How Do You Measure Light Intensity?
This seems like a simple question with an obvious answer but quite complex. Depending on your field of study, application, and area of expertise, the units and methods used to measure light vary drastically. The following chapter covers the various methods and ways we measure light, but first, we need to understand the difference between radiometry and photometry.
The Difference Between Radiometry and Photometry
Radiometry is the science of measuring light of any wavelength, that is, in any portion of the electromagnetic spectrum.
Photometry, on the other hand, is only concerned with measuring visible light, with a specific view (i.e. weighting) toward how strongly or weakly the human eye responds to these wavelengths.
Even though our eyes only perceive the visible portion of the electromagnetic spectrum, other wavelengths the sun produces (such as UV or IR) also play an essential role in many light-sensitive processes.
Here are a few areas that wavelength ranges in the UV or IR may be required:
- Solar cell material research on tandem and newer devices.
- Materials Degradation Testing to accelerate wearing (UV) or warping from heat (IR).
- Photochemistry applications to photocatalytic processes.
The list goes on depending on the field and application. What is important to remember is that the Sun emits visible light as well as many other useful and necessary wavelengths. Therefore, it makes most sense to use radiometry to measure sunlight.
Radiometric units of measurement
Radiometry measures light of any wavelength, comprising the most broadly applicable measurement units for the entire electromagnetic spectrum.
Radiant Flux (Power)
Radiant flux is the light energy per unit time which is emitted, transmitted reflected or received by an object. It has units of Watts (W, or Joules of energy per second, J/s). It is also sometimes called radiant power or optical power. Because this unit of measurement doesn’t depend on wavelength, it can be used to measure any electromagnetic radiation.
Spectral Flux
Spectral flux is like the radiant flux but specific to a wavelength interval. If we want to know how much power is received, transmitted or emitted per wavelength of light, then we talk about spectral flux. This quantity is helpful because it tells you how widely your radiant power is spread over the electromagnetic spectrum. It has units of Watts per nanometer (W/nm). If the radiation is being described in terms of frequency (instead of wavelength), the spectral flux can have units of Watts per Hertz (W/Hz).
For example, let’s say we have two 1 W light sources. One has a spectral flux of 2 W/nm, whereas the other has a spectral flux of 1 W/nm. The first source’s light is twice as concentrated in wavelength space.
Usually, though, light sources vary in spectral flux depending on the wavelength or colour of light, so you’ll see spectral flux plotted as a curve (a function of wavelength).
Irradiance
Irradiance is the radiant flux shining on or received by a specific surface area. In other words, it’s the received power of light per unit area. It has units of Watts per square meter (W/m2) or other variants like mW/cm2 (because most photodetectors have dimensional areas in the range of cm2 rather than m2).
This is one of the most commonly used radiometric units simply because it’s easy to measure, report, and share.
Most measurements are made by a detector with a finite area. It’s hard to measure the full power (radiant flux) emitted by a source, but it’s much easier to put a detector of a given area in the path of light and make one measurement.
Sometimes irradiance is also referred to as intensity or optical intensity, but this naming should be avoided because it’s too easy to confuse with radiant intensity.
Spectral Irradiance
There’s a similar quantity called spectral irradiance, which is the irradiance per unit of wavelength. As with other spectral quantities, it describes the irradiance for a given wavelength interval of the spectrum. When you see a plot of the solar spectrum, it will very often be given in spectral irradiance.
Radiance
Radiance is defined as irradiance per unit of solid angle. If you’re unfamiliar with a solid angle, you can think of it as two-dimensional. A rough way to distinguish this from irradiance is that irradiance describes the power striking a specific surface from all angles, whereas radiance describes the power striking a specific surface from a specific angle. It is not nearly as commonly used as irradiance.
One of the uses of radiance is that, because it considers distance through the calculation of solid angle, radiance itself doesn’t depend on distance. So you can go to other planets in the solar system, and the Sun will have a different irradiance but still have the same radiance.
Radiant Intensity
Radiant Intensity of a light source is its radiant flux per unit of solid angle. We won’t go into too much detail here because it’s unnecessary to fully understand solar simulators.
Briefly, though, this quantity captures how the light emission is changing as a function of the source’s angle.
Spectral Intensity
Similar to spectral flux’s relationship to radiant flux, spectral intensity is the radiant intensity per unit wavelength and describes the angular dependence of light for a specific wavelength interval.
So many measures and units! Which ones are the most important?
It can be overwhelming if you don’t use these units of measure every day.
The key units most often used (and most worth remembering!) are those of radiant flux (W) and irradiance (W/cm2).
If you understand these, it’s an easy step to add the extras: spectral flux (W/nm) and spectral irradiance (W/cm2/nm). Knowing these will equip you to fully understand the coming sections.
Photometric units of measurement
As mentioned earlier, photometric units of light measurement concern how light is perceived by the human eye, i.e., visible light. They are less useful when measuring sunlight, but because they are used so often in commercial lighting, they are worth a brief discussion.
