Candela

**Brad Barker** · Sep1-04, 08:44 PM

This is the SI unit for luminous intensity. The definition relates to blackbody radiation emitted at a certain temperature for a certain material (so I guess it ISN'T blackbody!), platinum, I think.

Except... I don't understand the necessity for the introduction of this unit.

Isn't intensity equal to power per area? Or is this something totally different?

**Galileo** · Sep2-04, 06:14 AM

It's slightly different.
From a physical point of view we are interested in quantities like:

Radiant Energy

(J=Ws)
Radiant energy density

Radiant flux (or just electric flux).
etc.
These are called Radiometric quantities. It's what you learn in EM-class.

From a optical point of view, we are more interested in that portion of the EM-spectrum which is visible light (optical spectrum). This is photometry.
Radiometry involves purely physical measurements, while photometry takes into account the response of the human eye to radiant energy at various wavelenghts. So it involves pseudo-physical measurements.
The distinction rests on the fact that the human eye, as a detector, does not have a "flat" spectral response. It does not respond with equal sensitivity to all wavelenghts.
If three sources of light with equal radiant power but radiation blue,yellow and red light are observed visually, the yellow source will seem much brighter than the others.

That is what photometric quantities are for. To measure properties of visible radiation as they appear to the normal eye, rather than as they appear on a "unbiased" detector.

A few photometric quantities are:
Luminous Energy (photometric counterpart of Radiant energy)
Luminous energy density (photometric counterpart of Radiant energy density)
Luminous flux (photometric counterpart of Radiant flux)
etc.

Since not all human eyes are the same, a standard response has been determined by the International Commision of Illumination (CIE).
The function that relates the relative response or sensation of brightness for the eye versus the wavelenght is called the CIE luminous efficiency curve.
I don't have a scanned picture of it, but it appears kinda gaussian with the peak on the yellow color.
There's a efficiency curve for daylight vision and one for night vision.

Radiometric quantities are related to photometric quantities through this curve.
The relation is simple:
photometric unit = $LaTeX Code: K(\\lambda) \\times$ radiometric unit
where $LaTeX Code: K(\\lambda)$ is the luminous efficacy.
If $LaTeX Code: V(\\lambda)$ is the luminous efficiency, then
$LaTeX Code: K(\\lambda)=685V(\\lambda)$

phew...

**Brad Barker** · Sep2-04, 08:02 AM

ok. that's all new to me!

...but...how is luminous (and i suppose also, radiant) intensity defined? Is it luminous flux times...something...?

**Galileo** · Sep2-04, 10:31 AM

The radiant intensity is the radiant flux emitted per unit of solid angle by a point source in a given direction. It's measured in Watts per steradian.

Intensity is very often confused with irradiance, which is the flux per unit area. It's measured in Watts per square meter.

NOTE: I say they are often confused, but since most physicist are often interested in the power delivered per square meter, it's often called the intensity of the radiation. So often that, in fact, it may be wrong to speak of confusion, in which case we have two different meanings for the same word.

For the luminous quantities, it's very simple. Instead of using Watts, you measure in lumen (lm). The dimensions are the same as in the radiant case, but this time it's multiplied by the luminous efficacy.
So 'luminous intensity' is (also called 'candlepower') is lumen per steradian (also called 'candela' (cd)).
Instead of 'luminous irradiance', the word 'Illuminance' is used. It's measured in lumen per square meter.

**Brad Barker** · Sep2-04, 10:39 AM

ok. making sense now. the candela is introduced as a standard for photometric quantities and not radiometric ones.

what is the unit of flux, now?

**Galileo** · Sep2-04, 12:05 PM

Well. The flux through a surface is the amount of 'flow' through that surface. So it depends on what you measure.
When we talk about the electric flux:
$LaTeX Code: \\Phi_E = \\int\\vec E \\cdot d\\vec a$
I think it's appropriate to measure it in Vm.
The magnetic flux:
$LaTeX Code: \\Phi_B = \\int\\vec B \\cdot d\\vec a$
is measured in Weber (Wb).

In our context we were talking about the energy flux. (The energy crossing through a surface per unit time). So it's Joules per second, or Watts.

Radiant flux is in Watts (W) or (J/s)
Luminous flux is in lumen (lm).

**Brad Barker** · Sep2-04, 05:28 PM

Originally Posted by Galileo

Well. The flux through a surface is the amount of 'flow' through that surface. So it depends on what you measure.
When we talk about the electric flux:
$LaTeX Code: \\Phi_E = \\int\\vec E \\cdot d\\vec a$
I think it's appropriate to measure it in Vm.
The magnetic flux:
$LaTeX Code: \\Phi_B = \\int\\vec B \\cdot d\\vec a$
is measured in Weber (Wb).

In our context we were talking about the energy flux. (The energy crossing through a surface per unit time). So it's Joules per second, or Watts.

Radiant flux is in Watts (W) or (J/s)
Luminous flux is in lumen (lm).

yeah, i'm familiar with electric and magnetic flux. and in those cases, the equations incorporate the surface through which the fields pass through.

...but it seems like radiant flux doesn't if the unit is just Watts and not Watts/steradians, since flux seems to, by definition, need to incorporate some sort of surface...

i guess it's just something you have to accept by definition.

so...radiant intensity is just what would be considered the energy of radiation passing through a solid angle.

and luminous intensity is that, with a correction factor for it to be useful for human perception.

pretty much have it.

**Brad Barker** · Sep3-04, 12:47 AM

Introduction to heat Transfer by Incropera and DeWitt define Intensity to be "Rate of radiant energy propogation in a particular direction, per unit area normal to the direction, per unit solid angle about the direction." Units of W/(m^2*sr).

Also, about flux, it normally doesn't incorporate rates, right? Just an amount of field (or in this case, energy) passing through some surface. Why is the radiometric/photometric definition any different? (ESPECIALLY with the lack of a specified area.)

**Galileo** · Sep3-04, 03:17 AM

Originally Posted by Brad Barker

Introduction to heat Transfer by Incropera and DeWitt define Intensity to be "Rate of radiant energy propogation in a particular direction, per unit area normal to the direction, per unit solid angle about the direction." Units of W/(m^2*sr).

Also, about flux, it normally doesn't incorporate rates, right? Just an amount of field (or in this case, energy) passing through some surface. Why is the radiometric/photometric definition any different? (ESPECIALLY with the lack of a specified area.)

Ok, this is pretty unsatisfactory. In my book on Optics the power (rate of radiant energy) per unit area per per unit of solid angle is called the 'Radiance'. It describes the 'radiant intensity' per unit of projected area perpendicular to the specified direction. (Hopefully not another rival convention term)
It's photometric counterpart is 'Luminance' (candela per square meter).

Flux DOES incorporate rates. Since you must be integrating over a vector field. Energy isn't vectorial, so I guess energy flux is pretty ill termed.
A better word would be power flux, since you CAN talk about the rate at which energy passes through a surface. (The integrand would be the Poynting vector, which is the energy flux density).

The radiometric and photometric definitions don't differ (apart from the human-eye correction).
Radiant flux is the rate at which radiant energy is passing through the surface.
Luminous flux is the rate at which 'uminous energy energy is passing through the surface.
A 'lumen' has the dimension of power, like a Watt.

**Brad Barker** · Sep3-04, 11:17 AM

okay, i'm not extremely familiar with the poynting vector (know it has something to do with energy and light), so i assume that it is responsible for the lack of an "area" term in this version of flux?

(and it certainly looks like the electric and magnetic flux equations don't have a "per time" term.)