Lighting Series Part 5 – Photometry

In this post from Lighting Series, we are going to talk about Photometry. The previous post in this series is Lighting Series Part 4 – Irradiance and Radiant Intensity.

What is Photometry?

Suppose we want to determine the relative brightness of light at different wavelengths. For that, we can do the following experiment. We will show 2 lights: first light is a 555 nm reference monospectral light source; second light is a monospectral light source whose wavelength λ will be varied over the range 400nm to 700nm (the visible spectrum of light).

Example of visible spectrum of light:

uv_vis_ir

We choose and fix a particular wavelength λ and we have a knob with which we can control a multiplier for the 555 nm reference light source. We adjust it until it has the same brightness as the one at the fixed wavelength λ.

We record the setting g(λ) and reset λ to a new value and we repeat the experiment. For each value λ, the number g(λ) tells how much less effective light at wavelength λ is in provoking a response than light at wavelength 555 nm.

When we are done, we have a tabulation of how effective light at frequency λ is at seeming bright, compared to light at the 555nm reference wavelength. Scaling so that the largest value of g(λ) is 100%, we can plot the resultant function. In the following picture, you can see the resultant graph that represents the luminous efficiency function for the human eye. In this case, “efficiency” refers to how efficient energy at a particular wavelength is in provoking the sensation of brightness.

luminous_efficiency_function.png

It is important to mention, that this graph varies from person to person, based on the person’s age as well. Given this, a standard luminous efficiency curve was derived by averaging many observations. There are many other factors (physical,
psychological, and physiological) that can affect the eye’s response to light,
but photometry does not attempt to address these.

The science that measures light in terms of its perceived brightness to the human eye is called Photometry. It is based on subjective judgements as we saw in the experiment. It should not be considered perfectly accurate in every case, but it is a very good representation of visual sensitivity of the human eye.

How are Radiometry and Photometry related?

As we described in previous articles, Radiometry deals purely with physical quantities, without taking account of human perception (photometry).

Each radiometric quantity has an equivalent metric photometric quantity. In the following picture we show them.

photometry_radiometry

The results of radiometric computations are converted to photometric units by multiplying by the CIE (Commission Internationale de l’Éclairage) photometric curve.

As you can read in The RGB Color Model article, we explained that rods and cones are stimulated by light. They are stimulated in a different way. The cones are the dominant receptor in high-light situations (for example, daytime), while the rods dominate in low-light situations (for example, outdoors at night). The first of these is called photopic vision, and the second scotopic vision. The scotopic response curve is different from the photopic response curve. You can see both curves in the following picture

scotopic_photopic

The rods cannot detect the sort of light we perceive as “red“. As both kinds of receptors perform some adaptation to average light levels, this makes red a good color for instruments that will be used in low-light situations (the red light from the instruments does not affect the average light-level adjustment for the rods, which are the primary receptors in use for seeing things in the dark).

There are two luminosity functions in common use. For everyday light levels, the photopic luminosity function best approximates the response of the human eye. For low light levels, the response of the human eye changes, and the scotopic curve applies.

The standarized tabulation, that we mentioned previously, can be used to define the luminance (in nits) of a light source. It is the photometric term corresponding to radiance in radiometry.

If we multiply the radiant intensity at each of the tabulated wavelengths by the luminous efficiency value for that wavelength, we get the luminous intensity (in candelas). One candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation at a frequency of 540 * 10^12 Hz (555nm wavelength), and whose radiant intensity in that direction is 1 / 683 watt per steradian.

For example, you could have an LCD screen that emits about 250 candelas per square meter (250 nits), while the light from the screen at a movie theatre is about 40 candelas per square meter, and a studio broadcast monitor has a reference brightness of 100 candelas per square meter.

In the following picture, you can see how all these photometric units are related.

photometry_example

References

Real-Time Rendering, 3rd Edition

Physically Based Rendering, 3rd Edition: From theory to implementation

Fundamentals of Computer Graphics, 4th Edition

Essential Mathematics for Games and Interactive Applications, 3rd Edition

Introduction to Computer Graphics: A Practical Learning Approach, 1st Edition

Computer Graphics: Principles and Practices, 3rd Edition

Foundations of 3D Computer Graphics

 

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