Radiometry vs photometry

Radiometry and photometry describe the same geometric quantities (power, power per area, power per solid angle and power per area per solid angle) and differ only in how the power is counted. Radiometry counts energy: a radiant flux is measured in watts, whatever the wavelength. Photometry counts the energy as the standard human eye would weight it, multiplying the spectral power at each wavelength by the photopic luminosity function $V(\lambda)$, which peaks at 555 nm, and by the constant $K_m = 683$ lm/W. One watt of 555 nm light is therefore 683 lumens, one watt of red light at 650 nm is 73 lumens, and one watt at 1550 nm is zero lumens. Laser safety, detector specifications and optical communications use radiometric units; lighting, displays and vision use photometric ones.

Paired quantities

Each radiometric quantity has a photometric twin: radiant flux (W) and luminous flux (lm); radiant intensity (W/sr) and luminous intensity (candela, lm/sr); irradiance (W/m²) and illuminance (lux, lm/m²); radiance (W/(m²·sr)) and luminance (cd/m², also called nit). The full table and the three senses of "brightness" are in the brightness entry. The geometric relations between the quantities, the inverse-square law and the conservation of radiance by passive optics hold identically in both systems, because the spectral weighting is applied before any geometry.

Conversion formula

For a source with spectral radiant flux $\Phi_{e,\lambda}$ in W/nm, the luminous flux is

$$\Phi_v = K_m \int \Phi_{e,\lambda}(\lambda)\,V(\lambda)\,d\lambda,$$

integrated over the visible range, roughly 380–780 nm. For a monochromatic source this reduces to $\Phi_v = 683\,V(\lambda)\,\Phi_e$. Using CIE 1924 values of $V(\lambda)$:

A 5 mW red laser at 650 nm emits 0.37 lm, while the same power at 555 nm would be 3.4 lm. The inverse conversion from lumens to watts requires the spectrum; a lumen value alone does not determine the radiant power of a broadband source.

The constant 683 lm/W comes from the SI definition of the candela, which fixes the luminous efficacy of monochromatic radiation at 540 × 10¹² Hz, a vacuum wavelength of 555.17 nm, to exactly 683 lm/W. For night (scotopic) vision a separate function $V'(\lambda)$, peaking near 507 nm with a maximum efficacy of about 1700 lm/W, applies; nearly all practical photometry uses the photopic function.

A photometric worked example

A lamp emitting 1000 lm uniformly into all directions has a luminous intensity of $1000/(4\pi) = 79.6$ cd. At 2 m, the illuminance on a surface facing the lamp is $I/r^2 = 19.9$ lx. The same calculation in radiometric units, starting from the lamp's radiant flux, gives the irradiance in W/m².

Measurement

Radiometric measurements use detectors with known spectral responsivity, such as a calibrated photodiode or thermal optical power meter. Photometers use a silicon detector behind a filter designed so that the combined response follows $V(\lambda)$; lux meters add a cosine-corrected diffuser, and total luminous flux is measured in an integrating sphere. The alternative, and the more accurate route for colored sources, is a spectroradiometer that measures the spectral power distribution, from which any photometric quantity is computed numerically.

Pitfalls

The match between a photometer filter and $V(\lambda)$ is imperfect, especially at the steep blue and red wings, so photometers calibrated on an incandescent source can read narrowband LEDs and lasers with errors of many percent. The CIE 1924 function underestimates the eye's sensitivity below about 460 nm, a known deficiency retained for continuity. Photometric units say nothing about power outside the visible: an infrared source can deliver a hazardous irradiance while reading zero lux, and ultraviolet exposure is likewise invisible to photometry. Luminous efficacy of a source (lumens per electrical watt) and luminous efficacy of radiation (lumens per optical watt) are different quantities and are often confused. Some fields, such as plant biology, count photons instead of watts, quoting photon flux in µmol/s; converting that to watts uses the photon energy at each wavelength: 1 W at 555 nm carries 4.64 µmol of photons per second.

Common questions

What is the difference between radiometry and photometry?

Radiometry measures optical power in watts at all wavelengths; photometry measures the part of that power the human eye responds to, in lumens, by weighting each wavelength with $V(\lambda)$. The two agree in geometry and differ only in the spectral weighting.

How many lumens are in a watt?

It depends on the spectrum. The maximum is 683 lm/W for monochromatic light at 555 nm. At other wavelengths it is $683\,V(\lambda)$, and for broadband sources it is an integral over the spectrum; for infrared and ultraviolet light it is zero.

Is lux radiometric or photometric?

Photometric. Lux is illuminance, lumens per square metre; its radiometric counterpart is irradiance in W/m².

References: BIPM, The International System of Units (SI Brochure), 9th ed. (2019); W. R. McCluney, Introduction to Radiometry and Photometry, 2nd ed. (Artech House, 2014); G. Wyszecki, W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982).