ISO 11421:1997

IS0
INTERNATIONAL
11421
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)

---------------------- Page: 1 ----------------------
IS0 11421:1997(E)
Page
Contents
1 Scope .
....................................................................
2 Normative reference
3 Definitions and symbols .
..........................
4 Sources of inaccuracy in measuring equipment
10
Methods of assessing levels of accuracy .
5
.; 18
.............. ......
6 Calculation of overall accuracy of a measurement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7 Specifying a general equipment accuracy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*. 22
8 Routine performance evaluation
Annexes
24
A Accuracy of PTF measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
B Determination of rate of change of MTF various parameters . . . . . .
C Example calculation of NAV ,.~.,. 27
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*. 30
D Bibliography
0 IS0 1997
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 the publisher.
International Organization for Standardization
Case postale 56 l CH-1214 Geneve 20 l Switzerland
Internet central @ iso.ch
x.400 c=ch; a=400net; p=iso; o=isocs; s=central
Printed in Switzerland
ii

---------------------- Page: 2 ----------------------
IS0 11421:1997(E)
@ IS0
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.
. . .
111

---------------------- Page: 3 ----------------------
@ IS0
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

---------------------- Page: 4 ----------------------
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).
1

---------------------- Page: 5 ----------------------
@ IS0
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
1
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).

---------------------- Page: 6 ----------------------
IS0 11421:1997(E)
@ IS0
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).

---------------------- Page: 7 ----------------------
@ IS0
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:
2
f
Al ’= -
1
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) = m ’(r, w)& ‘(o)
where & ‘(a) is this mechanical error, and m ’(r,w) is the rate of change of MTF with focus.
Other sources of error are inaccuracies in setting field angle and in setting the object distance to be infinity.
The resulting MTF errors are given by the relevant equations of 4.1.2, i.e.:
AMTF(r) = p ’(r,w)-Aw+q ’(r, h ’)-Al’
whereas before
2
f
Al ’= -
1

---------------------- Page: 8 ----------------------
IS0 11421:1997(E)
@ IS0
4.1.4 Image intensifiers and other systems with physically defined object and/or image surfaces
An accepted procedure when testing this type of system is to refocus the test target onto the object plane
and/or the image plane onto the image analyser, for every test position in the image/object plane. With this
procedure, focus errors arising from mechanical bench errors are eliminated. The only other source of error
is from incorrectly setting the specified test positions in the object or image surfaces. The resulting MTF
errors are usually negligible, and are given as in 4.1.1 by:
AMTF(r) = p ’(r,h ’) l Ah’
If a test procedure is used where no refocusing is carried out when the object/image position is changed
and reliance is placed on the TTU and image analyser slideways being straight and parallel to their
respective object/image surfaces, then MTF errors are given by:
AMTF(r) = m(r,h)[&(h) + h 1 Aa] + m ’(r,h ’)[Az ’(h ‘) + h ’- Aa ’]
4.1.5 Mounting of test piece
The test piece may not always I ocate exactly as intended on the mount to which it is attached on the
equipment. This will introduce some variability in the results of a sequence of measurements where the
test piece has been removed from and remounted on the equipment between each measurement. The
main effect is likely to be a small tilt of the image plane. The effect on the measured MTF, which can be
very significant, is given by the same equations as for angular errors in the slideways (see 4.1.1).
4.2 AZIMUTH CHANGING
With most OTF equipments a change in measurement azimuth is achieved by rotating the TTU and the
image analyser. This rotation can result in a movement of the TTU and or the image analyser along the
direction of the axis of rotation. This will produce a focus change which will be denoted as:
k(w) and &ly/),
,for the TTU and image analyser respectively, where w is the azimuth angle. The MTF error resulting from
this focus change is given in 4.2.1 to 4.2.4 for each of the bench configurations.
4.2.1 Object and image at finite conjugates
AMTF(r) =
m’(r, h’)[M(ly) + M2 l +)I
4.2.2 Infinite object and finite image conjugates
AMTF(r) =
mt(r, h’@‘(ly) + R2 l A&j
(test lens focal length)
where R is the ratio
(collimator focal length) ’
Usually R2 will be small and the second term in the brackets may be ignored.
4.2.3 Infinite object and image conjugates
AMTF(r) = m ’(r,u)[& ‘(W) + (M-R)2Az(w)l
(decollimator focal length)
where R is the ratio ) and M is the magnification of the test telescope.
(collimator focal length)
5

