Part III: Making Sense of Light Measures

A large amount of confusion about light measurements comes from the fact that there are several different ways of measuring light. Many terms are used to measure aspects of lighting, and a simple cruise on the Internet will take you through a plethora of terms such as: lumens, lux, candlepower, foot-candles, lamberts, phot, nit, irradiance, illuminance, Color Rendition Index (CRI), Kelvin and Photosynthetic Photon Flux Density (PPFD), among others. Why are there so many measures to describe light? This article will sort through this abundance of lighting measures.

There are basically three categories of light measures based on the particular application and interpretation, each with its own set of terminology.

1. Recall that light is a form of radiation, and hence can be measured as radiant energy using energy based measures. These units of light measurement are termed radiometric measures of light.

2. Light is also used to illuminate for visual purposes, hence light can also be measured for this application based on how the human eye perceives light. Measures of light based on visual perception are called photometric measures, and are by far the most commonly used and available metrics because they are used by the large lighting industry.

3. The form of measurement that we, as reefkeepers, are concerned about is the Photosynthetically Available Radiation (PAR), which measures the number of photosynthetically useful photons, and has been discussed in detail in Part II.

There are two main ways light can be measured: 1) at the source, and 2) at the surface of the object being illuminated.

The quantity of light at the source is termed flux, and is measured as "quantity" per unit of time. This is very similar to measuring the flow of a pump in gallons/hr or liters/min. We can think of a light source as a pump emitting radiation and measure this pumping capacity over time. It represents the total light output from the source per unit of time. What this measured "quantity" is depends on whether the light is interpreted using radiometric, photometric or photosynthetic standards.

The light radiating from the source ultimately falls onto an object, and we can measure the amount of light falling onto a given area of the object. This quantity is measured per unit area, and measures the light's density on a unit area.

The light emanates in several directions and we can either measure this without regard to the direction from which it comes, or measure it in a given direction. When measuring light in a given direction, it's helpful to visualize the light as radiating from all directions in a sphere. This sphere can be broken down into cones whose apex is at the center of the sphere with the cone specified by the solid angle at the apex. Thus the light can be measured as the amount of flux contained in such a cone and measured per unit angle. The unit angle used is called a steradian (similar to a radian in three dimensions). A complete sphere has 4p steradians.

The different quantities used in light measurements and their units of measure are summarized in the table below, and will be discussed in further detail.

Radiometric Measurement of Light

Because light is radiant energy, the energy is measured in typical units of energy - joules (J).

Radiant Flux, also called radiant power, is the flow rate of radiant energy. It is measured in terms of power units called watts, which are basically a measure of energy per unit time. 1 watt = 1 joule/sec.

Radiant Intensity is the radiant flux per unit solid angle and is measured in watts/steradian. The radiant intensity is independent of the distance because it measures only the amount of radiant flux contained in the cone with an angle at the apex equal to one steradian.

As we move further from the source, the cone's spread increases so the radiant intensity falls onto a larger surface. Thus, the density of light falling onto the surface decreases as the area increases (following the inverse square law for a point source), even when the angle at the cone's apex does not change. This is measured as radiance. Radiance is the radiant flux density per unit solid angle and is measured in watts/m2/steradian.

If we do not care about the light's direction and want to measure the light falling onto a source from all directions, then we measure this as irradiance. Irradiance, also known as radiant flux density, is the radiant flux per unit area at a point on the surface. Hence, its units are expressed in watts/m2 or joules/sec/m2. It is denoted as E.

Spectral Irradiance is the irradiance per unit wavelength interval at wavelength λ. This is denoted as Eλ and its units are expressed in watt/m2/nm. Recall that the spectral power distribution plot discussed in Part II is plotted using spectral irradiance values.

Photometric Measurements

Photometric measurements are geared toward how the human eye perceives light. The sensitivity of human eyes is different for different wavelengths. In the late 1920s the Commission Internationale de L'Eclairage (CIE), based on experimentation using human subjects, established how the human eye responds to light at different wavelengths. The human eye is more sensitive to light at 555 nm (green) and less sensitive to blues and reds. This characteristic of human vision established the standard observer response curve known as the luminous efficiency function to represent how the human eye responds to light at different wavelengths. Per this standard, detectors in the eye respond differently to different regions of the spectrum, and the response is scaled with respect to the peak values.

The change in the eye's spectral response can be explained by the presence of two types of receptors, rods and cones, in the retina. Cones are active at high light levels and are most densely situated in the central part of the field of view. The cones' spectral response corresponds to the photopic sensitivity curve. The rods are responsible for human vision at low light levels and are prevalent in the peripheral field of view, away from our direct line of sight. As light levels are reduced, cones become less active and rods become active with established spectral sensitivity gradually switching toward the scotopic response curve. The peak spectral sensitivity for photopic vision is 555 nm, and 507 nm for scotopic vision. From this it is quite clear that the human eye finds light at 555 nm to be the brightest, with the blues and reds tending to be less bright. The luminous efficiency functions are shown in Figure 1.

