ISO/TR 14999-2:2005

TECHNICAL ISO/TR
REPORT 14999-2
First edition
2005-03-01

Optics and photonics — Interferometric
measurement of optical elements and
optical systems —
Part 2:
Measurement and evaluation techniques
Optique et photonique — Mesurage interférométrique de composants
et systèmes optiques —
Partie 2: Mesurage et techniques d'évaluation




Reference number
ISO/TR 14999-2:2005(E)
©
ISO 2005

---------------------- Page: 1 ----------------------
ISO/TR 14999-2:2005(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.


©  ISO 2005
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
ISO's member body in the 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 copyright@iso.org
Web www.iso.org
Published in Switzerland

ii © ISO 2005 – All rights reserved

---------------------- Page: 2 ----------------------
ISO/TR 14999-2:2005(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Measurement objects . 1
2.1 Surfaces . 1
2.2 Optical components in transmission. 2
2.3 Optical systems. 3
2.4 Indirect examination of the function of optical elements . 3
3 Hardware aspects of an interferometer and test environment. 4
3.1 General. 4
3.2 Construction principles and influences on the quality of measurements. 5
3.3 Test environment . 15
4 Methods for evaluating the optical path difference. 18
4.1 General. 18
4.2 Visual inspection of interferograms. 18
4.3 Manual evaluation of interferograms . 24
4.4 Phase measurements with temporal carrier . 26
4.5 Phase measurements with spatial carrier . 32
4.6 Removal of phase ambiguities (phase unwrapping). 34
4.7 Registration of wavefronts; coordinate systems, coordinate system definition . 35
4.8 Polynomial and other representations of wavefronts. 36
5 Test reports and calibration certificates. 38
5.1 General. 38
5.2 Content of test reports and calibration certificates . 39
5.3 Test reports . 39
5.4 Calibration certificates . 39
5.5 Opinions and interpretations. 40
5.6 Electronic transmission of results . 40
5.7 Format of reports and certificates. 40
5.8 Amendments to test reports and calibration certificates . 41
6 Data format . 41
Annex A (informative) Orthogonal polynomials. 42
Annex B (informative) Orthogonal functions on “unusual areas” . 56
Bibliography . 59

© ISO 2005 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO/TR 14999-2:2005(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.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published 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 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 14999-2 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee
SC 1, Fundamental standards.
ISO 14999 consists of the following parts, under the general title Optics and photonics — Interferometric
measurement of optical elements and optical systems:
 Part 1: Terms, definitions and fundamental relationships (Technical Report)
 Part 2: Measurement and evaluation techniques (Technical Report)
 Part 3: Calibration and validation of interferometric test equipment (Technical Report)
 Part 4: Interpretation and evaluation of tolerances specified by ISO 10110
iv © ISO 2005 – All rights reserved

---------------------- Page: 4 ----------------------
ISO/TR 14999-2:2005(E)
Introduction
A series of International Standards on Indications in technical drawings for the representation of optical
elements and optical systems has been prepared by ISO/TC 172/SC 1, and published as ISO 10110 under
the title Optics and photonics — Preparation of drawings for optical elements and systems. When drafting this
standards series and especially its Part 5, Surface form tolerances and Part 14, Wavefront deformation
tolerance, it became evident to the experts involved that additional complementary documentation is required
to describe how the necessary information on the conformance of the fabricated parts with the stated
tolerances can be demonstrated. Therefore, the responsible ISO Committee ISO/TC 172/SC 1 decided to
prepare an ISO Technical Report on Interferometric measurement of optical wavefronts and surface form of
optical elements.
When discussing the topics which had to be included into or excluded from such a Technical Report, it was
envisaged that it might be the first time, where an ISO Technical Report or Standard is prepared which deals
with wave-optics, i.e. that is based more in the field of physical optics than in the field of geometrical optics. As
a consequence only fewer references than usual were available, which made the task more difficult.
Envisaging the situation, that the topic of interferometry has so far been left blank in ISO, it was the natural
wish to now be as comprehensive as possible. Therefore there was discussion, whether important techniques
such as interference microscopy (for characterizing the micro-roughness of optical parts), shearing
interferometry (e.g. for characterizing corrected optical systems), multiple beam interferometry, coherence
sensing techniques or phase conjugation techniques should be included or not. Other techniques, which are
related to the classical two beam interferometry, like holographic interferometry, Moiré techniques and
profilometry were also mentioned as well as Fourier transform spectroscopy or the polarization techniques,
which are mainly for microscopic interferometry.
In order to complement ISO 10110 the guideline adopted was to include what presently are common
techniques used for the purpose of characterizing the quality of optical parts. Decision was made to complete
a first Technical Report, and to then up-date it by supplementing new parts, as required. It is very likely that
more material will be added in the near future as more stringent tolerances (two orders of magnitude) for
optical parts and optical systems become mandatory when dealing with optics for the EUV range (wavelength
range 6 nm to 13 nm) for microlithography. Also, testing optics with EUV radiation (the same wavelength as
they are later used, e.g. at-wavelength testing) can be a new challenge, and is not covered by any current
standards.
This part of ISO 14999 should cover the need for qualifying optical parts and complete systems regarding the
wavefront error produced by them. Such errors have a distribution over the spatial frequency scale; in this part
of ISO 14999 only the low- and mid-frequency parts of this error-spectrum are covered, not the very high end
of the spectrum. These high-frequency errors can be measured only by microscopy, measurement of the
scattered light or by non-optical probing of the surface.
A similar statement can be made regarding the wavelength range of the radiation used for testing. ISO 14999
considers test methods with visible light as the typical case. In some cases, infrared radiation from CO -lasers
2
in the range of 10,6 µm is used for testing rough surfaces after grinding or ultraviolet radiation from excimer-
lasers in the range of 193 nm or 248 nm is used for at-wavelength testing of microlithography optics. However,
these are still rare cases, which are included in standards, that will not be dealt with in detail. The wavelength
range outside these borders is not covered.

