SIST EN ISO 11146:2000
(Main)Laser and laser-related equipment - Test methods for laser beam parameters - Beam widths, divergence angle and beam propagation factor (ISO 11146:1999)
Laser and laser-related equipment - Test methods for laser beam parameters - Beam widths, divergence angle and beam propagation factor (ISO 11146:1999)
This Standard specifies methods for measuring beam widths (diameter), divergence angles and beam propagation factors of laser beams.
Laser und Laseranlagen - Prüfverfahren für Laserstrahlparameter - Strahlabmessungen, Divergenzwinkel und Strahlpropagationsfaktor (ISO 11146:1999)
Diese Internationale Norm legt Verfahren zur Messung von Strahlabmessungen (Durchmesser), Divergenzwinkeln und Strahlpropagationsfaktoren von Laserstrahlen fest. Diese Verfahren dürfen nicht auf stark gebeugte Strahlen angewandt werden, wie z.B. diejenigen, die von instabilen Resonatoren oder beim Durchgang durch scharf begrenzte Aperturen erzeugt werden.
Lasers et équipements associés aux lasers - Méthodes d'essai des parametres des faisceaux laser - Largeurs du faisceau, angle de divergence et facteur de propagation du faisceau (ISO 11146:1999)
Laserji in laserska oprema – Preskusne metode za parametre laserskega žarka – Širina žarka, kot divergence kota in faktor širjenja žarkov (ISO 11146:1999)
General Information
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Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 11146:2000
01-januar-2000
Laserji in laserska oprema – Preskusne metode za parametre laserskega žarka –
Širina žarka, kot divergence kota in faktor širjenja žarkov (ISO 11146:1999)
Laser and laser-related equipment - Test methods for laser beam parameters - Beam
widths, divergence angle and beam propagation factor (ISO 11146:1999)
Laser und Laseranlagen - Prüfverfahren für Laserstrahlparameter - Strahlabmessungen,
Divergenzwinkel und Strahlpropagationsfaktor (ISO 11146:1999)
Lasers et équipements associés aux lasers - Méthodes d'essai des parametres des
faisceaux laser - Largeurs du faisceau, angle de divergence et facteur de propagation du
faisceau (ISO 11146:1999)
Ta slovenski standard je istoveten z: EN ISO 11146:1999
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
SIST EN ISO 11146:2000 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN ISO 11146:2000
INTERNATIONAL ISO
STANDARD 11146
First edition
1999-06-01
Lasers and laser-related equipment — Test
methods for laser beam parameters —
Beam widths, divergence angle and beam
propagation factor
Lasers et équipements associés aux lasers — Méthodes d'essai des
paramètres des faisceaux laser — Largeurs du faisceau, angle de
divergence et facteur de propagation du faisceau
A
Reference number
ISO 11146:1999(E)
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SIST EN ISO 11146:2000
ISO 11146:1999(E)
Contents
1 Scope .1
2 Normative references .1
3 Terms and definitions .1
4 Coordinate systems.3
5 Test principles.4
6 Measurement arrangement and test equipment.5
7 Beam widths and beam diameter measurement .6
8 Divergence angle measurement.7
9 Combined determination of laser beam propagation parameters.8
10 Determination of beam propagation factor and times-diffraction-limit factor .9
11 Test report .11
Annex A (normative) Alternative methods for beam width measurements .14
Annex B (normative) Equations for non-circular beams.21
Annex C (informative) Derivation of equations .24
© ISO 1999
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
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ISO 11146:1999(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.
International Standard ISO 11146 was prepared by Technical Committee ISO/TC 172, Optics and optical
instruments, Subcommittee SC 9, Electro-optical systems.
Annexes A and B form a normative part of this International Standard. Annex C is for information only.
