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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

The basic question of this paragraph is
"how will the received amount of light [*] decrease if we increase the distance
between transmitter and receiver (between source and sink, between lamp and detector)?"

Why do we spend thoughts on this topic? - Well, this topic is simply important. Right here, I'll mention just two out of many applications:

First Application

If you knew how the radiometer/fotometer reading decreases with distance from light source, then you could increase your instrument's range:

* Reading too low, instrument's resolution getting coarse? -
 Approach the light source, take the bigger reading
 and calculate the reading at the intended location.

* Reading too high, instrument saturated? -
 Increase distance to light source
 and calculate the reading at the intended location.

* Light source too far away, too hot, too wet, out of reach? -
 take a measurement at some easy distance
 and calculate the reading at the intended location.

Second Application

For designing an illumination system, you can certainly prescribe a certain illuminance at a certain distance to the luminaire. But tasks of this simplicity are rare. In most cases, an extended stereoscopic scene is to be illuminated. With different scene points having different distances to the luminaire.

At least for the direct light (from luminaire to scene points), illuminance at various scene points should be easy to calculate. (With respect to light that has been reflected within the scene, you'd better use ray tracing programs.) Like you define a 'depth of focus' at optical imaging, you could now define a 'depth of illumination'. Within this depth of illumination, a prescirbed range of illuminances is maintained.

In this respect, an ample range of applications opens up in the areas of indoor illumination, stage illumination, headlights, and exterior lighting. And, last not least, in the area of lighting for machine vision.

Point-, line-, and area-sources:

For deriving the "distance to light amount"-relation, we will proceed from the easier to the more complicated cases: we'll look at point sources (para. 6.1), at line sources (para. 6.2), and at area sources (para. 6.3). These paragraphs offer criteria for classifying your problem into the "point", "line", or "area" source domain. Some problems, however, fall in-between. Para. 6.4 offers an easy solution for these transitional domains.

Admitted: The area source is the only one to have some relation to physical reality.
But anyway, point sources
* are very easy to mould into a mathematical model,
* lend themselves to constructing line source models as well as area source models,
* are an ideal that is closely resembled by sources of finite area at (near to) infinite distance.

Note [*]: the blurred expression "amount of light" is deliberately chosen. In most cases, the quantity in question will be illuminance or irradiance.

Continued: 6.1 Point Source and Distance

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Last modified April 28th 2004 00:29