Investigation of a measurement technique to determine led

HSE
Health & Safety
Executive

Investigation of a measurement technique to determine
the apparent source size for light emitting diodes

Prepared by National Physical Laboratory and Europtics Ltd
for the Health and Safety Executive 2005

RESEARCH REPORT 345

HSE
Health & Safety
Executive

Investigation of a measurement technique to determine
the apparent source size for light emitting diodes

Simon Hall
Laura Crane
David Gibbs
National Physical Laboratory
Hampton Road
Teddington
Middlesex
TW11 0LW

Brooke Ward
Europtics Ltd

Current ocular safety standards associated with the application of light emitting diodes (LED), and
other intermediate sources, cite the angular subtense of the apparent source as an essential quantity
for optical hazard assessment. Under these standards, the angular subtense parameter is calculated
from the apparent source size of the LED package and the specified most hazardous viewing distance.
However, an international standard for the measurement of the apparent source size parameter does
not yet exist.
This report describes the results of a study that provide rigorous practical support for a technique
proposed for the measurement of apparent source size when observed from the most hazardous
viewing distance. The results of this study allow, for the first time, an estimate of the potential optical
hazard of LEDs and other intermediate sources, in accordance with current safety standards. This is a
significant step in reducing the ambiguity that currently exists in the application of these optical safety
standards. The results also verify earlier numerical modelling of an improved method for the estimation
of the critical angular subtense parameter for extended sources, such as LEDs and intermediate
sources.
This report and the work it describes were funded by the Health and Safety Executive (HSE). Its
contents, including any opinions and/or conclusions expressed, are those of the authors alone and do
not necessarily reflect HSE policy.

HSE BOOKS

© Crown copyright 2005

First published 2005

ISBN 0 7176 6108 3

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ii

ACKNOWLEDGEMENTS

We would like to acknowledge the software development expertise provided by Oxford
Framestore Applications Ltd.

iii

CONTENTS

Executive Summary......................................................................................................... v ii
1 Introduction .............................................................................................................. 1
2 Theory....................................................................................................................... 2
2.1 Angular subtense .............................................................................................. 2
2.2 Beam measurements ......................................................................................... 5
2.3 The optical system ............................................................................................ 6
3 Description of Apparatus.......................................................................................... 7
3.1 Initial System Design ....................................................................................... 7
3.2 8-Bit System Design......................................................................................... 7
3.3 12-Bit System Design....................................................................................... 7
4 Measurement Procedure ......................................................................................... 11
4.1 Preparation for measurement.......................................................................... 11
4.2 Calibration of CCD array and associated equipment ..................................... 11
4.3 LED beam width measurement ...................................................................... 11
4.4 Transform Validation Experiment.................................................................. 14
5 Results .................................................................................................................... 15
5.1 Initial results ................................................................................................... 15
5.2 8-Bit Transform Validation Experiment results ............................................. 17
5.3 12-Bit Transform Validation Experiment results ........................................... 20
5.4 Yellow LED - Ligitek LUY 3833/A29 .......................................................... 25
5.5 Blue LED - Nichia NSPB500 Rank WS ........................................................ 27
5.6 Green LED - Nichia NSPG500 Rank GS....................................................... 29
5.7 Red LED - Kingbright L-53SRC/E ................................................................ 31
5.8 White LED - Nichia NSPW500 Rank BS ...................................................... 33
5.9 Orange LED - Toshiba TLOH190P................................................................ 35
5.10 High Power Blue LED - Luxeon Star............................................................. 37
6 Uncertainty Analysis .............................................................................................. 39
7 Conclusions ............................................................................................................ 46
7.1 Future directions ............................................................................................. 50
Appendix 1: Second moment, azimuth and principle width derivation ......................... 51
Appendix 2: Design And Technical Specification For A Facility To Determine The
Apparent Source Size Of Light Emitting Diodes ........................................................... 53
Appendix 3: LED techinical data sheets......................................................................... 58
References ...................................................................................................................... 59
Glossary.......................................................................................................................... 61

v

EXECUTIVE SUMMARY

The work detailed in this report was commissioned to allow the optical hazard level of light
emitting diodes (LEDs), and more laser-like intermediate sources, to be quantified. The
dramatic increase in the use of superbright LEDs for consumer, medical and industrial
applications necessitates a responsible assessment of the hazard presented by these devices.

The International Electrotechnical Committee (IEC) and Commission Internationale de
l'Eclairage (CIE) cite that the angular subtense of the apparent source is an essential quantity for
the assessment of optical hazard. Under current optical hazard safety standards the angular
subtense parameter is calculated from the apparent source size and a specified most hazardous
viewing distance. However an international standard for the measurement of the apparent
source size parameter does not exist.

The aim of this current study is to provide rigorous practical support for a technique proposed
for the measurement of apparent source size when observed from the most hazardous viewing
distance. Development of the practical technique required the recognition of the apparatus
limitations and the development of strategies to overcome these limiting factors. Both an 8-bit
and 12-bit system were tested. The 12-bit systems’ superior dynamic range and cooled array
highlighted the effect of stray light and noise. This demonstrated the need for a large dynamic
range in the measurement facility to measure second moment beam diameters effectively.

A validation experiment suggested by the International Standards Organisation (ISO/TC 172/SC
9) comprehensively verified the suitability of the technique. It is therefore proposed that the
results of this work should be used to underpin the adoption of this methodology within
international standards for the assessment of the optical hazard potential of LEDs and other
intermediate sources.

The report highlights the following:

Technical specification of the critical components and the design of a facility for the
measurement of apparent source size of LEDs and intermediate sources.
Verification of an 8-bit and a 12-bit apparent source size measurement facility. This was
achieved by computerized processing of images of spatial beam profile using a
converging second moment method.
High level of agreement between the propagation parameters derived through the 8-bit
and 12-bit methods using the IR LED. This was an unexpectedly good correlation
between results, considering the dynamic range limitations of the 8-bit camera.
Evaluation of the astigmatic state of the beam by analysis of the change of azimuth as
the beam propagates. This was carried out by azimuth determination of the beam by the
comparison of the second moment widths in perpendicular axes.
Measurement of a selection of 8 LEDs with differing peak emission wavelengths,
construction and beam propagation characteristics.
Visualisation of real beam propagation using a montage of beam images and spatial
profiles related to the propagation envelope for one of the LEDs.
Effective demonstration that the point in the beam envelope where a sharp image of the
electronic structure of the LED is obtained does not necessarily correspond to the beam
waist or location of the apparent source.

vii

Identification of general astigmatism (as opposed to simple astigmatism) in the output
beam from one of the LEDs.
Populated angular subtense contour plot with results from this work. This plot enables
the easy estimation of the angular subtense of real LEDs and intermediate sources from
the measured beam propagation characteristics.
Verification of the technique using a test suggested by the International Standards
Organisation (ISO/TC 172/SC 9) identifying that this method can be applied
successfully to the analysis of beam propagation parameters and hence the apparent
source size determination for stigmatic and simple astigmatic beams from LEDs.
Development of this technique would allow the assessment of generally astigmatic
beams in line with ISO 11146-2 ‘Lasers and laser-related equipment. Test methods for
laser beam widths, divergence angle and beam propagation ratio. Part 2: General
astigmatic beams’.