Luminous Flux
Like radiant flux, luminous flux is the emitted optical energy per unit of time. However, luminous flux is weighted by the sensitivity of the human eye, which varies as a function of wavelength. The human eye’s response is usually separated into two categories: photopic and scotopic vision. Photopic vision is the eye’s response under well-lit conditions (mediated by cone cells), whereas scotopic vision is the eye’s response under low-light conditions (mediated by rod cells). Luminous flux specifically accounts for the photopic response of the human eye. The curves that describe the human eye response are usually called luminosity functions.
The two different responses, or luminosity functions of the human eye, correspond to the behaviour of rods and cones. Data source: Colour & Vision Research Laboratory of the University College London.
Luminous flux is measured in lumens, which are also known as lm. Commercial indoor lights are usually expressed in lumens because regular illumination needs only concern the visible part of the spectrum.
Luminous Intensity
The luminous intensity of a source is the luminous flux per unit solid angle (remember, solid angles are a bit like two-dimensional angles). This quantity accounts for directional variances in light.
The units of luminous intensity are lumens per steradian (lm/sr), also known as candelas (cd).
Illuminance
Illuminance is the photometric analogy to irradiance. In other words, it is the visible light power per unit area. It has units of lumens per square meter (lm/m2), also known as lux (lx).
Luminance
Luminance is the photometric analogy to radiance. In other words, it is the visible light power per unit area per unit solid angle. It has units of lumens per square meter per steradian (lm/m2/sr).
How to Convert between radiometric and photometric units
There are some online calculators that can convert between lumens and watts. Most of these, if they don’t mention wavelength, are trying to convert the brightness of an LED in lumens into the equivalent brightness of an incandescent light bulb.
We’re not talking about that type of conversion here. Instead, we’re talking about converting the number of lumens (visible energy per unit time) to the radiant flux (total energy per unit time). For this, we need to know the wavelength range of light involved, as well as the photopic luminosity curve of the human eye.
The photopic luminosity curve of the human eye has a peak at a wavelength of 555 nm. The curve is usually normalized to that point, and we define 683 as the number of lumens per watt at 555 nm. The fall-off in the human eye’s efficiency is described by this function, where lambda is given in units of micrometres (or microns):
The conversion between radiant flux (radiometric unit) and luminous flux (photometric unit) proceeds as follows.
The computation is more straightforward for a single-wavelength (i.e., monochromatic) source. Let’s say we have a one mW green laser (at 532 nm).
First, we calculate the photopic efficiency using the formula above:
Then we multiply this by the known conversion factor of 683 lm/W and the initial radiant flux in W:
For non-monochromatic sources, i.e. those sources that consist of more than a single wavelength of light, the calculation is more involved. In this case, we need to know the Spectral flux as a function of wavelength for our source (in units of W/nm). We then need to integrate (broadly speaking, sum up) the contributions over the full visible wavelength range, considering the change in photopic response at each wavelength. Mathematically, this is written as
Summary Table of Radiometric and Photometric Units
|
Quantity |
Metric Units |
Unit Name |
Radiometric or Photometric |
What it measures |
How Common? |
|
Radiant Flux |
W (or J/s) |
Watts |
Radiometric |
Light energy per unit of time |
Very Common |
|
Luminous Flux |
lm |
lumens |
Photometric |
Visible light energy per unit of time |
Very Common |
|
Spectral Flux |
W/nm |
Watts per nanometer |
Radiometric |
Distribution of light power in the spectrum |
Common |
|
Irradiance |
W/cm2 |
Watts per square cm |
Radiometric |
Concentration of light power |
Very Common |
|
Illuminance |
cd (or lm/m2) |
Candelas |
Photometric |
Concentration of visible light power |
Very Common |
|
Spectral Irradiance |
W/cm2/nm |
Watts per square cm per nanometer |
Radiometric |
Distribution of light concentration in the spectrum |
Very Common |
|
Radiance |
W/cm2/sr |
Watts per square cm per steradian |
Radiometric |
Angular distribution of light concentration |
Uncommon |
|
Luminance |
cd/sr (or lm/m2/sr) |
Candelas per steradian |
Photometric |
Angular distribution of visible light concentration |
Uncommon |
|
Radiant Intensity |
W/sr |
Watts per steradian |
Radiometric |
Angular distribution of light power |
Uncommon |
|
Luminous Intensity |
lm/sr |
Lumens per steradian |
Photometric |
Angular distribution of visible light power |
Uncommon |
|
Spectral intensity |
W/sr/nm |
Watts per steradian per nanometer |
Radiometric |
Angular and spectral distribution of light power |
Uncommon |
How Many Lumens is the Sun?
The short answer is that the sun has an illuminance of about 100k lux (lumens per square meter) on a sea-level perpendicular surface.
As we discussed earlier, though, the unit of lumens is a photometric one, which only considers wavelengths of light visible by the human eye. So, this measure misses out on much of the radiation the sun emits.
The solar industry prefers radiometric units (e.g., radiant flux in W/m2 instead of luminosity in lumens).
Please refer to the above sections for more details on the difference between radiometric and photometric units and what these units mean.
Light Measurement Summary
This chapter covered a lot of dense information on the difference between radiometry and photometry. What is critical to remember is that your area of study will most likely have units similar to it. For most, that will be radiant flux in either W/m2 or mW/cm2, which is analogous to the way light is measured from solar simulators.
Our next chapter brings the last few chapters together by exploring the field of solar simulation. Read on to learn more!
