ISO 11421:1997

IS0
INTERNATIONAL
STANDARD
First edition
1997-09-l 5
Optics and optical instruments - Accuracy
of optical transfer function (OTF)
measurement
Exactitude du mesurage de la fonction
Optique et instruments d ’optique -
de transfer? optique (OTF)
Reference number
IS0 11421:1997(E)
IS0 11421:1997(E)
Page
Contents
1 Scope .
....................................................................
2 Normative reference
3 Definitions and symbols .
..........................
4 Sources of inaccuracy in measuring equipment
Methods of assessing levels of accuracy .
.; 18
.............. ......
6 Calculation of overall accuracy of a measurement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7 Specifying a general equipment accuracy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*. 22
8 Routine performance evaluation
Annexes
A Accuracy of PTF measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B Determination of rate of change of MTF various parameters . . . . . .
C Example calculation of NAV ,.~.,. 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*. 30
D Bibliography
0 IS0 1997
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IS0 11421:1997(E)
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Foreword
IS0 (the International Organization for Standardization) is a world-
wide federation of national standards bodies (IS0 member bodies).
The work of preparing International Standards is normally carried out
through IS0 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. IS0 collaborates closely with the International
Electrotechnical Commission (IEC) on all matters of electrotechnical
standardization.
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 IS0 11421 was prepared by Technical
Committee ISO/TC 172, Optics and optical instruments, Subcommittee
SC 1 Fundamental standards.
Annex A forms an integral part of this International Standard.
Annexes B, C and D are for information only.
. . .
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IS0 11421:1997(E)
Introduction
The optical transfer function (OTF) is one of the main criteria used for
objectively evaluating the image-forming capability of optical, electro-
optical and photographic systems.
The terms used in the measurement of OTF are defined in IS0 9334,
whilst IS0 9335 covers the actual principles and procedures of
measurement. A further International Standard, IS0 9336, deals with
specific applications in various optical and electro-optical fields and is
in several parts, each dealing with a particular application.
Although IS0 9335 lists the main factors which influence the accuracy
of OTF measurement and describes procedures which are aimed at
achieving accurate and repeatable results, it does not cover in detail
the techniques and procedures for evaluating the accuracy of OTF
measuring equipment and for estimating the uncertainty in
measurements made on specific imaging systems.
The present International Standard lists the main sources of
inaccuracy in OTF measuring equipment and provides guidance on
how these can be assessed and how the results of these assessments
can be used in estimating the error band in any measurement of OTF.
One of the aims in preparing this International Standard is to
encourage the setting of more realistic uncertainty levels for the
results of OTF measurements. Another is to encourage the use of
methods of expressing the accuracy of OTF test equipment which
recognize the fact that the accuracy of a particular measurement is a
function of both the equipment and the test piece.
iv
IS0 11421:1997(E)
INTERNATIONAL STANDARD o Is0
Optics and optical instruments - Accuracy of optical
transfer function (OTF) measurement
1 SCOPE
This International Standard gives general guidance on evaluating the sources of error in optical transfer
function (OTF) equipment and in using this information to estimate errors in a measurement of OTF. It also
gives guidance on assessing and specifying a general accuracy value for a specific measuring equipment,
as well as recommending methods of routine assessment.
The main body of this International Standard deals exclusively with the modulation transfer function (MTF)
part of the OTF. The phase transfer function (PTF) is dealt with relatively briefly in annex A.
2 NORMATIVE REFERENCE
The following standard contains provisions which, through reference in this text, constitute provisions of
this International Standard. At the time of publication, the edition indicated was valid. All standards are
subject to revision, and parties to agreements based on this International Standard are encouraged to
investigate the possibility of applying the most recent edition of the standard indicated below. Members of
IEC and IS0 maintain registers of currently valid International Standards.
Definitions and mathematical
IS0 9334:1995 Optics and optical instruments - Optical transfer function -
relatbnships
3.1 DEFMWTiONS
For the paarposes of this International Standard, the following definitions apply.