The results of this study allow, for the first time, the effective characterisation of the optical
hazard of LEDs and other intermediate sources, in accordance with the IEC and CIE standards.
This is a significant step in reducing the ambiguity that currently exists in the application
of these optical safety standards. The results also verify earlier numerical modelling of an
improved method for the estimation of the critical angular subtense parameter for extended
sources, such as LEDs and intermediate sources.

viii

1 INTRODUCTION

The assessment of the optical hazard associated with beams from sources of light intermediate
in quality between a laser and light emitting diodes (LED)1 has been a challenging problem for
the international standards community for a large number of years.

This report has been produced to contribute to the international debate regarding the optical
hazard due to LEDs. The current requirements for the classification of LEDs follows IEC 60825
3
and requires a measurement of “apparent source size and its location”. The CIE publication
CIE S 009/E:2002 “Photobiological Safety of Lamps and Lamp Systems” cites apparent source
size as part of the methodology to calculate angular subtense and hence Retinal Hazard.
However a procedure for establishing apparent source size and location is not described.

The apparent source size of an LED is a critical parameter used in the assessment of the ocular
viewing hazard of these devices under ISO 60825-1 ‘Safety of laser products. Equipment
classification, requirements and user’s guide’. Under the committee draft IEC 60825-13
‘Measurements for the classification of laser products’ a proposed measurement method is
described to determine the apparent source size of LEDs. The validity of this method has been
questioned at a national and international level and continues to be debated within the various
standards bodies such as IEC, ISO and CIE. Specifically, the applicability of propagation
models to low divergence beams from LEDs has been challenged.

Previously the validity of these models has not been demonstrated through physical
measurement of LED devices. This project aimed to resolve this situation through the
construction of a suitable measurement facility and by performing an assessment of a range of
commercially available LED sources.

1

2 THEORY

Figure 1 is a schematic diagram of the proposed measurement method for the determination of
the apparent source size and beam characteristics of LEDs. A CCD diode array camera system
is placed on a movable carriage in front of the LED source. The relay lens of the camera system
allows the CCD to capture a spatial intensity profile of the beam at a particular plane. The beam
width is then calculated using a modified second moment technique. It is necessary to ensure
that enough of the beam power has been captured to allow an accurate determination of the
beam width. To address this problem a self-converging width measurement technique is used to
estimate the beam width at each measurement plane and represent the true value to an
acceptable level of uncertainty. This measurement is repeated at a number of locations along the
test beam axis until sufficient data points have been obtained to allow the fitting of a maximum
likelihood hyperbola using a least squares fitting technique. The coefficients of the fitted
hyperbola allow the derivation of the beam propagation parameters of the source.
A’ B’
u v
LED
CCD

do

A B
AA’ – plane of beam waist
BB’ – plane of transformed beam waist
u - distance from beam waist to lens
v – distance from lens to transformed beam waist
do – beam waist diameter

Figure 1 Proposed methodology to determine apparent source size of LEDs

If the beam waist is not accessible for direct measurement then using an aberration-free
focussing system, or transform lens can create an artificial waist. This may be necessary if, for
example, the beam waist is formed within the LED package or there is insufficient space to
perform the required number of measurements either side of the waist. The position and
diameter of this artificial waist can then be used, along with the known properties of the
transform lens, to calculate the location and size of the original beam waist. The equations used
to calculate the location and size of the original beam waist using this procedure are given in
Section 6 as part of the uncertainty derivation process.

2.1 ANGULAR SUBTENSE

The angular subtense of an apparent source of radiation in the 400 nm to 1400 nm wavelength
range is required by current laser safety standards 3 to permit calculation of the relaxation factor
C6, for thermal retinal damage from extended sources. It is the ratio of the angular subtense of
the source in question to that of a source that would form the realistic minimum spot size on the
retina (1.5 mrad). Classification or assessment of the thermal hazard from a source requires that
both the angular subtense (see Figure 2) and location of an extended source be known before
there can be a relaxation of the maximum permissible exposure (MPE). The location of the
source is required so that the angular subtense can be calculated for viewing this from the

2

minimum conceivable eye accommodation distance of 100 mm (in IEC standards) 3. It should be
noted that this latter assumption may not describe the full range of potential hazards. It is
possible that some large divergence sources, when held closer than 100 mm from the eye, might
produce a significant thermal hazard in a blurred retinal spot even though the eye cannot
achieve a sharp focus.
Optical Image of
Source Optical
Source

Angular Eye
Subtense

Figure 2 Classical representation of Angular Subtense
It is a simple matter to measure the physical size of the chip of a LED that has a Lambertian
radiation pattern but it is more difficult to know or measure the location or size of the apparent
source with low divergence beams from a LED. Such beams can have a near planar wavefront,
which would imply that the apparent source is located at infinity with an unknown angular
subtense. However, recent advances in the characterization of optical beams, both coherent and
incoherent, enable prediction of their propagation envelopes 2,16,17. It is now possible to assess
the intrabeam-viewing hazard by using known beam characteristics to estimate the angular
subtense of an extended source that would present the greatest hazard to a retina 3.

The level of the thermal hazard to the retina is defined here as the power or energy per
millimeter of beam diameter falling on the retina 19. The process of calculation of the size of the
beam formed on a retina and the fraction of incident power passing through the pupil has been
performed for a wide range of feasible conditions. The calculations assume that the beam has a
divergence of less than 30° and has a power density profile that produces the greatest peak
irradiance on the retina (i.e. a Gaussian profile).

Measurements of the enclosed power envelope of beams from lasers have confirmed that they
propagate with a hyperbolic profile, the constants of which are modified when passing through a
lens. The new constants can be used to estimate the location of the waist of the new hyperbola
and its Gaussian beam diameter as a function of propagation distance. In this way it is possible
to determine the spot size on the retina formed by a beam after passing through the lens of the
eye.

d01 – beam waist diameter of input beam
L1 – waist to lens distance
Zr1 – Rayleigh length of input beam
fe – focal length of lens
L2 – lens to transformed waist distance
Zr1 – Rayleigh length of output beam
d02 – beam waist diameter of output beam
dr – beam diameter on retina
Lr –transformed waist to retina distance

Figure 3 Calculation of spot size (dr) on the retina of the eye.

3

For a given set of beam propagation constants (waist diameter and divergence say) it is possible
to predict the hazard level (P/d) at the retina. The hazard level results from calculations of the
fraction of beam power that passes through the 7mm iris of the eye as a function of both the
strength of the eye lens (assumed to vary anywhere between 14.5 mm and 17 mm) and the
distance of the incident beam waist from the eye. The maximum hazard occurs when the eye
accommodates itself at the most hazardous viewing distance. In the interests of simplicity, IEC
60825-1 assumes that this most hazardous viewing distance is 100 mm but this is not always
found to be the case.

