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i
OPTICAL METROLOGY OF LENSES IMMERSED IN WATER
A FOURTH YEAR THESIS IN Physics
In partial fulfilment of the requirements for the degree
BACHELOR OF SCIENCE
ii
Abstract An experiment was conducted with the aim of completely characterising the optical and physical properties of an intraocular lens (IOL). A theoretical software model of the IOL would then be used to verify the experimental metrology.
A FISBA OPTIK μPhase® HR interferometer was used to characterise a 21.5D IOL of the type Bausch & Lomb Akreos™ Adapt AO. The optical properties were measured as wave aberration in double transmission through the IOL; physical properties were measured as anterior-posterior surface radii of curvature and deviation from a perfect sphere, apparent apical thickness and back focal length. The hydrophilic nature of this particular IOL material necessitated measurement of the IOL submerged in liquid. The success of a previously performed experiment within the group was built upon, whereby the design and development of a new experimental apparatus allowed measurement of total wave aberration in transmission through the IOL. Accordingly, a high-quality mirror was submerged in the liquid.
Some problems encountered in measurement at autocollimation required measurement of a dry Pharmacia 17D IOL in air. ‘Dry’ IOLs are packaged in a dry atmosphere, thus they are well-suited to measurement in air. Measurement in air was assessed as perfectly adequate; however, measurement in balanced salt solution (BSS) would more closely represent the in situ environment.
The anterior and posterior surface deviations and radii of curvature were used together with the apical thickness to create a lens model in Zemax ray-tracing software. The software was then used to confirm experimentally determined values of total IOL transmission wavefront error. The modelled and experimental values of root mean square error differed by just 2.5%.
Further refinement of the experimental method and software model would allow transformation of this qualitative proof-of-concept model into an accurate quantitative analysis. With consequent reduction and/ or removal of variables, it would be possible to determine the source of discrepancy between experiment and theory. Complete control of all variables would in fact allow for attribution of any discrepancies to internal lens material inhomogeneities.
iii
List of Figures Figure 1.1. IOL Variations. .................................................................................................... 1
Figure 1.2. Schematic diagram of a cataracteous crystalline lens. ........................................ 2
Figure 2.1. 3D render of Zernike polynomials two to eleven. ................................................. 4
Figure 2.2. Schematic diagram of the relative measurement positions. ................................. 5
Figure 2.3. Schematic diagram of the confocal position. ....................................................... 5
Figure 3.1. Photograph of the Interferometer. ....................................................................... 8
Figure 4.1. Photograph of the initial IOL stage. ................................................................... 10
Figure 4.2. Photograph of the prototype Meccano stage and liquid bath. ............................ 11
Figure 4.3. Pharmacia (AMO) 17D IOL [8]. ......................................................................... 13
Figure 4.4. Photograph of the prototype Meccano ‘dry’ stage. ............................................. 14
Figure 4.5. 3D-rendered simulation of the experimental setup. ........................................... 17
Figure 4.6. 2D side-view of the Zemax double pass model. ................................................ 17
Figure 4.7. 2D side-view of the Zemax single pass model. .................................................. 18
Figure 5.1. Interferogram of the water meniscus. ................................................................ 19
Figure 5.2. Confocal interferogram of Bausch & Lomb 21D IOL in water............................. 20
Figure 5.3. Confocal interferogram of Pharmacia 17D IOL in air. ........................................ 21
Figure 5.4. Autocollimated interferogram of Pharmacia 17D IOL anterior surface in air. ...... 21
Figure 5.5. Autocollimated interferogram of Pharmacia 17D IOL posterior surface in air. .... 22
Figure 5.6. Comparison of modelled and experimental anterior 17D IOL surface. ............... 23
Figure 5.7. Comparison of modelled and experimental posterior 17D IOL surface. ............. 23
Figure 5.8. Comparison of modelled and experimental 17D IOL wave aberration. .............. 23
Figure 5.9. Final Zemax user-interface showing lens editor fields. ...................................... 24
Figure 5.10. Final Zemax user-interface showing total wave aberration and 2D layout. ...... 24
Figure 6.1. Examples of the lensing effect of the water meniscus. ...................................... 27
iv
Contents
Abstract................................................................................................................................... ii
List of Figures......................................................................................................................... iii
1. Introduction .................................................................................................................... 1
1.1 Intraocular Lens ...................................................................................................... 1
1.2 Cataract Surgery ..................................................................................................... 1
1.3 Project Aims............................................................................................................ 2
2. Background .................................................................................................................... 3
2.1 Aberration Theory ................................................................................................... 3
2.2 Interferometry ......................................................................................................... 3
2.3 Phase-Shifting Interferometry ................................................................................. 3
2.4 Zernike Polynomials ................................................................................................ 4
2.5 The ‘Cat’s Eye’ Position .......................................................................................... 4
2.6 The Autocollimated Position .................................................................................... 5
2.7 The Confocal Position ............................................................................................. 5
