ISO/TR 11826:2024

Technical
Report
ISO/TR 11826
First edition
Ophthalmic optics — Spectacle
2024-07
lenses — Aspects of three-
dimensional properties and
reference markings
Optique ophtalmique — Verres de lunettes — Aspects des
propriétés tridimensionnelles et marquages de référence
Reference number
© ISO 2024
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Technical background. 1
4.1 General .1
4.2 Spectacle lenses .1
4.3 Spectacle frames .2
5 Influence of three-dimensional effects and necessity to deal with them . 3
5.1 Optical effects . . .3
5.2 Reference points on front surface versus back surface meeting the eye in as-worn
position .7
5.3 Positioning errors from the images of markings on the back surface .10
5.3.1 General .10
5.3.2 Simulation results . 12
6 Different approaches to specifying measurement positions and alignment .15
6.1 General . 15
6.2 Reference coordinate systems defined by engravings .16
6.2.1 General .16
6.2.2 Reference coordinate system for front side engravings .16
6.2.3 Reference coordinate system for back side engravings .17
6.2.4 Data Communication Standard (DCS) from the Vision Council .19
6.3 Summary .21
7 Conclusion .22
Bibliography .24

iii
Foreword
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Ophthalmic optics and instruments.
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.

iv
Introduction
In current standards, spectacle lenses are mostly treated as two-dimensional objects.
However, knowing their three-dimensional geometrical properties is helpful to fully understand their
optical effects. Therefore, these are already taken into account in the industry in some instances, e.g. to
increase the performance of products and the accuracy of measurements.
The aim of this document is to deliver background information on this topic, to provide helpful terminology
including parameters, and to present some ways of dealing with their impacts. It is intended as a source of
information to the manufacturers of spectacle lenses, measurement systems, and mounting equipment as
well as to the optometric and dispensing professions.

v
Technical Report ISO/TR 11826:2024(en)
Ophthalmic optics — Spectacle lenses — Aspects of three-
dimensional properties and reference markings
1 Scope
This document is applicable to the three-dimensional aspects of spectacle lenses and their mounting in
frames. It gives possible details of how these aspects can be taken into account, particularly for lenses with
their permanent reference engravings (markings) on their back surface.
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 13666, Ophthalmic optics — Spectacle lenses — Vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 13666 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Technical background
4.1 General
Changes in the method of manufacture of spectacle lenses and in the styling of some spectacle frames have
th
generated problems of positioning lenses correctly in the frame that did not occur in the 20 century.
Conversely, free form manufacture allows the benefits of individualized computer enhancement and more
sophisticated lens designs but requires an improved, and available, ability to position lenses.
[1]
Many aspects related to the use of free form technology are explained in ISO/TR 18476 , which also covers
optical effects relevant to the topics discussed in this document.
4.2 Spectacle lenses
The reference points and design reference points are specified in ISO 13666 to be on the front surface of the
lens. This is logical, in that the marking device on focimeters dots the front surface of the lens, in particular
the optical centre for single-vision lenses. This dot is used for positioning the uncut lens correctly for edging it
to shape for mounting in the frame. Although errors in prism imbalance (relative prism error) are generated
if lenses are not correctly centred in the frame in front of the eyes, there is no or little effect on the binocular
field of view for single-vision lenses or for the far and near fields of view with multifocal lenses. Position-
specific single-vision lenses and power-variation lenses have, however, to be positioned so that their optical
properties including, where applicable, the (intermediate) corridor and near portion are aligned with the
eyes. The conventional construction of progressive-power and degressive-power lenses was to use a blank
with the power-variation surface moulded (or sagged for glass blanks) on the front surface of the blank, then