Previous calculations (numerically verified by workers in Austria and the UK) have
concentrated on determining the spot size on the retina at the most hazardous viewing condition
as a function of the two beam propagation parameters, beam waist diameter and far-field
divergence. Knowing the spot size at the retina and by assuming the eye to be 17 mm "long",
the artifact of the angular subtense of the apparent source has been estimated over the most
relevant range of incident beam parameters. The values of angular subtense can be displayed as
contours in the two-dimensional map of waist diameter and divergence. Further calculations
based on the measured values of these parameters will also reveal the location of the apparent
source. If the Rayleigh length of the beam is significantly less than 50 mm then the source can
be assumed to coincide with the measured beam waist location.

While some rather extreme conditions have been assumed when modeling the beam (e.g. a
Gaussian beam profile), the procedure for estimating angular subtense from beam parameter
measurements is thought to offer an unambiguous and non-subjective result. While the
procedure may over-estimate the hazard level it can permit a greater relaxation of the MPE level
than simply assuming that C6=1.

A CCmap showing the range of angular subtense values as contours against the Beam waist
width and the beam divergence was produced from these calculations (Fig 4)2.

Contour of
equal angular
subtense in mrad
Beam waist
diameter and
divergence of LED

Angular subtense,
, of LED

Figure 4 Theoretical plot of beam waist diameter (width) vs. beam divergence
showing contours of angular subtense

4

The contours show equal values of angular subtense in milliradian. To use the contour plot, the
waist diameter and the divergence of the LED beam are measured. The results are plotted on the
graph and the value of the angular subtense, , is then read from the contour just below the
measured point.

The objective of this investigation was to demonstrate that it is possible to determine the
propagation characteristics of the beam produced by a LED. This information could then be
used to estimate the size of the image formed on the retina and from this the angular subtense of
the apparent source at the eye at a given distance. These results then enable the population of a
theoretical contour map of the computed angular subtense as a function of the measured beam
characteristics of LEDs. The angular subtense for all beam types can then be determined by
measuring the beam waist diameter and the divergence.

2.2 BEAM MEASUREMENTS

Measurement of the optical constants of the propagation envelope of a beam has been the
subject of considerable research over the last ten years. A consequence of this work is the
evolution of ISO standards for the measurement of the diameter and divergence of a beam. ISO
11146:1999. “Test methods for laser beam parameters: beam widths, divergence angle and
beam propagation factor” 6 is the current draft standard being reviewed by ISO. The procedures
and techniques that are described here for the determination of the diameter and location of the
apparent source of a beam are based on the principles underlying the ISO standards7 for
stigmatic and simple astigmatic beams. The proposed methods are applicable to beams whose
full divergence angle is less that 30°. Relaxation of the laser safety criteria should not be applied
to a beam displaying general astigmatism.

There are a number of methods available for measurement of the diameter of a beam as well as
its far-field divergence. The basic principles for those methods have been established in an ISO
standard. They are applicable to laser beams with a relatively small beam propagation ratio, M2.
Recent research has demonstrated that adequate steps have to be taken to counter the effects of
noise and offset errors when measuring the transverse irradiance distribution of a beam. When
these steps are taken, the propagation behaviour of incoherent broadband beams as well as high-
quality laser beams can be predicted reproducibly with considerable precision.

To accurately measure the second moment beam diameter both the number of pixels and the
level of digitisation of the signal received on each pixel has to be considered. For beams with a
rapidly changing beam diameter the number of bits in the digitisation process becomes more
critical. Noise on the image acquired by the camera both from electrical and optical sources
must be removed by setting a discrimination level. This effectively reduces the dynamic range
of the camera and this favours cameras with an inherently large dynamic range due to a larger
number of bits available on the digitisation electronics.

The methods leading to estimates of the diameter of a beam use a procedure known as the
Converging Second Moment diameter or width measurement (CSM). The schematic of this
method is shown in Figure 5. These methods are being defined in the revision of ISO 11146 that
is currently in preparation.

5

Figure 5 Schematic of converging second moment iteration

The preferred method for measuring all the propagation characteristics of a beam is to perform
CSM diameter measurements at a number of locations either side of the beam waist. The
calculation of second moment width is described in Appendix 1.

2.3 THE OPTICAL SYSTEM

The beam measurement process consists of using a CCD sensor to image the irradiance profile
at a minimum of ten measurement locations either side of the beam waist. The proposed optical
system contains variable magnifying optics that are designed to facilitate imaging the transverse
irradiance profiles to occupy approximately one quarter of the sensor screen height. Other
components are included in the system to attenuate the beam power to avoid sensor saturation
and to provide spatial calibration of the pixel array of the sensor.

6

3 DESCRIPTION OF APPARATUS

3.1 INITIAL SYSTEM DESIGN

An initial specification of the 12-bit measurement system was written and can been found in
Appendix 2. This specification details the required elements to measure apparent source size of
LEDs.

3.2 8-BIT SYSTEM DESIGN

Both an 8-bit and 12-bit camera systems were used for measurement. The final system design
for the 8-bit system was identical to that described in Section 3.3, except for the camera and
zoom lens. The details of the 8-bit camera are given in Section 3.2.1. The details of the
associated zoom lens are presented in Section 3.2.2.

3.2.1 8-Bit Camera System

The 8-bit system consisted of a analogue CCD interline transfer camera connected to an 8 bit
frame grabber card. A Leica Monozoom optic was used to adjust the size of the image of the
propagating beam from the test LED. An 8-bit system would imply a digitised dynamic range of
28 =256 bits. This takes no account of noise or camera processing. The dynamic range in these
measurements was assumed at the start to be one of the greatest limiting factors of the
measurement. This assumption was later shown to be true by adjusting discrimination levels and
plotting the effect against the measured second moment values for identical camera frames.

3.2.2 Leica Monozoom 7

The camera zoom lens used for the 8-bit system was a 1:7 par-focal microscope zoom. During
zooming the focus could be maintained, whilst providing a wide field of view and a long
working distance. The zoom did not include an integral iris and the zoom setting could not be
locked. The latter meant that special care was required to ensure that the zoom was not
disturbed during measurements, otherwise the dimensional calibration would be lost. The
shortcomings of this zoom prompted the acquisition of a higher specification zoom system to
form part of the 12-bit set-up.

3.3 12-BIT SYSTEM DESIGN

3.3.1 Electrical Measurements

The LED sources were operated at a constant current using a power supply stabilised to 0.02%.
Setting a constant voltage is also possible, although this is more likely to be affected by
differences in contact potential. To measure the current to the LED, a standard resistor was
placed in series with the power supply and the LED source. The potential across the standard
resistor was measured using a calibrated digital voltmeter. Using this value, the current to the
LED was calculated and recorded. This ensured that the same electrical conditions were used
for each LED measurement.

7

3.3.2 Transform Lens

Following a survey of commercially available products, it was identified that a single large
diameter achromatic lens of sufficient power and quality for the measurements was not
available. Two high quality achromats were combined to provide an equivalent effect. The large
diameter was required to provide effective coupling of the LED output to the camera input to
reduce vignetting. Optics of large diameter also allows the inner portion of the lens to be used
which introduces less aberration to the measurement process. It is critical that the geometry of
the lens is known accurately, so that the lens transformation properties can be calculated (see
Figure 6 and Figure 7).

