Display Reflectance Model Based on the BRDF

Many flat panel displays (FPDs) have anti-reflection surface treatments that differ in character from those of traditional cathode-ray-tube displays. Specular reflection models (mirror-like, producing a distinct image) combined with diffuse (Lambertian) reflection models can be entirely inadequate to characterize the reflection properties of such displays. A third reflection component, called haze, exists between specular and diffuse. Display metrology should account for the haze component of reflection. That is best done using the bidirectional reflectance distribution function (BRDF). The effects of using oversimplified reflectance models are discussed in contrast with a parameterized BRDF. INTRODUCTION: Flat panel displays (FPDs) can have reflection properties that differ substantially from their cathode-raytube (CRT) counterparts. In the case of the CRT, the necessity of the thick front glass prevents strongly diffusing surface treatments from being used on the front surface. Such treatments, distant from the pixel surface, would compromise readability. With FPDs the front surface can be very close to the pixel surface, permitting surfaces that substantially diffuse incident light without seriously compromising the display’s resolution. (This is easy to see: Take wax paper and hold it about 1 cm above some text; compare the readability for that configuration with the readability when the wax paper is placed directly upon the text.) Therefore, CRTs are often made with very mild surface treatments to diffuse the specular light, but their surfaces cannot be as diffusing as those that can be used with some FPDs. Because strongly diffusing surfaces can be used in connection with FPDs, conventional reflection measurement techniques used to characterize display reflection for CRTs may well prove to be inadequate or, at the very least, irreproducible when applied to all FPDs. In this paper, when we refer to diffuse reflectance, we refer to an ideal Lambertian reflector that obeys the relation: L = qE = Ed /, (1) where L is the luminance, E is the illuminance, q = d / is the luminance coefficient, and d is the diffuse (Lambertian) reflectance. That is, the luminance is independent of direction. When we refer to specular reflection, we mean mirror-like reflection that produces a distinct virtual image of the source where the reflected luminance L is related to the source luminance Ls by: L = s Ls, (2) where s is the specular reflectance. A more general way to describe reflection is through the bidirectional reflectance distribution function (BRDF). It is the differential form of Eq. 1 and will be developed in the next section. Using the BRDF, we can account for the above specular and diffuse (Lambertian) properties, but also understand a third type of reflection that exists between the two extremes of specular and diffuse (Lambertian) reflection. This third component of reflection is quickly identified by the eye when it views electronic displays. For want of a better term we will call it haze (see ASTM E284 1 and D-4449 2 ). Haze reflection is similar to diffuse (Lambertian) reflection in that it depends upon the illuminance (source-display distance), whereas it is similar to specular reflection in that the luminance is peaked in the specular direction. In Fig. 1 we show drawings of the three types of reflection and their combinations. Using a bare bulb of a flashlight placed 200 mm or more in front of the screen, the significant components of the reflection are easily observed and appear distinct from one another. The diffuse (Lambertian) component is seen as an overall gray, as if it were a dark-gray matte paint, slightly brighter where the screen is nearest the source and gradually darker near the edges of the display because of the 1/r 2 falloff in illuminance. The specular (mirror-like) component is the virtual image of the point source seen in the display surface. The haze component is the distinct fuzzy ball of light that surrounds the specular image. Sometimes the