater than ordinary LCD displays with uniform backlights. The contrast reported in [3] is comparable to the dynamic range covered by the human eye. This means that an HDR display is able to show images with a luminance range that faithfully reproduces actual scenes. A PSF describes spatial luminance distribution on a screen, coming from a point source. If only one LED is illuminated in an HDR display, a circular patch of light with a bright center would be visible on the screen. This is the PSF of one LED. Without taking into account back reflections from diffusers or reflective polarizers, the rotationally invariant PSF of a Lambertian emitter, like an LED, can be described by the following equation:  2 a Ix  cos2 θ p  cos4 θ: a2  x2

3. Quadratic B-spline as Point Spread Function

In this paper, a new idea is presented—the use of a quadratic B-spline as an optical PSF. These piecewise connected polynomials are commonly used in signal processing or image up-sampling [13], but have never been used as PSFs in HDR displays. In one dimension, the function can be defined with these connecting polynomials, where x is in unit spacings: for for for

1 3 jxj ≤ ∶ f x  − x2 2 4   1 3 1 3 2 < jxj ≤ ∶ f x  jxj − 2 2 2 2 3 jxj > ∶ f x  0: 2

(2)

(1)

In Eq. (1), a stands for the fixed distance between the LED and the screen, and x denotes the position on the screen in one dimension. One cosine factor results from the fact that LEDs are approximately Lambertian emitters, and a second cosine is required since the light strikes the screen with the angle θ. In Eq. (1), the light falloff over large distances is governed by the inverse–square law and the two cosine factors. In HDR displays, the addition of diffuser sheets and reflective polarizers substantially increases the area of a PSF. This decreases the local contrast, since dark areas of the screen are still illuminated by distant bright LEDs. The PSF’s slow decrease toward zero also increases the number of LEDs that need to be taken into account when the nonuniformity of the backlight is computationally corrected by the front LCD [2,8]. For compensation by the front LCD, the backlight luminance for every pixel of the front screen (2.1 megapixel on a screen with 1080 p or 1080 i standard), needs to be calculated in real-time. A PSF that slowly decreases with distance to zero, increases the number of LEDs that are involved in this calculation. For a standard HDR screen, the calculation involves thousands of LEDs, which is difficult to do in real-time. It is known that uniformity can be improved by modifying the PSF [9–12]. Some authors have argued that a square step function is the optimal PSF [9,10]. In this case, the PSFs are not overlapping and each PSF is constant in its respective area. Work has been done on reasonable approximations of these step 8240

functions [11,12]. However, these nonoverlapping PSFs, with constant luminance, cannot produce smooth luminance gradients. Instead, discrete luminance steps are provided by the backlight. Artifacts caused by abrupt changes in the backlight are difficult to compensate using the front LCD, due to possible alignment and parallax issues.

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This PSF has three major benefits. First, it improves the local contrast, since the light from one LED falls off to zero after 1.5 unit spacings (see Fig. 1). Second, according to these equations, using an LED spacing of 1 unit causes the sum of all contributing LEDs to be constant across the screen. Third, if the output of each LED is tuned to be linearly increasing from one LED to the next, in theory, a perfectly linear luminance gradient can be created. This approach also works for a quadratic increase of LED outputs, which yields a perfectly quadratic luminance gradient. These constant, linear, and quadratic behaviors for a linear arrangement of seven LEDs are shown in Fig. 2. Imperfect edge effects can be seen in the areas of the first and the last unit spacing. A 2D version of this conceptual approach can be described by the following equation:

Fig. 1. 1D PSFs: quadratic B-spline (solid) and PSF of a Lambertian emitter (dotted) with the same full width at half-maximum.

