### 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
Message:
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Hi,

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:

--Luminous intensity is a photometric quantity, measured in lumens per
squared (W/m2). The equivalent quantity in other branches of physics is
intensity.
--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)

where
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
direction,
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)

Where

This integral is obtained in [0,infinite]
F is the luminous flux (lm)
y(lambda), (also known asV(ë)) 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)

where
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)

Where
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

Best Wishes,

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