Figure 6 Schematic diagram of achromat showing critical measurements needed to allow
the lens transformation properties to be calculated (all dimensions in mm).
A description of the parameters used can be found in the glossary.

The distance between the two lenses and the distance from the LED required calculation to
ensure that the beam would not overfill the aperture of the camera zoom. In addition, the
transformed waist diameter must not be too small as to cause measurement problems due to the
camera resolution. Additionally, the Raleigh length (distance for the beam diameter to increase
by 2) should be long enough to allow accurate distance measurement to be carried out. High
quality lens mounts with yaw and tilt adjustments were purchased to allow uniaxial alignment of
the measurement system.

Figure 7 Scale drawing of the two transform achromats showing some of
the calculated measurement distances, definitions of parameters are
given in section 6 (all dimensions in mm)

8

3.3.3 Optical Rail

A 2-metre cast iron optical rail was used as the primary bench for the mounting of the optical
components. A second, machined, aluminium rail was used to mount the LED and the achromat
lenses. This secondary rail was mounted on a roller carriage on the primary bench. All carriages
and benches carried vernier scales to ensure accurate measurement readings.

3.3.4 LED Mount

A stable LED clamp which could in turn be mounted on a 3 axis gimbal mount with height and
transverse adjustment was required. A commercially available solution was unavailable so a
clamp was designed and produced by the NPL workshop. This was mounted on a high stability
goniometric mount with height and transverse adjustment provided by two other stages. This
provided a low vibration mount with high resolution and repeatable displacement.

3.3.5 Beam Attenuation

Neutral Density (ND) optical filters were used to attenuate the light input to the camera. Critical
attributes were spectral neutrality and spatial uniformity. Tests were made on NPL’s primary
Zygo Fizeau interferometer to inform the purchase of a high quality set of filters with low
wavefront aberration. The filters were placed in a mount that allowed stacking of filters with an
adjustment for variable tilt to reduce inter-reflection. The proposed initial system did not include
a scatter screen and thus the use of an iris with the zoom system would have caused vignetting.
Later adoption of the scatter screen allowed this option.

3.3.6 Rotating diffuser

It was found to be necessary to use a rotating frosted scatter screen to allow visualisation of the
beam profile at the focal point of the zoom system. Measurements made without this system
caused vignetting problems. The rotating diffuser had the added advantage that it allowed the
use of the integral iris in the zoom lens to attenuate the LED light. Several measurements were
made to ensure that the real beam diameter was not greater than the diameter obtained by the
use of the screen.

3.3.7 Graticule

A photoetched transparent graticule with traceable calibration was used to calibrate the imaging
system (zoom in combination with the CCD array and analysis software).

3.3.8 12-Bit Camera System

The 12-bit system utilized a superior zoom system that had a larger input optic and a greater
magnification range. The CCD detector used produced a digital 12 bit output and incorporated a
two stage peltier cooler to both reduce the temperature of the array and the level of noise
acquired. The dynamic range of the system was 212=4096 bits, the software used a
“discriminator level” which allowed the baseline for detection to be raised above the ambient
noise level. The zoom system incorporated an iris which allowed the light levels to be reduced
within the range afforded by the detector integration time adjustment.

Calculations were performed to ensure that the LED and lens(es) were located so that the beam
could converge to a waist and re-expand within the travel range of the optical bench system. At
the same time the anticipated diameter of the beam at the transforming lens(es) was examined to

9

ensure that the beam size was not large enough to introduce significant aberration or vignetting
effects.

3.3.9 Leica Z16 Zoom

Two Leica zoom microscope systems were assessed, the Z6 and Z16 models. The Z16 was
found to have a greater focal range and would allow the measurement of a greater range of LED
types. The Z16 is an apochromatic zoom system with central beam path. A planapochromatic
0.5X objective was used and the zoom range was 0.57× – 9.2×. This high quality optic has a
similar field of view to the Monozoom 7 but has significantly lower aberrations. The inbuilt iris
can also be employed to attenuate light levels when used in conjunction with a scatter screen.
The lockable zoom setting allows calibration at a particular fixed zoom level.

3.3.10 Final 12-bit System Design

Figure 8 shows the final components used in the 12-bit system for the measurement of angular
subtense.

Achromats Rotating ND Filter and CCD camera
LED diffuser Filter holder

Planofocal
Zoom Lens
Secondary
optical bench
Primary optical
bench

Figure 8 Final optical arrangement of the 12-bit system for the measurement of
apparent source size

10

4 MEASUREMENT PROCEDURE

4.1 PREPARATION FOR MEASUREMENT

The optical arrangement for the measurement of apparent source size is detailed in the
schematic diagram, Figure 8. Prior to measurement the components must be carefully aligned to
ensure that the LED beam is parallel to the optical axis of the primary and secondary bench.

The following points detail the steps required to align the components used with the optical axis
of the bench.

a) Establish a reference He-Ne beam parallel to the optical bench by the use of at least two
movable irises or apertures.

b) Align the centre of the Zoom lens with the HeNe beam and use the imaging software to
ensure that the suitably attenuated beam is in the centre of the CCD array field of view.

c) Introduce the transform achromats one at a time and centre them on the beam. Ensuring
that the emerging beam is still creating a centred image in the camera.

d) Place the viewing screen at the focal point of the zoom lens by utilizing a reference grid
that can be resolved by the imaging software and can be coincident with the frosted side
of the screen.

e) A microscope, focused on the optical axis of the system, is used to locate and record the
positions of the components along the optical bench. This facility is used to set
accurately the appropriate distances between the LED and the achromat(s).

4.2 CALIBRATION OF CCD ARRAY AND ASSOCIATED EQUIPMENT

a) A reference grid or graticule is inserted in place of the frosted screen with the reference
grid plane coincident with the plane of the frosting, as determined using a telescope. A
CCD frame of the reference grid is recorded and analysed by the software to derive the
calibration factor (pixels/mm) to be used to convert subsequent beam pixel
measurements into linear dimensions.

b) All equipment used to measure the electrical characteristics of the LED were calibrated
and traceable to national standards, as is essential for such a system.

4.3 LED BEAM WIDTH MEASUREMENT

Once the system is aligned and the calibration procedures performed, the following steps are
required to predict the position of the beam waist from the vertex of LED.

a) A combination of ND filters and the iris of the Zoom lens are used to attenuate the
beam irradiance so that the full dynamic range of the CCD system is used. This is done
by locating the position of maximum irradiance, then placing filters in the beam path so
that the signal is just about saturating the CCD pixels. As readings are taken either side

11

of the maximum, the iris of the zoom lens and the exposure time of the camera can be
adjusted to maintain the signal level at the full dynamic range of camera. The Zoom is
also set so that approximately a quarter of the CCD field of view appears to be filled by
the largest diameter that is to be measured;

b) The image acquisition software is used to capture at least 10 equidistant beam images
either side of the beam waist. Each image has an associated image of background
optical noise captured at the same time by blanking out the LED with a black felted
beam stop;

c) The background frame is subtracted from the beam image frame before the digital width
analysis process is performed;

d) The corrected image is processed using the convergent second moment (CSM) method
to limit the dimensions of the CCD window that is subsequently analysed and hence
reduce noise contribution to the second moment evaluation. The CSM values of the
beam in the laboratory (CCD array) vertical and horizontal axes are calculated. A cross-
moment of the beam distribution in the converged window is used to calculate the
azimuth of the principal axes of potentially non-circular distributions. This figure
enables the calculation of the dimensions of the beam along its principal axes. The ratio
of the principal dimensions (ellipticity), the azimuth angle of the principal axes relative
to the laboratory axes; and the calibrated linear magnitude of the principal dimensions
are recorded. The convergence of the 2nd moment calculations can be seen in Figure 9
The program then outputs the final 2nd moment measurements in the X and Y axes;

