1、 Reference number ISO/TR 11146-3:2004(E) ISO 2004TECHNICAL REPORT ISO/TR 11146-3 First edition 2004-02-01 Lasers and laser-related equipment Test methods for laser beam widths, divergence angles and beam propagation ratios Part 3: Intrinsic and geometrical laser beam classification, propagation and
2、details of test methods Lasers et quipements associs aux lasers Mthodes dessai des largeurs du faisceau, des angles de divergence et des facteurs de propagation du faisceau Partie 3: Classification intrinsque et gomtrique du faisceau laser, propagation et dtails des mthodes dessai ISO/TR 11146-3:200
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6、SO 2004 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 either ISO at the address below or ISOs member body in th
7、e country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2004 All rights reservedISO/TR 11146-3:2004(E) ISO 2004 All rights reserved iiiContents Page Forewor
8、d iv Introduction v 1 Scope 1 2 Second-order laser beam characterization 1 2.1 General. 1 2.2 Wigner distribution . 1 2.3 First- and second-order moments of Wigner distribution 2 2.4 Beam matrix. 3 2.5 Propagation though aberration-free optical systems . 4 2.6 Relation between second-order moments a
9、nd physical beam quantities 4 2.7 Propagation invariants . 8 2.8 Geometrical classification 9 2.9 Intrinsic classification 9 3 Background and offset correction 10 3.1 General. 10 3.2 Coarse correction by background map subtraction . 10 3.3 Coarse correction by average background subtraction. 11 3.4
10、Fine correction of baseline offset . 11 4 Alternative methods for beam width measurements 13 4.1 General. 13 4.2 Variable aperture method. 14 4.3 Moving knife-edge method. 16 4.4 Moving slit method . 17 Annex A (informative) Optical system matrices 20 Bibliography . 22 ISO/TR 11146-3:2004(E) iv ISO
11、2004 All rights reservedForeword 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
12、 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 Commiss
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14、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. In exceptional circumstances, when a technical committee has collected data of a different kind from that which is normally publ
15、ished as an International Standard (“state of the art”, for example), it may decide by a simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely informative in nature and does not have to be reviewed until the data it provides are considered to
16、 be no longer valid or useful. 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/TR 11146-3 was prepared by Technical Committee ISO/TC 172, Optics
17、and photonics, Subcommittee SC 9, Electro-optical systems. This first edition of ISO/TR 11146-3, together with ISO 11146-1, cancels and replaces ISO 11146:1999, which has been technically revised. ISO 11146 consists of the following parts, under the general title Lasers and laser-related equipment T
18、est methods for laser beam widths, divergence angles and beam propagation ratios: Part 1: Stigmatic and simple astigmatic beams Part 2: General astigmatic beams Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods (Technical Report) ISO/TR 11146-3:2004
19、(E) ISO 2004 All rights reserved vIntroduction The propagation properties of every laser beam can be characterized within the method of second-order moments by ten independent parameters. However, most laser beams of practical interest need less parameters for a complete description due to their hig
20、her symmetry. These beams are stigmatic or simple astigmatic, e.g. due to the used resonator design. The theoretical description of beam characterization and propagation as well as the classification of laser beams based on the second-order moments of the Wigner distribution is given in this part of
21、 ISO 11146. The measurement procedures introduced in ISO 11146-1 and ISO 11146-2 are essentially based on (but not restricted to) the acquisition of power (energy) density distributions by means of matrix detectors, as for example CCD cameras. The accuracy of results based on these data depends stro
22、ngly on proper data pre-processing, namely background subtraction and offset correction. The details of these procedures are given here. In some situations accuracy obtainable with matrix detectors might not be satisfying or matrix detectors might simply be unavailable. In such cases, other, indirec
23、t methods for the determination of beam diameters or beam width are viable alternatives, as long as comparable results are achieved. Some alternative measurement methods are presented here. TECHNICAL REPORT ISO/TR 11146-3:2004(E) ISO 2004 All rights reserved 1Lasers and laser-related equipment Test
24、methods for laser beam widths, divergence angles and beam propagation ratios Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods 1 Scope This part of ISO 11146 specifies methods for measuring beam widths (diameter), divergence angles and beam propagat
25、ion ratios of laser beams in support of ISO 11146-1. It provides the theoretical description of laser beam characterization based on the second-order moments of the Wigner distribution, including geometrical and intrinsic beam characterization, and offers important details for proper background subt
26、raction methods recommendable for matrix detectors such as CCD cameras. It also presents alternative methods for the characterization of stigmatic or simple astigmatic beams that are applicable where matrix detectors are unavailable or deliver unsatisfying results. 2 Second-order laser beam characte
27、rization 2.1 General Almost any coherent or partially coherent laser beam can be characterized by a maximum of ten independent parameters, the so-called second-order moments of the Wigner distribution. Laser beams showing some kind of symmetry, stigmatism or simple astigmatism, need even fewer param
28、eters. The knowledge of these parameters allows the prediction of beam properties behind arbitrary aberration-free optical systems. Here and throughout this document the term “power density distribution E(x,y,z)” refers to continuous wave sources. It might be replaced by “energy density distribution