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Introduction
Any radially symmetric laser beam requires three parameters for characterization:
a) location of the beam waist z ;
0
b) waist diameter d ; and
s0
c) the far-field divergence angle Q for the beam under test.
s
With these three values, one can predict the beam diameter at any plane along the propagation axis. To a first
approximation (for divergence angles less than 0,8 rad), the beam propagates as
2
2 2 2
dz()=+d z z⋅ Q (1)
()-s s 0 0 s
The beam propagates according to equation (1) provided the second moments of the power (energy) density
distribution function are used for the definition of beam widths and divergences. The propagation is described by a
2
beam propagation factor K or a times-diffraction-limit factor M which can be derived from the above basic data. The
2
relationship between K and M , respectively, the actual waist diameter ds and the divergence angle Q, is:
0s
4l
1 14 1
l
0
== ⋅ =⋅ (2)
K
2
ppnd⋅⋅QQd ⋅
M
s00s s s
where
K is the beam propagation factor;
2
M is the times-diffraction-limit factor;
lis the wavelength in vacuum ;
0
lis the wavelength in medium with index of refraction n,
Qis the divergence angle,s
d is the waist diameter,s0
n is the index of refraction.
NOTE 1 The accuracy of measurement of beam propagation factors is expected to be in the region of 10 %. It is not
consistent with divergence angles (full angle according to ISO 11145) above 0,8 rad.
The product
2
44llM
0 0
nd⋅⋅Q= = (3)
0 s
s
Kpp
describes the propagation of laser beams and is invariant throughout the propagation of the beam as long as
aberration-free and non-aperturing optical systems are used.
For non-radially symmetric beams, the values of seven parameters are required for characterization:
locations of the beam waists z and z
0x 0y
waist widths d and d ;s0xs0y
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far-field divergence angles Q and Q; and
sxsy
azimuth angle j between the x-axis of the beam axes system and the x'-axis of the laboratory system. The x-
axis of the beam axes system coincides with the principal axis of the laser beam closest (within ±45°) to the
arbitrary x' coordinate.
In analogy to equation (3), the propagation of non-radially symmetric beams, which are however still characterizable
using two principal axes orthogonal to each other, can be described independently for the x- and y-axes using K
x
2 2
and K as beam propagation factors, or M and M as times-diffraction-limit factors, respectively.
y x y
NOTE 2 Beams that suffer from general astigmatism (twisted beams) require three additional parameters for their
characterization. The propagation in the x-z plane is not necessarily independent of the propagation characteristics in the y-z
plane and not necessarily along the propagation path will a generally astigmatic beam exhibit a circular power density
distribution. The measurement of generally astigmatic beams is outside the scope of this International Standard.
In this International Standard, the second moments of the power (energy) density distribution function are used for
the determination of beam widths. However, there may be problems experienced in the direct measurement of this
property in the beams from some laser sources. In this case, other indirect methods of measurement of second
moment may be used as long as comparable results are achievable.
In annex A, three alternative methods for beam width measurement and their correlation with the method used in
this International Standard are described. These methods are:
• Variable aperture method
• Moving knife-edge method
• Moving slit method
The problem of the dependence of the measuring result on the truncation limits of the integration has been
investigated and evaluated by an international round robin carried out in 1997. The results of this round robin testing
were taken into consideration in this document.
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SIST EN ISO 11146:2000
INTERNATIONAL STANDARD © ISO ISO 11146:1999(E)
Lasers and laser-related equipment — Test methods for laser
beam parameters — Beam widths, divergence angle and beam
propagation factor
1 Scope
This International Standard specifies methods for measuring beam widths (diameter), divergence angles and beam
propagation factors of laser beams.
These methods may not apply to highly diffractive beams such as those produced by unstable resonators or
passing through hard-edged apertures.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this International Standard. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this International Standard are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO 11145:1994, Optics and optical instruments — Lasers and laser-related equipment — Vocabulary and symbols.
IEC 61040:1990, Power and energy measuring detectors — Instruments and equipment for laser radiation.
