Lasers and laser-related equipment - Test methods for determination of the shape of a laser beam wavefront - Part 1: Terminology and fundamental aspects (ISO 15367-1:2003)

ISO 15367-1:2003 specifies methods for the measurement of the topography of the wavefront of a laser beam by measurement and interpretation of the spatial distribution of the phase of that wavefront across a plane approximately perpendicular to its direction of propagation. Requirements are given for the measurement and analysis of phase distribution data to provide quantitative wavefront parameters and their uncertainty in a test report.
The methods described in ISO 15367-1:2003 are applicable to the testing and characterization of a wide range of beam types from both continuous wave and pulsed lasers. Definitions of parameters describing wavefront deformations are given together with methods for the determination of those parameters from phase distribution measurements.

Laser und Laseranlagen - Prüfverfahren für die Bestimmung der Wellenfrontform von Laserstrahlen - Teil 1: Begriffe und grundlegende Aspekte (ISO 15367-1:2003)

Die vorliegende Internationale Norm legt Messverfahren für die Topografie der Wellenfront eines Laserstrahls durch Messung und Auswertung der räumlichen Verteilung der Phasen dieser Wellenfront in einer Ebene rechtwinklig zu ihrer Ausbreitungsrichtung fest. Es werden Anforderungen für die Messung und Analyse von Phasenverteilungen aufgestellt, die die quantitative Angabe von Wellenfrontparametern und deren Messunsicherheit in einem Prüfbericht ermöglichen.
Die in dieser Internationalen Norm beschriebenen Verfahren gelten für die Prüfung und Beschreibung vieler Strahlenarten von Dauerstrichlasern sowie Pulslasern. Es werden Parameterdefinitionen für die Verformung von Wellenfronten sowie Verfahren zur Ermittlung dieser Parameter aus Messungen der Phasenverteilung angegeben.

Lasers et équipements associés aux lasers - Méthodes d'essai pour la détermination de la forme du front d'onde du faisceau laser - Partie 1: Terminologie et aspects fondamentaux (ISO 15367-1:2003)

L'ISO 15367-1:2003 spécifie les méthodes pour le mesurage de la topographie du front d'onde d'un faisceau laser par le mesurage et l'interprétation de la distribution spatiale de la phase de ce front d'onde, à travers un plan approximativement perpendiculaire à sa direction de propagation. Les exigences sont données pour le mesurage et l'analyse des données de la distribution de phase pour inscrire les paramètres quantitatifs du front d'onde et leurs incertitudes dans un rapport d'essai.
Les méthodes décrites dans l'ISO 15367-1:2003 sont applicables à l'essai et à la caractérisation d'une grande variété de types de faisceaux issus à la fois de lasers continus ou pulsés. Les définitions des paramètres décrivant les déformations du front d'onde sont données avec les méthodes pour la détermination de ces paramètres à partir des mesures de distribution de phase.

Laserji in laserska oprema – Preskusne metode za ugotavljanje oblike valovne fronte laserskega žarka – 1. del: Izrazje in temeljni vidiki (ISO 15367-1:2003)

General Information

Status
Published
Publication Date
30-Dec-2003
Withdrawal Date
30-Mar-2004
Current Stage
9092 - Decision on results of review/2YR ENQ - revise - Review Enquiry
Start Date
17-Dec-2008
Completion Date
17-Dec-2008

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SLOVENSKI STANDARD
SIST EN ISO 15367-1:2003
01-december-2003
Laserji in laserska oprema – Preskusne metode za ugotavljanje oblike valovne
fronte laserskega žarka – 1. del: Izrazje in temeljni vidiki (ISO 15367-1:2003)
Lasers and laser-related equipment - Test methods for determination of the shape of a
laser beam wavefront - Part 1: Terminology and fundamental aspects (ISO 15367-
1:2003)
Laser und Laseranlagen - Prüfverfahren für die Bestimmung der Wellenfrontform von
Laserstrahlen - Teil 1: Begriffe und grundlegende Aspekte (ISO 15367-1:2003)
Lasers et équipements associés aux lasers - Méthodes d'essai pour la détermination de
la forme du front d'onde du faisceau laser - Partie 1: Terminologie et aspects
fondamentaux (ISO 15367-1:2003)
Ta slovenski standard je istoveten z: EN ISO 15367-1:2003
ICS:
01.040.31 Elektronika (Slovarji) Electronics (Vocabularies)
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
SIST EN ISO 15367-1:2003 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 15367-1:2003

