Radiant intensity of a Lambertian surface

In summary, the radiant intensity of a surface is maximum in the direction normal to the emitting surface and approaches zero as the direction becomes parallel to the surface.
  • #1
dougy
26
0
Hello everyone.

From what I've understood, the radiant intensity of a surface is defined as the number of photons emitted by the surface per unit solid angle (steradian) and per second, times a constant (that constant being the mean energy of a photon emitted by this surface). So radiant intensity is expressed in W·sr−1

The way I see it, the radiant intensity of a Lambertian surface (i.e. an isotropic source) is the same in every direction, so plotting the radiant intensity of such a surface for each direction should give in 3D a sphere (or a semisphere) with the source at the center, and in 2D a circle (or a semicircle) with the source at the center. Yet all the representations I find of the radiant intensity of an isotropic source are similar to this one :

500px-Lambert_Cosine_Law_1.svg.png



which, the way I see it, would mean that the radiant intensity is maximum in the direction normal to the emitting surface, and approach zero as the direction becomes parallel to the surface.

What am I not getting there?
 
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  • #2
Perhaps you are not accounting for the cos(q) term- dA*cos(q) is the apparent area of dA, as determined by the angle between the surface normal and the propagation direction.

Here's how I describe a Lambertian emitter (which is not an isotropic emitter) such as a piece of paper or the surface of the moon: each area element dA appears as dA*cos(q). Since the radiant intensity of the Lambertian surface is given by I cos(q)dAdW , the irradiance I/dA = I cos(q) dAdW/dA*cos(q) = I dW and is independent of the orientation of the surface with respect to propagation direction: the lunar surface appears flat, not curved.

Does that help?
 
  • #3
Hi Dougy,

The radiant intensity is not constant, it is proportional to cos(theta) for a Lambertian emitter. Lambertian emitters have a constant radiance (W/sr/m^2).

Claude.
 

1. What is the meaning of "radiant intensity" in relation to a Lambertian surface?

Radiant intensity refers to the amount of electromagnetic radiation, specifically visible light, emitted by a Lambertian surface in a particular direction. It is measured in watts per steradian (W/sr) and is a measure of the brightness or luminosity of the surface.

2. How is the radiant intensity of a Lambertian surface calculated?

The radiant intensity of a Lambertian surface can be calculated using the formula I = E x cosθ, where I is the radiant intensity, E is the irradiance of the surface, and θ is the angle of incidence. It is important to note that this calculation assumes the surface is perfectly diffuse, meaning it reflects light evenly in all directions.

3. What is the difference between radiant intensity and luminance?

Radiant intensity and luminance are related but distinct concepts. Radiant intensity is a measure of the total amount of light emitted by a surface in a particular direction, while luminance is a measure of the perceived brightness of a surface as perceived by an observer. Luminance takes into account factors such as the sensitivity of the human eye and the distance between the observer and the surface.

4. How does the radiant intensity of a Lambertian surface change with distance?

The radiant intensity of a Lambertian surface decreases with distance according to the inverse square law. This means that as the distance from the surface increases, the radiant intensity decreases exponentially. For example, if the distance is doubled, the radiant intensity will decrease by a factor of four.

5. Can the radiant intensity of a Lambertian surface be measured directly?

No, the radiant intensity of a Lambertian surface cannot be measured directly. It can only be calculated using the appropriate formula and measured values for irradiance and angle of incidence. However, specialized instruments such as radiometers and photometers can be used to measure irradiance, which can then be used to calculate radiant intensity.

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