ISO/TS 22247:2022

TECHNICAL ISO/TS
SPECIFICATION 22247
First edition
2022-04
Optics and photonics — Effective
numerical aperture of laser lenses —
Definition and verification procedure
Optique et photonique — Ouverture numérique efficace des lentilles
laser — Définition et procédure de vérification
Reference number
ISO/TS 22247:2022(E)
© ISO 2022

---------------------- Page: 1 ----------------------
ISO/TS 22247:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
  © ISO 2022 – All rights reserved

---------------------- Page: 2 ----------------------
ISO/TS 22247:2022(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Coordinate systems.4
5 Short description of the verification procedure . 4
6 Permitted beam sources. 5
7 Measurement of the beam propagation ratio of the initial probe laser beam (before
collimation) .5
8 Measurement of the divergence angle of the initial laser beam (before collimation) .5
9 Verification of the effective numerical aperture of rotational symmetric laser
lenses based on the beam propagation ratio . 6
10 Verification of the effective numerical aperture of rotational symmetric laser
lenses based on the residual divergence. 9
11 Verification of the effective numerical aperture of cylindrical laser lenses .11
12 Long cylindrical laser lenses.13
12.1 General .13
12.2 Sequential procedure .13
12.3 Parallel procedure . 14
13 Test report .16
13.1 General information. 16
13.2 Test lens . 16
13.3 Probe laser . 16
13.4 Measurement . 16
13.5 Measurement results . 16
13.5.1 “Beam propagation ratio” method. 16
13.5.2 “Residual divergence” method . 17
13.6 Lower limit for effective numerical aperture . 17
Bibliography .18
iii
© ISO 2022 – All rights reserved

---------------------- Page: 3 ----------------------
ISO/TS 22247:2022(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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 172, Optics and Photonics, Subcomittee
SC 9, Laser and electro-optical systems.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
  © ISO 2022 – All rights reserved

---------------------- Page: 4 ----------------------
ISO/TS 22247:2022(E)
Introduction
Lenses are used in the field of laser beam forming, typically for collimation of divergent radiation or
for focusing collimated radiation to obtain very small spots. A distinction is made between rotational
symmetric lenses on one hand and cylindrical lenses, which provide optical power only in one direction,
on the other hand.
Two crucial quality characteristics can be defined for such lenses: the trivial demand that the lenses
should not clip the laser beam during propagation and the more sophisticated requirement, that they
should not significantly increase the beam propagation factor of a traversing beam.
If the divergence angle of the beam before or after the lens is large, the geometric form of the surfaces
of the lens needs to be carefully designed to an aspherical or acylindrical form to fulfill the second
requirement. The desired form of the surfaces depends on the intended use of the lens and the
wavelength of the laser radiation.
In fabrication and application of such lenses the following problems may arise, even in combination:
— in fabrication of the lens the optimum surface form has not been reproduced;
— the lens is applied to a laser beam with a different wavelength than the design wavelength.
Non-well designed or non-well produced lenses or lenses applied to beams with wavelength for which
the lens has not been designed may still be useful as long as the involved divergence angles are small
enough.
To account for this, an effective numerical aperture is defined here as the sine of half of the maximum
divergence angle a laser beam may have before the lens, when it collimates the beam, or after the lens,
when it focuses the beam, to ensure that the aberrations introduced by the lens to the beam at the given
wavelength is acceptable.
This definition is in close relationship to ISO 11146-1, which is important in the field of laser beam
characterization. It provides the decisive parameter in the field of laser beam forming. Furthermore,
it is related to a fairly simple verification procedure, which can be applied by manufacturers of laser
lenses as well as users with acceptable effort.
v
© ISO 2022 – All rights reserved