2.8 Characterising the IOL ............................................................................................ 6
2.9 IOL Selection and Metrology Criteria ...................................................................... 6
3. Instrumentation .............................................................................................................. 8
3.1 The Twyman-Green Interferometer ......................................................................... 8
3.2 Zemax Ray-Tracing Software ................................................................................. 9
3.3 Meccano ................................................................................................................. 9
4. Techniques .................................................................................................................. 10
4.1 Design and Construction of the IOL Stage ............................................................ 10
4.2 Calibration of the Interferometer ............................................................................ 11
4.3 Characterisation of the Retro-Reflective Return Mirror .......................................... 12
4.4 Characterisation of the Water Meniscus Lensing Effect ........................................ 12
4.5 Metrology of Bausch & Lomb 21.5D IOL in Water ................................................. 12
4.6 Metrology of Pharmacia (AMO) 17D IOL in Air ...................................................... 13
4.7 Zemax Ray-Tracing Analysis ................................................................................ 15
5. Results ......................................................................................................................... 19
5.1 Characterisation of the Retro-Reflective Return Mirror .......................................... 19
5.2 Characterisation of the Water Meniscus Lensing Effect ........................................ 19
5.3 Metrology of Bausch & Lomb 21.5D IOL in Water ................................................. 19
5.4 Metrology of Pharmacia (AMO) 17D IOL in Air ...................................................... 20
5.5 Zemax Ray-Tracing Analysis ................................................................................ 22
6. Discussion. .................................................................................................................. 25
v
6.1 Design and Construction of the IOL Stage ............................................................ 25
6.2 Characterisation of the Retro-Reflective Return Mirror .......................................... 25
6.3 Characterisation of the Water Meniscus Lensing Effect ........................................ 25
6.4 Metrology of Bausch & Lomb 21.5D IOL in Water ................................................. 26
6.5 Metrology of Pharmacia (AMO) 17D IOL in Air ...................................................... 27
6.6 Zemax Ray-Tracing Analysis ................................................................................ 28
7. Conclusion ................................................................................................................... 30
8. Acknowledgements ...................................................................................................... 31
9. References .................................................................................................................. 31
1
1. Introduction
1.1 Intraocular Lens
This project was specifically concerned with the optical metrology of intraocular lenses
(IOLs) immersed in water. IOLs are small plastic lenses of typically 6mm diameter and less
than 1mm thick. Two particular IOL models are shown in Figure 1.1 below. The central
region is called the optic, whereas the odd-shaped features extending from the optic are
called the haptics. The haptics’ shape, size and angulation can vary largely, depending on
the manufacturer. IOLs are usually implanted in the eye to replace the existing crystalline
lens because it has been clouded over by a cataract, or as a form of refractive surgery to
change the eye's optical power.
Figure 1.1. IOL Variations.
Bausch & Lomb Akreos Adapt AO Aspheric IOL (a) and
Bausch & Lomb Akroes M160 IOL (b) [1].
1.2 Cataract Surgery
Cataract surgery is one of the world’s most successful procedures, with approximately 20
million carried out globally and 20,000 carried out in Ireland each year [2]. Due to the ageing
society, there are currently 5 million new cataract patients annually, worldwide.
The surgery typically involves the replacement of the aged, cataracteous, partially
opaque crystalline lens (see Figure 1.2 below) with an artificial intraocular lens (IOL) [3].
When the crystalline lens is removed, the eye is said to be aphakic; with subsequent
implantation of the IOL, the eye is said to be pseudophakic. The procedure dramatically
reduces internal light scattering and provides for unobstructed retinal image formation [4].
(a) (b)
2
Figure 1.2. Schematic diagram of a cataracteous crystalline lens.
IOL power calculation is currently based on regression analysis and has effective outcomes
for people with ‘normal eyes’. ‘Unusual eyes’ are those which are unusually long or short or
belong to those patients who have previously had refractive eye surgery. For unusual eyes,
the IOL selection method is ineffective in 80% of cases, where post-operative vision is
characterised by blurriness and lack of contrast and where satisfactory vision necessitates
the use of spectacles. Post-operative retinal image quality is not solely based on correct IOL
power calculation; it is also based heavily on the true post-operative position of the IOL and
its optical aberrations.
1.3 Project Aims
The main aim of the project was to completely determine the optical and physical
characteristics of a particular IOL and subsequently fully characterise their effect on
pseudophakic retinal image quality. The anterior and posterior IOL surfaces, together with
the apical thickness, could be modelled in Zemax ray-tracing software. The software could
then be used to determine the IOL’s imaging properties using this simple lens model.
However, as already stated, this method only gives a measure of the total wave aberration
attributable to individual surface imperfection and does not take into account any aberrations
introduced due to IOL material inhomogeneity. Therefore, to completely determine the
pseudophakic retinal image quality, it is necessary to experimentally measure the total wave
aberration in transmission through the IOL, with subsequent confirmation using the Zemax
ray-traced model. Any discrepancies between the two data sets can then be assigned to
inhomogeneities in the lens material.