33.71

Figure 9 CSM software illustrating the calculation of the second moment values.

e) A least-squares (maximum probability) process is used to discover the best fitting
hyperbolic envelope to the propagating beam in each of its principal planes. The
coefficients of the hyperbolas are processed to reveal: the locations of the beam waists
relative to the vertex of the LED; the transverse dimensions of the waists; the values of
the Rayleigh Lengths of the beam along their principal planes; and the far-field
divergences in those planes;

12

f) If the beam is found to be astigmatic (i.e. the ellipticity of the beam is found to be
greater than 1.15 or less than 0.83) and there is a monotonic variation in the azimuth of
the principal planes of the propagating beam (twist) then the beam is deemed to suffer
from general astigmatism and no further investigation or relief of the thermal hazard
factor C6 can be justified without a more detailed analysis procedure;

g) If the beam is identified as stigmatic or simple astigmatic the determined values of the
beam waist widths and far-field divergences can be placed on the angular subtense
contour map (Figure 4) and the contour below the lowest uncertainty ellipse can be used
to identify the angular subtense to be used to determine the appropriate value of the
thermal hazard relaxation factor C6.;

h) If the Rayleigh Length in the least divergent principal plane is less than 50 mm then the
location of the apparent source can be regarded as the location of the beam waist in that
plane. If the Rayleigh Length is greater than 50 mm then the possible error in hazard
assessment can be greater than 5% and the location of the centre of curvature of the
wavefront arriving at the most hazardous viewing distance should be used to identify
location of the apparent source.

Figure 10 shows the required optical elements of the system to measure the angular subtense of
an LED.

Transform achromats

LED in Rotating diffuser
goniometric mount Cooled CCD
Camera

Zoom lens
ND filters

Enclosure to reduce
scattered light

Figure 10 Experimental apparatus

13

4.4 TRANSFORM VALIDATION EXPERIMENT

To validate the suitability of the proposed measurement method for determining the beam
propagation parameters a Transform Validation Experiment can be undertaken. This technique
uses the beam propagation parameters to predict the size of a beam waist produced when a
known lens is inserted into the beam. This prediction is then verified by using the measurement
technique to measure the true diameter of the new beam waist with the lens inserted. The aim is
to achieve 10% (1 sigma) agreement between the predicted value and the measured diameter of
the beam waist. The transform validation experiment is shown in Figure 10 and schematically in
Figure 11. The points below detail the steps required in the transform validation method.

Measure the transformed waist and estimate original waist

Use the estimated waist to predict new waist formed by inserted lens

Measure and estimate new waist for comparison with step 2. If the estimate and the
prediction agree sufficiently well the validation is complete

Measure
LED
CCD

Step 1

Estimate

Predict
LED

Step 2

Compare

Measure

LED
CCD

Step 3

Figure 11: The three steps of the primary ISO Transform Validation Experiment 6

The results of the Transform Validation Experiment are presented in Section 5.2.

14

5 RESULTS

5.1 INITIAL RESULTS

The ideal methodology to measure the LED beam would be through direct imaging. Some
difficulties were encountered due to vignetting of the beam by the zoom lens. This effect can be
seen in the asymmetry of the hyperbolic plot produced from the second moment analysis, Figure
12.

IR LED measurement showing Vignetting effect

5.000

4.500

2
y = 0.0003x - 0.0142x + 3.4009
2
R = 0.9827
2nd moment Beam radius

4.000
Horizontal width (mm)
Vertical width (mm)
Poly. (Vertical width (mm))
Poly. (Horizontal width (mm))
3.500 2
y = 0.0003x - 0.0146x + 3.297
2
R = 0.9854

3.000

2.500
-60.0 -40.0 -20.0 0.0 20.0 40.0 60.0 80.0 100.0
Distance from Beam Waist

Figure 12 Skewed fit of second moment values obtained showing vignetting effect of
zoom aperture
Noise effects from the intereflections between the filters used to attenuate the light from the
LED were found to be a particular problem. The differences in measured second moment
diameter caused by different filter combinations can be seen on Figure 13. The stray light noise
levels on the camera were very high and a discriminator level of 50 was required to produce the
analysis.

For the final measurements the procedure was adapted to only utilise the minimum number of
filter elements by manually finding the camera position that resulted in the greatest local
irradiance. The integration time of the camera and/or the iris in the zoom lens were then reduced
as much as possible to reduce the signal output from the camera pixels to a point where a ND
filter would reduce the signal levels to just below saturation. This was to ensure that the greatest
dynamic range of measurement was employed.

15

IRED through 2 lens transform - X-axis (Aug 26 Disc 50)

20.0

18.0
Converged 2M beam width (mm)

LSq Fit Hyperbola
4 filter set A
16.0
2 filter set B
1 filter C

14.0 1 filter D
4 filter set E
3 filter set E
12.0 2 filter set F

10.0

8.0
280 285 290 295 300 305 310
Distance past vertex (mm)

Figure 13 IRED Led measurements demonstrating filter effects

Initial measurement work concentrated upon the confirmation of earlier work using an Osram
IR LED 2. Details of this LED can be found in Appendix 3. Early evaluations were pursued with
a 50 mm focal length singlet lens to examine the field of view required for the experiment.

16

5.2 8-BIT TRANSFORM VALIDATION EXPERIMENT RESULTS

5.2.1 Direct Measurements of IR LED

The 8-bit system using the Cohu CCD camera and Leica monzoom 7 lens was used for the
initial work to confirm the method for measurement of angular subtense. Figure 14 details the
required apparatus to measure the beam waist of an LED directly. Measurements of the beam
width were made using the procedure in Section 4.3.
Rotating ND Filter and CCD camera
diffuser Filter holder
LED

Planofocal
Zoom Lens
Secondary
optical bench
Primary optical
bench

Figure 14 Optical set-up for direct apparent source size measurement

SFH 400 IRED (950 nm) @ 50 mA Raw Beam (5 Aug)
Converged 2M beam

6.5
width (mm)

5.5

4.5

3.5

2.5
0 5 10 15 20 25

Figure 15 Plot of converged beam width for IRED LED

The results, shown in Figure 15 and Table 1, indicate that the IR LED produces a beam with a
waist external to the LED. The M2 value is very large but the beam still fits the hyperbolic

17

envelope well. The existence of an external beam waist allows the effective measurement of the
direct propagation envelope.

