ISO 9336-3:2020

INTERNATIONAL ISO
STANDARD 9336-3
Second edition
2020-01
Optics and photonics — Optical
transfer function — Application —
Part 3:
Telescopes
Optique et instruments d'optique — Fonction de transfert optique —
Application —
Partie 3: Télescopes
Reference number
ISO 9336-3:2020(E)
©
ISO 2020

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ISO 9336-3:2020(E)

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© ISO 2020
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ISO 9336-3:2020(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 General description of test specimen types and the relevance of OTF tests .1
5 Test arrangement . 2
5.1 General . 2
5.2 Arrangement of optical bench . 2
5.3 Collimators . 3
5.4 Spectral response. 3
5.5 Spatial frequency range . 3
5.6 Azimuths. 4
5.7 Preparing the test specimen. 4
5.8 Auxiliary equipment . 5
6 Normalization of OTF values . 5
7 Test condition . 5
8 Specification of the imaging state . 5
8.1 Test specimen . 5
8.2 Measuring equipment . 6
8.3 Measurement . 6
9 Presentation . 8
10 Accuracy of equipment. 8
Annex A (informative) MTF Test methods using detector arrays . 9
Annex B (informative) Deriving an objective image quality criterion from the MTF .13
Bibliography .17
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ISO 9336-3:2020(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, Subcommittee
SC 4, Telescopic systems.
This second edition cancels and replaces the first edition (ISO 9336-3:1994), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— update of the document based on the latest technical developments;
— Annex A regarding tests on components and sub-assemblies using azimuth scanning systems
removed, due to lack of practical relevance;
— two new Annexes added regarding test methods using detector arrays and deriving an objective
image quality criterion from the MTF.
A list of all parts in the ISO 9336 series can be found on the ISO website.
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.
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ISO 9336-3:2020(E)

Introduction
Methods of assessing the imaging quality of telescopic systems can be found in ISO 14490-7. The
methods described in this document are basically subjective, relying as they do on the judgement
of the observer and the quality of his vision. The technique of measuring the “limit of resolution” is
relatively easy and quick to perform and provides a single figure of merit for each orientation of the
test pattern. However, being a subjective measurement, it can be open to significant variations in its
results. Measuring the optical transfer function (OTF), or more usually just its modulus, the modulation
transfer function (MTF), provides a completely objective means of evaluating imaging quality that can
be compared directly with the theoretical assessment done by the optical system designer.
Integration of the system MTF over a certain domain of spatial frequencies and normalised to the
diffraction limited MTF will provide a single figure of merit that is a reasonable representation of the
system performance without relying on any subjective assessment. When the spatial frequency domain
is selected in accordance with the properties of the detector system the method can be applied to
telescopic systems operating with any detector type, thus not limiting the method to visual observation.
This is of importance as in state-of-the-art telescopes the same optical path can be used for visual
observation as well as for wavelengths outside the visual range (using appropriate detector systems).
As a special case, an “objective limit of resolution”, providing a single figure of merit, can be derived
from a measurement of MTF by using the latter in combination with a “contrast sensitivity” curve for
the eye and a measurement of MTF may also be used as the basis for several other image quality criteria
(see Annex B).
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INTERNATIONAL STANDARD ISO 9336-3:2020(E)
Optics and photonics — Optical transfer function —
Application —
Part 3:
Telescopes
1 Scope
This document specifies a method of testing telescopes in terms of imaging states aimed at making
valid optical transfer function (OTF) measurements.
This document includes two annexes (Annex A and B) that provide information on the more recent
techniques for measuring optical transfer function and methods of deriving image quality criteria from
such measurements.
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 9334, Optics and photonics — Optical transfer function — Definitions and mathematical relationships
ISO 9335, Optics and photonics — Optical transfer function — Principles and procedures of measurement
ISO 14132-1, Optics and photonics — Vocabulary for telescopic systems — Part 1: General terms and
alphabetical indexes of terms in ISO 14132
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 9334 and ISO 14132-1 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 http:// www .electropedia .org/
4 General description of test specimen types and the relevance of OTF tests
The specimens considered are telescopic observational instruments with direct view used for viewing
remote objects and include many instruments such as telescopes, binoculars, telescopic sights or
spotting scopes.
Ideally, instruments would be best with no astigmatism and no field curvature coupled with good
chromatic correction but frequently compromises as mentioned above shall be tolerated.
Many optical systems include roof prisms to give a compact instrument. However, the image produced
by such systems is basically made up of two superimposed images and the accuracy with which they
match will depend on the accuracy with which the roof edge has been constructed. In such cases the
orientation of the roof edge shall be noted (see 5.5).
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ISO 9336-3:2020(E)

