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

5. Photometric Measurements
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5.0 General
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Key words:
GREASE-SPOT PHOTOMETER | BUNSEN PHOTOMETER | STANDARD CANDLE | SPECTRAL LUMINOUS EFFICIENCY | V(lambda) | LUMINOUS EFFICACY OF RADIATION | K | DEFINITION OF "PHOTOMETRY" | INDEX v | TRANSFORM RADIO-/PHOTOMETRY


Definition:

I think that photometry is the oldest way of measuring light. Light was understood as some effect on the human eye, no matter what physics might later find out about nature of light. People started making comparative kinds of measurement while using the human eye as a detector. Need an example? - Here it is:

The GREASE-SPOT PHOTOMETER or BUNSEN PHOTOMETER (1), (2).
Look at fig. 5.0-a. A screen made of paper with a translucent grease-spot is illuminated from the right side by the device under test (d.u.t.).

    fig.5.0-a: grease-spot photometer (18 kByte)

From the left side, some "STANDARD CANDLE" illuminates the back of the screen (the unit "candela" for intensities  --  para.5.2.2  --  has its roots in this candle).
Now a grease-spot on paper works as follows:
* illuminated and seen from the front, backing dark, it is darker than its surrounding;
* illuminated from the back side, seen from the front side, it is lighter than its surrounding;
* illuminated with the same illuminance from the front and from the back side, it turns invisible.

People watched one side of the screen with the naked eye and adjusted the distances of one or both light sources until the spot disappeared. Then they used the "inverse distance squared law" (para.6) to calculate the intensity ratio of d.u.t. and standard candle.
Simple visual comparison is the base of this measurement. But since a zeroing technique is used, reasonable exactness is achieved.


Nowadays we like explanations which fit not only to common sense, but also to well-established theories from physics. And so, people have measured spectral characteristics of human eye sensitivity. The result is shown in the next figure.

fig.5.0-b: human eye sensitivity (14 kByte)

This  spectral luminous efficiency  V[(lambda)]  shows color information only. No amplitude information. That is, only relative values are given; curve maximum is simply 100% (located at 555 nm).
If you need absolute (intensity) information, then you must multiply every function value by the
factor    Km  =  683 lm/W    (3) .
Then, curve maximum is  683 lm/W  instead of 100%. And the curve is no more named "SPECTRAL LUMINOUS EFFICIENCY  V[(lambda)]" , but "LUMINOUS EFFICACY OF RADIATION  K" .


As a next step, light detectors were supplemented with optical color filters so as to emulate the human eye. With these detectors, we can perform "photometric" measurements.

And this is DEFINITION OF "PHOTOMETRY": The spectrum of the light to be measured is weighted in the same way as the human eye would do it.
The photometric nature of a quantity may be (but need not be) indicated by an INDEX v ("visual") at the quantity symbol.
And a photometric value neatly shows how strong the human eye will respond to the measured light.


Transforming radiometric values <---> photometric values:

I have often been asked, "what is the factor with which I have to multiply this radiometric value for making it a photometric value?" (or, vice versa).  --  Well, sad to say: there is no transformation factor of general validity. For transforming to and fro between radiometric and photometric data, you are always entangled in spectra. Only if the very same spectrum of light is measured once more with the very same bandwidth radiometrically ... then you can use the same transformation factor one more time.

In all other cases you'll need the following steps of transformation:
* Prerequisite is always: spectral characteristics of the light incident on the detector has to be known. *

a) TRANSFORMING RADIOMETRIC VALUE TO PHOTOMETRIC VALUE
Step 1: numerically integrate the spectral characteristics of the measured light within the bandwidth limits of the radiometric detector. Result is a number which you might call  SUM(e) .
Step 2: numerically multiply the spectral characteristics of the measured light with the sensitivity curve V(lambda)  --  see fig. 5.0-b.
Step 3: numerically integrate the product curve from Step 2. And multiply the result by 683 lm/W. Call the resulting number  SUM(v) . Advice: The spectrum of the light to be measured need not be known in absolute values. The amplitude may be given in percent or in arbitrary units. Just be sure to have it in the same units for Step 1 and for Step 2.
Step 4: Divide       F = SUM(v) / SUM(e)
Now multiply your radiometric value by  F   and result is the related photometric value FOR THIS AND ONLY THIS SPECTRUM OF MEASURED LIGHT.
A closely related calculation (deriving luminous flux from the radiant intensity spectral characteristics of a lamp) is shown in my numbercrunching example at para. 4.4.3.

b) TRANSFORMING PHOTOMETRIC VALUE TO RADIOMETRIC VALUE
Proceed like above in Step 1 through Step 4, but divide     1/F = SUM(e) / SUM(v)
Now 1/F is the conversion factor for transforming a photometric value to its radiometric relative FOR THIS AND ONLY THIS SPECTRUM OF MEASURED LIGHT.

If you use a spectrometric measurement system (like recommended in para.4.4) then your measurement system software will readily supply the radiometric as well as the photometric values. Because it applies Step 1 through Step 4 mentioned above. (Except for multiplication of discrete measurement values with  F  or with  1/F ; the measured spectra are already so corrected as to consist of absolute values.)



Link List and Literature
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Subject used in source
human eye spectral
sensitivity
fig.5.0-b German standard DIN5031, March 1982, table 2;
Publ. CIE Nr. 18.2(TC-1.2) "The basis of physical photometry", 1983;
Baer, "Beleuchtungstechnik Grundlagen", Berlin 1996, p.15 Bild 1.5 and p.41 Tabelle 1.13
grease-spot photometer text ref. (1) E.Jochmann, O.Hermes, P.Spies:
"Grundriss der Experimentalphysik",
18. Auflage, Berlin 1914, page 135
grease-spot photometer text ref. (2) Chambers Dictionary of Science and Technology,
Edinburgh and New York 1999, page 524
luminous efficacy of radiation text ref. (3) Harry Paul, Lexikon der Optik,
Band 2, Berlin 2003, page 204



Continued: 5.1 Photometry within the Beam / 5.1.1 Flux (Phi)

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Last modified April 30st 2004 21:47