Presentation on theme: "Richard Young Optronic Laboratories Kathleen Muray INPHORA"— Presentation transcript:
1Quantifying Photometric Spectral Mismatch Uncertainties in LED Measurements Richard Young Optronic LaboratoriesKathleen Muray INPHORACarolyn Jones CJ Enterprises
2IntroductionWe can see mis-matches at low response better on a logarithmic plot.Ideally, photometer response should match the photopic curve
3Introduction They often deviate in the Blue Photometer 2 Photometer 3 The highest response and best fit are normally around 555 nmAnd in the RedPhotometers use filter/detector combinations to approximate photopic responseThis approximation can sometimes be quite good, but is never perfect.This plot shows 3 photometers.
4IntroductionIf 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.
5Introduction 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.
6IntroductionHowever, 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).
7The calculation requires the photometer relative response. IntroductionTo remind you how f1’ is defined:Where:Illuminant APublication CIE : Methods of characterizing illuminance meters and luminance meters: Performance, characteristics and specificationsThe calculation requires the photometer relative response.
8LEDs are generally narrow band, and are very unlike illuminant A IntroductionEspecially in the BlueAnd in the RedMeasurements of LEDs can therefore have large errors associated with white light calibrations.LEDs are generally narrow band, and are very unlike illuminant A
9IntroductionIf 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*.
10Spectral Mismatch Factors We can therefore calculate the spectral mismatch factors for Photometer 1.Here are the spectral distributions for a range of LEDs
11Spectral Mismatch Factors LED measurements using this photometer, can be multiplied by the appropriate F* to give corrected results.
12Spectral Mismatch Factors 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).
13Spectral Mismatch Factors Using a Gaussian curve within the FWHM limits and an exponential curve outside, the LED spectrum is represented reasonably well.
14Spectral Mismatch Factors Mathematically, for lL l lH[lL is the lower and lH is the upper FWHM limit, lp is the peak wavelength]
15Spectral Mismatch Factors For l < lL and lH > l[lL is the lower and lH is the upper FWHM limit, lp is the peak wavelength]
16Spectral Mismatch Factors …and here are the predicted F* values using the modelled LED spectra (shown in red).So, here are the F* factors calculated from real LED spectra again…
17Spectral Mismatch Factors 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…
18Spectral Mismatch Factors And other ranges where F* hardly changes at allThere are wavelength ranges where F* changes rapidlyAnd other places where F* changes rapidly with FWHMWe see that the F* curve has places where FWHM hardly matters
19Spectral Mismatch Factors LEDs differ in peak wavelength and FWHM, so if we want to describe how F* changes for real LEDs:We must include a wavelength componentWe must include a FWHM component
20Spectral Mismatch Factors The mathematical model for the LED spectra works for this photometer, but does it work for all?
21Spectral Mismatch Factors It seems to work even better for Photometer 2 than it did for Photometer 1.
22Spectral Mismatch Factors 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 detectorHowever, 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
23Spectral Mismatch Factors 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.
24Spectral Mismatch Factors 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.
25Spectral Mismatch Factors Let us take a closer look at some of these F* values.Magnify
26Spectral Mismatch Factors 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 errorWhen we apply the F* factor, we are effectively offsetting the curve at one wavelength
27fLEDWe 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.
28fLEDThere 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.
29wLEDMathematically, 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.
30wLEDSimilarly, 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.
31wLEDThe 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.
32Where p1 and p2 are the wavelength limits of the region wLEDRecall 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
33wLED 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.
34wLEDWe 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.
35wLED The first stage is to calculate p,c over the region. This is the result for photometer 1 at 20 nm FWHM.
36wLED The next stage is to calculate wLED values. These results show that wLED varies strongly with FWHM.
37hLED 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:
38Where h1 and h2 are ± 5 nm limits around the central FWHM value, H hLEDWe can define hLED in similar mathematical terms to wLED:Where h1 and h2 are ± 5 nm limits around the central FWHM value, H
40hLED 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):
41You can see that high hLED is generally close to a low wLED. fLEDYou can see that high hLED is generally close to a low wLED.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.We add hLEDHere is an example of wLEDAnd finally fLED.
42fLEDGiving large errors with wavelength changesWhere the photometer response crosses the photopic curve, their slopes are very differentBut high and low contributions offset one another for changes in FWHM.This is the photometer response graph shown earlier but rescaled.
43fLED 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.
44fLED Photometer 4 is confirmed as generally the best for blue LEDS. But photometer 1 is best at 430 nm.
45fLED Photometer 3: f1’ = 2.51% Photometer 3 is the worst 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 worstAt 40 nm FWHM Photometer 4 is the best for blue LEDS even at 430 nmPhotometer 1: f1’ = 6.35%Photometer 2: f1’ = 1.98%
46fLEDA 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.
47We can overlay a plot of FWHM vs. wavelength for some modern LEDS fLED – Photometer 1We can overlay a plot of FWHM vs. wavelength for some modern LEDSThese would be measured with <1% fLED.These would be measured with <2% fLED.
48fLED – Photometer 2 Photometer 2 has <1% fLED for most LEDs. But offers no significant improvement for these LEDs.
49Photometer 3 also has a wide range of <1% fLED. fLED – Photometer 3Photometer 3 also has a wide range of <1% fLED.But up to 7% fLED for these LEDs.
50And has fLED<3% even for these LEDs. fLED – Photometer 4Photometer 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.
51Calibration LEDs shown in black fLEDThe “central” LED in each batch was used to calibrate the photometers for the measurement of all other LEDs in the batch.Each batch included similar LEDs in terms of peak and FWHM, regardless of manufacturerTo test the validity and usefulness of fLED, several batches of LEDs were measured.Calibration LEDs shown in black
52But the extent is not ± 5 nm like 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 batchBut the extent is not ± 5 nm like fLED.
53The blue line represents equivalence. fLEDThe blue line represents equivalence.
54fLED 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.
55fLED 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.
56fLEDfLED 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.
57Acknowledgements 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.