3 Terms and definitions
For the purposes of this International Standard, the terms and definitions given in ISO 11145 and IEC 61040, and
the following apply:
3.1
energy density
H(x,y)
that part of the beam energy which impinges on the area dA at the location x, y divided by the area dA
3.2
power density
E(x,y)
that part of the beam power which impinges on the area dA at the location x, y divided by the area dA
3.3
beam waist locations
z , z , z
0 0x 0y
positions where beam widths reach their minimum values along the axis of propagation
See Figure 1.
NOTE The locations are expressed as the distances to the beam waists (inside or outside the resonator) from a reference
plane defined by the manufacturer e.g. the front of the laser enclosure.
1
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3.4
beam diameter
ds
dz()z =22 s() (4)
s
where the second moment of the power density distribution function E(x, y, z) of the beam at the location z is given
by
2
rEr,zrddr j
()
∫∫
2
s ()z = (5)
Er(),z rddr j
∫∫
where r is the distance to the centroid (,xy)
and where the first moments give the coordinates of the centroid, i. e.
xE()x,,y z ddx y
∫∫
x = (6)
Ex(),,y z ddx y
∫∫
yE()x,,y z ddx y
∫∫
y = (7)
Ex,,y z x y
()dd
∫∫
NOTE 1 In principle, integration is carried out over the whole x-y plane. In practice, the integration is performed over an area
such that at least 99 % of the beam power (energy) is captured. Refer to practical limits in 6.4.
NOTE 2 The power density E is replaced by the energy density H for pulsed lasers.
NOTE 3 This definition differs from that given in ISO 11145:1994, for the reason that only beam propagation factors based
on beam widths and divergence angles derived from the second moments of the power (energy) density distribution function
allow calculation of the beam propagation. Other definitions of beam widths and divergence angles may be helpful for other
applications, but must be shown to be equivalent to the second-order moment definition to be used for calculating the correct
beam propagation.
3.5
beam widths
d ; d
sx sy
dz() =4s (z) (8)
sxx
dz() = 4s ()z (9)
s y y
where the second moments of the power density distribution function E(x, y, z) of the beam at the location z are
given by
2
()xx-E()x,y,z ddxy
∫∫
2
sz = (10)
()
x
Ex,,yz ddx y
()
∫∫
2
()yy-E()x,y,z ddxy
∫∫
2
sz = (11)
()
y
Ex,,y z ddx y
()
∫∫
where xx and yy are the distances to the centroid xy,
()-()-()
and where the first moments give the coordinates of the centroid, i. e.
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xE x,,y zddx y
()
∫∫
x = (12)
Ex,,y zddx y
()
∫∫
yE x,,y zddx y
()
∫∫
y = (13)
Ex,,y zddx y
()
∫∫
NOTE 1 In principle, integration is carried out over the whole x-y plane. In practice, the integration is performed over an area
such that at least 99 % of the beam power (energy) is captured. Refer to practical limits in 6.4.
NOTE 2 The power density E is replaced by the energy density H for pulsed lasers.
NOTE 3 This definition differs from that given in ISO 11145:1994, for the reason that only beam propagation factors based
on beam widths and divergence angles derived from the second moments of the power (energy) density distribution function
allow calculation of the beam propagation. Other definitions of beam widths and divergence angles may be helpful for other
applications, but must be shown to be equivalent to the second-order moment definition to be used for calculating the correct
beam propagation.
3.6
times-diffraction-limit factor
2
M
measure of how close the beam parameter product is to the diffraction limit of a perfect Gaussian beam
d Q
2 p
s 0 s
M =⋅ (14)
l 4
4 Coordinate systems
4.1 General
The x, y and z axes define the orthogonal space directions in the beam axes system. The x and y axes are
transverse to the beam and define the transverse plane. The beam propagates along the z axis. The origin of the z
axis is in a reference xy plane defined by the manufacturer, e.g. the front of the laser enclosure.
For elliptical beams, the principal planes of propagation, defined as xz and yz, are the planes containing the major
and the minor axes, respectively, of the ellipse. See figure 1.
