MadSci Network: Physics

Re: Is there a way to convert between light intensity and Luminance?

Date: Thu May 24 09:34:30 2007
Posted By: Zehra Sarac, PhD, Department of Electric and Electronic Engineering , Zonguldak Karaelmas University
Area of science: Physics
ID: 1179764501.Ph


First of all, you should check the equations, that you used them to 
convert the luminance to the light intensity. After that you can continue;
Several measures of light are commonly known as light intensity:

--Radiant intensity is a radiometric quantity, measured in watts per 
steradian (W/sr). 
--Luminous intensity is a photometric quantity, measured in lumens per 
steradian (lm/sr), or candela (cd). 
--Irradiance is a radiometric quantity, measured in watts per meter 
squared (W/m2). The equivalent quantity in other branches of physics is 
--Radiance is commonly called "intensity" in astronomy and astrophysics. 

Luminance is a photometric measure of the density of luminous intensity 
in a given direction. It describes the amount of light that passes 
through or is emitted from a particular area, and falls within a given 
solid angle.

The SI unit for luminance is candela per square metre (cd/m2). The CGS 
unit of luminance is the stilb, which is equal to one candela per square 
centimetre or 10 kcd/m2.

Luminance is often used to characterize emission or reflection from flat, 
diffuse surfaces. The luminance indicates how much luminous power will be 
perceived by an eye looking at the surface from a particular angle of 
view. Luminance is thus an indicator of how bright the surface will 
appear. In this case, the solid angle of interest is the solid angle 
subtended by the eye's pupil. Luminance is used in the video industry to 
characterize the brightness of displays. In this industry, one candela 
per square metre is commonly called a "nit". A typical computer display 
emits between 50 and 300 nits.
Luminance is invariant in geometric optics. This means that for an ideal 
optical system, the luminance at the output is the same as the input 
luminance. For real, passive, optical systems, the output luminance is at 
most equal to the input. As an example, if you form a demagnified image 
with a lens, the luminous power is concentrated into a smaller area, 
meaning that the illuminance is higher at the image. The light at the 
image plane, however, fills a larger solid angle so the luminance comes 
out to be the same assuming there is no loss at the lens. The image can 
never be "brighter" than the source.
Luminance is defined by

Lv= d^2(F)/(dA.dB.Cos(theta))				(1)

Lv, is the luminance (cd/m2), 
F, is the luminous flux or luminous power (lm), 
theta, is the angle between the surface normal and the specified 
A, is the area of the source (m2), and 
B,is the solid angle (sr). 

The luminous flux (or visible energy) in a light source is defined by the 
photopic luminosity function. The following equation calculates the total 
luminous flux in a source of light.

F=683. integral y(lambda).J(lambda).dlambda		(2)

This integral is obtained in [0,infinite]
F is the luminous flux (lm)  
y(lambda), (also known asV()) is the standard luminosity function (which 
is dimensionless). 
J(lambda), is the power spectral density of the radiation, in watts per 
unit wavelength. 

For J(lambda), the integral is obtained in [-pi,pi] interval

J(lambda)= integral (Iv(w)).e^(-ikw).dw			(3)

The luminous intensity for monochromatic light of a particular wavelength 
lambda is given by

Iv=683.I.y(lambda) 					(4)

Iv is the luminous intensity in candelas, 
I is the radiant intensity in W/sr, 

If more than one wavelength is present (as is usually the case), one must 
sum or integrate over the spectrum of wavelengths present to get the 
luminous intensity:
Iv=683 integral I.y(lambda).dlambda                      (5)

The integral is obtained in [0,infinite]

As a result,

The luminous intensity can be written due to luminous flux as follow

Power spectral density is calculated by substituting the equation (5) to 
the equation (3). After that the luminous intensity can be found 
substituting the equation (3) to the equation (2). Lastly equation (2) is 
placed to the equation(1)) and  the  luminance is obtained due to 
luminous intensity(light intensity).

So, we can convert the luminance to the light intensity 

I hope, this answer can solve your problem.

Best Wishes,

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