Lambertian surface

Under the typical summertime conditions, the thinner cloud shows an increase of 65% in the actinic flux above the cloud whereas the thicker cloud shows an increase of almost a factor of three, the maximum theoretically possible. This is due to scattering of diffuse light from the top of the cloud, as well as from the ground. As expected, below the thicker cloud, the total actinic flux is reduced, in this calculation, to 19% of the clear-sky value. However, for the thinner cloud of optical density 8, the actinic flux below the cloud is actually calculated to be greater than for the cloudless case. This occurs in the case of a small solar zenith angle and direct (rather than diffuse) incident light because the direct incident light is diffused as it traverses the cloud as discussed earlier for the case of the actinic flux above a Lambertian surface, conversion of a direct to diffuse source leads to an enhancement in the actinic flux. 

If we know the BRDF of the material of the viewed object, then we can compute the radiance using the preceding equation. We will now have a look at the BRDF for two idealized surfaces, a Lambertian surface and a perfect mirror. Let us address the BRDF of a perfect mirror first. If the incident light is coming from direction (9l, [Pg.54]

Let us now turn to a Lambertian surface. A Lambertian surface reflects the incident light equally in all directions. The radiance given off by matte objects can be approximated using the BRDF of a Lambertian surface. If the irradiance is reflected equally in all directions,... 

This BRDF allows us to compute the radiance given off by a Lambertian surface illuminated by a point light source. 

Macbeth 5000 K fluorescent, a Philips Ultralume fluorescent, and a Sylvania Cool White fluorescent tube. Some color constancy algorithms try to find out what type of illuminant produced the particular color sensation, which was measured by the sensor. If we measure the entire power spectrum for a particular patch of our object and also know the type of illuminant used, then it is easy to compute the BRDF. Let L(X) be the measured power spectrum and let E A.) be the power spectrum of the illuminant. Assuming a Lambertian surface, where the BRDF is independent of the normal vector of the patch Nobj, and also independent of the normal vector that points to the direction of the light source Ni, we... 

The factor due to the scene geometry does not depend on the position of the viewer relative to the object, i.e. we have a Lambertian surface. 

In particular, for any two Lambertian surfaces (surfaces that emit or reflect with an intensity independent of angle, a condition approximately satisfied by most nonmetallic, tarnished, oxidized, or rough surfaces), the fraction 1/ 2 of total energy from one of them, designated 1, that is intercepted by the other, designated 2, is given by... 

Thus a highly reflecting Lambertian surface can increase the actinic flux by as much as a factor of 3 relative to the actinic flux from direct sunlight alone. 

Gain is expressed as screen brighmess relative to a lambertian surface. Table 5.9 lists some typical front-projection screens and their associated gains. 

Screen gain The improvement in apparent brightness relative to a lambertian surface of a projection system screen by designing the screen with certain directional characteristics. 

The reflectance properties of a surface are characterized by its bidirectional reflectance distribution function (BRDF). The BRDF is the ratio of the scene radiance in the direction of the observer to the irradiance due to a Hght source from a given direction. It captures how bright a surface will appear when viewed from a given direction and illuminated by another. For example, for a flat Lambertian surface illuminated by a distant point light source, the BRDF is constant hence, the surface appears equally bright from all directions. For a flat specular (mirrorHke) surface, the BRDF is an impulse function as determined by the laws of reflection. 

Seeliger (in 1888) derived a diffuse reflectance law based on the assumption that the radiation striking the surface of a powder will penetrate into the interior of the powder sample and thus does not represent a perfect remitting (Lambertian) surface (Fig. 6). 

The first robust reflectance standard for mid-IR applications was produced by Frank J. J. Clarke at the National Physical Laboratory. The material is a flame-sprayed aluminum of sufficiently large particle size to produce a highly Lambertian surface. The drawbacks of this material are that the reflectance is in the range of 80%R, a bit low for a high-reflectance material, and that aluminum does form a surface oxide that shows absorbances in the spectral range of interest. 

On the contrary, if there are clouds, the discrepancy between flie observation and the model is large in general, and the cause of uncertainty is thought to be the contribution of albedo of clouds. When the actinic flux f tot is divided by direct radiation component Fq, and downward and upward diffusive radiation component Fj, and F, respectively, assuming a Lambertian surface i.e. a virtual completely diffusive surface for which radiance is constant being independent of the direction of observation (isotropic scattering),... 

A further nice property of Lambertian surfaces is the fact that if a passive, i.e. not self-luminous surface is illuminated by an illuminance E, the reflected luminance Lr (sometimes called borrowed luminance ) can be calculated in a straightforward way ... 

In the case of Lambertian surfaces, the perceived brightness is independent of object distance. 

If a (passive, not self-luminous) Lambertian surface is illuminated with an illuminance E, the reflected luminance can easily be calculated by Lr = E p/n, where p denotes the local reflectivity of the surface. 

FIGURE 9 Intensity distribution of light reflected from a perfectly diffuse (Lambertian) surface, showing proportion of reflected light within 5° of each indicated direction. [From Boynton, R. M. (1974). In Handbook of Perception (E. C. Carterette and M. P. Friedman, eds.), Vol. 1. Copyright 1974 Academic Press.]... 

---