Fig. 2. 1D luminance of seven LEDs with a quadratic B-spline as PSF. A uniform luminance level (solid) was achieved as well as perfectly linear (dashed) and quadratic (dotted) gradients.

f x; y  f xf y:

(3)

This multiplicative separable function is not rotationally symmetric, nor would we expect it to be, given the rectangular geometry of the LED array. With this 2D PSF and an array of LEDs located on a square grid with spacing of 1, a completely uniform screen is yielded. In addition, perfectly linear and quadratic gradients can be shown in any direction, not only along the x or y axis of the LED grid. This last feature is another advantage over all other methods of creating an HDR backlight, because many pictures contain linear and quadratic gradients, in arbitrary orientations and lengths, across a few pixels, or the whole screen. To evaluate this approach for modifying the PSF of an LED to a quadratic B-spline, we built a backlight consisting of a 4 × 5 array of LED modules with a unit spacing of 10 cm (see Fig. 3). The PSF of every LED was modified by a filter at a distance of 24 mm, which had a spatially variable transmission pattern. In addition, opaque baffles were placed in between the LEDs. All interior surfaces were painted black to reduce reflections. The screen was an acrylic bulk diffuser with 53% transmission at a distance of 76 mm from the LEDs. In the uniform state, with all LEDs outputting the same flux, we measured the luminance along a line scan across the diffuser screen and determined that there was a small oscillation pattern (called “contrast modulation”) with an amplitude of 1.3% overlaying the constant luminance level of 1. The wavelength of this modulating pattern was 10 cm, which corresponds to the spacing between the LEDs. After

Fig. 3. Schematic of a setup that creates PSFs on the screen. The PSFs have the shape of quadratic B-splines in the x and y directions. The walls between the LEDs were opaque to confine the light within the corresponding area on the screen. The filters consisted of a gray-scale pattern with spatially variable transmission to change the original PSF of the LEDs into the new shape.

adjusting the LED output to yield the desired gradients, we determined the relative root mean square (RMS) errors from the perfectly linear and quadratic gradients to be 2% and 2.1%, respectively. Some light leakage and back reflections from the diffuser screen caused the experimental PSF to be slightly different from the quadratic B-spline shape, which explains the measured imperfections. Since the filters and the baffles absorbed most of the light, the overall efficiency of the backlight (flux output of screen divided by flux of LEDs) was only 20%. These results show that it is difficult to create a PSF that matches the shape of the quadratic B-spline exactly, even in a highly absorptive environment. Since reflective materials tend to cause more light leakage and unwanted reflections, it would be even harder to create a good match in a highly reflective setup. 4. New Backlight Principle and Simulation

Our goal was to increase the efficiency, thus we tried to find a PSF that had similar characteristics to a quadratic B-spline and could be produced using a more practical and efficient optical structure. With this requirement in mind, we developed a theoretical model. In this new scheme, every backlight module consisted of a light-emitting plane (LEP) parallel to the screen, with certain predetermined luminance values across the LEP. There were opaque baffles between these modules. The height of the baffles was set to half the distance between the LEP and the screen. With this system, different PSFs could be created by different luminance patterns on the LEP. To find the best possible PSF, a simulation was created to calculate the PSF on the screen for a given luminance pattern on the LEP (see Fig. 4). The emitting luminance pattern Ex; y and the intensity pattern Ix; y on the screen were pixelated. We computationally simulated this system with specially developed ray-tracing software. With this program, rays were traced from each pixel on the LEP to each pixel on the screen. Since we assumed Lambertian emission by the LEP, the intensity deployed on Ix; y by each ray was calculated based on Eq. (1) and then the contributions of all rays were added to form the final intensity pattern. Rays that hit the opaque baffles were absorbed.

Fig. 4. Schematic side view of simulation setup. Through raytracing, the simulation determined the intensity pattern on the screen caused by a given luminance distribution of the source plane. Ex; y is the pixelated light emission plane (LEP) of one unit spacing and Ix; y is the pixelated intensity function of incident light on the screen at distance d. The width of Ix; y is three unit spacings. Opaque baffles of height d∕2 surround Ix; y. 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS

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In a first test, the emitting luminance pattern Ex; y was simulated as a 10 × 10 matrix. Due to the fourfold symmetry along the x and y axes, as well as along the diagonals, the number of variables is reduced from 100 to 15. In addition, the distance between the LEP and the screen was kept variable. Once Ex; y had been determined for a given Ix; y, this PSF was used to calculate the output of a backlight array in three different cases: (i) all LEDs having the same flux output, (ii) their output increases linearly in one direction, and (iii) their output increases quadratically in one direction. The relative RMS errors for these three cases (Δuni , Δlin , and Δquad for uniform brightness, linear, and quadratic gradients, respectively) were determined and combined into the following error function: F  Δ2uni  Δ2lin  Δ2quad 1∕2 :

(4)

The 16 variables were optimized by a MATLAB Pattern Search procedure to minimize the error function F. On a standard desktop PC, the optimization converged within a few minutes to a value of F  1.5% at a screen distance of 0.68 unit spacings. To make sure we were using sufficient resolution, we increased the resolution of Ex; y to 20 × 20 pixels; however, the final value of the error function was not substantially lower, at F  1.4%. The optimization described here can be used in a wide range of applications. When different luminance characteristics on the screen are desired, the error function needs to be adjusted.

We produced such a filter by using a bulk diffuser sheet having spatially varying thickness. Thinner sections transmitted more light than thicker sections, which reflected most of the light. To experimentally fabricate such structures, we formed patterned apertures within a stack of ten high-transmission diffuser sheets (each being 1 mm thick, with a transmission of 80%), to increase the transmission at selected locations. To enable very low transmission levels, we also included two sheets of white paper having a transmission of only 20%. The spatial varying transmission values of the filter were measured and then corrected by an absorptive filter that absorbed small amounts of extra light at each pixel position to ensure the transmission goals were met accurately (see Fig. 6). Given that the mathematical model had not included any internal reflections, we expected that the discrepancy between simulation and measurement would increase for more efficient reflective setups. Therefore, we developed a new approach to find the best PSF possible with this setup. As mentioned earlier, the 10 × 10 pixelated luminance pattern had 15 independent variables. Based on these variables, we created 15 black filters with holes corresponding to each variable (see Fig. 7). For each such filter we measured the luminance pattern. In MATLAB, we created a PSF through a linear combination of these 15 sub-patterns. We then changed the PSF by varying the 15 linear combination

5. Experimental Verification of a Practical PSF

The first step was to physically emulate the system described above. For the LEP with different luminance values, we used a uniform light box and added a calibrated filter on which a 10 × 10 gray scale matrix was printed (see Fig. 5). The LEP was surrounded by black baffles. A layer of neutral density filter was also added to reduce the amount of back reflections from the diffuser screen, which had not been simulated. The agreement between the simulated and the measured PSF was sufficient to take the next step: using a nonabsorbing (and hence, reflective) filter.

Fig. 5. Setup to verify simulation: 10 cm × 10 cm LEP made with a uniform backlight with a diffuser and an absorptive filter. 8242

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Fig. 6. Setup of reflective variable transmission filter, consisting of a stack of paper and diffuser films with holes. The more diffuse material at a given position, the lower the transmission.

Fig. 7. Fifteen calibration filters. Filters were black with hole positions based on horizontal, vertical, and diagonal symmetry of the system.

coefficients and optimized it by minimizing Eq. (4). A linear combination coefficient of 0 meant no light transmission, a coefficient of 1 meant highest transmission. We used this method for the next setup, where we used a single LED in a highly specular reflective cavity (25 mm × 25 mm, 3.25 mm high, R  98.5%). This backlight illuminated an almost Lambertian acrylic diffuser (t  2.75 mm, T  53%), which ensured an almost constant luminance when measured from an angle. The baffles were covered with retroreflective corner-cubes to recycle the light hitting them. When the 15 sub-patterns were measured and the PSF was optimized in MATLAB, the result was that only the 4 center pixels were needed to produce the best PSF. That meant that in this particular case we did not need a continuously variable transmission filter. Instead, reducing the size of the LED cavity to the size of the 4 center pixels (5 mm × 5 mm) gave the best result. Given this result, a new backlight was built with 5 columns of 3 LEDs with a spacing of 25 mm. Each column was dimmable in order to create gradients. The thickness of the backlight modules, including the LED backplane and the screen, was 34 mm.