© ISO 2005 – All rights reserved v

---------------------- Page: 5 ----------------------
TECHNICAL REPORT ISO/TR 14999-2:2005(E)

Optics and photonics — Interferometric measurement of optical
elements and optical systems —
Part 2:
Measurement and evaluation techniques
1 Scope
This part of ISO 14999 gives fundamental explanations to interferometric measurement objects, describes
hardware aspects of interferometers and evaluation methods, and gives recommendations for test reports and
calibration certificates.
2 Measurement objects
2.1 Surfaces
2.1.1 Mirrors: boundary surfaces of optical components in transmission
A common task in interferometry is measurement of the shape of a surface. This can be accomplished in two
different ways. Either reflected light or the light transmitted through the surface could be used for the
measurement.
Interferometric measurement is achieved by comparing the difference of two optical path lengths nd .
∫
Usually one path is called the reference path, the other the measurement path.
The resulting wave aberration, ∆W, for a displacement d of the surface, if measured in reflection, is ∆=Wn2d .
The same displacement measured in transmission results in the wave aberration ∆=Wn( −n )d .
21
2.1.2 Reflection degree
The Fresnel reflection from the boundary between two different media, R, can be calculated from the refractive
index n and n at the boundary surface.
1 2
2

nn−
21
R = (1)

nn+
21
For most optical glasses this value is between 4 % and 6 %, so an average of 5 % is usually a good estimate.
This reflection causes a loss of light from the transmitted wavefront at every surface. On the other hand, this
reflection is often used for the measurement itself. To obtain maximum fringe visibility, or contrast, the two
interfering beams should have approximately the same intensity. Changing the reflectivity of the beam splitter
within an interferometer only changes the amount of light in the interference pattern and does not change the
beam intensity ratio of the two beams because the light in both arms is transmitted through and reflected by
the beam splitter once. If the measurement path and reference path are separated, as in a Mach-Zehnder or
Twyman-Green set-up, it is usually possible to adjust the intensities of the light in both arms.
© ISO 2005 – All rights reserved 1