If the principle planes of propagation do not coincide with the x'z and y'z planes of the laboratory system x', y', z, then
one of two equivalent procedures can be chosen:
4.2 Description in the beam axis system
If the azimuth of the beam axis system relative to the laboratory system is known, then the beam parameters can be
measured directly in the beam axis system and the azimuth angle recorded with those measurements.
4.3 Description in the laboratory system
If the principal axes of the beam are not known, they can be determined by measuring the two second moments
2 2
2
s, s and the mixed moment s of the beam distribution in the laboratory system. It is then possible to
x' y' xy''
calculate the second moments in the beam axis system and the azimuth angle j between the two systems.
The mixed moment is given by
xx'--' y' y'Ex',y',zddx' y'
()()()
∫∫
2
s ()z = (15)
xy''
Ex()',y',zddx' y'
∫∫
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Figure 1 — Coordinates in the beam axis system
5 Test principles
5.1 Beam widths and beam diameter
For the determination of beam widths or diameter at location z, the power (energy) density distribution function of
the laser beam shall be determined in the x'y' plane at the location z. Additionally, the azimuth angle j shall be
determined.
From the measured cross-sectional distribution function, the first spatial moments xy, containing the beam axis are
2 2 2
determined. In a second step, the second moments s, s or s as well as the beam widths d , d or the beam
x ysxsy
diameter d are calculated. See equations (4) to (7) and (8) to (13), respectively.s
5.2 Divergence angles
The determination of the divergence angles follows from measurements of the beam widths or the beam diameter:
First, the laser beam shall be transformed by an aberration-free focusing element. The beam diameter d is thensf
measured one focal length f away from the rear principal plane of the focusing element. The divergence angle of the
laser beam before the focusing element is determined using the relationship
d
sf
Q = (16)
s
f
For non-radially symmetric beams, the divergence angles q or q in the xz or yz planes are determined by usingsxsy
the beam widths instead of the beam diameter.
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5.3 Beam propagation factor and times-diffraction-limit factor, respectively
2 2
For the determination of the beam propagation factors K , K or K and the times-diffraction-limit factors M , M or
x y x y
2
M , respectively, it is necessary to determine the waist widths d , d or the waist diameter d and the relateds0xs0ys0
beam divergence angles q, q or q.sxsys
5.4 Beam waist location, combined measurement of beam widths, beam divergence angle and
beam propagation factor or times-diffraction-limit factor
For determination of the waist location the beam widths, data along the propagation axis shall be fit to a hyperbola
as discussed in clause 9.
The other beam parameters can also be determined by this method.
6 Measurement arrangement and test equipment
6.1 General
The test is based on the measurement of the cross-sectional power (energy) density distribution function of the
entire laser beam.
6.2 Preparation
The optical axis of the measuring system should be coaxial with the laser beam to be measured. Suitable optical
alignment devices are available for this purpose (e.g. aligning lasers or steering mirrors).
The aperture of the optical system shall accommodate the entire cross-section of the laser beam. Clipping shall be
smaller than 1 % of the total beam power or energy.
The attenuators or beam-forming optics shall be mounted such that the optical axis runs through the geometrical
centres. Care should be taken to avoid systematic errors. Reflections, interference effects, external ambient light,
thermal radiation or air draughts are all potential sources of error.
After the initial preparation is complete, an evaluation to determine if the entire laser beam reaches the detector
surface shall be made. For testing this, apertures of different widths can be introduced into the beam path in front of
each optical component. The aperture which reduces the output signal by 5 % should have a diameter less than 0,8
times the aperture of the optical component.
6.3 Control of environment
Suitable measures such as mechanical and acoustical isolation of the test set-up, shielding from extraneous
radiation, temperature stabilization of the laboratory, choice of low-noise amplifiers shall be taken to ensure that the
contribution to the total probable error of the parameter to be measured is low.
Care should be taken to ensure that the atmospheric environment in high-power laser beam paths does not contain
gases or vapours that can absorb the laser radiation and cause thermal distortion in the beam to be assessed.