---------------------- Page: 5 ----------------------
TECHNICAL SPECIFICATION ISO/TS 22247:2022(E)
Optics and photonics — Effective numerical aperture of
laser lenses — Definition and verification procedure
1 Scope
This document covers terms, definitions, and a verification procedure to characterize the ability of
laser lenses to collimate divergent laser beams and to focus collimated laser to small spot sizes. The
aim of this document is to give users reliable information on the applicability of laser lenses in the field
of beam forming.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 11146-1, Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles
and beam propagation ratios — Part 1: Stigmatic and simple astigmatic beams
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
NOTE Within this document, the terms power density and energy density are used in units of areal densities.
According to the common understanding in the fields of optics, photonics and laser technology, the term power
density is generally perceived in unit of areal density. In this document, the term energy density also follows this
specification. In text books, this power density is also denoted as irradiance and this energy density as fluence.
3.1
beam diameter
d (z)
u
diameter of a circular aperture in a plane perpendicular to the beam axis
that contains u % of the total beam power (energy)
Note 1 to entry: For clarity, the term “beam diameter” is always used in combination with the symbol and its
appropriate subscript: d or d .
u σ
[SOURCE: ISO 11145:2018, 3.3.1]
3.2
beam diameter
d (z)
σ
diameter defined by using the second
moment of the power (energy) density distribution function
dz()= 22σ ()z
σ
1
© ISO 2022 – All rights reserved

---------------------- Page: 6 ----------------------
ISO/TS 22247:2022(E)
where the second moment of the power density distribution function E(x, y, z) of the beam z is given by
22
xx− ()zy+− yz() ⋅Ex(),,yz ⋅ddxy
() ()
()
∫∫
2
σ ()z =
Ex(),,yz ⋅ddxy
∫∫
where the first moments give the coordinates of the beam centroid xz() , yz()
[]
Note 1 to entry: For clarity, the term “beam diameter” is always used in combination with the symbol and its
appropriate subscript: d or d
u σ.
[SOURCE: ISO 11145:2018, 3.3.2]
3.3
beam widths
d (z), d (z)
x,u y,u
width of the smallest slit aligned with the x or y transverse axes of
the power (energy) density distribution function, transmitting u % of the total beam power (energy)
along x or y
Note 1 to entry: For circular Gaussian beams, d and d both equal d .
x,95,4 y,95,4 86,5
Note 2 to entry: For clarity, the term “beam width” is always used in combination with the symbol and its
appropriate subscripts: d , d or d , d .
σx σy x,u y,u
[SOURCE: ISO 11145:2018, 3.5.1]
3.4
beam widths
d (z), d (z)
σx σy
width defined by using the second
moment of the power (energy) density distribution function along x or y
dz()= 4σ ()z
σxx
dz = 4σ z
() ()
σ yy
where the second moments of the power density distribution function E(x, y, z) of the beam at z are
given by:
2
()xx− ()zE⋅ ()xy,,zx⋅ddy
∫∫
2
σ z =
()
x
Ex,,yz ⋅ddxy
()
∫∫
2
yy− zE⋅ xy,,zx⋅ddy
()() ()
∫∫
2
σ ()z =
y
Ex(),,yz ⋅ddxy
∫∫
where xx− z and yy− z are the distances from the current point’s coordinates to the beam
()() ()()
centroid xz , yz
()() ()
Note 1 to entry: For clarity, the term “beam width” is always used in combination with the symbol and its
appropriate subscripts: d , d or d , d .
σx σy x,u y,u
[SOURCE: ISO 11145:2018, 3.5.2]
3.5
beam waist
portion of a beam where the beam diameter or beam width has a local minimum
[SOURCE: ISO 11145:2018, 3.7.1]
2
  © ISO 2022 – All rights reserved

