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

4.2 Radiometry at Light Emitting Plane
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(Sorry: "light" in a narrow sense is visible and radiometry is not restricted to the visible portion of the electromagnetic spectrum. Please let me use the word "light" as an abbreviation for "electromagnetic radiation".)

There are some radiometric quantities which you use for characterization of light sources. You can assume that they were derived units (para. 2) using the base unit of flux, that is Watt(para. 4.1.1).

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Key words:
FLUX DENSITY | FLUX PER AREA | RADIANT EMITTANCE | EXITANCE | INTEGRATING SPHERE | ULBRICHT SPHERE | WATT PER SQUARE-METER | SPATIALLY RESOLVED | STRUCTURED LIGHT SOURCE | PIXELIZED CAMERA

Definition, other names, unit:

Radiant exitance  M  is a kind of FLUX DENSITY: it is FLUX PER AREA; or, more precise: the total emitted flux per unit emitting area:

M = (Phi) / A1

Other names for the same quantity are "RADIANT EMITTANCE" and simply "EXITANCE".

The unit of choice is
WATT PER SQUARE-METER = W / m^2

This is the very same unit like the one used for irradiance  E   (para. 4.3.1). So watch out when you see the unit alone and not the quantity name: is the area meant to be emitter area  A1 (--> radiant exitance  M ), or meant to be receiver area  A2 (--> irradiance  E ).

Measurement procedures and source examples:

I called  (Phi)  the "total" emitted flux. That means: flux emitted into   a l l   directions of space. That poses no problem, if the emitter is very directive (fig. 4.2.1-a). But with emitters that fill wide solid angles with radiation, you'll not be able to keep the detector aperture underfilled (like in para. 4.1.1 and in fig. 4.2.1-a). Then you'd better use an INTEGRATING SPHERE (sometimes called ULBRICHT SPHERE) for gathering the light that diverges into all directions ... see fig. 4.2.1-b. To be completely honest, I don't know whether you're going to find a ready-to-use "radiant exitance meter" on the market.

But of course you find a make-shift solution for the measurement procedure:
Step 1 - Consider whether to measure the entire emitting area or only part of it.
If the latter, place an appropriate field stop directly onto the emitting area.
Step 2 - Measure the total emitted flux  (Phi)  with your radiant power meter (para. 4.1.1).
Step 3 - Divide  (Phi)  by the area of the emitter or, if applicable, by the field stop area.

If  M  varies significantly across the emitting (or field stop-) area, then
* either you will only get a mean value of radiant exitance
* or you should resort to the more sophisticated formulation
M(x,y) = d(Phi(x,y)) / d(A1)

This means that field stop (or "aperture") area  d(A1)  should be chosen as small as possible and lots of values  M  are to be measured for lots of different locations  (x,y)  on the emitter. Result would be a diagram with SPATIALLY RESOLVED radiant exitance  M(x,y) . Figures 4.2.1-c and 4.2.1.-d show simple examples of more or less STRUCTURED LIGHT SOURCEs, where  M(x,y)  could be interesting.  By different lengths of the yellow arrows I've tried to indicate that the individual turns of the filament mutually warm up one another. This way, at filament ends and in short filament segments, the turns get lower temperatures and less radiant exitance than in the center of long filaments.
Neglecting this "marginal" effect, I show the well-known influence of field stop width in fig. 4.2.1-e. Here, two apertures of different widths were displaced along the filament of fig. 4.2.1-d and the number of turns within the aperture was simply counted. You might wish to scan the M/Mmax-structure with a PIXELIZED CAMERA of the CCD- or CMOS-type. But you would have to pass two hurdles:
a) The camera has to gather onto the sensor pixel the rays that emanate from the emitter pixel into   a l l   directions of space.
b) The camera's spectral response characteristics must be known and must be constant across the emitter's bandwidth (otherwise use spectral measurement, para. 4.4)

Continued: 4.2.2 Solid Angle (Omega)

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