---------------------- Page: 6 ----------------------
ISO/TR 14999-2:2005(E)
A major problem arises in a Fizeau interferometer. If the reference surface has high reflectance, the result will
be multiple beam interference fringes resulting in narrow fringes as in a Fabry-Perot interferometer. If
sinusoidal fringes are required as for the evaluation by phase shift interferometry, the reference surface shall
have low reflection and an element has to be introduced between the reference and the measurement surface
that will absorb light without distorting the wave aberration.
2.1.3 Roughness
For interferometric measurement the roughness of the measured surface should not exceed a certain limit that
is a fraction of the wavelength and of the difference of indices of refraction, if used in transmission.
2.1.4 Topology of the regions
Difficulties may arise with interferometer software when the wavefront area has breaks in it (e.g. because it is
split into segments by the mechanical supports of the secondary mirror of a mirror telescope). Problems are
most severe with static fringe analysis software that depends strongly on using neighbouring points to
determine the position and continuity of fringes. Phase shift software is not affected to the same extent as it is
a point-by-point evaluation of wave aberrations.
Similar problems may occur if the wavefront area has a complicated outline.
2.1.5 Continuity of the surface; gradient of the surface
Due to the inherent ambiguity of ± n⋅2π it is not possible to measure any arbitrary surface shape uniquely. The
evaluation of a surface is usually correct, if the wave aberration between two resolvable points is less than π.
The gradient of the surface under test relative to the reference surface results in a gradient of the measured
wave aberration and in high-density or closely spaced fringes. Interferograms cannot be evaluated, if the
fringe separation is less then twice the distance of two resolvable points. If this condition is not possible by
adjustment, or by changing the measurement set-up, compensating optics may be required in some cases.
Some of the problems caused by the ambiguity can be solved by multiple wavelength interferometry.
2.1.6 Stiffness of mirrors; finite-element-calculations
During measurement the method of supporting the optics being tested should not deform them other than
when used as intended. It is sometimes difficult to notice whether an object is deformed during the
measurement. As a first indication of the influence of the support, the object can be measured by supporting it
in two completely different ways. In the case of any doubt, a finite-element-calculation is recommended.
2.1.7 Temperature homogeneity of mirrors
During measurement the object shall have a homogeneous temperature. Inhomogeneous temperatures can
cause deformations as the expansion coefficient of optical materials is rather high and the thermal conductivity
is very low. Stabilization can take some minutes but may sometimes require several hours.
2.1.8 Examples of measurement objects
Items that can be measured by interferometry include optical flats, windows, raw glass, convex and concave
mirrors, lenses, prisms, and optical systems.
2.2 Optical components in transmission
2.2.1 Single-pass versus double-pass testing
Transmitting optical components can be measured in single-pass or double-pass, depending on the
interferometric set-up. Double-pass measurement increases the sensitivity by a factor of two but may also
2 © ISO 2005 – All rights reserved

---------------------- Page: 7 ----------------------
ISO/TR 14999-2:2005(E)
include the effect of the reflecting surface. In double-pass measurements consideration shall also be given to
the possibility that the returning light passes back through the component at different locations.
2.2.2 Windows (wavefront aberrations in transmission)
For windows the shape error of the surfaces is usually not important. Also, the measured transmitted
wavefront will include the homogeneity of the material. Depending on the application, a certain amount of
power may be tolerated separate from the other wave aberrations. Also, a tolerated wedge can be measured
by interferometry. However, it can be more convenient to measure angular errors by different equipment.
2.2.3 Prisms (wavefront aberrations and angle error)
As in the case for windows, the wave aberrations and angular errors of prisms can be measured by different
equipment. However, if the angular tolerances are in the interferometric region, and many parts are to be
measured, it can be more convenient to measure both features by interferometry. In this case a fixed set-up,
or a master specimen, is used as a reference.
2.2.4 Influence of temperature on the refractive index
For measurement of an optical component in transmission, it shall be noted that not only the objects might be
deformed by the thermal expansion but, also, that the refractive index of the material changes with
temperature. Therefore, thermal setting of the test piece before testing is even more important.
2.3 Optical systems
2.3.1 Single-pass versus double-pass testing
Complete optical systems can be measured by interferometry in a manner similar to the testing of single
components. It is, however, important that systems be measured in the same geometry as they were
designed to be used. This can lead to a complicated set-up in single or double pass. For long systems tested
in double pass and in the presence of severe aberrations, it is necessary to take into account that the light
path on the way back can be considerably different to that in the forward direction.
2.3.2 Examination in the pupil
Interferometric measurements should be made in the exit pupil of the optical system.
2.3.3 Chromatic aberrations
If systems are measured at wavelengths different than those they are designed for, the effects caused by
chromatic aberrations shall be computed. There will be some systems, where the wave aberrations can be
simply scaled by the ratio of the test and design wavelengths, whereas other systems are so different that a
measurement is not possible.
2.4 Indirect examination of the function of optical elements
2.4.1 Examination with different wavelength
Usually the measurement of windows is possible and can be scaled to the correct wavelength. It shall be
noted, however, that inhomogeneities of optical materials may to some degree depend on the wavelength
range. Because of the presence of chromatic aberrations no universal recommendation is possible.
2.4.2 Examination with different beam path
Usually the measurement set-up should be as similar as possible to the application. In some cases, however,
it is more convenient to measure optical elements in a way that is different from their use. In this case, it may
© ISO 2005 – All rights reserved 3