surfacing the prescription onto the back surface. The two permanent alignment reference markings were
positioned on the complicated surface, and thus automatically on the front, and were used to generate the
reference point for mounting the lenses.
The ability to combine the prescription and complicated surface of power-variation lenses on the back
[1]
surface and generate this using free form technology – see ISO/TR 18476 – means that the permanent
alignment reference markings are now usually positioned on the back surface of the lens. These markings
are, however, viewed through the front surface when positioning the uncut lens for mounting in the frame.
Prism incorporated in the lens, whether prism thinning or prism required by the lens order, displaces the
apparent position of these markings and hence the midpoint between them, while the convex front surface
will magnify their separation. Position-specific single-vision lenses also have complicated back surfaces
generated with free form technology, and are likely therefore also to be marked on the back surface.
In many respects, it is more logical to have the reference points on the back surface of the lens, since it is rays
leaving the back surface that enter the eye, but this change requires an enormous change to the methods of
working in the lens mounting industry, including non-permanent lens inking and edging block positioning
presently on the front. Moreover, nose pads and spectacle sides are likely to be in the way when measuring
the positioning of mounted lenses. Changing to using the back surface for reference points for lenses is
therefore a “non-starter”.
4.3 Spectacle frames
Until the early 2000's, spectacle frames had fronts which were relatively flat so that the two lenses lay in
the same plane, or nearly so. Since then, a minority of frames have been designed with a significant face
[2]
form or wrap angle (see ISO 8624 ). This can have an effect on the decentration needed – the geometrical
relationship between various distances is given in the notes to entry for the term “centration point” in
ISO 13666.
Key
α as-worn face form angle
d displacement
t centre thickness
c
Figure 1 — Displacement caused by the face form angle and lens thickness
An additional point for lenses in frames with significant face form angle is the thickness of the lens. The
front surface can lie in front of the plane of the lens shape or of the dummy/demonstration lens by an amount
depending upon the centre thickness of the lens and the position of the peak of the bevel relative to the edge
of the lens. This results in a nasal displacement between the centration point on the front surface and the

intersection of the normal to the front surface at this point with the back surface. As shown in Figure 1, this
displacement, d, can be calculated by Formula (1):
d = t tan α (1)
c
e.g. 0,67 mm for a lens 2,5 mm thick or thicker than the dummy lens for a face form angle of 15°.
The as-worn pantoscopic angle can have a similar effect on vertical centration, but at least the errors are in
the same direction in both lenses rather than additive with base in or base out for the face form angle. If the
vertical component of the centration point position is measured in the plane of the lens shape, no errors are
expected to occur, but if it is measured projected onto a vertical plane, e.g. by a digital dispensing system
that does not take account of the as-worn pantoscopic angle, then errors could occur. If the height measured
in the vertical plane is y and the as-worn pantoscopic angle is θ, then the height y' in the plane of the lens
shape as shown in Figure 2 is given by Formula (2):
y’ = y/cos θ (2)
Taking an example of an as-worn pantoscopic angle of 10° and a centration point height of 20 mm from the
tangent to the bottom rim, the required measurement in the plane of the lens shape is only about 0,31 mm
larger than the apparent measurement in the vertical plane, but for a pantoscopic angle of 15°, it is 0,71 mm.
At the centre of rotation of the eye, about 27 mm behind the lens, these distances correspond to just over
1,0 Δ and 2,5 Δ respectively. The wearer can compensate for such a small induced prismatic effect by an
upwards or downwards gaze movement.
Key
y apparent height measured in a vertical plane
y' height measured in the plane of the lens shape
θ as-worn pantoscopic angle
Figure 2 — Potential error in fitting height with the as-worn pantoscopic angle
5 Influence of three-dimensional effects and necessity to deal with them
5.1 Optical effects
Optical aberrations in conventional spectacle dispensing can be minimised by decentring the optical centre
of the lens horizontally and vertically in the spectacle frame so that the optical axis of the lens passes
approximately through the eye's centre of rotation, the "centre of rotation condition". With a relatively flat
fronted spectacle frame (see 4.3), matching the centration distance to the wearer's monocular centration

values is sufficient to achieve the horizontal requirement. In the vertical direction, the optical centre is
usually positioned below the pupil centre position, i.e. the visual point, V, when the wearer's eyes are looking
in the primary direction, (Key 1 in Figure 3), i.e. the eyes are in their primary position. This is because, as
[3]
pointed out by Jalie , most frames are designed to have the plane of the spectacle lens (‘plane of the lens
shape’) approximately parallel to the plane joining the supra-orbital ridge to the chin, giving an as-worn
pantoscopic angle of 5° to 15°. This centre of rotation condition is satisfied if the optical centre is displaced
downwards by 1 mm for each positive 2° of as-worn pantoscopic angle - the "dispenser's rule". In most cases,
the frame manufacturer's choice of vertical boxed lens size, bridge dimensions (including bridge height)
and angle of side (or ‘frame pantoscopic angle’) means that the horizontal centreline of the frame is usually
4 mm to 5 mm below the pupil centre so that very little vertical decentration from the horizontal centre line
is often needed. See Figure 3 a), which illustrates the back surface of the spectacle lens and the eye.
a) Conventional dispensing
b) Dispensing of a steeper base curve lens with high as-worn pantoscopic angle
Key
1 primary direction
O optical centre of the lens
V visual point in the primary position
Z centre of rotation of the eye
C centre of rotation of the back surface of the lens
ϕ angle of obliquity on leaving the lens when viewing in the same direction as in the upper diagram
Note that the centre of rotation rule is satisfied in a) but not in b).
Figure 3 — Conventional and sports-vision dispensing
Satisfying the centre of rotation condition means that when the eye rotates away from the optical axis of
the lens, relatively simple spherical surfaces can give good optical performance in the periphery when using
one of the various types of “best form” lens, for example, the choice of minimising the oblique astigmatism