3
2. Background
2.1 Aberration Theory
The properties of an optical system can be determined through the examination of wave
aberration introduced in single (or double) transmission through the system. For a single
optical element (e.g. a lens), this method only gives information about the optical
imperfections of the system as a whole, however, and does not portray any information
about the individual surfaces of the lens. Furthermore, it is impossible to determine whether
certain aberrations are due to surface imperfection or internal inhomogeneity. In order to
completely characterise the lens, it is necessary to measure not only both lens surfaces and
total wave aberration in transmission through the lens, but also the apical lens thickness.
The entire lens and consequent image degradation can then be modelled using ray-tracing
software.
The optical properties of a lens can be measured using an interferometer. The
associated software computes the lens imperfections and generates a set of Zernike
polynomials, which can be subsequently used to describe the lens properties in ray-tracing
software.
2.2 Interferometry
For many years interferometry has been an invaluable tool for the measurement of optical
surfaces and systems. Its capability was greatly extended with the advent of highly
monochromatic and coherent laser light. It was enhanced yet further with the development of
advanced numerical analysis techniques made possible by the power of computers in the
1990s. As a measurement technique it is extremely sensitive and can easily resolve
distances that are just a fraction of the wavelength of light. The measured parameter in
interferometry is usually the wavefront distortion, with interferometers measuring precisely
how an ideal wavefront is modified when it is reflected from a surface or transmitted through
an optical window or lens assembly.
2.3 Phase-Shifting Interferometry
The phase-shifting interferometric technique has an important advantage over static fringe
analysis whereby seemingly identical concave and convex surface maps can be deciphered.
The technique usually involves moving the reference surface, which is perpendicular to the
optical axis, by half a wavelength along the axis. This movement is effected by a piezo-
electric device and is usually separated into four or five steps, with measurements taken at
each step. The five step method has an advantage over the four step method whereby the
first and fifth measurements should be identical; thus the method is self-checking. The data
can then be ‘phase-unwrapped’ and the wavefront characterised to a very high degree of
accuracy.
If φ is the phase of the wave in radians, where:
,
4
then φ1 – φ2 = Δφ is the phase difference between the test and reference beams
and if OPD is the optical path difference between two beams, then:
Δφ
[5]
2.4 Zernike Polynomials
Zernike polynomials are a compact set of polynomials which are often used to describe the
aberrations of optical assemblies. The wave aberration of a given wavefront is described as
its deviation from a perfect wavefront of the same type. The aberration is then decomposed
into a finite number of Zernike polynomials so that the total root mean square (RMS)
wavefront aberration is minimised.
Zernike polynomials form a complete set in two variables that are orthogonal in a
continuous fashion over the unit circle, thus necessitating normalisation of pupil co-
ordinates. They are orthogonal only in a continuous fashion and will not, in general, be
orthogonal over a discrete set of data points [6-7]. Several common definitions exist for
Zernike polynomials, so caution must be exercised when comparing coefficients. For
example, the notation adopted in the FISBA µShape® software differs from that in the
Zemax ray-tracing software; see Section 4.7.
Figure 2.1 below is a 3D mesh-type render of Zernike polynomials two to eleven.
Figure 2.1. 3D render of Zernike polynomials two to eleven.
2.5 The ‘Cat’s Eye’ Position
If a surface is placed directly at the focus position of a convex lens, then an interference
pattern is observed, and this is referred to as a ‘cat’s eye’ reflection. The interferogram
obtained is generally unhelpful in terms of surface evaluation, as one of the characteristics of
the cat’s eye position is wavefront inversion i.e. the light rays are not retro-reflected. The
cat’s eye is, however, very useful for measuring the radius of curvature, vertex length, and
apparent thickness of an optical system.
5
2.6 The Autocollimated Position
The autocollimated position occurs where light from a focussing lens is normally incident on
a test surface, so that the beam is retro-reflected, with imperfections of the test surface
showing up as abnormalities in the interferogram. At this position, the focal point of the
focussing lens is coincident with the centre of curvature of the test surface, and is therefore
useful for measuring radius of curvature.
Figure 2.2. Schematic diagram of the relative measurement positions.
Top cat’s eye (Green)
Bottom cat’s eye (Blue)
Autocollimation (Red).
Note: The diagram is not to scale.
2.7 The Confocal Position
The focussing lens of the interferometer is positioned so that light enters through the focus
position of a convex test piece and emerges collimated (to be retro-reflected by a return flat).
The retro-reflected light then propagates back through the test piece and in this way,
information about the double pass aberration of the piece can be obtained. In this
arrangement, the focus positions of both the interferometer focussing lens and the test piece
are coincident.
Figure 2.3. Schematic diagram of the confocal position.
Note: The diagram is not to scale.
6
2.8 Characterising the IOL
There are many ways of characterising optical surfaces and systems. The particular setups
used in this experiment allowed the determination of:
1. Radius of Curvature. The radius of curvature was measured as the displacement
between the cat’s eye reflection from the top surface of the IOL and the
autocollimated position.