29、 H(x,y,z)” in the case of pulsed sources. Furthermore, a coordinate system is assumed where the z axis is almost parallel to the direction of beam propagation and the x and y axes are horizontal and vertical, respectively. 2.2 Wigner distribution The Wigner distribution h(x,y, x , y ;z) is a general
30、 and complete description of narrow-band coherent and partially coherent laser beams in a measurement plane. Generally speaking, it gives the amount of beam power of a beam passing the measurement plane at the lateral position (x,y) with a horizontal paraxial angle of xand a vertical paraxial angle
31、of yto the z axis, as shown in Figure 1. NOTE The Wigner distribution is a function of the axial location z, i.e. the Wigner distribution of the same beam is different at different z locations. Hence, quantities derived from the Wigner distribution are in general also functions of z. Throughout this
32、 document this z dependence will be dropped. The Wigner distribution then refers to an arbitrarily chosen location z, the measurement plane. ISO/TR 11146-3:2004(E) 2 ISO 2004 All rights reservedx,y spatial coordinates x , ycorresponding angular coordinates Figure 1 Coordinates of Wigner distribution
33、 The power density distribution E(x,y) in a measurement plane is related to the Wigner distribution by ()() , , , d d x yxy Exy hxy = (1) NOTE The integration limits in the equation above are finite, representing the maximum angles of the rays contained in the beam, in paraxial; they are conventiona
34、lly extended to infinity. 2.3 First- and second-order moments of Wigner distribution The first-order moments of the Wigner distribution are defined as () 1 , , ddd d xyx y xh x yx x y P = (2) () 1 , , ddd d xyx y yh x yy x y P = (3) () 1 , , ddd d x xyx xy hxy xy P = (4) () 1 , , ddd d yx y yx y hxy
35、 xy P = (5) where P is the beam power given by () , , ddd d xyx y Ph x y x y = (6) or, using Equation (1), ( ) ,dd PE x yx y = (7) ISO/TR 11146-3:2004(E) ISO 2004 All rights reserved 3The spatial moments x and y give the lateral position of the beam centroid in the measurement plane. The angular mom
36、ents x and y specify the direction of propagation of the beam centroid. The (centred) second-order moments are given by () () ()() () 1 , , ddd d n km kmn xyx yx x y yx y xy hxy x x y y xy P = (8) where , , and km n are non-negative integers and 2 km n + += . Therefore, there are ten different secon
37、d- order moments. The three spatial second-order moments 22 , and xy x y are related to the lateral extent of the power density distribution in the measurement plane, the three angular moments 22 , and x yx y to the beam divergence, and the four mixed moments , , and x yx y xxy y to the phase proper
38、ties in the measurement plane. More details on the relation between the ten second-order moments and the physical beam properties are discussed below. The spatial first- and second-order moments can be directly obtained from the power density distribution E(x,y). From Equation (1) it follows: () 1 ,
39、d d x Exyxxy P = (9) () 1 ,d d y Exyyxy P = (10) and ()() 2 2 1 ,d d xE x y x xx y P = (11) ()() () 1 ,d d xy E x y x x y y x y P = (12) ()() 2 2 1 ,d d y Exyy y xy P = (13) The other second-order moments are obtained by measuring the spatial moments in other planes and using the propagation law of
40、the second-order moments (see below). NOTE The details of measuring all ten second-order moments are given in ISO 11146-2. 2.4 Beam matrix The ten second-order moments are collected into the symmetric 4 4 beam matrix ISO/TR 11146-3:2004(E) 4 ISO 2004 All rights reserved2 2 T 2 2 xy xy xxxx y yyx yx
41、xx yxx xy y y y xy xy = WM P MU(14) with the symmetric submatrix of the spatial moments 2 2 xx y xy y = W (15) the symmetric submatrix of the angular moments 2 2 xy y yy y = U (16) and the submatrix of the mixed moments xy xy xx yy = M (17) 2.5 Propagation though aberration-free optical systems Aber
42、ration-free optical systems are represented by 4 4 system matrices S known from geometrical optics. The propagation of the second-order moments through such a system is given by T out in = PS PS (18) where P inand P outare the beam matrices in entry and exit plane of the optical system, respectively
43、. Examples for system matrices are given in Annex A. 2.6 Relation between second-order moments and physical beam quantities The ten second-order moments are closely related to well known physical quantities of a beam. The three spatial moments describe the lateral extent of the power density distrib
44、ution of the beam in the measurement plane. The directions of minimum and maximum extent, called principal axes, are always orthogonal to each other. Any power density distribution is characterized by the extents along its principal axes and the orientation of those axes. The beam width along the di
45、rection of the principal axis that is closer to the x-axis of the laboratory system is given by ( ) ( ) () 1 1 2 2 2 2 22 22 22 4 x dx yx yx y =+ (19) ISO/TR 11146-3:2004(E) ISO 2004 All rights reserved 5and the beam width along the direction of that principal axis, which is closer to the y-axis by
46、( ) ( ) () 1 1 2 2 2 2 22 22 22 4 y dx yx yx y =+ (20) where ( ) 22 22 22 sgn xy xy xy = (21) If the principal axes make the angle + or /4 with x- or y-axis, when x 2 = y 2 , then d xis by convention the larger of the two beam widths, and ( ) 1 2 22 22 2 x dxyx y =+ (22) ( ) 1 2 22 22 2 y dx yx y =+
47、 (23) The azimuthal angle between that principal axis, which is closer to the x-axis, and the x-axis is obtained by ( ) 22 1 arctan 2 2 xy x y = (24) valid for 22 xy ; for 22 xy = , (z) is obtained as () () sgn 4 zx y = (25) where () sgn xy xy xy = (26) See Figure 2. Figure 2 Azimuthal angle and bea
48、m widths along principal axes of power density distribution ISO/TR 11146-3:2004(E) 6 ISO 2004 All rights reservedVery similar, the three angular moments describe the beam divergence characterized by the orthogonal directions of its maximum and minimum extent. These directions are called the principal axes of the beam divergence and may not coincide with the principal axes of the power density distribution in the measurement plan
