Light Metrics

The Measurements of Light

Light is a radiated form of energy. Other forms of radiant energy include electro-magnetic, nuclear, and heat.   Light consists of photon particles and radiated waves.   Radiated energy flows from a point source toward the surface of a sphere surrounding it.   The amount of energy falling on the sphere follows the inverse square law of energy: E=1/r2.   There are three important metrics of radiated energy; force, distance, and time.   In some cases, direction should also be considered but it can be ignored in this discussion.  

Force is a measurement of the intensity of energy per unit of area, volume, angle, or similar unit.   For example, a joule is the unit of energy required to exert a force of one Newton over one meter.   Flux is the rate of energy or fluid distribution over a surface area.   An example of flux is the foot-pound.   The quantity of energy (flow) is measured over time.   For example, a watt-second is one joule (or one amp at one volt) per second.   A kilowatt-hour is 1000 watts for an hour.

There are five important measurements of the energy of light; intensity, flux, illumination, reflection, and quantity.   The intensity of the source is typically measured in candelas.   Light flux (transmitted through space) is measured in lumens.   Light illumination at a surface is measured in LUX or foot-candles.   The luminance of light reflected from a surface is measured in candelas per square meter or foot-lamberts.

The quantity of light can be measured in lumens or lux per second.   This can be translated into an exposure value.   The photographer or camera then matches the measured exposure value to a combination of film sensitivity, aperture size, and shutter speed.

The Intensity of Light

The intensity of light is measured at its source.   The basic unit is the candela.   It is equivalent to the light emission from an open flame (candlepower) or more scientifically, the light emission from one square centimeter of glowing platinum at 1042° Kelvin.   For lighting measurements, the light source is a point at the center of a sphere that contains the illuminated surface.   Since 1979 there has been a new official definition, the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540x1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.   This is more clearly a definition of power and can be more easily and accurately measured.   Note that this works out to a yellow/green light (555.6 nm) at the peak of our eyes sensetivity.   For most of us, the open flame from a candle is close enough for the concept.

A steradian is an angular measurement of a cone where the area covered is equal to the radius of the sphere squared.   Thus one square foot at one-foot radius and one square meter at one-meter radius are both one steradian.   A constant source will emit the same energy at either distance to the corresponding surface area.   You can think of the energy as the number of photons striking the surface of the sphere.   Whether you measure it in feet or meters, the same number of photons will cover each area, just at different densities.   The amount of energy does not diminish over distance, but it does spread out.


Luminous flux is measured in lumens.   A lumen is the flux unit of the light output from a light source that falls on one steradian of surface area.   One candela from a light source will produce one lumen of light at one steradian.   A lumen is the same in the English or metric systems.   Since the total surface area of the sphere is 4πr2, one candela produces a total of 12.57 lumens across the entire sphere.   The radiant energy efficiency of light does vary with the wavelength.   Again, at 555 nanometers (yellow-green light), it is defined as 1 lumen/683 watts of radiant flux.   For photographic applications, the flux (lumens) is frequently adjusted for the spectral response of visible light.

Illumination (or illuminance) from a source of light is measured in foot-candles or lux.   The standard metric unit for illuminance is the lux, lumens per square meter.   The standard English unit for illuminance is the FC, lumens per square foot.   One FC is 10.764 lux. Either is a measure of lumens per unit of surface area.   Illuminance is an area density measurement that decreases with distance from the source following the inverse square law of light (energy).   This is also called incident light when measuring the light falling on a subject.   Similarly, the term ambient light is used when the light is from multiple continuous sources including reflected and diffuse light.


Reflected Light

Luminance from a diffuse reflecting surface is measured in Lamberts.   A Lambertian surface provides perfectly uniform diffusion of the incident radiation such that its luminance is the same in all directions from which it can be measured.   Note that this is not a spectral reflecting (mirror) surface.   The Lambert is a measurement of reflected light from a diffused surface.   Luminance = illuminance x reflectance / π.   A perfectly diffuse white surface with one lux of illumination will reflect 1/π nits of light.   The metric unit of luminance is the apostilb. The English equivalent is the foot-lambert.   The term π sneaks into the formula because it is based on calculations of the cosine of angles of incidence and diffused reflection to a spherical surface again.


To determine the luminance of a tone we need to multiply the illumination by the surface reflectance.   For example, the standard photographic gray card is 18% reflectance.   This brings up an important point, a 50% (middle) gray tone has 18% surface reflectance.   The 50% tonal value is the middle tone between the darkest and lightest reproducible tones (contrast range).   But the reflectance follows logarithmic progressions.

A typical gray scale mapped into the standard photographic zone system.

In the zone system each tone represents one f/stop or EV difference.   Black and white on the scale are not technically pure, but represent the paper white and ink black.   So, the contrast or density range of the media would have to be a factor in any attempted calculations.   A reflected light meter or inboard camera meter is calibrated to exposure values assuming that the target or scene is mid tone at 18% reflectance.   So, 18% gray reflectance has become the standard photographic exposure target.

