Quantifying photometric spectral mismatch uncertainties in led measurements
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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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Quantifying photometric spectral mismatch uncertainties in led measurements l.jpg

Quantifying Photometric Spectral Mismatch Uncertainties in LED Measurements

Richard Young Optronic Laboratories

Kathleen Muray INPHORA

Carolyn Jones CJ Enterprises


Introduction l.jpg
Introduction LED Measurements

Ideally, photometer response should match the photopic curve

We can see mis-matches at low response better on a logarithmic plot.


Introduction3 l.jpg
Introduction LED Measurements

They often deviate in the Blue

Photometer 1

Photometer 2

Photometer 3

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.


Introduction4 l.jpg
Introduction LED Measurements

  • If the photometer is calibrated with a white light source, such as illuminant A:

    • Correct measurements will only be made if the test source is also illuminant A.

  • The errors in measuring other sources depend on:

    • The accuracy of matching the photometer response to the photopic curve.

    • The difference between the test source and illuminant A.


Introduction5 l.jpg
Introduction LED Measurements

  • If the photometer response is very close to photopic:

    • There is little error, relaxing the need for similarity between calibration and test sources.

  • If the test source is very close to illuminant A:

    • There will be little error, relaxing the accuracy requirements of the photometer response.


Introduction6 l.jpg
Introduction LED Measurements

  • However, an LED is so different from illuminant A that the photometer needs to match the photopic response curve very closely.

  • A “goodness of fit” parameter, f1’, has been used for many years as the selection parameter for photometers.

    • It is intended to apply to white light sources and DOES NOT WORK for LEDs (with the possible exception of white LEDs).


Introduction7 l.jpg
Introduction LED Measurements

  • To remind you how f1’ is defined:

Where:

Illuminant A

Publication CIE 69-1987: Methods of characterizing illuminance meters and luminance meters: Performance, characteristics and specifications

The calculation requires the photometer relative response.


Introduction8 l.jpg
Introduction LED Measurements

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.


Introduction9 l.jpg
Introduction LED Measurements

  • If the relative spectral distribution of the LED and photometer response are known, the measured photopic value can be corrected for the difference between the calibration source and the LED.

    • This is called the spectral mismatch correction factor, F (also known as color correction factor in some older documents).

    • When the calibration source is illuminant A, the spectral mismatch factor is given the symbol F*.


Spectral mismatch factors l.jpg
Spectral Mismatch Factors LED Measurements

Here are the spectral distributions for a range of LEDs

We can therefore calculate the spectral mismatch factors for Photometer 1.


Spectral mismatch factors11 l.jpg
Spectral Mismatch Factors LED Measurements

LED measurements using this photometer, can be multiplied by the appropriate F* to give corrected results.


Spectral mismatch factors12 l.jpg
Spectral Mismatch Factors LED Measurements

  • Can we calculate the spectral mismatch factors without measuring a whole range of LEDs?

    • Although spectral distributions of LEDs are often asymmetric, they have a similarity of shape that might be reproduced by calculation.

    • To keep the calculation simple and relevant, it should be based on information readily available: peak wavelength and full-width-at-half-maximum (FWHM).


Spectral mismatch factors13 l.jpg
Spectral Mismatch Factors LED Measurements

  • Using a Gaussian curve within the FWHM limits and an exponential curve outside, the LED spectrum is represented reasonably well.


Spectral mismatch factors14 l.jpg
Spectral Mismatch Factors LED Measurements

  • Mathematically, for lL l  lH

    • [lL is the lower and lH is the upper FWHM limit, lp is the peak wavelength]


Spectral mismatch factors15 l.jpg
Spectral Mismatch Factors LED Measurements

  • For l <lL and lH > l

    • [lL is the lower and lH is the upper FWHM limit, lp is the peak wavelength]


Spectral mismatch factors16 l.jpg

…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…


Spectral mismatch factors17 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

  • The agreement between real and modelled LED spectral calculations means we can express F* as a smooth curve rather than individual points.