2. Apparent Central Thickness1. The apparent thickness was measured as the
displacement between the cat’s eye reflections from the top and bottom surfaces of
the IOL respectively.
3. Back Focal Length. The back focal length was measured as the displacement
between the cat’s eye reflection from the top surface of the IOL and the confocal
position. Information about the back focal length can be used to calculate the
refractive index of a lens material.
4. Double Pass Wave Aberration. Information about the double-pass wave aberration of
the IOL was obtained from double-pass measurements in the confocal arrangement.
5. Surface Deviation in Single reflection at Normal Incidence. Pits/hollows in the IOL
surface will cause any light incident there to be phase delayed, with bumps/hills
causing phase advancement. In this way, surface abnormalities show up as visible
fringes in the interferogram, with each fringe representing an area of equal phase.
The phase-shifting software can be used to process the resulting interferogram and
calculate the corresponding Zernike coefficients.
2.9 IOL Selection and Metrology Criteria
A dioptric series of Bausch and Lomb Akreos Adapt AO IOLs were received prior to
experimentation. It was decided to measure the 21.5D Bausch & Lomb IOL, which, out of the
series of received IOLs, best matched the most commonly implanted IOL power of 21D
[2].The particular type of IOL material was a hydrophilic acrylic copolymer, with the IOLs
packaged in liquid. A model of the IOL is shown in Figure 1.1 (a); the haptic features are
seen on the top right and bottom left and serve to indicate that the anterior lens surface is
facing forwards.
A recent experiment performed by the author, in collaboration with Matt Sheehan,
indicated that measuring this IOL material in air was highly problematic. The thin layer of
liquid that covered the IOLs after removal from their containment was unsurprisingly found to
dry out. However, this drying out of the liquid caused any interferograms to fluctuate wildly
due to the induced constantly-changing aberrations. Thus problems similar to, for example,
the drying of the tear film in retinal imaging were encountered. Without the use of a
sophisticated adaptive optic system, the method of hydrophilic IOL measurement in air was
deemed impossible. Furthermore, there was some ambiguity as to whether the IOL’s
physical characteristics changed through drying out in air. Consequently, it was decided to
measure the IOL submerged in liquid.
The measurement of an IOL is a difficult task. The lens itself is small and fragile and
requires delicate manipulation using a tweezers or other sensitive instrument. Care must be
taken to ensure that at no point is the optic region touched with anything but the cleanest
and smoothest of devices, lest any damage be caused there. It is not simply sufficient to
1 Note that due to refraction at the air/ IOL interface, it was necessary to model the system in
ZEMAX® to calculate the real thickness of the IOL.
7
place the IOL on an optical bench, since that would damage or dirty the optic region.
Furthermore, the haptics which extend from the optic would be weighted downwards,
causing strain on the (often flexible) optic and incorrectly introducing artefacts there.
Therefore, it is necessary to place the IOL on a stage which not only allows light to pass
unobstructed through the IOL, but also provides adequate haptic and optic support.
When measuring an IOL, particular care must be taken to ensure that the rotation of
the IOL about its optical axis is kept constant, or at least well-defined, for all measurements.
If it was not, then the surfaces would be measured as being incorrectly rotated relative to
each other. For example, when measuring the anterior and posterior IOL surfaces, the IOL
must be flipped about a particular known axis; otherwise the measured surfaces will give
incorrect total wavefront aberration when modelled in software.
The aforementioned recent experiment was carried out to determine the
characteristics of the Bausch & Lomb IOL series. However, the particular experimental
technique adopted allowed only determination of the anterior & posterior surface deviations,
radii of curvature and back focal lengths; and apical thickness. It was deemed too difficult,
too time-consuming, or too complicated to measure the wave aberration in double
transmission through the IOL. Improvement upon the success of this previous experiment
therefore necessitated the design and development of a new apparatus and experimental
technique which would allow effective measurement of wave aberration in double pass
through the IOL.
8
3. Instrumentation
3.1 The Twyman-Green Interferometer
All measurements of IOL properties were performed using a FISBA Optik µPhase® HR
Twyman-Green Interferometer. It allows implementation of the phase-shifting interferometric
method owing to the inclusion of a piezo-electric actuator contained within the device. It
operates using a frequency-stabilised He-Ne auxiliary laser ( =632.8nm). The interferometer
was mounted vertically on a µPhase® ophthalmic platform. Vertical translation of the
interferometer was accurately performed using the in-built micrometer with smallest ruled
division of 0.01mm. A photo of the apparatus is shown in Figure 3.1 below.
The interferometer was accompanied by µShape® interferometry software. The
software facilitates calibration of the system and measurement of surface deviation in single
reflection at normal incidence and wave aberration in double transmission, amongst others.
The phase-shifting technique is utilised in deciphering interferograms, with the resultant
wave aberration displayed as measurement maps on the user interface. The software can
then be used to resolve the maps into a user-specified number of Zernike coefficients for
subsequent export.