---------------------- Page: 9 ----------------------
@ IS0
IS0 11421:1997(E)
4.2.4 Image intensifiers and other systems with physically defined object and/or image surfaces
If a test procedure is used where the test target is refocused on to the object plane and/or the image plane
on to the image analyser, for every test azimuth (see 4.1.4) then no errors will result. If a test procedure is
used where no refocusing is carried out when the object/image azimuth is changed, then MTF errors are
given by:
AMTF(r) = m(r,h) - AZ&) + m ’(r,h ’) - & ‘(W,
4.3 ALIGNMENT (ORIENTATION) OF TTlJ AND IMAGE ANALYSER
If both the TTU and the image analyser use mask patterns which are not circularly symmetric, then their
relative orientation is important. Usually one or both of the masks is in the form of a slit perpendicular to
the scan direction. The effect of any angular misalignment Aw between the two (see figure I) will result in
an effective increase in width of the slit, given by:
where L ’is the length of the shorter of the two slits, referred to the image plane. The error in MTF resulting
from this is given by:
1
AMTF(r) = n-r* L ’-AtpMTF(r)- ’
(n+g ’)- tan(nr-g ’)
where g’ is the assumed width of the slit, referred to the image plane.
It is important to note that in some types of equipment a combination of a slit and a grating is used to
generate a periodic target whose spatial frequency can be altered by changing the orientation of the grating
with respect to the slit. Spatial frequency errors will usually result from any errors in the relative orientation
of the slit and grating. The user must make his own assessment of the effect of such errors (see 4.6 for the
effect of spatial frequency errors on MTF).
LSF S
W = g ’+ L ’sinAy
LSF Line spread function
S Image analyser slit
L’ Length of slit
Width of slit
g’
Ay Angular misalignment
Effective slit width
W
Figure 1 - Errors from alignment of analysing slit with respect to object pattern

---------------------- Page: 10 ----------------------
IS0 11421:1997(E)
@ IS0
4.4 CORRECTION FACTORS
Correction factors are applied to MTF measurements to allow for the effect of equipment constants such as
the finite width of target and/or analyser slits, the MTF of incoherently coupled relay lenses and the effect of
off-axis measurement geometry on spatial frequency (see IS0 9335). Errors in MTF will occur either if these
factors are not applied, or if there is an error in the value of the applied correction factor. Only the most
common correction factors are considered here. However, these may be taken as examples of how to deal
with other types of correction factor.
4.4.1 Slit width errors
Errors or uncertainties in the widths of slits will introduce errors in the measured MTF, given by:
1
AMTF(r) = IwMTF(~) ’ - Ag“
(7c+g ’)- tan(n:.r.g ’)
where g ’is the width of the slit, referred to the image plane and Ag’ is the error or uncertainty in its value.
4.42 Correction for MTF of incoherently coupled relay lenses
Incoherently coupled relay lenses are frequently used in equipment for measuring the MTF of electro-
optical devices and systems such as image intensifier tubes. The reciprocal of the MTF of these relay lenses
is applied to the measured MTF as a correction factor. Any errors in the value of MTF of such relay lenses
will therefore introduce errors into the final MTF value for the system under test. If the error in the MTF of
such a relay lens is AMTF,(r) and the actual value of its MTF is MTF,(r), then the error in the MTF of the test
system is given by:
AMTF, (r)
AMTF(r) = MTF(r) .
MTF, 0-J
where MJF(r) is the MTF of the system.
Similar considerations apply to other measure ment situations where a correcti on is applied for the MTF of a
device i n the measurement train.
4.4.3 Spatial frequency correction for field angle
In making off-axis measurements with a grating test pattern positioned on the axis and in the focal plane of
a collimator, a correction of the frequency scale should be performed (this also applies whenever frequency
is measured in this plane). The corrected frequency is given by:
r = ro-cos2(o) for the tangential azimuth and
r = rocos(w) for the radial azimuth, where r. is the on-axis frequency
Errors in the value of r will be produced by errors in the value of w the field angle.
The values of these
errors are given by:
Ar = 2*r,sin( w)-cos( &Am
Ar = rOsin(& Act,
The effect of such errors on the MTF can be calculated in the manner indicated in 4.6.