In use, the eye is coherently coupled to the telescope, so it may be contended that the only valid test
would be one that included the eye: reference is made to the case of cascaded optical systems in the
introduction to ISO 9334. However, in observer tests using telescopes, improved performance has been
obtained with instruments with better measured OTF performance in a variety of tests, including
contrast sensitivity using sinusoidal grating targets, which confirms the value of OTF tests.
OTF tests also enable performance to be compared with that computed by the telescope designer and
provide effective quality assurance tests of production specimens.
When considering the details of tests, some features of the eye need to be borne in mind, especially its
ability to accommodate for varying object distances and to adjust the working aperture, varying the
iris size, according to the ambient illumination. Thus firstly, unlike the photographic lens testing case,
refocusing for off-axis tests is necessary. Secondly, the working aperture of the telescope, i.e. the exit
pupil diameter, will need to match the receiving eye pupil, which generally has a range of 7 mm down
to 2 mm diameter for different ambient illumination levels. The size of the evaluation pupil for the MTF
measurement (receiving pupil in the test setup) is specified in the corresponding imaging state tables.
5 Test arrangement
5.1 General
MTF values can typically be obtained by
a) direct measurement of frequency response to targets of different spatial frequencies,
b) calculating from measurements of wavefront aberration in the exit pupil,
c) calculating from measurement of the intensity distribution generated through the system under
test of a (quasi-ideal) point source.
Cases b) and c) obtain two-dimensional MTFs from which one-dimensional MTFs may be deduced.
5.2 Arrangement of optical bench
For case 5.1 a) direct measurement of the frequency response to targets of different spatial frequencies,
a typical test setup is shown schematically in Figure 1. The separation between the test pattern unit
and the collimator is adjusted to give an infinite conjugate for the test. The separation between the
image analyser collimator (“decollimator”) and the image analyser needs to be adjustable by a suitable
micrometer, operating on the image analyser focus slideway, to position the image analyser at the image
of the test pattern.
When the object generator assembly (test pattern unit and collimator) and the image analyser assembly
(image analyser collimator and image analyser) are aligned, without the optical system to be tested,
the micrometer setting for optimum response of the test system will be the datum. When the optical
system to be tested is positioned for an on-axis test, refocusing of the image analyser is needed and
any change from the datum setting gives a measure of the on-axis dioptre setting of the system being
tested. In off-axis tests, a different setting from that for on-axis tests will be found and the new change
from the datum will give the dioptre setting for the particular field point and azimuth of the test; the
difference from that of the on-axis test gives a measure of the field curvature.
In off-axis tests with an arrangement where the test specimen is retained in a fixed position, the object
generator assembly will be rotated about a point on the reference axis, at or near the entrance pupil of
the specimen, through an angle ω . The image analyser assembly will be rotated about a point on the
p
reference axis, at or near the exit pupil of the specimen, through an angle ω' .
p
Descriptions of optical bench arrangements for testing a variety of different types of telescopic system
can be found in References [1] and [2].
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ISO 9336-3:2020(E)

5.3 Collimators
The object collimator shall be a well-corrected achromat with a focal length at least twice that of the
objective of the specimen and a working aperture diameter at least 10 mm greater than the objective of
the specimen. Reflective (off-axis) or catadioptric collimators may be preferred, especially for tests at
different wavelengths, thus providing a constant apparent test object distance without the requirement
for refocusing when changing the wavelength.
For the image analyser collimator, a convenient focal length would be 100 mm as this would ensure
that the movement of the image analyser along its focus slideway would be within the range of a readily
−1
available (e.g. 25 mm) micrometer movement if the field curvature reached 2 m . However, there may
be circumstances where the resolution of the image analyser may require a longer focal length to be
used. Alternatively, an image analyser collimator with fixed focal length in combination with well
corrected microscope objectives of different lateral magnifications can be used.
5.4 Spectral response
Unless otherwise specified, the spectral response of the test system shall match that of an observer
using the specimen in its normal viewing role or that of the detector if the specimen is intended for non-
visual use (e.g. infrared systems). This may be achieved by using a specially designed filter combination
to give the desired match in conjunction with the source emission and the detector spectral sensitivity
(see notes to Table 2).
Ideally, measurements shall be carried out with narrow bandwidth (quasi-monochromatic) radiation,
preferably at the dominant wavelength of the eye or the detector spectral response. If more than one
wavelength or a wavelength range is of interest, it is advisable to perform quasi-monochromatic tests
in succession to ensure the separation of chromatic and resolution deficiencies.
The most effective position for filters is after the image analysing element as the effect of stray radiation
is reduced. However, in good laboratory conditions, it is quite practicable to position the filter within
the test pattern unit.
5.5 Spatial frequency range
To a large extent, the test specimen will be the controlling influence on spatial frequency ranges as
derived in object space. In image space, the range might be limited by the resolution of the eye or the
detector. The lower and upper bound of the spatial frequency range shall be defined in the imaging
state table.
The corresponding frequency range in object space will be given by M times the lower and upper
bounds, where M is the magnification of the telescope.
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ISO 9336-3:2020(E)