---------------------- Page: 8 ----------------------
ISO/TR 14999-2:2005(E)
be difficult to find a correlation between the measured wave aberration and the tolerances and, therefore, not
possible to evaluate how the application is affected.
2.4.3 Tolerance range
Sometimes the relationship between the interferometric measurement and the tolerances of the measured
objects is not clear. Usually the complete test set-up shall be considered.
3 Hardware aspects of an interferometer and test environment
3.1 General
The purpose of this clause is to acquaint the user of an interferometer set-up to possible influences on the
accuracy of measurements. It is a matter of fact that two different persons using the same hardware and doing
their measurements in the same laboratory, will not necessarily achieve identical results with their
measurements. The skilled user might achieve a highly accurate result, whereas the unskilled user might have
severe errors in his result that he might not be aware of. It is important to keep in mind that good
reproducibility of measurement is no guarantee for a correct result, because systematic sources of errors
might have influenced the measured results. Knowledge about such possible influences, and how to avoid
them, is what experimental skill is about.
Such sources of errors can be, for example:
 improper use of the measuring instrument, because the optical principles are not well understood, e.g.
failure to image the surface under test onto the CCD camera of the interferometer;
 use of unsuitable fixtures to hold the test piece, inducing strain which causes bending;
 influence of gravity on the test piece;
 vibrations of the test set-up, which might induce phase-measuring errors;
 unsuitable use of polynomial fits with respect to the given shape of the aperture (for example due to some
obscured parts of the circular shape) and adjacent subtraction of error terms like tilt and focus terms, due
to an violation of the orthogonality assumption;
 presence of stable layers of air with different temperatures in the interferometer cavity, causing coma and
astigmatism;
 flipping (mirroring), or some other mismatch, of a calibration error map with respect to the actual
orientation, shape or magnification of the measured field;
 influence of different temperature or different focus settings between calibration and measurement;
 use of test pieces which are not homogeneous in temperature and have a considerable coefficient of
temperature expansion.
These are only examples; although there are a much greater number of “typical” sources of error. The only
way to overcome such types of error, which depend very much on the actual test situation and the demands
for the final accuracy, is that the operator planning and assembling the test should be aware of possible
influences on the accuracy of the measurement, which might be of optical or mechanical nature.
Conceptually, it is very important not to believe blindly the results which the instrument shows. At the same
time, it is equally important not to blame the instrument, or the principle of the interferometric measurement, if
there are inexplicable results. Note that in the majority of cases the instrument shows the “correct” readings
from what is presented to it, even if that is not the measurement task in question. If, for example, the
measured error map does not rotate by 72° when the test piece is rotated physically by 72°, this might indicate
4 © ISO 2005 – All rights reserved

---------------------- Page: 9 ----------------------
ISO/TR 14999-2:2005(E)
that the reference surface may contribute a considerable amount to the total error. The support of the test
piece can also influence the measurement, etc.
Another test might be, to repeat the measurement after 1 h without touching anything in the meantime. If the
results deviate from each other the reason might be that the temperature of the supports of the surface under
test, may have had an uneven temperature distribution in the first test. Normally, it may take more than 30 min
before the temperature has homogenized after handling a part. Also, the temperature in the laboratory might
have changed, the instrument might have warmed up, etc.
Such tests are imperative in order to exclude at least the most common sources of error. It is strongly
recommended to repeat a measurement at least three times and compare the results; this repetition should
include the demounting and remounting of the part in the test set-up, as well as all the adjustments of the
set-up and the settings of the interferometer. It is even better to repeat the whole test procedure on another
day, and, even by another operator.
All measurement conditions and settings have to be documented and the final data sets should be stored in
the computer in an organized way. Ideally, the documentation should be stored together with the measured
data sets. Any further treatment like subtraction of tilt or even higher order (Zernike) functions, number of
averages, any filtering like smoothing with a spatial low pass or median filter to remove “spikes”, shall be
documented and stored together with the data set. Such information is part of the result and when not given
together with the measured surface map, the result is useless and cannot be used for proof of quality for the
part under test.
3.2 Construction principles and influences on the quality of measurements
3.2.1 General
When the wavefront deviation of a test piece is measured by an interferometer, the test piece becomes part of
the optics of the instrument. The auto-collimation condition shall be met, as well as the condition to image the
surface under test onto the detector. In order to achieve high flexibility of possible locations for the surface
under test and for different test configurations, there will be stringent requirements on the spatial and temporal
coherence of the light source which need to be fulfilled. These can easily be attained by use of a laser and,
together with a very high intensity compared to other light sources, are the reason that the laser is the
standard light source for interferometers.
One of the consequences of the very high coherence of lasers is that all kinds of defects, such as impurities of
substrates, optical cements and coatings, tiny scratches, bubbles, holes, dust particles, micro-roughness of
surfaces, which can occur at any part of the light path through the interferometer, are “collected” and are
superimposed as an uncleanliness, i.e. unwanted amplitude and phase modulations of the wavefronts which
finally show clearly on the interferogram. The further away the disturbing defects are from an image plane of
the detector, the more the defects are altered in their phase distributions due to Fresnel diffraction and in
spatial frequency. A very narrow defect located on a surface near an image of the light source might spread
out to a big size in the detector plane. The specification of optical parts used in an interferometer set-up
therefore have to be much more stringent than in
...