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SIST EN ISO 15367-1:2003
EUROPEAN STANDARD
EN ISO 15367-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
September 2003
ICS 01.040.31; 31.260
English version
Lasers and laser-related equipment - Test methods for
determination of the shape of a laser beam wavefront - Part 1:
Terminology and fundamental aspects (ISO 15367-1:2003)
Lasers et équipements associés aux lasers - Méthodes Laser und Laseranlagen - Prüfverfahren für die
d'essai pour la détermination de la forme du front d'onde du Bestimmung der Wellenfrontform von Laserstrahlen - Teil
faisceau laser - Partie 1: Terminologie et aspects 1: Begriffe und grundlegende Aspekte (ISO 15367-1:2003)
fondamentaux (ISO 15367-1:2003)
This European Standard was approved by CEN on 1 September 2003.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Management Centre has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2003 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 15367-1:2003 E
worldwide for CEN national Members.

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SIST EN ISO 15367-1:2003
EN ISO 15367-1:2003 (E)
Foreword
This document (EN ISO 15367-1:2003) has been prepared by Technical Committee ISO/TC 172
"Optics and optical instruments" in collaboration with Technical Committee CEN/TC 123 "Lasers
and laser-related equipment", the secretariat of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by March 2004, and conflicting national
standards shall be withdrawn at the latest by March 2004.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium, Czech
Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Luxembourg, Malta, Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and
the United Kingdom.
NOTE FROM CMC  The foreword is susceptible to be amended on reception of the German
language version. The confirmed or amended foreword, and when appropriate, the normative
annex ZA for the references to international publications with their relevant European
publications will be circulated with the German version.
Endorsement notice
The text of ISO 15367-1:2003 has been approved by CEN as EN ISO 15367-1:2003 without any
modifications.
2

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SIST EN ISO 15367-1:2003


INTERNATIONAL ISO
STANDARD 15367-1
First edition
2003-09-15


Lasers and laser-related equipment —
Test methods for determination of the
shape of a laser beam wavefront —
Part 1:
Terminology and fundamental aspects
Lasers et équipements associés aux lasers — Méthodes d'essai pour la
détermination de la forme du front d'onde du faisceau laser —
Partie 1: Terminologie et aspects fondamentaux




Reference number
ISO 15367-1:2003(E)
©
ISO 2003

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
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All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
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ii © ISO 2003 — All rights reserved

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references. 1
3 Terms and definitions. 2
3.1 General definitions. 2
3.2 Definitions associated with power (energy) density distribution . 4
3.3 Definitions associated with astigmatism. 4
3.4 Definitions related to the characteristics and topography of the wavefront. 5
3.5 Definitions related to wavefront gradient measurements . 7
4 Test methods. 8
4.1 Laser types. 8
4.2 Safety. 8
4.3 Test environment. 8
4.4 Beam modification. 9
4.5 Detector system. 10
4.6 Wavefront measuring instruments. 10
5 Test and measurement procedures . 11
5.1 Alignment. 11
5.2 Calibration. 11
5.3 Visual inspection of automated data analysis . 11
5.4 Measurement procedures. 12
6 Analysis of wavefront quality . 12
6.1 Polynomial representation of wavefronts . 12
6.2 Computation of wavefront quality. 12
7 Uncertainty. 13
7.1 Requirements for uncertainty estimation. 13
7.2 Sources of uncertainty . 14
8 Test report. 14
Annex A (informative) Astigmatism and laser beams . 15
Bibliography . 20

© ISO 2003 — All rights reserved iii

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(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 2.
The main task of technical committees is to prepare International Standards. 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.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 15367-1 was prepared by Technical Committee ISO/TC 172, Optics and optical instruments,
Subcommittee SC 9, Electro-optical systems.
ISO 15367 consists of the following parts, under the general title Lasers and laser-related equipment — Test
methods for determination of the shape of a laser beam wavefront:
 Part 1: Terminology and fundamental aspects
 Part 2: Hartmann-Shack sensors