a)  On-axis
b)  Off-axis
Key
1 test target unit 6 image analyser collimator (decollimator)
2 object collimator 7 image analyser
3 fixture for test specimen 8 image analyser focus slideway
4 test specimen ω , ω’ object and image pupil field angles
p p
5 diaphragm (with role of exit pupil); z reference axis
Figure 1 — Schematic setup — Object at infinity, image nominally at infinity
The spatial frequency in object space may be obtained either:
a) by calculation, using the linear spatial frequency of the test pattern in conjunction with the focal
length of the collimator; or
b) by measurement of the angular subtense of a number of cycles of the collimated test pattern,
followed by the appropriate calculation to give the spatial frequency.
5.6 Azimuths
It is permissible to measure one-dimensional MTFs. These shall be taken at the azimuths with highest
and lowest MTF values. For off-axis image points, this will generally be in the radial and tangential
directions. In case of rotational asymmetry (e.g. for on-axis points) this fact shall be noted and
measurement results given for the directions of highest and lowest MTF values.
A special case is that of systems containing roof prisms where one of the measurements shall be made
with the direction of variation of intensity of the test pattern normal to the roof edge.
5.7 Preparing the test specimen
The exposed optical surfaces shall be clean and the specimen shall have attained the stable temperature
of the test laboratory.
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ISO 9336-3:2020(E)

−1
Unless otherwise specified, focusing eyepieces shall be set for an infinite conjugate (0,0 m ). It is
permissible to refocus for best MTF (e.g. when measurements at different off-axis positions or at
different wavelengths are taken). In cases 5.1 a) and c), refocusing shall preferably be accomplished on
the analyser side (Key 8 of Figure 1). For case 5.1 b), refocusing with the eyepiece (or on the objective
side of the specimen) is permissible. In any case, the amount of refocusing required shall be noted in the
test report.
For tests assessing performance with a reduced exit pupil, uncertainties can arise due to the difficulty
of correctly positioning a stop at the exit pupil especially when making off-axis measurements. This is
due to a combination of vignetting, pupil distortion and pupil wander along the reference axis relative
to the on-axis pupil position. Consequently, it is preferable to position a stop of the corresponding
diameter at the entrance pupil. The size of the stop is given by the product of the desired exit pupil and
the magnification of the specimen.
5.8 Auxiliary equipment
In addition to fixtures for holding test specimens, some means for aligning the test beam with the
input axis of the specimen can be needed particularly for instruments having large offsets between
input and output axes. Mechanical means should be used for this if practical; otherwise, adjustable
periscopic beam deviators using a framework and plane mirrors may be employed. The combined effect
of all auxiliary equipment on the wavefront aberration shall be significantly lower than the accuracy of
measurement.
6 Normalization of OTF values
The normalization arrangement with equipment which permits the response at zero cycles to be set to
1,0 will generally be satisfactory but further checks can be used if needed.
7 Test condition
The testing shall be carried out in accordance with the general principles and procedures given in
ISO 9335.
8 Specification of the imaging state
8.1 Test specimen
Table 1 specifies an imaging state for the test specimen.
Table 1 — Imaging state of test specimens
Parameter Value/Setting Notes Clause
in line
Some configurations require
configuration 5.8
in line with offset angled
auxiliary equipment.
periscopic
example: these examples give exit pupils of
6 × 42 7 mm
magnification and
—
objective diameter
8 × 40 5 mm
10 × 30 3 mm
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ISO 9336-3:2020(E)

