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

4. RADIOMETRIC MEASUREMENTS (continued)

4.4 Spectrally Resolved Measurements (continued)


4.4.3 Applying Spectral Resolution
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Key words:
APPLICATION SOFTWARE | DATA EXPORT | COLOR CO-ORDINATES | DOMINANT WAVELENGTH | COLOR TEMPERATURE | SPECTRUM INFORMATION | ABSOLUTE SPECTRAL DATA | DELTA LAMBDA | NUMERICAL INTEGRATION | SPIKE and NOTCH | BANDWIDTH DEPENDENCE | BROAD-BAND FLAT | WEIGHTING |

Whereas in para. 4.4.2, we learnt some applicational facts about spectroradiometer internal technology, we will now ask: what can we really do with those neatly measured spectral characteristics?


The merits of "APPLICATION SOFTWARE":

In most cases, you will get it from the instrument manufacturer.
And again in most cases, this manufacturer has one (or some) special application(s) in mind when developping his software. This might be colorimetry, paint blending, analytical chemistry, mineralogy, biology, or the like.
If your application fits directly into this template: very good.
In all other cases: make sure that you buy only those types of software, which are able to export their spectral measurement results into your spreadsheet and presentation graphics program (Excel, Lotus, or similar). Or which, at least, offer DATA EXPORT in the form of ASCII strings. So that you can make your own use of it.

What can application software do for you?

Most of the systems will deliver on a few keystrokes:

* COLOR CO-ORDINATES of various co-ordinate systems, e.g. CIE-x,y,z; CIE-L,a,b; H,L,S; ...
(see my essay on color, para. 1.3 "measuring color sensation");
* DOMINANT WAVELENGTH;
* COLOR TEMPERATURE (if reasonably usable);
* full SPECTRUM INFORMATION (displaying a table and/or graphics of the spectral characteristics curve).
And many systems will also deliver radiometric or photometric flux (in most cases, flux per solid angle; that is, intensity  I .)


What you will need:

Perhaps you want to use the instrument for deriving those radiometric data like
* Flux  (Phi)
* Emittance  M
* Intensity  I
* Radiance  L
* Irradiance  E
by yourself.
Then your system should be able to
+ output ABSOLUTE SPECTRAL DATA (e.g. flux in Watts, not only in percent or "arbitrary units").
Otherwise you would have to perform an amplitude calibration which is indicated in item "g) amplitude calibration" in para. 4.4.2 Instrumentation
+ multiply an entire spectral characteristics curve by some geometry factor that you derive from the optical setup. Anyway, this multiplication can be done outside the spectroradiometric system in your spreadsheet program. As well as
+ perform multiplication  "curve * curve"  (needed e.g. for spectral simulation of an optical signal chain)
+ perform subtraction  "curve - curve"  (needed for dark signal subtraction)
+ perform division  "curve / curve"  or producing reciprocal values (needed for amplitude calibration)


The "DELTA LAMBDA"-challenge:

The spectral characteristics curve will be output in terms of spectral flux density; that is, "power per wavelength interval" in "Watt per nanometer". If you need the total flux between two wavelength limits, then you'll at first check whether your spectroradiometer software produces this result voluntarily. If not so, you're going to perform a NUMERICAL INTEGRATION of the measured spectral flux density function  from the lower wavelength limit up to the upper one. Wavelength intervals are of constant width all over your function and hence, integration can easily be done with your spreadsheet program.

Your tabulated spectral functions look very simple and easy to understand:
They contain
* a column indicating the wavelength - usually with equal step widths;
* at least one column of function values (e.g. spectral flux, spectral sensitivity, spectral transmission, ...).

Looking at this simple structure, you think that handling these tables should be easy. If you have to join two tables and their wavelength steps do not fit, then simply compress one of them by omitting every second value. Or expand the other one of them by interpolating "new" values between two each of the old values.
But the "challenge" is hidden in two properties of these functions.
One of them is plain to see, but the other one does not strike the eye.

1st hidden property: SPIKEs
If your spectral function contains a SPIKE (or a NOTCH), then interpolation will broaden the spike (or notch). And file compression by data omission might totally suppress a spike / a notch. Both effects might really hurt you; so, before expanding or compressing, search the diagram for spikes and for notches. And try to preserve them.