Fig. 9. Data points extracted from line scans across the screen of the backlight, showing the linear gradient setting (circle) and the quadratic gradient setting (cross). The lines are fits using first (linear) and second (quadratic) order polynomials. The fractional RMS error between the measured line scans and the fits are 1.6% (linear) and 1.8% (quadratic).

6. Measurements and Simulations

Using a calibrated CCD camera positioned at normal angle, we measured the luminance distribution in several cases. With all LEDs of the backlight emitting the same flux we measured a contrast modulation of 0.8% and relative RMS error of 0.6% for a line scan along the longer axis (see Fig. 8). The RMS errors were also determined for the linear (1.6%) and quadratic (1.8%) gradients (see Fig. 9). The light falloff, a measure of the local contrast, is shown in Fig. 10. For this measurement only one column of LEDs was switched on. A contrast of 5∶1 was found at the location of the next LED and a contrast of 33∶1 at the distance of 2 unit spacings. The exponential character of this falloff can be seen by the

Fig. 8. Variation on the “uniform” screen of the backlight measured from normal angle. The line scan has a fractional RMS deviation of 0.6%. A cosine function was fitted to the data (solid) to determine a contrast modulation of 0.8%.

Fig. 10. Line scan demonstrating decrease of light level with increasing distance from the LED (dashed). The active LED is positioned at ‘0’. The solid line is plotted on a logarithmic scale, which is shown on the axis on the right-hand side. The linearity of these data suggested an exponential drop of the light level.

linearity of the data when plotted on a logarithmic scale (see Fig. 10). Another way to show the local contrast is by measuring the flux transfer from one backlight module to its neighbor modules (sideways and diagonal). We determined the flux transfer with (a) retro-reflective and (b) opaque baffles. With this information, we simulated the two different light falloffs in a larger display and compared it to the theoretical falloff of an LED, which is placed on a perfect reflector. A diffuser screen with Lambertian reflectance of 50% is added at the same distance as in the previously discussed backlight setup (20 mm). This situation mimics the backlight without baffles. The results in Fig. 11 show that the best contrast can be achieved with black baffles, but the retro-reflective baffles still represent a substantial improvement over the case without baffles. The efficiency of the backlight was measured to be 60.9% with retro-reflective baffles and 25% with 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS

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a few dozen LEDs. In the latter case, a uniform screen can be achieved with a limited number of LEDs without losing the capability of local dimming and smooth gradients. The next steps could be to combine this new backlight with a high-definition LCD screen to measure its performance under more realistic conditions. References

Fig. 11. Based on measurements of the small backlight, the flux transfer from one LED module to the next was determined, and a larger display was simulated. The given scenario is that one LED at position 0 is switched on and the amount of flux which traveled to a distant module is shown in the graph. The triangle data points show the flux transfer for a backlight with opaque baffles; the crosses are data points for the same backlight with retro-reflective baffles; and the round data points show the simulation results for a backlight without baffles.

opaque baffles. These efficiencies were verified using the ray-tracing software TracePro. For this verification, a CAD model of the two setups was created. With reasonable surface properties, efficiencies were found that agreed with the measured efficiencies. 7. Conclusions

It has been shown that a new backlight configuration producing a new PSF is efficient, uniform, and can show smooth gradients. Due to rapid light falloff, the image processing necessary for HDR displays based on such a backlight would be reduced by about one order of magnitude. The new design is sufficiently thin for a direct-LED backlight and is, therefore, suitable for large-scale use. These advantages may help make HDR displays more useful in a wide range of applications, such as medical technologies and movie editing. The fact that the backlight modules are easily scalable makes them applicable for high-end displays, with unit spacings of only a few millimeters, as well as for low-cost displays with only

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Modified point spread function for efficient high dynamic range LED backlight capable of high uniformity, high contrast, and smooth gradients.

We investigate the effect of new point spread functions (PSFs) on the uniformity and contrast of high dynamic range displays that use local dimming of...
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