Table 1 (continued)
Parameter Value/Setting Notes Clause
7 mm
5 mm
To obtain reduced exit pupil
exit pupil 5.7
diameters appropriate stops are used.
3 mm
2 mm
field of view e.g. ±3° In object space. Clause 4
infinite conjugate
eyepiece focus setting Specify if other setting is used 5.7
−1
(0 m )
8.2 Measuring equipment
Table 2 specifies an imaging state for the measuring equipment.
Table 2 — Imaging state for measuring equipment
Parameter Value/Setting Notes Clause
bench configuration object at infinity focus adjustment is needed 5.2 and 5.3
cases 5.1 a) and c): image
side decollimator forms
an image in the plane of
the image analyser
wavefront sensor in exit
pupil
spectral characteristics dominant (monochromatic specify source 5.4
wavelength for nominal characteristics (i.e. center
V(λ) = spectral luminous
use) bandwidth)
efficiency for photopic
vision
wavelength(s) selected for specify source —
measurement characteristics (i.e.
center wavelength and
bandwidth)
polychromatic source: band filter and —
analyser combination
should have overal
spectral characteristics
which match the V(λ)
curve of the eye
8.3 Measurement
Table 3 specifies an imaging state for the measurement.
Table 3 — Imaging state for measurement
Parameter Value/Setting Notes Clause
MTF MTF is essential — —
PTF (phase transfer
function) if specified
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ISO 9336-3:2020(E)

Table 3 (continued)
Parameter Value/Setting Notes Clause
focusing on-axis: maximum integral — datum focus for infinity to be —
MTF (specify lower and established
upper bound of spatial
— different focussing criteria have
frequency)
to be specified
— focus for both radial and
tangential sections can be
required
— off-axis: refocusing for both
radial and tangential sections
will be needed
exit pupil full aperture and 3 mm Other if requested as defined in —
Table 1.
Maximum aperture for eye related
measurement shall be 7 mm.
pupil field angles on-axis — —
optional: off-axis
±0,5 semifield
±0,7 semifield
±0,85 semifield
reference angle 0°, 90°, 180° and 270° In case of rotational symmetry one —
angle is sufficient.
angles of roof edge
azimuth radial and tangential — —
dioptre setting infinite conjugate For fixed focus specimens adjust de- —
collimator accordingly.
Calculated from the difference be-
tween the datum focus and the
on-axis focus setting. Specify how
refocusing is accomplished.
field curvature — Calculated from the difference —
between the on-axis focus and
off-axis focus setting in both radial
and tangential sections for selected
field angles.
astigmatismus — Calculated from the difference —
between radial and tangential focus
settings at selected field angles.
reference plane — Object at infinity, no test specimen; —
image analyser focused for
maximum MTF.
selected spatial The sampling has to be — 5.5
frequencies in image sufficient to represent
space the measured MTF curve.
Generally 8 sampling
points over the represent-
ed frequency range should
be sufficient.
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ISO 9336-3:2020(E)

9 Presentation
The measured MTF shall be plotted together with the diffraction limited MTF in a diagram versus
10 equidistant frequencies over the practical measurement range.
10 Accuracy of equipment
The uncertainty of measurement shall be assessed either by using recognized or known test telescopes,
or by estimation of all systematic and random sources of error.
One method is to replace the test specimen and image analyser collimator with a collimator, which is
similar to the object collimator, to form an image of the test target without the test specimen.
Then, using a narrow bandwidth filter at 546 nm, and assuming that the collimators have diffraction
limited performance, the correct response should be obtained through a range of spatial frequencies.
Specify if different wavelengths are used.
Alternatively, special instruments of stable construction can be used. To facilitate the alignment of the
test setup, for all field points considered, a graticule with circles is incorporated so that each field point
is identified as the centre of a circle (see Reference [3]).
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ISO 9336-3:2020(E)

Annex A
(informative)

MTF Test methods using detector arrays
A.1 Measurement technique
Digital video cameras and digital still cameras can form the basis of a convenient facility for measuring
OTF, or just the MTF, of telescopic systems. Figure A.1 is a diagram of such an arrangement (note
similarities to Figure 1).
The test target can be of several forms, but in general the most convenient are illuminated pinholes,
slits or straight edges mounted so that their orientation can be varied, or a special form of radial
grating (Siemens star) where the transmission or reflectance of the grating lines varies sinusoidally
perpendicular to their length. The image analyser is either a digital video camera or a digital SLR still
camera, where the normal lens is in effect replaced by the decollimator or a decollimator combined
with well corrected microscope objectives
...