Quantifying Photometric Spectral Mismatch Uncertainties in LED Measurements. Richard Young Optronic Laboratories Kathleen Muray INPHORA Carolyn Jones CJ Enterprises. Introduction. Ideally, photometer response should match the photopic curve.
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Richard Young Optronic Laboratories
Kathleen Muray INPHORA
Carolyn Jones CJ Enterprises
Ideally, photometer response should match the photopic curve
We can see mis-matches at low response better on a logarithmic plot.
They often deviate in the Blue
The highest response and best fit are normally around 555 nm
And in the Red
Photometers use filter/detector combinations to approximate photopic response
This approximation can sometimes be quite good, but is never perfect.
This plot shows 3 photometers.
Publication CIE 69-1987: Methods of characterizing illuminance meters and luminance meters: Performance, characteristics and specifications
The calculation requires the photometer relative response.
Especially in the Blue
And in the Red
LEDs are generally narrow band, and are very unlike illuminant A
Measurements of LEDs can therefore have large errors associated with white light calibrations.
Here are the spectral distributions for a range of LEDs
We can therefore calculate the spectral mismatch factors for Photometer 1.
LED measurements using this photometer, can be multiplied by the appropriate F* to give corrected results.
…and here are the predicted F* values using the modelled LED spectra (shown in red).Spectral Mismatch Factors
So, here are the F* factors calculated from real LED spectra again…
We see that the F* curve has places where FWHM hardly matters
And other places where F* changes rapidly with FWHM
There are wavelength ranges where F* changes rapidly
And other ranges where F* hardly changes at all
It seems to work even better for Photometer 2 than it did for Photometer 1.
This is because the mathematical model is symmetric and the LED spectrum is not. These LEDs are narrow band and highly asymmetric, combined with a poor photopic fit of the detector
However, it still matches the general shape of the F* curve, which is all that is required in this paper.
Photometer 3 shows some differences as the F* value increases
Magnify LED spectra (shown in red).Spectral Mismatch Factors
Let us take a closer look at some of these F* values.
The size of the error depends on how different the wavelength is and how quickly the F* factor changes in that region.
This means that measurements of LEDs that have a slightly different wavelength still have an associated error
When we apply the F* factor, we are effectively offsetting the curve at one wavelength
NOTE: It is NOT a correction factor to be applied, but it IS an indicator of the suitability and quality of the photometer for measurement of any single color LED.
NOTE: This equation no longer contains a reference to the calibration source, so it does not matter if it was calibrated with white light or a calibrated LED.
p,c depends only on the photometer and the LED spectral distributions. If the modelled spectral distributions are used, it is purely a photometer characteristic.
Where p1 and p2 are the wavelength limits of the region
The first stage is to calculate p,c over the region.
This is the result for photometer 1 at 20 nm FWHM.
The next stage is to calculate wLED values.
These results show that wLED varies strongly with FWHM.
Where h1 and h2 are ± 5 nm limits around the central FWHM value, H
Like wLED, hLED is strongly dependent on FWHM.
You can see that high h LED spectra (shown in red).LED is generally close to a low wLED.fLED
This means there are wavelengths where the photometer error is more sensitive to LED peak wavelength shifts and others where it is more sensitive to FWHM changes.
Here is an example of wLED
We add hLED
And finally fLED.
Where the photometer response crosses the photopic curve, their slopes are very different
Giving large errors with wavelength changes
But high and low contributions offset one another for changes in FWHM.
This is the photometer response graph shown earlier but rescaled.
Photometer 4 is confirmed as generally the best for blue LEDS.
But photometer 1 is best at 430 nm.
Values of fLED(c,H) show the suitability for LED measurement, but bear no relation to the f1’ value.
Photometer 3: f1’ = 2.51%
Photometer 3 is the worst
At 40 nm FWHM Photometer 4 is the best for blue LEDS even at 430 nm
Photometer 1: f1’ = 6.35%
Photometer 2: f1’ = 1.98%
A 3-D plot shows the variations of fLED(c,H). The value is color coded to show iso-value lines. Seen from above, this is a map.
These would be measured with <1% f LED spectra (shown in red).LED.
These would be measured with <2% fLED.fLED – Photometer 1
We can overlay a plot of FWHM vs. wavelength for some modern LEDS
Photometer 2 has <1% fLED for most LEDs.
But offers no significant improvement for these LEDs.
Photometer 3 also has a wide range of <1% f LED spectra (shown in red).LED.fLED – Photometer 3
But up to 7% fLED for these LEDs.
Photometer 4 data has a limited wavelength range, but <1% fLED extends further into the blue region than the others.
And has fLED<3% even for these LEDs.
To test the validity and usefulness of fLED, several batches of LEDs were measured.
Each batch included similar LEDs in terms of peak and FWHM, regardless of manufacturer
The “central” LED in each batch was used to calibrate the photometers for the measurement of all other LEDs in the batch.
Calibration LEDs shown in black
But the extent is not LED spectra (shown in red).± 5 nm like fLED.fLED
The smaller the spread in wavelengths, the lower the batch error. We can scale the errors to a ± 5 nm region to compare directly with fLED.
The spectra of each of these LEDs is known, so we can calculate the error in measurement and hence the standard deviation for each batch
The blue line represents equivalence.