---------------------- Page: 11 ----------------------
@ IS0
IS0 11421:1997(E)
4.5 FOCUS ERROR
An error or uncertainty in focus of & ‘(referred to the image plane) will result in an MTF error or uncertainty
given by:
AMTF(r,h ’) = m ’(r,h ’) - AZ’
where m ’(r,hl) is the rate of change of MTF with focus for a spatial frequency r and an image height h ’.
The value of & ‘will depend on several factors. The most important of these are: the sensitivity of the focus
control, the technique of focusing used, the spatial frequency at which the MTF is maximized (low
frequency will generally result in a low focusing accuracy), the numerical aperture (NA) of the test lens, the
MTF of the test lens, the signal/noise ratio associated with the particular equipment and test configuration.
Uncertainties in the focus position will normally only lead to small errors in MTF at the field position where
the lens is focused (usually on-axis). However large errors may result at other field positions, particularly
where astigmatism and/or field curvature are present.
4.6 SPATIAL FREQUENCY ERRORS
An error Ar in the spatial frequency will produce an MTF error given by:
AMTF(r,h) = n ’(r,h ’) - Ar
where n ’(r,h ’) is the rate of change of MTF with spatial frequency. Some sources of spatial frequency errors
are: calibration errors, non-linearity and/or zero offset in transducers or mechanisms generating the spatial
frequency reading. Note that the relationship between spatial frequency in image and object space may
change with image height in the presence of distortion.
4.7 RESIDUAL ABERRATIONS IN RELAY OPTICS
Any optical system in the MTF measurement chain which is coherently coupled to the system under test
(e.g. collimators and image relay lenses) should be aberration-free, since corrections cannot be applied for
their effect on the measured MTF.
Accurate assessment of the errors resulting from known residual wavefront aberrations in relay lenses
require the aberrations of the test system to also be known.
Moreover, complex calculations are required
for its determination.
If information is available about the MTF errors AMIF, which would result from the aberrations of the
relay system when testing a diffraction-limited lens with the same NA and aperture diameter as the test
system, then this represents the largest error which will be introduced into the measurements from this
source. The value of AMTF,,(r) can either be measured directly or can be computed from the measured
aberrations of the relay lens.
Unfortunately this approach will overestimate the errors when the system under test is poorly corrected.
4.8 SPECTRAL CHARACTERISTICS
The mismatch between the actual and desired spectral response characteristics of the measurement
equipment will introduce errors in the measured MTF. The magnitude of the errors will depend on the
sensitivity of the MTF of the system under test to the particular mismatch.
If the design data for the system under test is available and the characteristics (or likely characteristics) of
the spectral mismatch are known, then the associated MTF errors can be calculated using a computer
program for calculating polychromatic MTF. An alternative to this is to estimate the errors from the results

---------------------- Page: 12 ----------------------
@ IS0 IS0 11421:1997(E)
of MTF measurements made using appropriate narrow-band filters (see 5.4). Where a spectral mismatch is
known to occur and where the resulting error cannot be determined, this should be clearly indicated on the
measured MTF data and a curve provided showing the actual overall spectral response characteristics used.
It is important to realize that even low levels of response, at wavelengths where the response is assumed to
be zero, can result in a significant error in the measured MTF. This is particularly so when making
measurements on optical systems designed for use with monochromatic radiation, which may have little or
no correction for chromatic aberrations. It can be a mistake to attempt to use a filter with a very narrow
bandwidth for such measurements since this increases the relative effectiveness of any transmission
outside the intended pass band.
4.9 EXTENT OF TEST TARGET AND/OR SCAN
If the correct boundary conditions are not satisfied during a measurement of MTF, an error will result. It is
difficult to estimate in a particular case what error can be introduced in this way. However there are several
tests that can be made to check if this is likely to be a significant source of error. In general terms, an
increase or decrease in the lateral extent of a test target or analysing mask and (where applicable) the
extent of a scan, should produce no change in the absolute signal level, or in the measured MTF, if the
boundary conditions are correct. The minimum or maximum acceptable extent of test targets etc. is related
to the size of the point spread function. An approximate knowledge of this can allow one to determine if the
boundary conditions for a particular measurement technique are satisfied.
4.10 ANGULAR RESPONSE CHARACTERISTICS OF IMAGE ANALYSER
For the result of an MTF measurement to be correct, the image analyser must respond to the full angular
cone of radiation from the test system. Any truncation, or nonuniform attenuation of this response, will
introduce errors in the measurement. The polar response of an image analyser should be measured and
the possible errors evaluated using the method described in 5.7.
4.11 POLAR LUMINANCE/RADIATION CHARACTERISTICS OF OBJEC T GENERATOR
(4.10). The requirements are
Similar considerations apply as for the Ipolar response of image analysers
is only required to uniformly
usually easier to satisfy in this instance, ‘since in most situations the TTU
;iVlumina%e the aperture of a collimator.
4.12 ~EQUIWIEMT \SdGNAL PROCESSI ’NG
Err.ors in the MTF measurement can arise from limitations and inaccuracies in the signal processing of the
measuring equipment. The magnitude of such errors can be estimated from measurements carried out
using standard test lenses or special artefacts such as accurately measured slits (see 5.6).
4.13 STRAY RADIATION
Stray radiation from such sources as room lighting may affect the performance of an equipment. This
should be checked by the user and any undesirable sources of radiation eliminated or reduced to a level at
which their effects are insignificant.
4.14 COHERENT RADIATION
The concept of OTF as it is dealt with in this International Standard applies only to objects which are
illuminated incoherently. The use of coherently, or partially-coherently, illuminated test objects for the
measurement of OTF will give incorrect results. No easy means of assessing the degree of coherence or
partial-coherence of a test object exists. The necessary steps to avoid coherent illumination are part of the
design of an equipment and are not dealt with in this standard. Apart from avoiding the use of coherent
sources such as lasers, a necessary condition of illumination is that the numerical aperture (NA) of the
optical system illuminating the test object shall be greater than the object-side NA of the test piece (for
collimated radiation the pupil of the collimator shall also be greater than that of the test piece). When
9

---------
...