2nd hidden property: BANDWIDTH DEPENDENCE
Monochromator bandwidth  (lambda)_bw  is a property of your monochromator. It is defined in para. 4.4.2, fig. 4.4.2-d, where it has been named (delta)(lambda). It depends on the monochromator's dispersive element and on the optical setup. But it does not necessarily depend on the width  (lambda)_step  of the steps from one spectral value to the next. Especially with those older "scanning" monochromators (see para. 4.4.2 instrumentation).
 Now does a difference between bandwidth  (lambda)_bw  and step width  (lambda)_step  mislead the process of summing up the  (Phi)-area  or the  sensitivity-area ?
 No, it does not. Thanks to a kind property of these "spectral" functions:
Consider the description of the "histogram-like" fig. 4.4.1-b in para. 4.4.1 and also consider fig. 4.4.3-a just below:

fig.4.4.3-a: Area, width, and height of histogram column (10 kByte)


The height of these columns is but the derivative or slope of  (Phi)  as a function of  (lambda) . And since slope values may be arranged along the x-axis as densely as you want, step widths  (lambda)_step  differing from bandwidth  (lambda)_bw  are no problem at all. Just remember to multiply with step width  (lambda)_step  when summing up the entire area.

But anyway: given a certain value of  (lambda)_bw  you should not choose any value of  (lambda)_step  at will. As explained in the following figure there is only one way to the safe capture of a single spectrum line: sample every bandwidth intervall at least once, i.e.
       (lambda)_step  <=  (lambda)_bw


fig.4.4.3-b: Evaluation of a single spectrum line (13 kByte)



Concluding for the "delta lambda"-challenge:
Before numerically integrating a spectral function, you should check
- In the case that the file has been blown up by interpolation (or compressed by omission): whether your raw data contained spikes or notches ... and if they are preserved;   and
- In any case: whether your sampling comb  (lambda)_step  is fine enough for making full use of monochromator wavelength resolution  lambda_bw .


BROAD-BAND FLAT with evident wavelength limits:

And here we are at last arrived at the first main advantage of measuring radiometric quantities spectrally: You get an instrument with BROAD-BAND FLAT response, capable of measuring a big variety of sources. And you can even look at the source's spectral characteristics; if it is spread out to your instrument's spectral limits, then you know that in your measurement there might be a bandwidth deficiency. And you can give reasonable bandwidth limits when publishing your result.


Simulating spectral weights:

The second main advantage: the measured spectral characteristics curve can afterwards be WEIGHTed with any other function. Not important? -- But imagine:

* Weighting with  V(lambda)  (and integration) will yield the photometric measurement result (see para.5, "photometric measurements" and numbercrunching example)

* weighting with any system of three colorimetric functions (and three times integration) will yield color co-ordinates of the item you've measured

* weighting with a CCD sensor's spectral responsivity characteristics (and integration) will yield relative CCD signal strength

* weighting with filter or surface color spectral characteristics (and integration) enables you to quantify the influence of colored matter (see my essay on color, fig. 2.6 in para. 2.6 "surface color and colored light")

* even scanning, displaying, printing can capitalize on spectral resolution:
  a) simulating device spectral characteristics (e.g. calculating scanner spectral sensitivity from its component spectral characteristics)    AND:
  b) improving device gamut as explained in my essay on color, para. 3.3 "gamuts of reproducible color space"

All together: lots and lots of attractive applications arise. And they just work with a one-time measurement which is afterwards treated and used in all the various ways you like.


Link and Literature
-------------------

Subject used in source
slit function;
sampling comb
figure 4.4.3-b,
reference (1)
Publication CIE No. 63 (1984)
"The Spectroradiometric Measurement of Light Sources"
Commission Internationale de l'Éclairage
(= International Commission on Illumination),
Kegelgasse 27, A-1030 Wien, Austria



If you would like to see details of multiplying and integrating spectral characteristics, then look how a lamp radiant intensity spectrum is converted into the corresponding luminous flux value in my
numbercrunching example.

Continued: 5. Photometry / 5.0 General

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Last modified April 30st 2004 19:24