Figure 3.1. Photograph of the Interferometer.
The interferometer is a two-beam system, whereby an expanded and collimated
beam of the highly monochromatic He-Ne laser light is incident on a beam splitter, where
equal beam intensities are reflected and transmitted. One of these beams is referred to as
the reference beam and is created by reflection from an extremely accurate reference
surface. The second beam is reflected from the test surface, and is referred to as the object
beam. The two beams are then made to interfere, with the resulting interferogram on the
CCD camera displayed as a live image intensity distribution on the software interface.
The interferometer functionality can be extended through the use of spherical
objectives. A µLens EF 15/43 spherical objective, together with a µLens DCI 2 10/∞ beam
Interferometer
Coarse
Adjust
Screw
Micrometer
µPhase®
Ophthalmic
Mount
Tip/Tilt Table
Objective
9
expander were employed in this experiment. The notation for lens specifications is µLens
[Model] [Diameter/Focal_length]. Thus, the employed objective had an f-number of f/2.9.
3.2 Zemax Ray-Tracing Software
Zemax is a comprehensive ray-tracing software package which allows the design,
optimisation and characterisation of optical systems and lens assemblies. It has a user-
friendly and intuitive interface allowing easy description and modification of optical element
parameters. It is a powerful tool for the analysis and visualisation of system performance
such as spot diagrams and ray-fan plots and boasts a comprehensive suite of in-built
optimisation tools for the optimal design of a particular optical arrangement.
In this experiment, the measured IOL surface deviations, radii of curvature and apical
thickness could be inserted into Zemax, with the software used to calculate the resultant
total wave aberration. This theoretical result could then be compared to the experimentally
determined value of double pass aberration.
3.3 Meccano
Meccano is a robust construction system comprising re-usable metal components, with nuts
and bolts to connect the pieces. It enables the construction and implementation of simple
working models and mechanical devices. The combination of its relatively low cost and large
range of components makes it ideal for constructing almost any conceivable structure.
Meccano was highly suitable for this project since it required custom-built structures over a
short period of time. It would have been impractical to wait for the manufacture of such
structures in the department workshop.
10
4. Techniques
4.1 Design and Construction of the IOL Stage2
As already stated, the design and development of a new apparatus and experimental
technique was necessary to improve upon the success of previous experiments. The
particular difficulty which previously hindered the measurement of double pass wave
aberration was the availability of an apparatus which allowed independent tip/tilt and
translation of both the high-quality retro-reflective mirror and the IOL itself. Consequently, a
considerable amount of time was spent in designing and constructing an IOL stage which
not only provided adequate IOL support, but also provided for relative tilt of the IOL and
return mirror. Note that measurement of the submerged IOL also necessitated submersion of
the IOL platform and the high-quality return mirror in a liquid bath.
Initially, an IOL stage was successfully constructed using Linos optical bench
components, shown in Figure 4.1 below. Although optical bench components are
manufactured to exacting dimensions, they are relatively expensive and typically only a few
components will be readily available in the laboratory environment. Due to the lack of
multifarious components, the apparatus design was not ideal. In particular, the small rod
suspending the IOL platform entered the water quite close to the IOL itself, resulting in large
curvature of the water meniscus due to larger surface tension at that point; see Figure 4.1.
Figure 4.1. Photograph of the initial IOL stage.
The outer ‘legs’ would surround the liquid
bath, with the IOL and supporting platform submerged in the liquid.
It became increasingly clear that high-quality components were not necessary, and
that a large variety of components was highly desirable. Accordingly, it was decided to
create a new prototype stage using Meccano. A suitable stage was constructed, with the
Meccano components offering a much wider range of customisation possibilities. A photo of
the stage is shown in Figure 4.2 below. The IOL stage rested on the µPhase® ophthalmic
table, enabling tip, tilt and horizontal translation of the IOL.
2 The ‘stage’ is defined here and throughout as the entire structure used to hold the IOL, whereas the ‘platform’ is that
particular part of the stage which the IOL actually rested on.
IOL Platform
11
Figure 4.2. Photograph of the prototype Meccano stage and liquid bath.
The outer ‘legs’ can be seen to surround the bath, with the IOL platform and
mirror submerged in the bath. Note that the IOL platform was covered
with black tape to avoid any unwanted reflections there from.
As can be seen from the photo, the water bath with submerged mirror was also placed
on its own tip & tilt platform. The construction of this bath platform was vital to the success of
the experiment, since it allowed essential alignment of the mirror with the interferometer.
This therefore ensured that any collimated light emerging from the aligned IOL would re-
trace its path back to the interferometer. The bath platform was supported using Linos
cageplates and rods, with the delicate tip & tilt control achieved using three upward-facing
potentiometer-type screws.
