Radiance

Radiance is a fundamental measurement used in the field of radiometry. It describes the radiant flux that is emitted, reflected, transmitted, or received by a specific surface. This measurement is calculated per unit solid angle and per unit projected area.

Radiance helps scientists characterize how electromagnetic radiation is reflected or emitted in a diffuse way. It is also used to quantify the emission of other particles, such as neutrinos. The standard SI unit for radiance is the watt per steradian per square metre. Because it is a directional quantity, the radiance of a surface changes based on the direction from which you observe it.

To understand how radiance works, we must look at its mathematical components. The radiance of a surface is denoted as Le,Ω. The "e" stands for energetic, which helps distinguish it from photometric quantities. The symbol Ω indicates that it is a directional quantity. The formula involves the radiant flux, which is the total power. This flux is divided by the solid angle and the projected area, which is written as A cos θ. This projected area depends on the viewing direction through the angle θ and the azimuth angle.

For a special type of surface called a Lambertian surface, the radiance is uniform. This means it is isotropic, or independent of the viewing direction.

Scientists often study a related concept called spectral radiance. This describes radiance as a function of frequency or wavelength. It is denoted as Le,Ω,ν for frequency or Le,Ω,λ for wavelength. You can think of spectral radiance as a more detailed breakdown of light. The total radiance of a surface is actually the integral of its spectral radiance over all frequencies or wavelengths.

This allows researchers to look at specific parts of the light spectrum rather than just the total power.

History shows that the names for these concepts have changed over time. Historically, radiance was simply called "intensity." Spectral radiance was known as "specific intensity." You will still see these older terms used frequently today. They are especially dominant in the fields of heat transfer, astrophysics, and astronomy.

However, the term "intensity" is used in many ways in physics. Most commonly, it refers to power per unit area, which is different from radiance.

Radiance is highly significant because it predicts how much power an optical system will receive. This includes systems like the human eye. If you look at a surface from a specific angle of view, the radiance tells you how much light enters the system's entrance pupil. Because the eye is an optical system, radiance and luminance are great indicators of how bright an object appears.

In some fields, like laser physics, people still use the nonstandard term "brightness" to describe radiance and luminance.

There is also a very important rule known as the conservation of radiance. In geometric optics, if you divide radiance by the index of refraction squared, the value remains invariant. This means that for an ideal optical system in air, the output radiance is the same as the input radiance.

For example, if a lens creates a smaller, demagnified image, the irradiance at the image is higher. However, the light at the image plane fills a larger solid angle. Therefore, the radiance remains the same if there is no loss at the lens.

In real-world, passive optical systems, the output radiance is at most equal to the input. It can only be less if the index of refraction changes. Radiance is also related to a concept called étendue. In an ideal system, both the étendue and the radiant flux are conserved. However, in real systems, the radiant flux might decrease due to absorption. The étendue might increase due to scattering. Because of these factors, the basic radiance in a real system may decrease, but it cannot increase.