How to Calculate Illuminance

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When installing light bulbs or controlling the brightness of your computer screen, an understanding of the brightness of light can assist you in determining how effective they are.

The illuminance of a surface, a feature different from luminance, measures how much light falls on it while luminance is the amount of light reflected or emitted from it. Staying clear with terminology when it comes to brightness and electricity can help you make better decisions.

Calculating Illuminance

You measure illuminance as the amount of light that falls on a surface in units of foot-candles or lux. 1 lux, the SI unit, is equal to about 0.0929030 foot-candles. 1 lux is also equal to 1 lumen/m2 in which lumen is a measure of luminous flux, the amount of visible light a source emits per unit of time, and 1 lux also equals .0001 phot (ph). These units let you use a wide range of scales for determining illuminance for different purposes.

You can calculate illuminance E related to luminous flux "phi" Φ using E = Φ / A over a given area A. This equation denotes luminous flux with Φ, the same symbol for magnetic flux, and it shows similarity to the equation for magnetic flux Φ = BA for a surface area parallel to a magnet A and magnetic field strength B. This means illuminance parallels magnetic field in the way scientists and engineers calculate it, and you can convert the units of illuminance (flux/m2) directly to watts using the intensity (in units of candelas).

You can use the equation Φ = I x Ω for flux Φ, intensity I and angular span "ohm" Ω for the angular span in steradian (sr), or square radian, and a full sphere has an angular span of . The light calculated in illuminance falls onto the surface and spreads out causing the object to become bright, so illuminance may be used as a measure of brightness.

For example: The illuminance on a surface is 6 lux and the surface is 4 meters from the light source. What is the intensity of the source?

Because light travels in a radiating pattern, you can imagine the light source is the center of a sphere with a radius equal to the distance between the light source and the object. This means the corresponding surface area to use is the surface area of the sphere that corresponds with this arrangement.

Multiplying the sphere's surface area with radius 4 as 4π42 m2 by illuminance 6 lumen/m2 gives you 1206.37 lumens of flux Φ . The light travels directly to the surface, so angular span Ω is candelas, and, using Φ = I x Ω, the intensity I is 15159.69 lumens/m2.

Calculating Other Values

The candela used in the angular span is used as a measurement of the amount of light that a light source emits in a range in a three-dimensional span. As shown through the example, the angular span is measured through steradian over the surface area which the light is applied. A full sphere's steradian is candelas. Make sure to not mix up lux and candela.

While candela is a measurement of the angular span, the lux is the illumination of the surface itself. At points farther away from a light source, the lux is less as less light is able to reach that point. This is important in real-world applications and precise calculations that need to account for the exact source of a light that would be in, for example, the tungsten wire of a light bulb, not the case of the light bulb itself. For smaller light bulbs such as certain LED light sources, the distance may be more negligible depending on the scale of your calculations.

One steradian of a sphere with a one-meter radius would encompass a surface of 1 m2. You can obtain this from knowing that a full sphere covers candelas so, for a surface area of (from 4πr2 with a radius of 1) steradians, the surface this sphere would covers is 1 m2. You can use these conversions by calculating real-world examples of light bulbs and candles giving off light using the surface area of a sphere to account for the geometry of the light. They can then be related to luminance.

While illuminance measures light incident on a surface, luminance is the light emitted or reflected by that surface in candela/m2 or "nits". The values of luminance L and lux E are related through an ideal surface that emits all light with the equation E = L x π.

Using a Lux Measurement Chart

If it may seem daunting to have so many different ways of measuring the same quantities, online calculators and charts perform calculations to convert between different units to make the task easier. RapidTables offers a lumens to watt calculator that calculates power for different light standards. The table on the website shows these values so you can see how they compare against one another. Note the units of lumens and watts when performing these conversions which also use the luminous efficacy by "eta" η.

The EngineeringToolBox also offers methods of calculating illuminance and illumination for standards of light bulbs and lamps alongside a lux measurement chart. Illumination is another method of calculating illuminance that uses electrical standards of the lamp or light source instead of the experimental measurements of light given off itself. It's given by the equation for illumination I as I = Ll x Cu x LLF / Al for luminance of the lamp Ll (in lumens), coefficient of utilization Cu, light loss factor LLF and area of the lamp Al (in m2).

Lighting Efficiency

As calculated by the RapidTables website, the luminous efficacy of radiation is a common way of describing how a light bulb or other light source uses its energy resources well, but the official method of determining the efficiency of light sources is the luminous efficacy of a source, not radiation.

Scientists and engineers typically express lighting efficiency as a percent value with the maximum theoretical value of lighting efficiency 683.002 lm/W, which emits a 555 nm wavelength of light. As one example, a typical modern day white watt "lumiled" can reach efficiencies of over 100 lm/W with an efficiency of 15%, which is actually more than many other types of light sources.

Measuring luminance and illuminance in science and engineering take into account the ways eyes themselves perceive the brightness of light to obtain more refined, objective measurements. Examining the distribution of the brightness of light using experiments try to understand whether the response to brightness is due to cone or rod photoreceptor signals within the human eye.

Other research, such as photometry research, seeks to detect specific forms of radiation based on their response linearity. If two fluxes of light Θ1 and Θ2 were to produce two different signals, photometry detectors measure the signal generated as a result of both of the fluxes added linearly. The response linearity is the measure of this relationship.

References

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.

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