Table 1 Calculated beam parameters for Osram IRED LED

Parameter Value Units
Waist position from LED vertex zo 5.61 mm
Waist diameter Wo 3.38 mm
Rayleigh distance Zr 9.76 mm
Divergence 347 mrad
M2 969

5.2.2 Two Lens transform of IR LED

Achromats Rotating ND Filter and CCD camera
LED diffuser Filter holder

Planofocal
Zoom Lens
Secondary
optical bench
Primary optical
bench

Figure 16 Optical set-up for apparent source size measurement
using two achromat lenses
The second step in the validation of the measurement method is to predict the beam waist
diameter. This requires the use of a transform lens in the optical arrangement (see Figure 16).
Two achromats were used to produce a beam waist that would not overfill the field of view of
the CCD. The lenses also ensured that the Rayleigh Length was sufficiently long to provide an
appropriate number of measurement planes. Figure 17 shows the results of these measurements
with a hyperbolic fit to the data points.

18

IRED 2 Lens Transform X-axis

7.5
7.0
6.5
CSM width (mm)

6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
220 230 240 250 260 270

Figure 17 Hyperbolic fit to data from IR LED through two achromat lenses

A summary of the beam characteristics for the Osram LED is presented in Table 2. The
complete summary of the Transform Validation Experiment is located in Tables 4 and 5 of
Section 5.3 as it was thought more appropriate to put them in the context of the 12-bit system
and hence allow comparison.

Table 2 Summary of beam characteristics for IRED LED using 8-bit camera system
SFH 400 IRED using 8-bit Camera
Transformed Beam
Beam property Goodness of fit
Waist position from LED vertex Zo 254.1 mm 0.01
Waist diameter Wo 3.12 mm 0.10
Rayleigh distance Zr 8.6 mm 0.27
Divergence 361 mrad 16
M2 950 67

Original Beam from Inverse Transform
Beam property Uncertainty
M2 950 129

Uncertainties Used
Focal length etc. 0.5 %
Datum positions 0.1 mm
Width measurements 0.025 mm
Measurement locations 0.15 mm

19

5.3 12-BIT TRANSFORM VALIDATION EXPERIMENT RESULTS

The 12-bit PCO Sensicam camera with the Leica Z16 zoom lens was used for further
measurements of apparent source size on the Osram IRED LED and a range of visible LEDs.
The details of all LEDs measured can be seen in Appendix 3.

5.3.1 Low Level Noise

It was found that the discriminator level used to eliminate low level noise caused a much greater
effect upon measured beam width than might be expected. The intensity of the imaged LED was
always set as close as possible to the saturation point of the CCD to produce the greatest
dynamic range possible. With the 12-bit system, the maximal number of bits of dynamic range
would be 4096. Figure 18 shows the effect upon the second moment beam size due to change of
discrimination level. Hereafter the discrimination setting was kept at 5 bits.

IRED raw beam width vs Discriminator Level

48 Pos 1
Pos 3
Second moment (X-axis)

Pos 6
43
Pos 6
Pos 10

38 Pos 11
Pos 12
Pos 13
33 Pos 14
Pos 15

28
0 5 10 15 20
Discriminator Level

Figure 18 Variation in discriminator level with beam width

5.3.2 Transform Validation Experiment results from IRED LED

The measurements performed using the 8-bit system (described in section 5.2) were repeated to
demonstrate the differences between the two systems and to validate the procedure for
measurement of angular subtense. The beam width of the LED was measured directly using the
measurement arrangement shown in Figure 14.The resulting data is plotted in Figure 19.

The next step in the Transform Validation Experiment was to measure the beam of the LED via
two achromat lenses. Several measurements were made and a hyperbolic fit was made to the
resulting data. The fit is shown in Figure 20.

20

IRED Raw - X-axis (SEP 30)

7.0
Converged 2M beam width (mm) - 2% uncertainty

6.5

6.0

5.5

5.0

4.5

4.0

3.5

3.0
5 10 15 20 25 30

Figure 19 Plot of converged beam width for IR LED

IRED 2 Lens Transform X-axis

7.5
7.0
6.5
CSM width (mm)

6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
220 230 240 250 260 270

Figure 20 Hyperbolic fit to data through two achromats from IR LED

21

Table 3 Summary of beam characteristics for IRED LED using 12-bit camera system

SFH 400 IRED

Transformed Beam

M2 588 43


M2 588 78

Uncertainties Used

Measurement locations. 0.15 mm

Beam propagation parameters calculated from the hyperbola equation. These parameters
were then back propagated by calculation through the lens using the known lens
parameters allowing calculation of the LED emitted beam properties. The beam
parameters are presented in Table 3.

These can then be compared with the previous measurements of the LED direct beam.
Tables 4 and 5 give a complete summary of the Transform Validation Experiment
results for both the 8-bit and 12-bit camera systems.

22

Table 4 Validation results for IRED LED - X axis

LED SFH 400 IRED (950 nm) X – Axis
12-bit camera + Z16 lens
Property Direct UC Trans. UC Inverse UC Difference Agreement %
beam % beam % transformed % (ITB-RB) (Difference/RB
(DB) beam (ITB) x 100)
Waist
location
4.28 0.04 252.8 0.03 4.7 9.7 -0.42 -9.8
(mm from
vertex)
Waist
diamter 3.06 0.01 2.73 0.14 3 0.58 0.06 2.0
(mm)
Rayleigh
length 12.13 0.03 10.7 0.56 13 1.8 -0.87 7.2
(mm)
Divergence
253 1 255 19 232 55 21 8.3
(mrad)

8-bit camera system + monozoom 7 lens
Waist
location
5.6 254.1 4.9 0.7 12.5
(mm from
vertex)
Waist
diamter 3.38 3.12 3.47 -0.09 2.7
(mm)
Rayleigh
length 9.76 8.6 10.7 -0.94 9.6
(mm)
Divergence
346 361 324 22 6.4
(mrad)

Note: UC = Uncertainty (%)

23

Table 5 Validation results for IRED LED - Y axis

LED SFH 400 IRED (950 nm) Y - AXIS
12-bit camera + Z16 lens
Property Direct UC Trans. UC Inverse UC Difference Agreement %
beam % beam % transformed % (ITB-RB) (Difference/RB
(DB) beam (ITB) x 100)
Waist
location
4 0.03 252.8 0.03 4.5 9.9 -0.5 -12.5
(mm from
vertex)
Waist
diamter 3.19 0.007 2.77 0.16 3.05 0.61 0.14 4.4
(mm)
Rayleigh
length 11.93 0.03 10.3 0.58 12.5 1.8 -0.57 -4.8
(mm)
Divergence
267 1 270 21 245 60 22 8.2
(mrad)

8-bit camera system + monozoom 7 lens
Waist
location
5.66 253.9 4.45 1.21 21.4
(mm from
vertex)
Waist
diameter 3.34 3.09 3.45 -0.11 3.3
(mm)
Rayleigh
length 10.01 8.36 10.43 -0.42 4.2
(mm)
Divergence
333 370 331 2 0.6
(mrad)

24

5.4 YELLOW LED - LIGITEK LUY 3833/A29

The measurements of the yellow LED were performed using an arrangement of two
achromats. Images of the beam were taken and the beam width calculated. The
measurement points and the resultant hyperbolic fit are plotted in Figure 21. The
hyperbolic fits the measured data well. It is always difficult to make an initial estimate
of the position of the waist from the LED vertex. Ideally iterative measurements would
allow the spread of data to be symmetric around the beam waist position.

