Converting From Radiometric Units to Photometric Units

You can convert from radiometric terms to the matching photometric quantity; however the photometric quantity depends on how the source appears to the human eye. This means that the variation of eye response with wavelength, and the spectrum of the radiation, determines the photometric value. Remember that invisible sources have no luminance, so a very intense ultraviolet or infrared source does not register a value on a photometer.

The conversion between photometric units and straight radiometric units for a monochromatic light source (see note 2) is given by the following formula: (photometric unit) = (radiometric unit) x Km x V(λ)

Figure 1 - the relationship between emission
wavelength and luminosity for modern LED lamps.

Where:

V(λ) = the "luminous efficiency," and is a function of the wavelength of light.

Km = 683 lm/W, the maximum sensitivity for photopic vision, which occurs at 555nm (see Note 2).

Basically the luminous efficiency tells us how efficiently the eye picks up certain wavelengths of light. Illustrated below is a graph of V(λ) and the Photonic Response Table of Wavelength and corresponding V(λ):

Example Of Conversion:

Let's say you have an ultra Red LED with a peak wavelength of 660nm and a power output (Radiant Flux) of 4mw. What is the Luminous Flux?

At 660nm, V(λ) = 0.061 lm/watt.

Therefore:

Luminous Flux = 0.004 watts x 683 lm/watt x 0.061 = 0.167 lm

Conversion Note 1:

The CIE selected the wavelength 555nm, the peak of the photopic luminous efficiency function, as the reference wavelength for the lumen, the standard photometric unit of light measurement. This wavelength corresponds to the maximum spectral responsivity of the human eye. By definition there are 683 lm/W at 555 nm. The lumens at all other wavelengths are scaled according to the photopic luminous efficiency functions.

Conversion Note 2:

The conversion technique described above is only true for monochromatic (single wavelength) light sources. Most LEDs are monochromatic light sources with the exception of White LEDs or LEDs with phosphors added on top of the die to create a variable amount of hues.

The conversion technique for non-monochromatic light sources is more complicated. It requires multiplying the spectral distribution curve by the photopic response curve, integrating the product curve and multiplying the result by a conversion factor of 683. This is illustrated in the following formula:

Where:

θv = Photopic Luminous Flux (lm)
Km = 683 lm/W
V(λ) = the "luminous efficiency"
θλ = Spectral Radiant Flux (W)

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