6.4 Detector system
Measurement of the cross-sectional power (energy) density distribution function requires the use of a power
(energy) meter with high spatial resolution and high signal-to-noise-ratio.
The accuracy of the measurement is directly related to the spatial resolution of the detector system and its signal-to-
noise ratio. The latter is important for laser beams with low power (energy) densities at larger diameters (e.g. for
diffracted parts of the laser beams).
In practice, noise in the wings of the density distribution function [either E(x,y,z) or H(x,y,z)] may readily dominate the
second moment integral. Thus it is usually necessary to subtract a background map (the detector response with the
beam blocked) from the signal map in determining the experimental distribution function.
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NOTE For example, consider calculating the second moment of a Gaussian beam at diameter 2w. Truncating the
integration at r/w = 1,9 clips off only 0,5 % of the value of the second moment. Assuming a 0,8 % peak-to-peak amplitude noise
to simulate the real experimental profile, truncation within these limits is required to be reasonably assured of a ± 5 %
uncertainty in the measured second moment.
The smallest spatial structures which are to be resolved should be sampled more than twice (sampling theorem).
Therefore the detector resolution necessary for the measurement is directly correlated to the structures of the beam
to be measured.
The provisions of IEC 61040:1990 apply to the radiation detector system; clauses 3 and 4 are particularly important.
Furthermore, the following points should be noted.
It shall be confirmed, from manufacturers' data or by measurement, that the output quantity of the detector
system (e.g. the voltage) is linearly dependent on the input quantity (laser power). Any wavelength
dependency, non-linearity or non-uniformity of the detector or the electronic device shall be minimized or
corrected by use of a calibration procedure.
Care shall be taken to ascertain the damage thresholds of the detector surface so that they are not exceeded
by the laser beam.
When using a scanning device for determining the power density distribution function, care shall be taken to
ensure that the laser output is spatially and temporally stable during the whole scanning period.
When measuring pulsed laser beams, the trigger time delay of sampling as well as the measuring time interval
play an important role because the beam parameters may change during the pulse. Therefore it is necessary to
specify these parameters in the test report.
6.5 Beam-forming optics and optical attenuators
If the beam cross-sectional area is greater than the detector area, a suitable optical system shall be used to reduce
the beam cross-sectional area on the detector surface. The change in magnification shall be taken into account
during the evaluation procedure.
Optics shall be selected appropriate to wavelength.
An attenuator may be required to reduce the laser power density at the surface of the detector.
Optical attenuators shall be used when the laser output-power or power density exceeds the detector's working
(linear) range or the damage threshold. Any wavelength, polarization and angular dependency, non-linearity or non-
uniformity, including thermal effects of the optical attenuator, shall be minimized or corrected by use of a calibration
procedure.
None of the optical elements used shall significantly influence the relative power (energy) density distribution.
6.6 Focusing system
The focusing system for the divergence angle measurement shall conform with the requirements relating to the
beam-forming optics given in 6.5. The total error contributed by the focusing system shall be less than 1 % of the
beam width.
7 Beam widths and beam diameter measurement
7.1 Test procedure
Before the measurements are started, the laser shall warm up for at least 1 h (unless otherwise stated by the
manufacturer) to achieve thermal equilibrium. The measurements shall be carried out at the operating conditions
specified by the laser manufacturer for the type of laser being evaluated.
Repeat at least five times the measurement of the cross-sectional power (energy) density distribution function at
each location z at which the beam widths are determined.
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7.2 Evaluation
The following calculations are carried out using equations (4) to (7) and (15), given in 3.4 and 4.3.
Calculate the first moments of the power (energy) density distributions.