  • We don’t have to do all those LED spectral measurements.

  • We can express F* for different FWHM values at each peak wavelength.

    • And then something interesting happens…


Spectral mismatch factors18 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

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


Spectral mismatch factors19 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

  • LEDs differ in peak wavelength and FWHM, so if we want to describe how F* changes for real LEDs:

    • We must include a wavelength component

    • We must include a FWHM component


Spectral mismatch factors20 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

  • The mathematical model for the LED spectra works for this photometer, but does it work for all?


Spectral mismatch factors21 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

It seems to work even better for Photometer 2 than it did for Photometer 1.


Spectral mismatch factors22 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

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


Spectral mismatch factors23 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

  • The point of this presentation is not to replace LED spectral measurement in the calculation of spectral mismatch factors.

    • Though it seems to do a good job of this.

  • The point is, when testing LEDs in a production environment, there are small changes in peak wavelength and FWHM between devices of the same type.

    • And measuring the spectrum, or even peak wavelength, to get a new F* for each device is not practical.


Spectral mismatch factors24 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

  • At this point it is worth noting that if a calibrated LED is used to calibrate the photometer rather than a white light source, the photometer will already read correctly for that LED.

    • It is equivalent to calibrating and applying the F* factor in one process.

  • All other LEDs will still need a spectral mismatch factor, F, to correct the measurement result.

    • And that includes the production devices.


Spectral mismatch factors25 l.jpg

Magnify LED spectra (shown in red).

Spectral Mismatch Factors

Let us take a closer look at some of these F* values.


Spectral mismatch factors26 l.jpg
Spectral Mismatch Factors LED spectra (shown in red).

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


F led l.jpg
f LED spectra (shown in red).LED

  • We can define a “goodness of fit” parameter, like f1’ but specifically applying to LEDs – fLED.

  • The fLED parameter is “the average absolute spectral mismatch error over a wavelength region relative to the central wavelength of that region.”

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.


F led28 l.jpg
f LED spectra (shown in red).LED

  • There is one value of fLED for each wavelength and FWHM, but because we can effectively model the LED spectral distribution, it can be easily calculated from the photometer response.

  • fLED has two components.

    • Errors introduced by measuring LEDs at different wavelengths to the calibration –wLED.

    • Errors introduced by measuring LEDs at different FWHMs to the calibration – hLED.


W led l.jpg
w LED spectra (shown in red).LED

  • Mathematically, the F* value for an LED at the central wavelength, c, is:

    • Where s() is the photometer response and ScLED() is the LED spectral distribution.


W led30 l.jpg
w LED spectra (shown in red).LED

  • Similarly, the F* value for an LED at some other wavelength, p, is:

    • Where s() is the photometer response and SpLED() is the LED spectral distribution.


W led31 l.jpg
w LED spectra (shown in red).LED

  • The error when measuring an LED at wavelength p using the Fc* value at wavelength c is:

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.


W led32 l.jpg
w LED spectra (shown in red).LED

  • Recall the definition of fLED:

    • “the average absolute spectral mismatch error over a wavelength region relative to the central wavelength of that region.”

  • We can now define wLED in mathematical terms:

Where p1 and p2 are the wavelength limits of the region


W led33 l.jpg
w LED spectra (shown in red).LED

  • So wLED can be calculated for any central wavelength and FWHM.

  • It should be shown as wLED(c,FWHM) to reflect this.

  • Since it is independent of calibration source, a full photometer response curve is not required.

    •  3 FWHMs around the central wavelength should be sufficient.

  • The photometer response does need to be done at 1nm intervals or smaller for good results.


W led34 l.jpg
w LED spectra (shown in red).LED

  • We still need to define the wavelength “region” in order to calculate wLED(c,FWHM).

  • Based on data for over 900 LEDs in 63 batches, covering most of the visible range, we propose ± 5 nm around the central wavelength.