1) 1)
error or the mean oblique error . Figure 5 a) shows that the angles of refraction ϕ and ϕ at angles of gaze
a b
25° above and below the optical centre are equal.
Frames with deeper lens shapes and probably smaller angles of side to avoid the lower rim resting on the
cheeks and, conversely, frames, often for sports-vision, with larger angles of side giving larger as-worn
pantoscopic angles and probably with significant face form angles are likely to make it difficult to apply
the dispensing rule mentioned above without creating excess lens thickness at the upper or lower rim.
Figure 3 b) shows the situation of a steeper-than-normal base curve for the lens combined with a high
as-worn pantoscopic angle so that the optical axis of the lens does not pass through the eye's centre of
rotation. Even when viewing through the optical centre of the lens, positioned in the same relative place
as in the Figure 3 a), the oblique ray path induces oblique astigmatism. An approximate expression for this
[4]
astigmatism, A, is given by Jalie in Formula (3):
AF≈⋅tan φ (3)
s
where:
ϕ is the angle of obliquity, and n is the refractive index;
F is the sagittal power of the lens, given by
s
 
2n+sin φ
F ≈ F (4)
 
s
 
2n
 
and F in Formula (4) is the power of the lens.
This oblique astigmatism compounds with any cylindrical correction required in the lens. The obliquity also
produces the very small change in the spherical component of the lens power from F to F . For example, for a
s
+5,00 D sphere lens in 1,6 index material tilted through 12°, F = +5,068 D and A = 0,23 D.
s
Provided the lens manufacturer is supplied with the dispensing data (centration point and visual point
positions for single-vision lenses and just the centration point position for power-variation lenses vertically
and horizontally relative to the frame, vertex distance, as-worn pantoscopic and face form angles), the lens
manufacturer can calculate the compensated power of the lens at the optical centre or design reference
point that gives the wearer the ordered power when viewing through the lens. To take care of any potential
difference between the power experienced by the wearer and the power displayed by a focimeter (see
[1]
ISO/TR 18476 and ISO 13666:2019, 3.10.15, Note 2 to entry, for details) the manufacturer can provide the
value of the power (termed “verification power” in ISO 13666) that is expected to be found as the measured
[7] [8] [9]
power when verifying the lens on a focimeter according to ISO 21987 , ISO 8980-1 and ISO 8980-2 .
Figure 4 gives an idea of the relationship between the various powers mentioned.
[5]
1)  BS 3521-1 defines this as the difference between the tangential and sagittal oblique vertex sphere powers, the
latter being subtracted algebraically from the former.

a
In some countries, the person dispensing the spectacles is permitted to refine the prescribed power.
b
As-worn position and other applicable parameters such as the chosen working distance and physiological factors.
Figure 4 — Relationship between the various powers
[SOURCE: ISO 13666:2019, Figure 8]
Conversely, in Figure 5 b), the distance between the eye and back surface of the lens and the angle of
refraction of rays leaving the lens varies asymmetrically above compared with below the optical centre. The
[6]
same effect applies in the horizontal where there is significant face form angle. As pointed out by Jalie , this
compensation, if applied to a standard best form single-vision lens, is correct for only the distance design
reference point of the lens (in the case of a lens designed for distance vision), not the periphery. Compensation
for both the distance design reference point and for the varying angles on incidence in the periphery of
the lens can be carried out using modern computing methods and free form lens manufacture. As always
with free form technology, the effect of the optimization varies widely with the level of sophistication of the
2)
algorithm used . Since tolerances on lens powers apply only at the reference points, no verification powers
or methods for the periphery are specified in the international standards.
2)  While a simple toric superimposition does not achieve much more than can be done with conventional tooling,
an algorithm providing sophisticated pointwise optimization allows for eliminating power errors due to the as-worn
orientation of the lens even in the far periphery. However, there is a growing trade-off between eliminating power errors
and generating other unwanted optical effects like image distortion when moving away from the design reference point.
This is especially noticeable in binocular assessment of large lenses with high as-worn face form angles. (For a detailed
[11]
assessment, see Becken et al. ).