Figure 1. Luminous Efficiency Functions.

All photometric light measurements evaluate light in terms of this standard visual response described by the luminous efficiency function and, hence, all are weighted measures. Not all of the wavelengths are treated equally. The wavelength at 555 nm is assigned a weight of 1, and the others are scaled according to this function. According to this function, light at a wavelength of 450 nm is given a weight of 0.038. This explains why a light source with large amounts of radiation in the "blue" region will have a low reading when using photometric units.

The quantities used for photometric measurements correspond to those used for radiometric measurements, with the main difference being that the measurements are evaluated with respect to the human eye's response.

Luminous Flux is the amount of radiation coming from a source per unit time, evaluated in terms of a standard visual response. Unit: lumen (lm). You will see most data from lighting companies refer to light output in terms of lumens. Think of this as the amount of light produced by the lamp as perceived by the human eye.

Luminous Intensity is the luminous flux per unit solid angle in a given direction. Unit: candela (cd). One candela is 1 lumen/steradian.

Illuminance is the luminous flux per unit area. It is measured in lux (lumen/m2) or footcandles (lumen/ft2). The light emanating from a lamp is used to illuminate objects and the amount of light (measured in lumens) falling onto a specific area of the object, usually one square meter, is termed lux. When we measure this same area in square feet, the unit is footcandles. These units are often used in photography, where we are interested in how much light is falling onto the subject.

Conversion from Radiometric Units to Photometric Units

The following method is used to convert between photometric units and radiometric units. As defined, 1 watt = 683 lumens at 555 nm (peak photopic response), and it is scaled for other wavelengths based on the Luminous Efficiency Function V (λ) shown in Figure 1.

To determine a lamp's lux values, the spectral irradiance at each wavelength (taken from the spectral power distribution) in the spectral range (380-780nm) is multiplied by the luminous efficiency function at the equivalent wavelengths. Then, all of these multiplied values are summed and multiplied by 683 to find the total lux output. As you can see, the conversion requires knowledge of the spectral power distribution and cannot be done without it.

So far we have been dealing with metric units. To convert to English units, or to other measurement systems, appropriate conversions need to be made. These converted units are often given different names (thereby adding to the confusion)! As an example we can look at the different terms and units used for measuring luminance.

1 lm/m2/sr (lumens per sq. meter per steradian)
= 1 candela/m2 (cd/m2)
= 1 nit
= 10-4 stilb (sb) (or 1 candela/cm2)
= 9.290 x 10-2 cd/ft2
= π apostilbs (asb)
= π x 10-4 lamberts (L)
= 2.919 x 10-1 foot-lamberts (fL)

Units for Photosynthesis Measurements

In keeping corals and plants we should not be concerned about light as humans see it, but rather as the plants and corals see it. For the purpose of photosynthesis, light is termed Photosynthetically Available Radiation (PAR). This radiation's range is identical to what humans can see in the 400-700 nm range, but each photon is treated uniformly in this measurement (unlike the photometric measurement, which weights the photons according to how the human eye sees them).

The reason for expressing PAR as a number of photons instead of energy units is that the photosynthetic reaction takes place when a plant absorbs the photon, regardless of the photon's wavelength (provided it lies in the range between 400 and 700 nm). That is, if a plant absorbs a given number of blue photons, the amount of photosynthesis that takes place is exactly the same as when the same number of red photons is absorbed. Note, however, that the plant or coral may have an absorption response that preferentially absorbs more photons of certain wavelengths (more on this later).

Recall from Part II, PAR is measured as PPFD, which are Einstein/m2/s or µmoles/m2/s. One Einstein = 1 mole of photons = 6.022×1023 photons, hence, 1 µEinstein = 6.022×1017 photons.

Conversion from Radiometric Units to PPFD

If we know the spectral irradiance at any given wavelength (we can get this from the spectral power distribution), then we can determine the PPFD for the given wavelength by multiplying the spectral irradiance (watts/m2) by the watts to Einstein conversion factor for each wavelength (recall from Part I how to convert energy at a given wavelength into the number of photons). To compute the total PPFD over the range of 400-700 nm, compute the PPFD for each wavelength and sum over the range of 400-700 nm.


There are three basic forms of light measurement - radiometric, photometric and photosynthetic - and these can be measured at the source or at the object onto which the light falls. Photometric measurements are derived from the radiometric measurements by factoring in the human eye's response, and do not treat all radiation equally. Photosynthetic measures, on the other hand, treat all radiation equally. The starting point for all these measures is the spectral power distribution, from which all other entities can be derived. Conversion from one set of units to the others is simply not possible unless the spectral power distribution is known.

In addition to these lighting measures, additional measures such as Color Rendition Index (CRI) and Correlated Color Temperature (CCT) are used to describe light. These will be covered in the next part of this series.

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Facts of Light – Part 3: Making Sense of Light Measures by Sanjay Joshi -