3.M standard lens
Single- or multi-element lens which has been constructed with a level of accuracy which is sufficient to
ensure that for precisely specified conditions of measurement the MTF will be equal to that predicted from
theoretical calculations to an accuracy of better than 0,05 (MTF units).
NOTE - In order to achieve this accuracy, standard lenses are usually of simple construction and therefore of
limited performance. An example of a widely used lens is the 50 mm focal length plano-convex lens described
in reference [3]. This and several other standard test lenses (including afocal systems and lenses operating in
the infrared wavelength bands) are available commercially.
3.1.2 audit lens
Single- or multi-element lens of stable construction whose accuracy of construction is not sufficient to
enable the MTF to be predicted by calculation from design data (usually as a result of the complexity of the
lens), but whose “accepted” values for the MTF under precisely defined measuring conditions have been
obtained by measurements done by a reputable authority (preferably a national standards laboratory, if
such a service is available).
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IS0 11421:1997(E)
3.2 SYMBOLS
Unit
Meaning
Symbol
mm, mrad, degree
object height
h
mm, mrad, degree
h’ image height
mm, mrad, degree
error in image height
Ah’
mm
object conjugate
mm
image conjugate
1’
mm
error in image distance
Al1
mm
departures from straightness of object slide
AZ
mm
departures from straightness of image slide
AZ/
angular departure of object slide from perpendicularity to
Aa
rad
reference axis
angular departure of image slide from perpendicularity to
Aa’
rad
reference axis
mm
total departure from ideal object plane
AZ
mm
total departure from ideal image plane
ti
dimensionless
M magnification
mm -I, mrad-I, degree-l
r spatial frequency
Ar error in spatial frequency mm -I, mrad-I, degree-l
-1
rate of change of MTF with object focus (for image mm
d-h)
intensifier and similar systems)
-1
rate of change of MTF with image focus mm
m ’(r,h ’) or m ’(r,cu)
rate of change of MTF with image height mm -I, mrad-I, degree-l
p ’kh ’) or p ’(w)
-1
rate of change of MTF with image distance mm
q ’( rh ’)
0 field angle mrad, degree
AW error in field angle mrad, degree
focal length mm
f
azimuth angle degree
w
error in azimuth angle between slits degree
Aw
R
(test lens focal length)/(colIimator focal length) or
(decollimator focal length)/(collimator focal length) dimensionless
width of slit referred to image plane mm
g’
L’ length of shorter slit referred to image plane mm
MTFc MTF of relay lens dimensionless
r -I, mrad-I, degree-l
spatial frequency for zero field angle mm
n ’( r, ‘h ’) rate of change of MTF with spatial frequency
mm, mrad, degree
AMTF(r) error in MTF dimensionless
AMTFJ r) MTF error of the relay lens dimensionless
AMTF, dimensionless
MTF errors resulting from aberrations of relay lens error
Al
error in setting collimator focus mm
AMTF(random)
total error in MTF random sources dimensionless
AMTF (systematic)
total error in MTF systematic sources dimensionless
AMTF(totaI) total error in MTF from all sources
dimensionless
AMTF( rand)”
error in MTF from nth source of random error dimensionless
AMTF(syst)n
error in MTF from rzth source of systematic errors dimensionless
NOTE - The notation I&-,/Z), m ’(r,h ’), $(I#) etc. denotes that these parameters are functions of both spatial frequency r and
image height h’ or h (i.e. the value of the parameter will be different for different frequencies and different image heights).

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4 SOURCES OF INACCURACY IN MEASURING EQUIPMENT
In this clause the main sources of inaccuracy in OTF measuring equipment are listed and the effects on a
measurement of MTF described (brief comments on the measurement of PTF will be found in annex A).