a) Conventional dispensing
b) Dispensing of a steeper base curve lens with high as-worn pantoscopic angle
Key
1 primary direction
O optical centre of the lens
V visual point in the primary position
Z centre of rotation of the eye
C centre of rotation of the back surface of the lens
ϕ angle of obliquity on leaving the lens when viewing in the same direction as in the upper diagram
ϕ , ϕ angle of refraction on leaving the lens when viewing 25° above and below O
a b
Note that the centre of rotation rule is satisfied in a) but not in b).
Figure 5 — Conventional and sports-vision dispensing
5.2 Reference points on front surface versus back surface meeting the eye in as-worn
position
[7] [8] [9]
The standards ISO 21987 , ISO 8980-1 and ISO 8980-2 stipulate that position-specific single-vision
lenses and power-variation lenses such as progressive-power lenses have permanent alignment reference
markings comprising two marks located nominally 34 mm apart, equidistant to a vertical plane that passes
through the fitting point or prism reference point and contains the normal (perpendicular) to the surface at
that point.
When the markings are engraved on the front surface (see Figure 6 a)), the determination of the location of
the different reference points can be done with a fair precision as all these points are defined with respect to
the front surface according to ISO 13666. The positioning of the lens with respect to the eye's pupil centre in
the as-worn condition is done taking into account the prismatic deviation induced by the lens as illustrated
with the horizontal ray passing through the pupil centre of eye and deviated by the lens. In Figure 6 a), we

consider that O corresponds to the fitting point. When the markings are engraved on the back surface
F
(Figure 6 b)) of the lens, no information is usually provided on how to transfer their position to the front
surface's coordinate reference system in order to determine the location of the reference points. This can
however influence the fitting of the lens into the frame or the position of the reference points at which the
lens is verified.
Indeed, when the markings are engraved on the back surface and one looks at their images produced by the
lens's front surface, one can notice that their location changes with the viewing direction. If the lens is, for
instance, in a frame with a significant face form angle, the apparent position of the images of the markings
on the front surface can be inaccurate with respect to their theoretical position, which then can lead to a
shift of all reference points.
a)  Markings on front surface b)  Markings on back surface
Key
E and E markings positioned on the front surface (±17 mm apart from its centre O )
1F 2F F
O origin of front surface, midpoint between E and E
F 1F 2F
E and E markings positioned on the back surface (±17 mm apart from its centre O )
1B 2B B
O origin of back surface, midpoint between E and E
B 1B 2B
O’ theoretical centre on the front surface when information is provided on how to pass O from the back
F B
surface’s coordinate system into the front surface's one
Figure 6 — Illustration of markings engraved on the front and the back surface, as viewed from above
This is illustrated in Figure 7 for a +4 D lens with a prism thinning of 2 Δ at 270°. The grey dots represent the
markings E and E engraved on the lens's back surface. The black dots are the apparent positions on the
1B 2B
front surface of the images of the engravings when viewed with an angle of about 27° from the normal to the
front surface at O’ and with an azimuth of 135°. The black cross represents the midpoint between the black
F
dots projected onto the lens's front surface. Finally, the rectangular boxes show the nominal locations of the
markings E and E if they had been put on the front surface and the white cross shows the nominal centre
1F 2F
O’ on the lens's front surface. As can be observed, the two crosses do not match. The front surface position
F
obtained from the image of the markings does not match the nominal one.

Key
front reference marks (E and E )
1F 2F
images of back surface marks
back surface marks (E and E )
1B 2B
nominal centre on the lens's front surface (O’ )
F
midpoint between the black dots projected onto the lens's front surface
Figure 7 — Apparent displacement of back surface marks when viewed through the lens
Another issue can arise if the lens has semi-permanent (removable) ink markings on its front surface that
are not in line or centred with respect to the image of the back surface markings through the lens: is the lens
to be fitted with respect to the semi-permanent ink markings or the image of the markin
...