1. Richard Young Richard Young Optronic Laboratories Kathleen Muray Kathleen Muray INPHORA Carolyn Jones Carolyn Jones CJ Enterprises

2. Ideally, photometer response should match the photopic curve We can see mis- matches at low response better on a logarithmic plot.

3. They often deviate in the Blue Photometers use filter/detector combinations to approximate photopic response This approximation can sometimes be quite good, but is never perfect. And in the Red The highest response and best fit are normally around 555 nm This plot shows 3 photometers. Photometer 1 Photometer 2 Photometer 3

4.  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.

5.  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.

6.  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, f 1 ’, 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).

7.  To remind you how f 1 ’ is defined: Where: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.

8. LEDs are generally narrow band, and are very unlike illuminant A Measurements of LEDs can therefore have large errors associated with white light calibrations. Especially in the Blue And in the Red

9.  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*.

10. Here are the spectral distributions for a range of LEDs We can therefore calculate the spectral mismatch factors for Photometer 1.

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

12.  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).

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

14.  Mathematically, for L   H  [ L is the lower and H is the upper FWHM limit, p is the peak wavelength]

15.  For  L and H >  For  L and H >  [ L is the lower and H is the upper FWHM limit, p is the peak wavelength]

16. So, here are the F* factors calculated from real LED spectra again… …and here are the predicted F* values using the modelled LED spectra (shown in red).

17.  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…

18. 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

19.  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

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

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

22. Photometer 3 shows some differences as the F* value increases 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.

23.  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.

24.  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.

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

26. When we apply the F* factor, we are effectively offsetting the curve at one wavelength This means that measurements of LEDs that have a slightly different wavelength still have an associated error The size of the error depends on how different the wavelength is and how quickly the F* factor changes in that region.

27.  We can define a “goodness of fit” parameter, like f 1 ’ but specifically applying to LEDs – f LED.  The f LED 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.

28.  There is one value of f LED for each wavelength and FWHM, but because we can effectively model the LED spectral distribution, it can be easily calculated from the photometer response.  f LED has two components.  Errors introduced by measuring LEDs at different wavelengths to the calibration –w LED.  Errors introduced by measuring LEDs at different FWHMs to the calibration – h LED.

29.  Mathematically, the F* value for an LED at the central wavelength, c, is:  Where s( ) is the photometer response and S c LED ( ) is the LED spectral distribution.

30.  Similarly, the F* value for an LED at some other wavelength, p, is:  Where s( ) is the photometer response and S p LED ( ) is the LED spectral distribution.

31.  The error when measuring an LED at wavelength p using the F c * 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.  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. 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.  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.

32.  Recall the definition of f LED :  “the average absolute spectral mismatch error over a wavelength region relative to the central wavelength of that region.”  We can now define w LED in mathematical terms: Where p1 and p2 are the wavelength limits of the region

33.  So w LED can be calculated for any central wavelength and FWHM.  It should be shown as w LED (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.

34.  We still need to define the wavelength “region” in order to calculate w LED (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.

35. The first stage is to calculate  p,c over the region. This is the result for photometer 1 at 20 nm FWHM.

36. The next stage is to calculate w LED values. These results show that w LED varies strongly with FWHM.

37.  Using similar reasoning to w LED calculations  The error when measuring an LED at FWHM h using the F H * value at FWHM H, both at peak wavelength c is:

38.  We can define h LED in similar mathematical terms to w LED : Where h1 and h2 are ± 5 nm limits around the central FWHM value, H

39. Like w LED, h LED is strongly dependent on FWHM.

40.  So now we have the two components:  w LED (c,H) gives the error for peak wavelength change.  h LED (c,H) gives the error for FWHM change.  We can combine them to give the general error indicator, f LED (c,H):

41. Here is an example of w LED We add h LED And finally f LED. You can see that high h LED is generally close to a low w LED. 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.

42. This is the photometer response graph shown earlier but rescaled. 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.

43.  f LED (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.

44. Photometer 4 is confirmed as generally the best for blue LEDS. But photometer 1 is best at 430 nm.

45. At 40 nm FWHM Photometer 4 is the best for blue LEDS even at 430 nm Photometer 3 is the worst Values of f LED (c,H) show the suitability for LED measurement, but bear no relation to the f 1 ’ value. Photometer 2: f 1 ’ = 1.98% Photometer 1: f 1 ’ = 6.35% Photometer 3: f 1 ’ = 2.51%

46. A 3-D plot shows the variations of f LED (c,H). The value is color coded to show iso-value lines. Seen from above, this is a map.

47. We can overlay a plot of FWHM vs. wavelength for some modern LEDS These would be measured with <2% f LED. These would be measured with <1% f LED.

48. Photometer 2 has <1% f LED for most LEDs. But offers no significant improvement for these LEDs.

49. Photometer 3 also has a wide range of <1% f LED. But up to 7% f LED for these LEDs.

50. Photometer 4 data has a limited wavelength range, but <1% f LED extends further into the blue region than the others. And has f LED <3% even for these LEDs.

51. To test the validity and usefulness of f LED, 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

52. 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 But the extent is not  5 nm like f LED. 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 f LED.

53. The blue line represents equivalence.

54.  f LED and and LEDs:  f LED is specific to LED measurement.  f LED is based on variations in spectral mismatch factors.  f LED reflects actual measurement procedures.  f LED agrees with results.  f LED applies to all LEDs and photometers investigated and is robust enough for future developments.

55.  f LED and manufacturers:  f LED helps in design of better photometers.  f LED does not require any more measurements than is currently done for calculation of f 1 ’.  f LED can be calculated from limited range data – it does not require the full visible range.  f LED should be calculated from data at 1 nm or smaller intervals.

56.  f LED and users:  f LED provides a much better selection criterion than f 1 ’.  f LED is a property of the photometer, eliminating confusion on calibration requirements.  f LED allows for optimization of photometer selection across all the user’s LED requirements.  f LED gives an indication of errors in measurement.  Advances in quality of photometers and better selection will reduce uncertainties in measurement.

57.  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.