iv © ISO 2003 — All rights reserved

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
Introduction
It is important, when designing, operating or maintaining a laser system, to be able to ensure repeatability,
predict the propagation behaviour of the laser beam and to assess the safety hazards. There are four sets of
parameters that could be measured for the characterization of a laser beam:
 power (energy) density distribution (ISO 13694);
 beam width, divergence angle and beam propagation factor (ISO 11146);
 phase distribution (ISO 15367);
 spatial beam coherence.
This part of ISO 15367 defines the terminology and symbols to be used when making reference to or
measuring the phase distribution in a transverse plane of a laser beam. It specifies the procedures required
for the measurement of
 the azimuth of the principal planes of the phase distribution;
 the magnitude of astigmatic aberrations;
 evaluation of the wavefront aberration function and the RMS wavefront deformation.
A useful technique for qualitative assessment of a beam is visual inspection of the fringe pattern in
interferograms or an isometric view of a wavefront surface. However, more quantitative methods are needed
for quality assurance and transfer of process technology. The measurement techniques indicated in this part
of ISO 15367 allow numerical analysis of the phase distribution in a propagating beam and can provide
recordable quantitative results.
While it is quite possible to ascribe other conventional aberrations (e.g. coma or spherical aberration) as well
as astigmatism to a laser beam, these are not commonly used. Departure of the wavefront of a beam from
some ideal surface is a more common indication of quality. On the other hand, rotational asymmetry has a
much wider range of effects in a laser beam than is usually associated with astigmatism imposed on a beam
of optical radiation by conventional optical systems. For this reason, various forms and characteristics of
astigmatism in beams are now defined in detail.
The provisions of this part of ISO 15367 allow a test report to be commissioned with measurements or
analysis of a selection of beam characteristics. Measurements of astigmatism are important to system
designers who wish to specify optical elements for the correction of astigmatic beams. The measurement
techniques defined in this part of ISO 15367 can also be used to assess any residual astigmatism after the
addition of corrective elements and to aid with alignment.
A major application of phase distribution measurements comes with the possibility of combining those
measurements with a simultaneous measurement of the power (energy) density distribution (ISO 13694) at
the same location in the path of a beam. Digital processing of the data can reveal much more detailed
characteristics of the propagating beam than can measurements of the power (energy) envelope resulting
from calculation of the beam propagation ratio (ISO 11146). The more detailed information can be important to
assessors of laser damage and safety hazards as well as process development engineers when it is
necessary to know the power (energy) density distribution at the process interaction point.
© ISO 2003 — All rights reserved v

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SIST EN ISO 15367-1:2003

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SIST EN ISO 15367-1:2003
INTERNATIONAL STANDARD ISO 15367-1:2003(E)

Lasers and laser-related equipment — Test methods for
determination of the shape of a laser beam wavefront —
Part 1:
Terminology and fundamental aspects
1 Scope
This part of ISO 15367 specifies methods for the measurement of the topography of the wavefront of a laser
beam by measurement and interpretation of the spatial distribution of the phase of that wavefront across a
plane approximately perpendicular to its direction of propagation. Requirements are given for the
measurement and analysis of phase distribution data to provide quantitative wavefront parameters and their
uncertainty in a test report.
The methods described in this part of ISO 15367 are applicable to the testing and characterization of a wide
range of beam types from both continuous wave and pulsed lasers. Definitions of parameters describing
wavefront deformations are given together with methods for the determination of those parameters from
phase distribution measurements.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 9334, Optics and optical instruments — Optical transfer function — Definitions and mathematical
relationships
ISO 10110-5, Optics and optical instruments — Preparation of drawings for optical elements and systems —
Part 5: Surface form tolerances
ISO 11145, Optics and optical instruments — Laser and laser-related equipment — Vocabulary and symbols
ISO 11146, Lasers and laser-related equipment — Test methods for laser beam parameters — Beam widths,
divergence angle and beam propagation factor
ISO 13694, Optics and optical instruments — Lasers and laser-related equipment — Test methods for laser
beam power (energy) density distribution
ISO 15367-2, Lasers and laser related equipment — Test methods for determination of the shape of a laser
beam wavefront — Part 2: Hartmann-Shack sensors
IEC 60825, (All parts), Safety of Laser Products
IEC 61040, Power and energy measuring detectors, instruments and equipment for laser radiation
© ISO 2003 — All rights reserved 1

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3 Terms and definitions
For the purposes of this document, the definitions given in ISO 9334, ISO 10110-5, ISO 11145, ISO 11146,
ISO 13694 and IEC 61040 as well as the following apply.
3.1 General definitions
3.1.1
average wavefront shape
w(x,y;z )
m
continuous surface w(x,y) that is normal to the time average direction of energy propagation in the
electromagnetic field at the measurement plane z = z
m
NOTE 1 In the case of highly coherent radiation, the continuous surface w(x,y) is a surface of constant phase. The
phase distribution Φ(x,y) is then related to the wavefront distribution according to

Φ(,xy)=⋅w(x,y)
λ
where λ is the mean wavelength of the light.
NOTE 2 A continuous surface does not always exist.
3.1.2
wavefront surface
continuous surface w(x,y) that minimizes the power density weighted deviations of the direction of its normal
vectors to the direction of the energy flow vectors in the measurement plane
NOTE w(x,y) is the surface that minimizes the expression
2
GG
ˆ
E(,xy,z )P (,xy,z )−∇ w(,xy,z ) dxdy
∫∫
mm⊥ ⊥ m
where
G
ˆ
G
P (,xy,z )
ˆ
⊥ m
Px(,y,z) = is the normalized transverse Poynting vector;