W led35 l.jpg
w LED spectra (shown in red).LED

The first stage is to calculate p,c over the region.

This is the result for photometer 1 at 20 nm FWHM.


W led36 l.jpg
w LED spectra (shown in red).LED

The next stage is to calculate wLED values.

These results show that wLED varies strongly with FWHM.


H led l.jpg
h LED spectra (shown in red).LED

  • Using similar reasoning to wLED calculations

    • The error when measuring an LED at FWHM h using the FH* value at FWHM H, both at peak wavelength c is:


H led38 l.jpg
h LED spectra (shown in red).LED

  • We can define hLED in similar mathematical terms to wLED:

Where h1 and h2 are ± 5 nm limits around the central FWHM value, H


H led39 l.jpg
h LED spectra (shown in red).LED

Like wLED, hLED is strongly dependent on FWHM.


H led40 l.jpg
h LED spectra (shown in red).LED

  • So now we have the two components:

    • wLED(c,H) gives the error for peak wavelength change.

    • hLED (c,H) gives the error for FWHM change.

  • We can combine them to give the general error indicator, fLED(c,H):


F led41 l.jpg

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.


F led42 l.jpg
f LED spectra (shown in red).LED

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.


F led43 l.jpg
f LED spectra (shown in red).LED

  • fLED(c,H) values can aid in the design of photometers.

    • It provides instant feedback on the performance of the photometer for LED measurements.

    • It shows that it is the slope of the response rather than the absolute value that is important.

    • It does not require spectral data over the full visible region.

  • Photometer 4, specially designed for blue LEDs, can now be added to our list.


F led44 l.jpg
f LED spectra (shown in red).LED

Photometer 4 is confirmed as generally the best for blue LEDS.

But photometer 1 is best at 430 nm.


F led45 l.jpg
f LED spectra (shown in red).LED

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%


F led46 l.jpg
f LED spectra (shown in red).LED

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.


F led photometer 1 l.jpg

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


F led photometer 2 l.jpg
f LED spectra (shown in red).LED – Photometer 2

Photometer 2 has <1% fLED for most LEDs.

But offers no significant improvement for these LEDs.


F led photometer 3 l.jpg

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.


F led photometer 4 l.jpg
f LED spectra (shown in red).LED – Photometer 4

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.


F led51 l.jpg
f LED spectra (shown in red).LED

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


F led52 l.jpg

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


F led53 l.jpg
f LED spectra (shown in red).LED

The blue line represents equivalence.


F led54 l.jpg
f LED spectra (shown in red).LED

  • fLED and and LEDs:

    • fLED is specific to LED measurement.

    • fLED is based on variations in spectral mismatch factors.

    • fLED reflects actual measurement procedures.

    • fLED agrees with results.

    • fLED applies to all LEDs and photometers investigated and is robust enough for future developments.


F led55 l.jpg
f LED spectra (shown in red).LED

  • fLED and manufacturers:

    • fLED helps in design of better photometers.

    • fLED does not require any more measurements than is currently done for calculation of f1’.

    • fLED can be calculated from limited range data – it does not require the full visible range.

    • fLED should be calculated from data at 1 nm or smaller intervals.


F led56 l.jpg
f LED spectra (shown in red).LED

  • fLED and users:

    • fLED provides a much better selection criterion than f1’.

    • fLED is a property of the photometer, eliminating confusion on calibration requirements.

    • fLED allows for optimization of photometer selection across all the user’s LED requirements.

    • fLED gives an indication of errors in measurement.

    • Advances in quality of photometers and better selection will reduce uncertainties in measurement.


Acknowledgements l.jpg
Acknowledgements LED spectra (shown in red).

  • Thanks to NIST and Lumileds.

    • For the great quantity and quality of data provided by them.

  • Thanks to all the members of CIE TC2-45 and TC2-46.

    • For their useful input and discussions.

  • Special thanks to Yoshi Ohno, NIST.

    • For all his help.


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