Yellow LED 2 Lens Transform X-axis

7.5
7.0
6.5
CSM width (mm)

6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
220 230 240 250 260 270

Figure 21 Hyperbolic it to data from a yellow LED through two achromats

25

Table 6 Summary of beam characteristics for Yellow LED using 12-bit camera system

Yellow LED - Ligitek LUY 3833/A29

Transformed Beam

M2 735 20


Waist position from LED vertex Zo -3.9 mm 2.8
M2 735 64

Uncertainties Used
Focal length etc. 0.50%

Table 6 presents a summary of the beam characteristics for the yellow LED. From the results
the waist position of the inverse transformed beam (the direct beam) can be seen to be inside the
LED chip. This provides an interesting contrast to the IR LED. It should also be noted that the
divergence of this LED is significantly less than the other "display" LEDs examined in this
study.

26

5.5 BLUE LED - NICHIA NSPB500 RANK WS

Measurements of the 2-lens transformed beam from the blue LED were made at positions either
side of the beam waist and the results are shown in Figure 22.

The departure of data from the smooth fitted curve, shown in Figure 22, was thought to be due
to filter changes creating intereflections and problems for the CSM beam width measurement.

Blue LED 2 Lens Transform X-axis

5.4

5.2
CSM width (mm)

5.0

4.8

4.6

4.4

4.2

4.0
235 240 245 250 255 260

Figure 22 Hyperbolic fit to data from Blue LED through two achromats

27

Table 7 Summary of beam characteristics for Blue LED using 12-bit camera system
Blue LED - Nichia NSPB500 Rank WS

Transformed Beam

M2 1171 112


M2 1171 170

Uncertainties Used
Focal length etc. 0.50%


With these results an externally located beam waist location outside the Blue LED package can
be seen from the positive waist position in the inverse transform section of Table 7. This is
similar to the Osram SFH 400 IRED, but the waist is not as conveniently far away from the
LED vertex which facilitated the direct beam measurement in section 5.2.

28

5.6 GREEN LED - NICHIA NSPG500 RANK GS

Measurements of the beam width were made at positions either side of the beam waist and the
results are shown in Figure 23.

Green LED 2 Lens Transform X-axis

5.4

5.2
CSM width (mm)

5.0

4.8

4.6

4.4

4.2

4.0
235 240 245 250 255 260

Figure 23 Hyperbolic fit to data from Green LED through two achromats

Figure 23 shows a smaller data divergence from the fitted curve. These deviations can be
disregarded because the rest of the data fits so well.

29

Table 8 Summary of beam characteristics for Green LED using 12-bit camera system

Green LED - Nichia NSPG500 Rank GS

Transformed Beam

M2 1129 93


M2 1129 148

Uncertainties Used


The results in Table 8 summarise the beam characteristics for the green LED. It shows an
external waist from the LED. The measurement procedure requires at least 10 measurements of
the beam width either side of the waist position, therefore the waist would not be positioned far
enough away from the LED vertex to be easily measured as a direct beam.

30

5.7 RED LED - KINGBRIGHT L-53SRC/E


Red LED 2 Lens Transform X-axis

5.4

5.2
CSM width (mm)

5.0

4.8

4.6

4.4

4.2

4.0
235 240 245 250 255 260

Figure 24 Hyperbolic fit to data from Red LED through two achromats

31

Table 9 Summary of beam characteristics for Red LED using 12-bit camera system

Red LED - Kingbright L-53SRC/E

Transformed Beam

M2 1052 75


M2 1052 126

Uncertainties Used


A summary of the beam characteristics for the red LED is presented in Table 9. As seen with
the yellow and blue LEDs in sections 5.4 and 5.5, a beam waist location inside the red LED
package can be seen from the negative waist position in the inverse transform section of Table
9.

32

5.8 WHITE LED - NICHIA NSPW500 RANK BS


White LED 2 Lens Transform X-axis

5.0
4.8
4.6
CSM width (mm)

4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
235 240 245 250 255 260

Figure 25 Hyperbolic fit to data from White LED through two achromats

33

Table 10 Summary of beam characteristics for White LED using 12-bit camera system

White - Nichia NSPW500 Rank BS

Transformed Beam

M2 911 90


M2 911 131

Uncertainties Used

Measurement locations. 0.15 mm

A summary of the beam characteristics for the white LED is presented in Table 10.

34

5.9 ORANGE LED - TOSHIBA TLOH190P

Orange LED One Lens Transform. X-axis

13.

12.

11.
CSM width (mm)

10.

9.0

8.0

7.0

6.0
180 200 220 240 260 280

Figure 26 Orange LED one achromat transform

The orange LED only used one achromat to perform the beam transformation to give an
appropriate image to analyse on the 12-bit camera.

The orange LED data did not fit well to a hyperbola. This is clearly demonstrated in Figure 32.
Further study of the measurement data indicated that the propagating beam was astigmatic and
hence would not fit to the beam propagation model. Astigmatic beams could be treated using the
methodology described in ISO 11146-2 7 but this is beyond the scope of this study.

The astigmatic nature of the beam can be discovered from the steady change of azimuth angle as
the beam propagates, see Figure 33. The apparent sudden jump of the angle is due to the beam
widths in the X and Y direction reaching the same value at that point in the Z direction. This
indicates a nearly circular beam and makes the azimuth angle indeterminate. As described in the
ISO standard 11146-2 the insertion at this point of a cylindrical lens at the right azimuth angle
may remove the astigmatism.

35

Astigmatism in beam from Orange LED

20.00

15.00

10.00
WoX
WoY
5.00
Elipticity x 10
Azimuth (degrees)
0.00
170 190 210 230 250 270 290 310

-5.00

-10.00
Distance past Vertex (mm)

Figure 27 Plot demonstrating the astigmatism of the orange LED and hence the lack
of fit to a hyperbola.

36

5.10 HIGH POWER BLUE LED - LUXEON STAR

Figure 28 Photo of Luxeon Star LED with Fraen 10° lens

The Luxeon Star LED, including the Fraen 10° lens associated with the LED, is shown in
Figure 29. Details for the Luxeon Star are given in Appendix 3.

Luxeon V-Star Batwing LED (Royal blue) + Fraen 10° Lens. (x-axis)

13.0

12.0
CSM width (mm)

11.0

10.0

9.0

8.0

7.0
340 350 360 370 380 390 400 410

Figure 29 Hyperbolic fit to data from high power royal blue LED through one achromat

37

The values for the beam width of the Luxeon Star LED are plotted in Figure 30. The angular
subtense of this device far exceeds max (100 mrad) and hence falls outside the region where the
coefficient C6 (IEC 60825-1) value depends upon angular subtense. It should be noted that this
LED carries a Class 2 warning label.

38

6 UNCERTAINTY ANALYSIS

18
With reference to the ISO Guide to Uncertainty in Measurement the uncertainties are
separated into:
Type A, those uncertainties evaluated by statistical methods
and Type B, those evaluated by other methods.

