Sources Lambertian

The luminous intensity (luminance) can be determined by measuring the flux in any given solid angle, Q (the ratio of the size of aperture divided by the square of the distance between the light and the aperture). Consider a flat emitting surface, each point of which emits light equally in all directions i. e. a Lambertian source. A PLED/OLED is a Lambertian source if the luminous intensity follows... 

Fig. n.l3 The angular radiation characteristic of the multilayer OLED of the type shown in Fig. 11.9 in comparison to a Lambertian source. The agreement is nearly perfect. 

Flow line concentrator (trumpet) Nonimaging collector in which the reflecting wall follows the lines of vector flux from a Lambertian source. 

Collection efficiency is partially a function of the light source, and the figure given is typical for a lambertian source (CRT) and lens having a half-field angle of approximately 25°. 

Figure 2.4 shows some types of refractive microlenses that can be fabricated utilizing the standard microfabrication procedures in materials convenient for the MWIR and LWIR ranges. Most of them are loosely based on the solutions for microlenses used in fiber optics to improve coupling between laser sources and fibers [98]. These immersion lenses were thus intended for the operation with coherent and monochromatic radiation, while most of the microlenses in the field of IR detector technology are intended for incoherent, mono- or polychromatic Lambertian sources and, of course, they operate in different atmospheric windows. 

A diffuse or Lambertian source [2] is one where each differential area dA of source area emits light in all directions, i.e. 0g = 7t/2 in Eq. (4-1). The cross-section of such a source is illustrated schematically in Fig. 4-3(a). This is the most typical source in practice and approximates the output of a light-emitting... 

Fig. 4-3 Cross-sections of (a) a diffuse or Lambertian source, and (b) a collimated beam.

A final practical note involves instrument intensity measurement calibrations. The intensity measurement is self-calibrating relative to the incident beam from the source. However, measurements typically have a dynamic range of 10 -10 , and care must be taken to insure the detection system is linear. A method of calibrating the scatterometer is to characterize a diffuse reflector having a known scattering characteristic. For example, a surface coated with BaS04 makes a nearly Lambertian scatterer, which has a BRDF of 1/Jt at all angles. 

For a Lambertian emitting OLED source, where V is the operating voltage, rjie is the luminance efficiency (in cd/A), the power efficiency (rj) is given by... 

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. 

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... 

Assuming a Lambertian intensity profile and a disc-shaped source with radius r, the light intensity on a point detector placed a distance d away (see Fig. 4.5) can be expressed as follows [17, 18] ... 

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. 

Packed PTFE exhibits extremely high reflectance and is close to a perfect Lambertian scatterer over a very wide reflectance range (190-2500 nm/0.19-2.5 /on). The material is nonhydroscopic and is very easily prepared from commercially available sources. The powdered PTFE is also reasonably inexpensive—currently about 8.00/pound in bulk. 

A fundamental difference between the conic mirror and integrating sphere devices is in how absolute reflectance values are determined. Absolute measurements in conic mirror reflectometers are direct and simple. Sources of error, as discussed in Section V, need to be accounted for. However, absolute reflectance values from measurements made with integrating sphere reflectometers are based on integrating sphere theory. Also, integrating sphere theory is based on a variety of assumptions including that of a perfect Lambertian inner wall coating. The effects of deviations from the assumptions of the theory are difficult to quantify (43). This dependence of absolute results on the sphere theory restricts the use of most integrating sphere reflectometers in the infrared primarily to relative measurements. 

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. 

For 2nlQ mode reflectometers, an inverted CPC can be used in front of cavity radiation sources (46, 54) in order to reduce the non-Lambertian properties of such sources at larger angles. The HDR 100 hemiellipsoidal reflectometer from Surface Optics Corporation uses a reflective cone above a cavity radiation source (55). 

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... 

Real reflectance can be described analytically or empirically [261]. There are several analytic reflectance models that can be used to describe various types of surfaces. The simplest diffuse source is Lambertian. The Mie theory can compute light scattering by spherical particles, as well as some other simple shapes like elongated ellipsoids [266]. 

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