---------------------- Page: 7 ----------------------
ISO/TS 22247:2022(E)
3.6
beam waist diameter
d
0,u
diameter d of the beam at the location of the beam waist
u
[SOURCE: ISO 11145:2018, 3.7.4, modified — Note 1 to entry was deleted.]
3.7
beam waist width
d , d
x0,u y0,u
beam widths d and d at the locations of the beam waists in the x
x,u y,u
and y directions, respectively
[SOURCE: ISO 11145:2018, 3.7.8, modified — Note 1 to entry was deleted.]
3.8
beam waist location
z , z , z
0x 0y 0
location where the beam widths or the beam diameters reach their minimum values along the beam
axis
[SOURCE: ISO 11145:2018, 3.7.2, modified — Note 1 to entry was deleted.]
3.9
astigmatic beam waist separation
Δz
a
axial distance between the beam waist locations in the orthogonal principal planes of a beam possessing
simple astigmatism
[SOURCE: ISO 11145:2018, 3.7.3, modified — Note 1 to entry was deleted.]
3.10
divergence angle
Θ , Θ , Θ
u x,u y,u
full angle formed by the asymptotic cone of the envelope
formed by the increasing beam diameter (width)
[SOURCE: ISO 11145:2018, 3.8.1, modified — Notes 1 to 4 to entry and the example were deleted.]
3.11
divergence angle
Θ , Θ , Θ
σ σx σy
full angle formed by the asymptotic
cone of the envelope formed by the increasing beam diameter (width)
[SOURCE: ISO 11145:2018, 3.8.2, modified — Notes 1 to 3 to entry were deleted.]
3.12
Rayleigh length
z , z , z
R Rx Ry
distance from the beam waist in the direction of propagation for which the diameter and beam width
are equal to 2 times their respective values at the beam waist
[SOURCE: ISO 11145:2018, 3.9.1, modified — Notes 1 and 2 to entry were deleted.]
3
© ISO 2022 – All rights reserved

---------------------- Page: 8 ----------------------
ISO/TS 22247:2022(E)
3.13
beam propagation ratio
2
M
measure of how close the beam parameter product is to the diffraction limit of a perfect Gaussian beam
Note 1 to entry: In contrast to ISO 11145:2018, 3.10.2, in this document the beam propagation ratio is not defined
by the second order moments based definitions of beam diameter, beam width, and divergence angles, but
instead by the power content based counterparts given in 3.2, 3.4, and 3.11 of this document and ISO 11145:2018,
3.7.5 and 3.7.9.
3.14
residual divergence angle
angle of divergence Θ , Θ , Θ , Θ , Θ , Θ of a divergent laser beam after collimation by a laser lens
u xu yu σ σx σy
3.15
effective numerical aperture
NA
eff
sine of half of the maximum divergence angle, which a nearly diffraction limited beam can have before
it is truncated by the finite geometry of the lens or its beam propagation ratio along the collimating
direction of the lenses is increased by more than 0,5 due to aberrations
Note 1 to entry: The effective numerical aperture is always less or equal to the geometrical aperture of the lens.
4 Coordinate systems
The coordinate system is defined according to ISO 11146-1.
The laser beam propagates along the z-axis. In case of simple astigmatic laser beams the x- and y-axis
are aligned parallel to the principal axes of the beam.
5 Short description of the verification procedure
For the verification procedure a divergent probe laser beam source with known divergence angle and
beam propagation ratio is required. Simple-astigmatic laser beams with equal divergence angles in
2
both principal directions shall have a beam propagation ratio M of less than 1,5 along at least one
principal direction. Simple-astigmatic laser beams with non-equal divergence angles shall have a beam
2
propagation ratio M below 1,5 along the principal axis having the larger divergence angle.
The divergent laser beam is collimated by the laser lens under investigation. If a cylindrical laser lens
is under investigation, the laser beam shall be orientated such, that the higher divergent principal
direction is parallel to the working direction of the lens.
In the following the probe laser beam before collimation by the laser lens under investigation will be
called the initial beam. Its divergence will be called the initial divergence and its beam parameters the
initial beam parameters.
2
In the preferred version of the verification procedure the beam propagation ratio M of the collimated
beam in the principal direction with higher initial divergence or in working direction of the collimating
lens will be measured according to ISO 11146-1. If the initial beam propagation ratio has been increased
due to the collimation by the laser lens under investigation by less than absolute 0,5, then the sine of
half the divergence angle of the divergent laser beam is considered a proven lower limit of the effective
numerical aperture of the lens at the wavelength of the laser beam.
In another version of the verification procedure only the residual divergence after collimation in the
principal direction with higher initial divergence or in working direction of the collimating laser
lens will be measured and compared to a theoretical residual divergence, calculated from the initial
divergence angle and the initial beam propagation factor before collimation and the focal length of the
laser lens under investigation. If the measured residual divergence angle differs from the theoretical
one less than a limit, which again depends on the initial divergence angle and the focal length of the
4
  © ISO 2022 – All rights reserved

-----
...