4.2 Calibration of the Interferometer
Calibration of the interferometer was necessary in order to remove aberrations inherent in its
optical assembly, thus ensuring that the measurements obtained related directly to the part
under test. When measurements were performed using collimated light, the system was
calibrated using a large plane FISBA calibration surface of 4% reflectivity and surface
flatness of greater than /20 ( =632.8nm). Calibration of the µLens EF 15/43 spherical
objective employed in the experiment required use of a spherical reference. A FISBA
spherical calibration surface with a radius of curvature of 10mm, surface accuracy of /20
( =632.8nm) and reflectivity of 4% was used for this purpose. At the confocal position, the
rays of light striking the surface at 90o were retro-reflected and a ‘null fringe condition’ was
obtained.
A virtual electronic ‘Calibration Mask’ was used in the µShape® software to mask out
any undesirable outer fringing due to diffraction effects, ghost images on the CCD camera
and indistinct aperture edges.
IOL Platform
Mirror
Liquid Bath
Bath
Tip/Tilt
Controls
12
4.3 Characterisation of the Retro-Reflective Return Mirror
It was desired to measure the optical properties of an IOL using a spherical objective. This
required calibration using the FISBA spherical calibration surface. However, at the confocal
position, the light is retro-reflected from the plane mirror and thus any imperfections in the
mirror would incorrectly show up as aberrations in the IOL. If the system has already been
calibrated for use with the spherical objective, then it can only be used with that objective
and cannot be used to account for imperfections in the mirror.
Consequently, it was necessary to characterise the mirror prior to any measurements
of wave aberration in double transmission through the IOL. The interferometer was fitted with
a diameter 10mm beam expander and was first calibrated using the large FISBA flat. The
mirror was then aligned with the collimated interferometer output and a measurement of the
mirror surface was taken sixteen times. The average mirror surface error could then be
added to the ‘error budget’ of the double-pass wave aberration measurements.
4.4 Characterisation of the Water Meniscus Lensing Effect
Due to the finite radius of the employed water bath, surface tension caused some curvature
of the water meniscus at the periphery. Note that this lensing effect occurs even for a
perfectly flat water surface and can be easily modelled in Zemax; however extra care must
be taken to measure and account for the meniscus curvature.
To reduce curvature of the water meniscus, a large diameter of approximately 9cm
was chosen for the water bath. It was decided to measure the meniscus curvature by simply
reflecting collimated light from the top surface of the water. The resultant interferogram could
then be studied with the Zernike defocus term indicating the amount of curvature. A large
amount of time was spent aligning the water surface with the interferometer. It was not
simply a case of tilting the water bath, since the bath simply ‘moved around’ the water, with
the water surface remaining flat according to gravity. It was thus a case of aligning the entire
interferometer mount with the (level) water. After much deliberation, a satisfactorily low
number of tilt fringes were observed in the interferogram and so a measurement of the water
surface was taken. It was found to take an unreasonably large amount of time to completely
remove all tilt fringes. Since the primary interest was in determining the curvature of the
water, it was decided to ignore any rotationally invariant terms obtained in the interferogram;
the tilt fringes were accordingly ignored.
4.5 Metrology of Bausch & Lomb 21.5D IOL in Water
Prior to any measurement/alignment, it was necessary to switch on the laser, after which a
20 minute period was required to facilitate stabilization of the laser output.
The IOL, IOL platform and mirror were submerged in water, as per Figure 4.2 above.
However, before placement and alignment of the IOL stage, it was necessary to align the
mirror with the interferometer. The spherical interferometer objective was removed, and the
mirror adjusted using the three bath platform screws to obtain a null fringe condition.
The IOL was handled by the haptics and centred over a hole of diameter approx
6.5mm in the IOL platform. The hole was slightly larger than the IOL optic body to eliminate
the possibility of damaging the optic through contact with the platform. The hole was also
small enough to ensure that the optic was adequately supported, and that the IOL was not
suspended purely by the outer regions of the haptics. This therefore reduced possible effects
13
of strain caused by suspension from the haptics, such as flattening of the top surface and
introduction of surface artefacts. Below the IOL platform was the aligned mirror, which
allowed the confocal position to be determined.
Alignment of the IOL was carried out by ensuring that each of the confocal, cat’s eye
and autocollimated fringe patterns were centred on the CCD camera when the
interferometer was at their respective vertical locations. Any misalignment saw the patterns
drift to one side with vertical movement of the coarse adjustment/ micrometer gauge, and
was removed with suitable adjustment of the tilt and/ or lateral translation of the IOL stage.
After alignment of the mirror and IOL, it was decided to proceed with measurements.
The micrometer screw was used to accurately move the interferometer between successive
points of interest, with the value on the micrometer scale recorded at any particular point. At
the confocal and autocollimated locations, a virtual electronic ‘Measurement Mask’ was
applied to mask out any unwanted fringing due to edge effects of the IOL and/or the
interferometer’s optical assembly itself.
