How to Measure Light

Before anyone can start reproducing sunlight, they have to have a way of measuring and talking about it. There are two main methods of counting and quantifying light, known as 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 the measurement of 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 produced by the sun (such as UV or IR) also play an important role in many light-sensitive processes. Light-sensitive chemical reactions are also known as photochemical processes, and there are many that humans and all life rely on. For example, depending on the type of chlorophyll, plants wavelengths ranging from the UV to the IR to produce useful energy. Additionally, materials (organic or inorganic) can be designed to absorb light in a broad spectrum of wavelengths even outside of visible light.

Because the Sun emits visible light as well as many other useful and necessary wavelengths, it makes most sense to use radiometry to measure sunlight.  

Radiometric units of measurement

Radiometry measures light of any wavelength, so comprises the most broadly-applicable measurement units when talking about 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 kind of 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 useful because it tells you how widely spread out your radiant power is 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).

As an example, let’s say we have two 1 W light sources. One of them 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 color 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 detectors have dimensional areas in the range of cm2 rather than m2).

This is one of most commonly used radiometric units, simply because it’s easy to measure, report and share, for 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 not familiar with solid angle, you can think of it as a two-dimensional angle. A rough way to distinguish this from irradiance is that irradiance describes the power striking a specific surface from all angles, whereas the 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 takes distance into account 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 not needed for fully understanding 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 a bit overwhelming if you don’t use these units of measure everyday.

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 are concerned with how light is perceived by the human eye, i.e. visible light. It is less useful when talking about measuring sunlight, but because it’s used so often in commercial lighting, it’s 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.

Luminous flux is measured in a unit called lumens, written as lm. Commercial indoor lights are usually expressed in lumens because regular illumination needs are only concerned with 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 to convert between lumens and watts, but most of these, if they don’t mention wavelength, are trying to convert 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 how to convert 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 micrometers (or microns):

The conversion between radiant flux (radiometric unit) and luminous flux (photometric unit) proceeds as follows.

For a single-wavelength (i.e. monochromatic) source, the computation is more straightforward. Let’s say we have a 1 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

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 perpendicular surface at sea level.

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 is really missing out on a lot of the radiation the sun is actually emitting.

As far as the solar industry is concerned, radiometric units are preferred (for example, radiant flux in W/m2 instead of luminosity in lumens).

For more details on the difference between radiometric and photometric units, and what these units mean, please reference the above sections.