4.1 GEOMETRY OF OPTICAL BENCH SYSTEM
The function of the optical bench is to provide a means for supporting the “test target unit ”, the “test
specimen” and the “image analyser” in the correct geometrical relationship (i.e. that defined by the chosen I-
state, in accordance with IS0 9334). To achieve this one normally relies on such things as the straightness
of slideways, their parallelism to each other and/or to the surface to which the test specimen is referenced,
the accuracy of angle scales etc. Departures from the assumed geometry result in deviations from the ideal
l-state and therefore errors in the measured OTF. The important bench parameters depend on the test
arrangement being used (note that for bench arrangements such as “nodal slide benches” which are not
covered by this International Standard, the user must make his own assessment of errors). For the
arrangements recommended in IS0 9335, the main sources of inaccuracy and the resulting MTF errors are
as follows.
4.1.1 Object and image at finite conjugates
Both the test target unit (TTU) and image analyser slideways shall be straight and perpendicular to the
“reference axis ”.
Departures from straightness and perpendicularity will produce departures from the ideal focal planes given
.
.
bY
AZ(h) = Az(h) + h - Aa
for the TTU and
AZ ’(h ’) = Az ’(h ’) + h ’-Aa’
for the image analyser, where h an;d Jz” are object and image heights, & and AZ’ are departures from
straightness and Aa and Aa ’angular (radian) departures from perpendicularity to the reference axis, for the
lTU and image analyser slideways respective!y.
The combined effect is given by:
&7f(hg+M2. #g
AZ ’(h ’),,,l -=
h’
is the magnification.
where M=h
If m ’(r,h ’) is the rate of change of MTF(r) with focus, then the error in MTF is given by:
AMTF(r) = m ’(r, h ’) l AZ ’(h ’),o,,l
Two further possible sources of error are in the accuracy with which the image height h’ is set and the
accuracy with which the object and/or image distances are set. The error in MTF is in this case given by
(assuming image height and image distance are the parameters set):
AMTF(r) = p ’(r, h ’)dh ’+q ’(r, h ’)-Al’
where Ah’ and AZ’ are the errors in image height and image distance respectively and p’ and 4/ are the
corresponding rates of change in MTF. Usually p/and q ’are small and this source of error may be ignored
(i.e. errors will be less than 0,O ’l in MTF units).

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IS0 11421:1997(E)
4.1.2 Infinite object and finite image conjugates
Departures from the
Similar considerations as for 4.1.1 apply except that there is only a single slideway.
ideal focal plane are given in this instance by:
= & ‘(h ’) + h ’-Aa’
m ’(h ’AotaI
and the corresponding error in MTF is given once again by:
AMTF(r) = m ’(r, h ’)dZ ’(h ’),,,al
Errors may also arise from errors in setting image height or field angle (whichever is used in defining the I-
state) and in setting the object distance to be infinity. These give MTF errors as previously, i.e.:
AMTF(r) = p ’(r, h ’)-Ah ’+q ’(r, h ’).Al’
or, if field angle rather than image height is specified:
AMTF(r) = p ’(r,w)-Aw+q ’(r, h ’)-Al’
In the above equations h ’, AZ ’, p ’and q ’are as defined in 4.1.1, w is the field angle and Ao is the error in the
field angle. The value of AZ/shall be determined from the known departure of the object conjugate from
infinity. The relevant equation is:
f
Al ’= -
wherefis the focal length of the lens and I is the actual object conjugate.
Usually errors in MTF from these latter two sources are small and may be ignored except where, instead of
using a collimator, a very long object conjugate is used on the assumption that it provides a sufficiently
close approximation to an infinite conjugate.
$. ‘I.3 infinite object and image conjugates
With the recommended bench arrangement for this type of measurement (see IS0 9335) the separation
between image analyser and decollimator should not change as the image angle varies. There is therefore
no MTF error resulting from a change in focus setting with image angle (or field angle).
If bench arrangements are used where this error can occur, or, if as a result of mechanical flexing of the
focal slide which supports the decollimator and image analyser their separation may change, then an error
in the MTF may result, given by:
AMTF(r) =
...