Illumination Lambertian

Enhanced backscattering can lead to near-ideal Lambertian illumination and super-white coatings, or superdiffusers . Diffuse reflectors are described by the theory of disordered media. Generally, this theory is very complex and the methods... 

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... 

Figure 20 Angular distribution of the intensity L z,6) within the photobioreactor shown in Fig. 6. The results were obtained by the Monte Carlo method (A) for collimated normal incidence and (B) for Lambertian incidence (diffuse illumination).

Figure 26 (A) A 25 L prototype of the solar volumetrically illuminated photobioreactor DiCoFluV (Cornet, 2010). (B) EDStar geometric structure both the reactor 1Z) and the 979 light-diffusing optical fibers [T) are cylinders 1 m high the reactor s diameter is 16.5 cm, the distance between two fiber axes is djr = 4.8 mm, and the fiber radius is ryr = 1.2 mm.Tl and T are diffuse-reflective with uniform reflectivity p and pT, respectively.. is Lambertian emitting with the uniform surface flux density qn,v (Q Two-dimensional hexagonal lattice fiber arrangement an optical-path example in the culture medium V.

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. 

For InjO mode reflectometers, a non-Lambertian radiation source may introduce a measurement error. Wood et al. (31) described a typical cavity blackbody source that exhibits a monotonic drop in emitted radiance (52) with angle. The percentage decrease in radiance from the normal incidence value is 3 to 4% at 45° and 6 to 7% at 70°. Beyond 80°, the falloflf is very rapid due to direct viewing of the cavity wall near the exit aperture of the source. If a Lambertian sample is illuminated with radiance having an angular dependence L 6), where L(0) = 1, then the ratio of the measured reflectance to the true reflectance will be given by... 

If a Lambertian sample was illuminated with the source radiance profile given in Ref. (31), the sample reflectance would be measured to be 0.92 of the actual value. 

Some radiation reflected from the sample in the Bjln mode may be lost out of the entrance port when external optics are used or off of the focusing mirror or lens and its support structure when internal optics are used. This effect can result in an error in the measured reflectance. Similarly, for 2nl6 mode reflectometers, the optics used to collect reflected radiation from the sample reduces the radiant power striking the sample and may affect the measured reflectance. If the sample is a Lambertian reflector and the illumination (0/27i) or viewing (2ti/0) is near normal, then the fraction of radiation intercepting the sample optics is given by... 

In order to illustrate the dependence on the variables defined previously, we slightly modify Qarke s method. It is assumed that the source and sample are Lambertian reflectors, that a viewing port in the conic mirror is symmetrically placed with respect to the sample and source, and that the sample area is defined by a perfectly black mask. If this sample area were fully illuminated, the image of the sample would just underfill the source aperture. Under these assumptions, the reflected sample power, as measured through the viewing port, is given by... 

The effective reflectance of the detector can be further reduced by using Paschen s (11) method. In particular, an inverted CPC, when positioned in front of a detector (9/2it) or source (2ti/0) to reduce variations from ideal angular response as described in Section V,C, will also enhance the effective absorptance. Radiation reflected from the detector or source at angles larger than the CPC s critical angle is reflected back to the detector or source. If the detector or source is a Lambertian reflector and if the illumination of the CPC is Lambertian, then the effective reflectance of a CPC-detector combination is given by... 

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 ... 

To define the optical property of the scene, it is not sufihcient to stipulate only one scalar luminance value per source point—also the angular distribution of the (possibly reflected) luminance has to be specified (e.g. lambertian [L = const], isotropic [L cos 0 ] or collimated [L 8(0]). This is particularly important for the definition of test semps, as for example certain illuminance values required for a realistic simulation of glare scenarios can only be achieved with collimated sources. 

In an imaging process, luminance is an invariant quantity. Therefore, the image plane illuminance responsible for the sensory impression on the retina and the resultant grey value on the camera chip can easily be calculated by E = L d (Lambertian case). 

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. 

The Voyager spacecraft has a large plate mounted on the main bus so that the instruments on the scan platform can view the plate almost normally. The surface of the aluminum plate is chemically etched and scatters light in all directions when illuminated by the Sun. From the visible to 20 /tm, the scattering characteristic is that of a near perfect Lambertian diffuser, as verified by laboratory measurements one or two years before launch. Exposure of the calibration plate to sunlight requires a complex maneuver of the spacecraft Since the telemetry antenna does not point in the Earth direction at that time, such calibration sequences cannot be performed frequently. Cahbrations have been carried out a month or so before and after each planetary encounter, except following the Saturn encounter by Voyager 2, where... 

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