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M E A S U R I N G   L I G H T (continued)

6. Using the Inverse Distance Squared Law (continued)

6.3 Area Source and Distance

Key words:

Description of area source:
An area source is quite a good model for a real source: it is extended in two dimensions and so, represents a real light source like it might be seen from the detector.

The easiest case: INFINITE SOURCE SIZE. Here, boundary effects at the source rim need not be considered.

I regret, but I cannot draw a plane of infinite size; please imagine this plane. And please imagine it to emit light. Again the most simple case: Let luminous exitance  M  (or, radiant exitance  M) be constant all over the plane.

An experiment:
We hold the aperture of an illuminance meter detector against this source. What will the meter reading be?
 --  simple: outgoing and incoming flux density are the same, and hence, illuminance  E = M .

But now we increase the distance between the bright plane and the detector. How will the received illuminance  E  (or, irradiance  E ) change?  --  Not at all!

Since the detector's field of view is and remains filled up entirely with the emitting plane, illuminance meter reading will remain unchanged.

The deplorable remainder of the  "1/r^2 -law": there is CONSTANT ILLUMINANCE independent of distance!

Approximation limits:
But this cannot be the whole truth. Our common sense tells a different story.

Of course. The assumption of infinite source size is unrealistic.
It will only hold as long as detector distance  r  and detector aperture diameter  d  are small enough, compared to the width  w  of the emitting area. We are looking at a "NEAR FIELD" effect.
The figure uses about the greatest allowable relations of  r/w  and  d/w .

    fig.6.3: area source and detector (21 kByte)

Continued: 6.4 Distance and Illuminance: Overview

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Last modified April 29th 2004 23:33