Luminance (reflectance) measurements are independent of distance.   Unlike light from a point source, diffuse reflected light arrives at all angles.   Therefore, it does not spread over distance and the inverse square law does not apply.   That is why the gray card does not have to be positioned exactly at the subject plane as long as it gets the same illumination.   It does need to fill the viewfinder or angle of view of your light meter so that it is the only light being measured.   Of course if you consider the reflected light a source or the distance is great enough that the light becomes a point source, it is now providing illuminance and distance is a factor.

Summary

MeasurementUnitDefinition
Intensity
(force)
candle
candlepower
candela
1cm2 glowing platinum @1042K
source producing 1/683 watt/steradian at 540x1012 Hz
Flux lumen1 candela @ 1 steradian
Illuminationlux
foot-candle
phot
1 lumen/meter2
1 lumen/foot2
1 lumen/centimeter2
Luminanceapostilb
foot-lambert
nit
1/π * candela/meter2
1/π * candela/foot2
1 lux on @ 100% reflection = 1/π nits off
Quantity
(power)
lumen-second
lumen-hour
EV
Lumen seconds
Lumen hours
Photographic exposure value

Photographic Exposure Values: EV

Exposure values (EV) are a measure of the quantity of light over time, not the intensity.   EV was defined by the photographic industry as a unit that could be used to calculate aperture settings and shutter speeds based on film sensitivity.   The standard starts with EV0 for a one-second exposure and an aperture at f/1 using ISO 100 film.   It is also the basis for the sunny f/16 rule.


The quantity of light can also be measured in lumens, lux, or apostlib per second.   Therefore, there is a direct relationship between LUX per second or apostlib per second and EV.  

EV to illumination (lux)LUX=2EV * 2.5
LUX to exposure valuesEV = Log2(LUX / 2.5)
EV to luminance (apostilb)Apostlib = (1/π) x (2EV * 2.5)
Luminance (apostilb) to EVEV = Log2((π x apostlib) / 2.5)

Exposure meters measure the number of photons striking an electronically sensitive surface.   This is essentially the same as measuring illumination or luminance.   A count of photons (quantum units) in a given area for a given time is measured in Einsteins, also called moles.   Since this also varies across the light spectrum it is adjusted to visible light in PARs.   A PAR is a Photosynthetically Active Radiation unit.   Of course, you also have to know the sensitivity and other characteristics of the photo diode or photomultiplier tube.   Otherwise, how could a light meter work?

The following chart shows exposure values and the corresponding illuminance and luminance.  

EVLUX/secApostlib/secComments
-3.3125.099Night, away from city lights.
-2.625.199Full moon lit night, away from city lights.
-11.25.398Subjects lit by dim ambient artificial light.
02.5.796Subjects lit by dim ambient artificial light.
151.59Distant view of lighted skyline.
2103.18Total eclipse of moon.
3206.37Lightning or fireworks at night.
44012.73Subjects under bright street lamps. Candle lit close-ups.
58025.46Average nighttime building interiors.
616051Brightly lit home interiors at night. Fairs, amusement parks.
7320102Bottom of forest canopy. Indoor sports. Stage shows.
8640204Brightly lit city streets (Las Vegas or Times Square).
91.280407Landscapes and skylines 15 minutes after sunset.
102,560815Landscapes and skylines immediately after sunset.
115,1201,630Subjects in open shade. Sunsets.
1210,2403,259Subjects in heavy overcast skys.
1320,4806,519Subjects in cloudy-bright light (no shadows).
1440,96013,038Subjects in weak, hazy sun. Photo of a full moon.
1581,92026,076Subjects in bright or hazy sun (Sunny f/16 rule).
16163,84052,152Subjects in bright daylight on sand or snow.
17327,680104,304Rarely encountered in nature.

Note that the constants used are approximations and valid for the visible spectrum only.   They do seem to correlate to other published technical information.   They are only useful as a rough gauge for understanding the nature of light.   They did help me validate my research into the photographic nature of light and understanding how light meters work.

Exposure Matrix

If you would like to read more about aperture and shutter settings:


Physical Measurements and Human Perception

Note that these physical measurements codify the physical intensity and quantity of light.   They do not tell us about the human perception of light.   This is a separate field of study undertaken by the CIE (Commission International de L'Eclairage).

There are three basic classes of vision based on excitation of rods and cones in the eye.   These are called photopic, mesopic, scoptic.   Photopic is based on the cones and includes color vision.   This is the normal daylight vision.   The rods in the eye are effectively turned off.   Scoptic is based on the rods and is devoid of color.   The cones in the eye are effectively insensitive.   This is the normal nighttime vision.   Mesopic is the in-between area.   This would represent our vision at dawn and dusk.

The point of this is that vision is based on our perception of relative stimulus.   An automobile headlight viewed directly at night is strong enough to almost blind one.   The same headlight light viewed at mid day is barely perceptible.   The intensity of the light source has not changed.

The objective in photography is to match the scene illumination to our visual perception.   The CIE helps us achieve this mathematically with color models and color spaces.


I hope you also gained some new insight from this article.   If you have any comments, or suggestions, I would welcome your input.   Please send me an  Email.


Rags Gardner
Rags Int., Inc.
204 Trailwood Drive
Euless, TX 76039
(817) 267-2554
Send Email
www.rags-int-inc.com
May 28, 2004

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