Light measurements

We should specify a standard source in order to define properly the light intensity. A standard source is any body which radiates energy. However, not all the energy is considered lighting energy (the one we perceive through the sense of sight), because part of that energy is converted into heat or non visible radiations, so that, part of the source energy is invisible. The lighting radiations come from the warming of a given material by which energy radiates.

The standard source consists of a cylindrical tube made of heat-resistant material (Torio), with the highest melting point, surrounded by pure platinum. The tube gets wider in its end forming a solid angle of a steradian.Once this total radiator is heated over a temperature of 2045 K ,it emits a certain quantity of radiant energy, 1m²/600000 of this energy is our measurement of reference and it is what we call candle (cd).

The light intensity (I), fundamental feature of the radiation source is given by the lighting flux (F) which is emitted in a specified way by a unit of solid angle (W) or what is the same, the lighting power of the source which is expressed in watts (W).

Since the lighting flux is measured in lumens, the unit of light intensity will be the lumen in a steradian, which is called candle (cd).

However, measuring the power that belongs exclusively to the visible area is not an easy task because most of the sources emit in a broader area of the electromagnetic spectrum. In order to measure the intensity of a source it is necessary to define a unit which must be constant and invariable in relation to a given surface in order to measure the intensity of a source. For this aim, the International System of Unities (IS) included the CANDLE as a unit of measure of a source light intensity.

The candle (cd) may be defined as the lighting intensity in a certain direction of a source which emits monochromatic radiation with a 540 x 1012 Hz frequency equivalent to 555nm in the vacuity. The candle has an intensity of radiation in that direction of 1/683 watts per each steradian.

The "chosen frequency" is the one to which the eye is more sensible and is usually quantized in the Light Literature as one wavelength of 555 nanometers. The wavelength varies according to the environment through which the light goes right, so if we want to specify this, we could say that the light wavelength we understand is not the one used by the standard mode. Our strange choice of the 683 factor is because we want the value to be identical to the one obtained with the previous version of the unit: the 1cm² emission of solidified platinum shine.

The steradian (sr) is the cone light that is given off from the source which lights 1m² of a dark surface in a meter radius around the source. (What is the same, 1 steradian covers 1m² of a surface of 1meter diameter sphere).

The apparent source shining when is looked directly must not be confused with its light emission. The source shining is measured through the candle by square meter (cd/m²) and its magnitude is called luminance.

The luminance (L) is the lighting magnitude which determines the impression of a more or less brightness produced by a surface. The luminance is a common concept in the object shining, either with relation to the own produced light or reflected (source which emits light, source of light which is only reflected or source of light which has both emissions). It is defined as the luminous sensation which is produced in the retina of the eye because of the effect of the light. It is the superficial density of the light intensity and is expressed as the relation between the luminous intensity and the surface from which is emitted:

The measurement of the light intensity requires information about the relative sensitivity of the human eye for different wavelengths.

The eye has two different sensitivities according to the lighting type: the photopic vision for normal and strong lighting modes and the scotopic vision for the low ones. Due to this fact, the sensation of shine is not the same for equal quantities of lighting flux on different wavelengths. For instance, the sensation of shine for the yellow-green is higher than for the ends of the red-purple.

White light intensity source is defined by the product of the watts which are emitted for each wavelength through the output of that wavelength exciting the human eye, which output is 555nm. This factor of output is known as V-lambda curve.

This curve defines the relation between the sense of human light and the physical concept of light, which is the quantity the measure instruments react to.

The source of light emitted watts can be measured by absorbing all the light in a black ideal surface and by measuring the heat that has been produced. A filter which belongs to the V-lambda curve can be placed in front of a black surface in order to convert the result so that the eye and the human brain could value the brightness. The measurement instruments have filter sensors which are able to turn the V-lambda absorbed light into electric current.

The lighting flux (F) is the power (energy per one unit of time) of the lighting energy which is measured according to its visual effect (it is equivalent to one candle per each steradian). Clearly explained, it indicates the quantity of light which is emitted in a unit of time in a specific direction (spatial distribution of the source emitted light). Its unit is the lumen (lm).683 lumens are the equivalent of one watt, emitted to 555nm wavelength, which is the equivalent of the highest sensitivity of the human eye.

The lumen definition, the unit of a lighting flux, is: 'The lighting flux (dF) is a source of light Intensity I (cd) at an angle with a solid element is given by dF=IdR'

This means that the light source flux equals its intensity in candle multiplied by the solid angle over which the light is emitted, taking into account the variation of intensity that it produces in different directions.

We can observe from image a light point of the green ray emitting a 300 cd light intensity for a 30º angle.

Having already seen the concept of solid angle, if we take under consideration a source which emits a certain radiant energy and that this supposedly does it in all directions, we can consider this one as a sphere. The solid angle will determine one cone which takes up a certain surface or area (s), in relation to the radius unit. In these conditions, the measurement in steradians of the solid angle W is defined due to:

Since the sphere area is 4πr², if we replace it, we will get:

When S = r² the solid angle will be of one steradian. According to this, we could redefine the lumen:

'Lumen is the lighting flux that goes through a solid angle of a steradian in one second, emitted by a precise source whose intensity is of one candle.'

The output is a magnitude derived from lighting flux. When we talked about light intensity before, we mentioned that not all electric current consumed by a lamp (light bulb, fluorescent, etc.) is turned into visible light. Part of it gets lost by heat, part by non visible radiation (infrared or ultraviolet) etc.

We define the lighting output (h) as the quotient between the produced lighting flux and the consumed electric power, characterized by the lamps (25 W, 60 W, etc.). The bigger it is, the better the lamp will be and the consumption will be less. The unit is lumen per watt (lm/W).

The lumen formally derives from the candle, based on a simple wavelength light. A several wavelength lamp has a lumens exit which is calculated from the watts emitted as the radiation multiplied by the luminous efficiency in each wavelength, as it was described in the candle case.

The designer needs to translate the values of cd into Luminous Energy which reaches an object to a certain distance from the lamp. It is this energy which makes the object visible and which turns pale its nuances of color. The energy density which reaches the object is expressed in lumens per square meter (Lm/m²) , what is known as lux.

This value can be easily calculated from the diagram by a starting point. The candle value (300cd) given by 60° is the same that 300 lumens flowing in the cone of a steradian (sr), that by definition takes up 1m² of the surface of 1m diameter sphere.

If our object were in that distance, it would be receiving 300 lm/m².

In order to deduce the value of any other distance, the same rule must be used the other way round. Three meter away of the lamp, the flux over 1m² declines to 1/9 from the 300lm. The lux value is 33.

The luminance (E) is the lighting flux that falls on a surface, divided by that surface size (s). The luminance is the assessment magnitude of the light level on a surface or spatial zone.

The luminance unit of measure is the Lux (Lx), equivalent to the light which falls on each m² of a surface and on which a lumen lighting flux is uniformly distributed.

The luminance depends on the distance from the focus to the lighted object. It is something similar to what happens when we listen to a car moving away; at the beginning we can hear it loud and clear, but later it decreases until it gets lost. What happens with the luminance is known as the reverse law of the squares which relates lighting intensity and source distance. This law is only valid if the incidental light ray direction is perpendicular to the surface.

Reverse law of squares:

In case the light ray that falls on is not perpendicular, we have to break up the luminance into a horizontal and a vertical component.

The horizontal component of lighting (EH) is known as the cosine law. It is not difficult to see that if = 0 we have the inverted law of the squares. For this reason, if we express EH y EV depending on distance from focus to the surface (h) we have:

Normally, if a point is being lighted by more than a lamp, its total lighting is the sum of the light received.