Ex(,y,z )
m
G ∂

x
∇= is the transverse, two-dimensional gradient or Nabla operator.
⊥ 

y

3.1.3
phase
Φ
fraction of a wave period that has elapsed relative to that at a nominated origin
NOTE Phase is expressed in radians, modulo 2π.
3.1.4
measurement plane
z

m
axial location along the beam axis of the transverse plane in which the wavefront shape/surface is measured
2 © ISO 2003 — All rights reserved

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3.1.5
mechanical axes
x, y, z
orthogonal transverse axes defined by the construction axes of the laser or the measuring system
NOTE The origin of the mechanical axis system should be identified and be coincident with some accessible and
obvious location on the beam axis, be it a manufacturer's specification on the laser or reproducible location on the
measuring instrument. The orientation of the transverse axes can be those associated with the laser or the vertical and
horizontal axes in the measurement environment.
3.1.6
principal planes of wavefront shape/surface propagation
x'z and y'z
planes containing the principal axes of the wavefront and the beam axis
NOTE The principal planes of wavefront propagation will not necessarily coincide with the xz and yz planes of the
laboratory system.
3.1.7
wavefront shape/surface co-ordinate system
x', y', z
co-ordinate system used as reference axes for denoting the orientation of the principal axes of the astigmatic
wavefront shape/surface relative to the mechanical axes of the measuring environment
NOTE The x’, y’ and z axes define the orthogonal space directions of wavefront shape/surface in the beam axis
system. The x’ and y’ axes are transverse to the beam and define the transverse plane. The origin of the z-axis is in a
mechanical reference xy plane defined either by the manufacturer of the laser (e.g. the front of the laser enclosure) or by
the measuring system. A schematic diagram of the axes system is shown in Figure 1.

Figure 1 — The co-ordinate system of an astigmatic wavefront relative to the mechanical axes
3.1.8
wavefront azimuth angle
Ψ
angle between the principal planes of the wavefront shape/surface and the mechanical axes
See Figure 1.
© ISO 2003 — All rights reserved 3

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3.2 Definitions associated with power (energy) density distribution
3.2.1
power (energy) density distribution co-ordinate system
x'', y'', z
co-ordinate system used as reference axes for denoting the orientation of the principal axes of the astigmatic
power (energy) density distribution relative to the mechanical axes of the measuring environment
NOTE The defining parameters of the power (energy) density distribution of a simple astigmatic beam are shown in
Figure 2. Means for the evaluation of the major and minor beam widths and their azimuth angle are contained in
ISO 11146.
3.2.2
power (energy) density distribution azimuth angle
ϕ(z)
angle between the principal planes of propagation of the power (energy) density distribution and the
mechanical axes
See Figure 2.
NOTE 1 For simple astigmatic beams, ϕ remains constant.

NOTE 2 The waist locations z and z are shown for both the beam axes
ox oy
Figure 2 — Co-ordinates of the beam axis system for the power (energy) density distribution
3.3 Definitions associated with astigmatism
3.3.1
astigmatism
property of a laser beam having non-circular power (energy) density profiles in most planes under free space
propagation or having a phase twist
NOTE An outline description of astigmatic properties and the requirement to extend their descriptions beyond those
used conventionally to describe astigmatic properties of optical elements is contained in Annex A.
4 © ISO 2003 — All rights reserved

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3.3.2
simple astigmatism
property of the beam in which the transverse power (energy) density distribution does not possess rotational
symmetry but whose principal planes of wavefront shape/surface and power (energy) density distribution are
orthogonal and fixed in space, whose azimuth angles are equal (ϕ = ψ)
See Figures 1 and 2.
3.3.3
general astigmatism
property of a laser beam having non-circular power (energy) density distributions in most planes and where
the orientation of the principal axes of power (energy) density distributions changes during propagation
NOTE For coherent general astigmatic beams, the azimuth angles of the power (energy) density distribution and
wavefront differ in any plane.
3.3.4
astigmatic waist separation
∆z

a
axial distance between the beam waist locations in the orthogonal principal planes of a beam possessing
simple astigmatism
NOTE Astigmatic waist separation is also known as astigmatic difference.
3.3.5
astigmatic wavefront curvature
C , C
x’ y’
values of the maximum and minimum orthogonal curvature of the wavefront of a beam at a specified location.
NOTE 1 Curvature is the reciprocal of the radius of curvature.
NOTE 2 The difference between the two radii of curvature becomes essentially identical with both the astigmatic focal
difference and astigmatic waist separations when measurements are made in the farfield of the laser beam.
3.4 Definitions related to the characteristics and topography of the wavefront.
3.4.1
measured wavefront
w (x, y)

m
surface resulting from analysis of the measured phase distribution data
3.4.2
corrected wavefront
w (x, y)

c
theoretical surface derived by removing the effects of the average linear trend in the x- and y-direction
(average tilt and average tip) from the measured wavefront
NOTE The analytic definition can be summarized as:
wx(,y)=−w (x,y) xββ−y
cm xy
© ISO 2003 — All rights reserved 5

