Lambertian diffuser

This requirement is not critical since the property of a Lambertian diffuser makes the spectrometer response independent of this angle. The distance of the diffuser plate from the entrance slit is arbitrary so long as the slit aperture is... 

When an integrating sphere is used for a Lambertian (diffuse reflecting surface), the following equation applies ... 

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... 

For calculating the intensity of the signal at the detector one has to take into account the solid angle of collection for the chromophore embedded into a medium with refractive index n and acting as a non-Lambertian diffuse point source (i.e. the intensity of which in a given direction is not proportional to the cosine of the angle with respect to the direction of maximum irradiance). This solid angle is equal to ... 

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. 

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. 

Initially, we will focus on the mesoscopic description associated with the radiative transfer equation. Then, we will introduce the single-scattering approximation and two macroscopic approximations the PI approximation and two-flux approximation. AH of these discussions are based on the configuration shown in Fig. 6. Collimated emission and Lambertian emission wiU also be considered in the discussion later they correspond to the direct component and the diffuse component of solar radiation, respectively. Throughout our study, the biomass concentration Cx is homogeneous in the reaction volume V (assumption of perfect mixing), and the emission phenomena in V are negligible. The concentration Cx is selected close to the optimum for the operation of the photobioreactor the local photon absorption rate. 4 at the rear of the photobioreactor is close to the compensation point A.C (see Section 5 and chapter Industrial Photobioreactors and Scale-up Concepts by Pruvost et al.). 

In addition to this information, it is necessary to specify angular distribution of the intensity. A Lambertian distribution corresponds to isotropic intensity for the incoming directions (ie, diffuse incidence)... 

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).

In this section, we present a Monte Carlo algorithm for estimation of the specific photon absorption rate (xq) at any location Xq within any photobioreactor s reaction volume confined by two diffuse-reflective surfaces (7Z and JF) with uniform reflectivity and p, respectively, where T is Lambertian emitting with uniform surface flux density n,i/ is non-... 

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.

Lambert s law of reflection The flux reflected per unit solid angle is proportional to the cosine of the angle measured from the normal (perpendicular) to the surface. If the reflected flux is isotropic, the surface is said to be a perfect Lambertian reflector or a perfect diffuser. 

Reflectance spectroscopy concerns the measurement of four distinct types of materials and their interaction with light. Specular materials reflect the predominant amount of radiation at an angle equal and opposite to the incident radiation. Diffusely reflective materials scatter light over a wide range of angles, with the perfectly diffuse (or Lambertian) scatterer exhibiting a cosine response to the incident radiation. Gonioapparent... 

Another problem arises in integrating sphere measurements when the sample cannot be placed flush against the port of the sphere, ff the sample is specular, the reference should be recessed by an identical distance as the sample to be measured. For materials that are primarily diffuse in character, we have determined the measured reflectance for a lambertian material decreases by approximately 3% (absolute) per millimeter of distance of the sample from the sphere up to approximately 4 mm. Beyond that, it is difficult to predict. Measurement of the reference at a similar distance helps but is still very inexact. 

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). 

A perfect reflecting diffuser is defined as an idealized object with a reflected radiance independent of the angle of viewing (i.e., a Lambertian reflector) and a reflectance equal to 1. 

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... 

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]. 

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),... 

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.]... 

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.

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