To ensure that the orientation of the IOL was well-defined when measuring the
anterior and posterior surfaces, one of the non-featured haptics was marked. It was
consequently possible to not only determine which of the IOL surfaces was facing forwards,
but also the rotation of that particular surface. Between measurements, the IOL was flipped
carefully about a vertical axis through the IOL.
Unfortunately, some complications were observed while measuring the anterior and
posterior surface deviations at the autocollimated position. Firstly, a weak reflection caused
by the small change in refractive index at the water/IOL interface resulted in very low
contrast interferograms. Secondly, the water meniscus served to diverge the converging
objective beam at the autocollimated position. This resulted in a slower beam in the water,
and consequently only a small portion of the IOL surface was covered at that position.
Without the availability of a faster objective lens, it was decided to alternatively measure a
dry-packed hydrophobic IOL in air.
4.6 Metrology of Pharmacia (AMO) 17D IOL in Air
Without a faster objective lens, the unavoidable complications associated with metrology in
water necessitated measurement of a dry IOL. It was decided to measure a Pharmacia
(AMO) 17D IOL, since, due to limited availability of various IOL powers, it best matched the
most commonly implanted 21D. The IOL is shown in Figure 4.3 below. Note in particular the
‘s’, or ‘backwards s’ shaped haptics as distinct from the haptics of the Bausch & Lomb
model.
Figure 4.3. Pharmacia (AMO) 17D IOL [8].
14
Measurement of the IOL in air obviated the need for the water bath and accordingly,
the IOL stage could be made less unwieldy. A new IOL stage was constructed, as illustrated
in Figure 4.4 below.
Figure 4.4. Photograph of the prototype Meccano ‘dry’ stage.
The outer ‘legs’ can be seen to surround the mirror.
Note that the IOL platform was again covered with black tape to avoid unwanted reflections.
Once again, pre-alignment of the mirror with the interferometer was necessary and
was performed using the three vertical tip/tilt screws. The IOL stage was then placed
carefully over the mirror, taking great care not to touch it directly. The IOL was handled
carefully by the haptics and was placed over a diameter 6.5mm hole in the platform.
As was the case for wet metrology, alignment of the IOL was carried out by ensuring
that each of the confocal, cat’s eye and autocollimated fringe patterns were centred on the
CCD camera when the interferometer was at their respective vertical locations. Any
misalignment was removed with suitable adjustment of the tilt and/ or lateral translation of
the IOL stage.
After alignment of the mirror and IOL, it was decided to proceed with the dry
measurements. The micrometer screw was again used to move the interferometer between
successive points of interest, with the value on the micrometer scale recorded at any
particular point. The points of interest were located and recorded four times for each IOL
orientation. At the confocal and autocollimated locations, another (different) virtual electronic
Measurement Mask was applied to mask out any unwanted fringing.
To ensure that the orientation of the IOL was well-defined when measuring the
anterior and posterior surfaces, one of the s-shaped haptics was marked with a felt-tipped
pen. Thus, it was possible to determine which of the IOL surfaces was facing forwards, and
also the rotation of that particular surface. Between measurements, the IOL was flipped
carefully about an axis joining the meeting points of the haptics with the optic region.
Clear measurement maps were obtained at both the confocal and autocollimated
positions, with full coverage of both the anterior and posterior surfaces in the autocollimated
position. With this in mind, it was decided to begin modelling of the measured IOL
parameters in Zemax.
IOL Platform
Mirror
IOL
Mirror
Tip/Tilt
Controls
15
4.7 Zemax Ray-Tracing Analysis
Before deciding the orientation of the IOL in Zemax, it was first necessary to determine
which IOL surface was actually anterior, and which was posterior. In terms of balancing
aberrations when illuminated by collimated light, it is advantageous for the most curved
surface of a lens to face the collimated light, with the less curved side facing the focal region
[2]. Measurements of the IOL surfaces indicated that one surface was indeed more curved
that the other. This surface was initially deemed the anterior surface since, when implanted
in the eye, the anterior lens surface is facing (almost) collimated light. Note that the light is
not actually collimated, due to corneal refraction; however, it will suffice to assume so in this
approximation. Furthermore, it seemed reasonable to assume that wave error in double pass
through the lens would exhibit less spherical aberration when the anterior surface faced the
collimated light. Indeed, it was found experimentally that least spherical aberration was
observed when the preliminarily appointed anterior surface faced the collimated light. With
these evidences, it was decided to model the appointed anterior surface as facing the
collimated light in Zemax.
It was noted that the experimentally determined apical IOL thickness was an
apparent thickness caused by refraction at the air/IOL interface. It was therefore necessary
to convert this to a real distance using Zemax. However, it was not simply a case of
multiplying by the refractive index of the IOL since the surface sag needed to be taken into
account.
The measurement maps obtained in the µShape® software were resolved into the
first eleven Zernike coefficients, up to and including spherical aberration. The coefficients
were exported to a text file after each successful interferometric measurement. Analysis of
the text file indicated that the µShape® convention for Zernike polynomials differed from that
in Zemax. It was therefore necessary to rearrange and normalise the exported µShape®
Zernike coefficients before subsequent importation to Zemax.