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3.4.3
approximating spherical surface
s(x, y)
22
spherical surface s(,xy)=+ax( y ) that minimizes the irradiance (energy) weighted deviation of its normal
vectors to the direction of the energy flow vectors in the measurements plane
NOTE The expression to be minimized is
∞∞
2 2

ˆˆ
E xy,,z22ax−+P ay−Pdxdy
()
∫∫ ()()
xy

−∞ −∞
ˆ ˆ
where P and P are the components of the normalized transverse Poynting vector.
x y
3.4.4
approximating paraboloid surface
c(x, y)
22
paraboloid surface cx(,y)=+Ax By+Cxy that minimizes the irradiance (energy) weighted deviation of its
normal vectors to the direction of the energy flow vectors in the measurements plane
NOTE 1 The expression to be minimized is
∞∞
2 2

ˆˆ
E xy,,z 22Ax+−Cy P +2By+2Cx−P dxdy
∫∫ ()()()
xy


−∞ −∞
ˆ ˆ
where P and P are the components of the normalized transverse Poynting vector.
x y
NOTE 2 The best fitting parameters A, B and C can be used to retrieve the wavefront azimuthal angle Ψ and the two
orthogonal radii of wavefront curvature R and R from:

1 2

1 C
Ψ = arctan


2
B −A

k 1
R =
1
22
2
ABcosΨΨ++sin 2C sinΨ cosΨ
k 1
R =
2
22
2
ABsinΨΨ+−cos 2C sinΨ cosΨ
3.4.5
defocus
R

ss
radius of curvature of approximating spherical surface
3.4.6
wavefront aberration function
w (x, y)
AF
theoretical surface given by the difference between the corrected wavefront and the approximating spherical
or approximating paraboloid surface
NOTE The analytic expression is
wx(,y)=−w (x,y)s(,xy)
AF c
6 © ISO 2003 — All rights reserved

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3.4.7
weighted RMS deformation
irradiance weighted RMS wavefront error
w

RMS
root-mean-square value of the power (energy) distribution weighted difference between the local values of the
wavefront aberration function and its average value
2
∑∑Ex(,y)w (x,y) −w
AF AF
E(,xy)w (x,y) dxdy
xy ∫
AF
NOTE ww==     where
RMS AF
∑∑Ex(,y) E(x,y) dxdy

xy
3.5 Definitions related to wavefront gradient measurements
3.5.1
tilt
tilt about the y-axis
β
x
local gradient of the wavefront in the x-direction
∂w
NOTE Tilt is given by β =
x
∂x
3.5.2
average tilt
β
x
irradiance (energy) weighted average value of tilt
NOTE The average tilt is calculated using
E(,xy)β (xy, ) dxdy
x

β =
x
Ex(,y) dxdy

3.5.3
tip
tilt about x-axis
β
y
local gradient of the wavefront in the y-direction
∂w
NOTE Tilt is given by β =
y
∂y
3.5.4
average tip
β
y
irradiance (energy) weighted average value of tip
NOTE The average tip is calculated using
E(,xy)β (xy, ) dxdy
∫ y
β =
y
Ex(,y) dxdy

© ISO 2003 — All rights reserved 7

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SIST EN ISO 15367-1:2003
ISO 15367-1:2003(E)
3.5.5
wavefront gradient
∇w(x, y)
vector sum of the tip and tilt
NOTE The wavefront gradient is given by
∂∂wx(,y) w(x,y)
∇=wx(,y) i+ j
∂∂xy
where i and j are the unit vectors in the x- and y-direction, respectively.
3.5.6
phase gradient
∇Φ(x, y)
local slope of the phase distribution surface, being the product of the wavefront gradient and the wave number
2π/λ
4 Test methods
4.1 Laser types
Test methods can be devised for measuring the phase distributions of a wide range of pulsed or continuous
laser beams. Interferometry principles can be applied to beams covering the full wavelength spectrum for
which detectors and optical materials are available, provided that the coherence is sufficient for detectable
levels of interference. Phase gradient measurement techniques can be used with
...

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