2 2 2
In the next step, calculate the second moments s' and s as well as s for each measurement.
x' y' x'y'
Calculate the azimuth angle j and the beam widths d and d using equations (17) to (20):sxsy
1
22 2
arctan 2 / ( )
js=- (17)
()ssxy'' x' y'
2
1
1
2
2 2
Øø
22 22 4
ssdz()==42ss()z 2 + + +4 (18)
x x ()sexy'' ()ss-xy' ' x'y'Œœ
ºß
1
1
2
2 2
Øø
22 2 2 4
ssss--dz()==42ss()z 2 + +4 (19)
y y ()sexy'' (xy' ') x'y'Œœ
ºß
where
22
ss-
xy''
22
es=-sgn()s= (20)
xy''
22
ss-
xy''
Perform these calculations for each measurement and calculate the mean values and the standard deviations for
the beam widths and the azimuth angle.
If the ratio d /d is smaller than 1,15:1, the beam may be considered circular at that measuring location and thessx y
equations for circular beams may be used (see 3.5).
8 Divergence angle measurement
8.1 Test procedure
Locate the focusing element in the beam path in such a way that its optical axis is coaxial with the laser beam to be
measured.
Locate the measuring plane of the detector system one focal length away from the rear principal plane of the
focusing element.
NOTE In general, this location is not identical with the waist location behind the focusing element.
Perform at least five measurements of the beam widths d , d or the beam diameter d at that location insfxsfysf
accordance with clause 7.
8.2 Evaluation
NOTE The following equations are given explicitly only for the radially symmetric case, but equivalent expressions for the
x
and y parameters of non-circular beams are given in annex B.
Calculate the far-field divergence angle(s) of the unfocused beam according to
d
sf
Q = (21)
s
f
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where
d is the beam diameter one focal length away from the focusing element;sf
f is the focal length of the focusing element.
for each measurement and calculate the mean value(s) and the standard deviation(s) for the divergence angle(s).
9 Combined determination of laser beam propagation parameters
If the beam waist is accessible for direct measurement, the beam waist location and the standard deviation shall be
determined by a hyperbolic fit to different measurements of the beam width along the propagation axis z. For this, at
least 10 measurements shall be taken. Approximately half of the measurements shall be distributed within one
Rayleigh length on either side of the beam waist, and approximately half of them shall be distributed beyond two
Rayleigh lengths from the beam waist.
The hyperbolic fit to the measured diameters along the propagation can be expressed in the following way (for the
equations given, see note in 8.2):
2 2
dA=+B⋅z+C⋅z (22)
s
When the coefficients A, B, C (or A , A , B , B , C , C ; see annex B), of the hyperbola(e) have been found by
x y x y x y
appropriate numerical or statistical curve-fitting techniques (see note), the values of the beam waist diameter or
widths and location(s) can be determined using:
-B
z = (23)
0
2C
2
B
dA=- (24)
s 0
4C
NOTE It is advisable to weight the data points inversely proportional to the variance of the data points.
If the beam waist is not accessible for direct measurement, the same procedure shall be applied to an artificial waist
created by using an aberration-free focusing element as defined in 6.6. According to Figure 2, the distance l from
the focusing element to the reference plane, as well as the distances s or s and s from the artificial waist to the
2 2x 2y
rear principal plane of the focusing element, shall be determined. In addition, the beam widths d or d and ds2s2xs2y
shall be determined at the artificial waist. From these data the waist location(s) of the original beam can be
calculated using
zl=-s (25)
01
(Symbols according to Figure 2.)
where s (or s and s , see annex B) is determined using
1 1x
1y
2
fs⋅-()s f+ f⋅ z
22
R2
s = (26)
1
2
2 2
sf-⋅2 ⋅s+f+z
2 2 R2
and where
f is the focal length of the lens;
z is the Rayleigh length of the artificial beam waist.
R2
The Rayleigh length of the artificial waist z can be determined by using the equations for the hyperbolic fit
R2
procedure (see clause 10).
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Key
1 Laser
2 Reference plane
3 Rear principal plane
4 Focusing element
Figure 2 — Scheme for calculation of beam waist location(s)
The beam waist diameter or widths can be calculated in the following way (using the relationship =⋅ ,
dVd
ss21
where V is the magnification):
1
d
...
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