Light intensity

We should specify a standard source in order to define the light intensity in a clearer way. A standard source is any body which radiates energy, although not all the energy is considered lighting energy (the one we perceive through the sense of sight) but part of that lighting energy is converted into heat and non visible radiations. So, part of that energy which is emitted by a source,  is not a visible energy. The lighting radiations come from the warming of a given material by which energy radiates.

This 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 source of radiation is given by the lighting flux F which is emited in a specified way by a unit of solid angle W, in other words, the lighting power of the source which is expressed in watts. 

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.

The International System of Unities (IS) included the CANDLE as a unit of measure of light intensity of a source.

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 555 nm 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. (That is to say, 1 steradian covers 1m² of a surface of 1m of diameter sphere).

The apparent shine of a source when is looked directly at it must not be confused with its light emission. The shine of a source is measured through the candle by square metre (cd/m²) and its magnitude is called luminance.

The  luminence (L) is the lighting magnitude which determines the impression of a more or less brightness produced by a surface. The luminence is a common concept in the shine of an object, 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:

 V-LAMBDA Curve

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 kind of lighting. The photopic vision for normal and strong lightings and the scotopic vision for the low ones. 

Because of this fact the same sensation of shine is not produced for equal quantities of lighting flux of different wavelengths. So, for example, for the same sensation of shine, it obtains a higher sensation of shine for the yellow-green than for the ends of the red-purple. 

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

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

The watts which are emitted by a source of light 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 and with that the eye and the human brain may value the brightness. The measurement  instruments have sensors of filtrate which are able to turn the  absorbed light by the V-lambda into electric current.

Lumen and lux

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). That is, it indicates the quantity of light which is emitted in a unit of time in an specific direction (spatial distribution of the light which is emitted by the source). Its unit is the lumen (lm).683 lumens are the equivalent of one watt, emitted to 555 nm wavelength, which is the equivalent of the highest sensitivity of the human eye.          

The definition of lumen, 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 given by dF=IdR" 

This means that the flux of a light source 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.

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

We have already seen the concept of solid angle; if we take into consideration a source which emits a certain radiant energy and that this supposedly does it in all  directions, we can consider this one as an 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 area of a sphere 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 define the lumen in this way:

"It 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 the lighting flux. When we talked about light intensity 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...). 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 light of simple wavelength. A lamp of several wavelength has an exit of lumens which is calculated from the watts emitted as the radiation multiplied by the luminous efficiency in each wavelength, as it was described in the case of the candle.

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 in the reverse way. As far as 3m of the lamp, the flux over 1m² declines to 1/9 from  the 300lm. The lux value is 33.

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

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

The illuminance 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 illuminance is known as the reverse law of the squares which relates the lighting intensity and the distance to the source. This law is only valid if the direction of the ray of incidental light is perpendicular to the surface.

Reverse law of squares:

In case the ray of light that falls on isn't perpendicular, we have to break up the illuminance to the surface in an horizontal and vertical component.  

The horizontal component of the lighting (E_H) is known as the cosine law. It isn't difficult to see that if   = 0 we have the inverted law of the squares. If we express  E_H y E_V  depending on the distance of the 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 received light.

Units and conversion tables.