The equations used to derive the beam propagation parameter are partially differentiated with
respect to all the measured quantities to produce contributions to the uncertainty budget.

A simplified summary of the Type B uncertainty budget is shown in the Table 11. The
uncertainties quoted are the reduced values (coverage factor k=1).

Table 11 List of Type B uncertainty values

Source of Uncertainty Value
Focal lengths 0.5 %

The second moment width measurements were fitted to a hyperbolic curve and the curve
coefficients were then used to derive the beam propagation parameters. The uncertainty of this
measurement was therefore derived by the partial differentiation of the equations defining the
propagation parameters. This was checked using a step-wise uncertainty analysis, which
produced close agreement with the original method (partial differentiation is a more rigorous
method).

Correlation has not been considered in this analysis but the uncertainties were combined using
sum of squares to give the most conservative estimate of uncertainty.

The uncertainty derivations had to consider three measurement configurations
a) No Transform lenses used (LED has an external waist)
b) One Transform lens used
c) Two Transform lenses used

The tables below give examples of each configuration. The Type B uncertainties listed in Table
11 are added in quadrature to provide the uncertainty values for component positions.

39

6.1.1 No Transform Lens Used

This example is for the 12-bit direct beam measurement of Osram IR LED. Table 12 details the
uncertainty components. The uncertainty references are at the end of the Section 6.

Table 12 Uncertainties for measurement of Osram IR LED
Waist position zo 4.28 mm +/- 0.04
Waist diameter Wo 3.06 mm +/- 0.0067
Rayleigh distance Zr 12.13 mm +/- 0.0287
Divergence 252 mrad 0.81
M2 639 +/- 3.17

The uncertainties for the raw beam were calculated by knowledge of the Type B uncertainty in
the measurement of distance modified by the local gradient of the hyperbola. The resulting
covariances were then added in quadrature to obtain estimates for the 1 standard deviation level.

6.1.2 One Lens datasheet

This example is for the 12-bit direct beam measurement of high power Luxeon Star LED Osram
IR LED (optical arrangement and dimensions are shown in Figure 31). Table 13 details the
uncertainty components for this measurement.

Figure 30 Diagrams illustrating the required dimensions for the Luxeon star LED

40

Table 13 Uncertainties for measurement of Luxeon Star LED

Distance 1 Uncertainty
Symbol Formulae
(mm) Uncertainty calculation code

LED Vertex to lens datum L4 253.00 0.21 RMS

Datum of Lens 1 to 1st principle
L8 19.7 0.16 M/F
plane
Separation of principle planes L9 5.3 0.11 M/F

Effective focal length of lens fe 76.2 0.38 M/F

Location of measured beam B
Zo1 Z0 370.08 0.04 Ref 1
waist 2 C

Distance of measured waist from
X1 X 1 Zo1 L4 L8 L9 fe 15.88 0.48 RMS
focal plane

Rayleigh Length of measured 1 1 2
Zr1 Zr A C B 24.51 0.50 Ref 2
beam C 4

B2
Waist width of measured beam Wo1 Wo A 7.56 0.16 Ref 3
4C

Far-field divergence of measured Wo
1
10 3 308.3 8.97 Ref 4
beam Zr

f2
Transform Parameter G1 G 2 2 6.81 0.24 Ref 5
( X1 Zr )

Distance of output waist from
focal plane
Y1 Y1 G X 1 108.1 5.0 Ref 6

Location of output beam waist
Zo2 Zo2 L4 L8 Y1 fe 88.4 5.0 Ref 7
wrt vertex of LED

Waist width of LED output beam Wo2 Wo 2 Wo1 G1 19.7 0.5 Ref 8

Rayleigh Length of LED output
Zr2 Zr2 G Z r1 166.9 6.8 Ref 9
beam

Far-field divergence of LED Wo
2
10 3 118.2 18.3 Ref 10
output beam Zr

41

6.1.3 Uncertainty Budget For Beam Waist (two lens transform)

Figure 32 illustrates some of the critical measurements made for the Ligitek LUY 3833/A29
Yellow LED evaluation.

Figure 31 Critical measurements for two lens transformation

Table 14 Uncertainties for measurement of Yellow LED
Uncertainty
Distance 1
Symbol Formulae calculation
(mm) Uncertainty
code
LED Vertex to lens 2
L5 161.8 0.14 RMS
datum
Datum of Lens 2 to
L10 13.23 0.15 M/F
1st principle plane
Separation of
principle planes of L11 4.9 0.10 M/F
Lens 2
Effective focal length
fe2 100 0.50 M/F
of Lens 2
LED Vertex to lens 1
L4 81.60 0.14 RMS
datum
Datum of Lens 1 to
L8 19.7 0.16 M/F
1st principle plane
Separation of
L9 5.3 0.11 M/F
principle planes
Effective focal length
fe1 76.2 0.38 M/F
of lens

Location of measured B
Zo1 Z0 242.43 0.02 Ref 1
beam waist 2 C
Distance of measured
waist from input X1 X1 Zo1 L4 L8 L9 fe -37.50 0.55 RMS
focal plane of Lens 2

Rayleigh Length of 1 1 2
Zr1 Zr A C B 16.70 0.20 Ref 2
measured beam C 4

42

Waist width of B2
Wo1 Wo A 3.81 0.05 Ref 3
measured beam 4C
Far-field divergence Wo
of measured beam 1 10 3 228.2 3.85 Ref 4
Zr
2
f2
Transform Parameter G1 G1 5.93 0.16 Ref 5
( X 12 Z r21 )
Distance of waist of
intermediate beam
Y1 Y1 G X1 -222.5 6.8 Ref 6
from focal plane of
Lens 2
Location of
intermediate beam
Zo2 Z o2 L5 L10 Y1 f e2 297.5 6.8 Ref 7
waist wrt vertex of
LED
Waist width of
Wo2 Wo 2 Wo1 G1 9.3 0.2 Ref 8
intermediate beam

Rayleigh Length of
Zr2 Zr2 G Z r1 99.1 2.9 Ref 9
intermediate beam

Far-field divergence
Wo 93.7 0.6 Ref 10
of intermediate beam 2 103
Zr
Distance between
intermediate waist X 2 Zo2 L4 L8 L9 f e1 114.7
X2 6.8 RMS
and input focal plane
of Lens 1
2
f1
Transform Parameter G2 G2 2
0.2526 0.018 Ref 5
(X2 Z r22 )
Distance of waist of
input beam from Y2 Y2 G2 X2 28.98 2.7 Ref 6
focal plane of Lens 1
Location of input
beam waist wrt Zo3 Z 03 L4 L8 Y2 f1 -3.88 2.8 Ref 7
vertex of LED
Waist width of LED
output beam
Wo3 Wo 3 Wo 2 G2 4.67 0.2 Ref 8

Rayleigh Length of
Zr3 Z r3 G2 Z r 3 25.03 0.73 Ref 9
LED output beam

Far-field divergence Wo3
3 3 103 186.41 9.36 Ref 10
of LED output beam Zr 3

43

Investigation of a measurement technique to determine led

Investigation of a measurement technique to determine led

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Investigation of a measurement technique to determine led