Table 4.1 below indicates the discrepancy between the two conventions.
µShape® Zemax
Coefficient Polynomial Description Polynomial Description
1 1 1
2
3
4
5
6
7
8
9
10
11
Table 4.1. Indication of the discrepancy between conventions adopted in µShape® and Zemax
16
The anterior and posterior IOL surfaces were modelled as ‘Zernike standard sag’
surfaces in Zemax. This option allowed definition of the optical characteristics of both
surfaces in terms of their standard (rearranged and normalised) Zernike coefficients
obtained from the µShape® software. The interferometer µLens 15/43 objective was
modelled as a paraxial lens. In Zemax, “the paraxial surface acts as an ideal thin lens” [9].
To simulate double pass wave aberration of the IOL, it was necessary to model the
system in the confocal arrangement i.e. when the emergent light was collimated. The
problem of optimising the objective-IOL distance for collimated emergent light was solved
using a second paraxial lens directly behind the IOL. The distance between this second
paraxial lens and the image plane, and its focal length were fixed to 100mm (the default
paraxial lens focal length in Zemax is 100mm). Now, the image plane RMS spot size is
clearly minimised if collimated light is incident on the paraxial lens, since that is the definition
of a lens’ focal length. Since the paraxial lens is placed directly after the IOL, it is therefore
clear that the minimum image plane RMS spot size occurs for collimated light emerging from
the IOL. The optimal objective-IOL distance can thus be found by minimising the image
plane RMS spot size. This was performed using a Zemax merit function. The merit function
is, after [10], “a numerical representation of how closely an optical system meets a specified
set of goals”. In this case, the goal is minimal image plane RMS spot size with the objective-
IOL distance as the single variable. After optimisation, the technique can be qualitatively
verified by ignoring the second paraxial lens; collimated light should emerge from the IOL.
The collimated light was then reflected by a MIRROR surface type. In Zemax, after
reflection from a mirror, surfaces are modelled a second time, as though the light propagates
through the mirror, with distances entered as negative values. Extra care must be taken,
however, when entering radii of curvature after the mirror element. “The convention is that a
radius is positive if the centre of curvature is to the right (a positive distance along the local z
axis) from the surface vertex, and negative if the centre of curvature is to the left (a negative
distance along the local z axis) from the surface vertex. This is true independent of the
number of mirrors in the system” [11]. Thus, on reflection from the mirror, the radii are not
negated as with distances. Figure 4.5 below is a 3D-render of the experimental setup, as
modelled in Zemax; Figure 4.6 is a 2D side-view of the Zemax model. Note that the light
does not appear to exactly re-trace its path through the IOL. This was an un-avoidable effect
caused by the spherical aberration induced in single pass through the IOL and was not
simply an error in objective-IOL distance optimisation. Note also that the IOL-mirror distance
was approximated experimentally by photographing a ruler beside the apparatus.
17
Figure 4.5. 3D-rendered simulation of the experimental setup.
Figure 4.6. 2D side-view of the Zemax double pass model.
The objective beam (left) enters the IOL at the confocal position and emerges collimated, to be retro-reflected
from the mirror (right). The beam then passes back through the IOL to the image plane (centre). Note
that the posterior surface is facing to the left, with the anterior surface facing to the right.
The next step was to define the surfaces in terms of their Zernike coefficients.
Particular difficulty arose when entering those coefficients for the first anterior surface (which
faced to the right) and the second anterior and posterior surfaces after the mirror. It was
noted that when measuring a surface with the interferometer, that surface ‘faced’ the
interferometer. However, when modelling the first anterior surface in Zemax, the light
entered from the ‘back’ of that surface. Thus, the sign of all coefficients required inversion to
account for looking at the back of the surface, with certain coefficients requiring inversion to
account for anti-symmetry about the vertical axis [2]. Taking these two factors into account,
coefficients three, four, six, seven, nine and eleven were inverted for the anterior surface
(using the Zemax naming convention). Further difficulty was encountered when entering the
coefficients for the surfaces after the mirror, since those post-mirror distances are negative.
It was decided to use the original anterior coefficients since the light faced that surface, with
the posterior coefficients inverted accordingly, with all coefficients inverted again to account
for post-mirror distances being negative. Finally, the image plane was modelled at the focal
18
point of the objective lens, where the wave aberration in double transmission through the
lens could be studied.
After modelling the system in double pass, it was noted that the coefficient negation
system could be erroneous, and that any slight variation of coefficients was time consuming;
a simpler model was therefore sought. It was remarked that the wave aberration induced in
double pass through a system is simply double that induced in single pass [2]. Accordingly,
the system could be modelled in single pass, with the resultant wave aberration simply
doubled to simulate double pass. Moreover, it was noted that the FISBA µShape® software
outputs the results of double pass measurements as single pass wave aberration errors [12].
Therefore, in any case, it was necessary to only model half of the experimental setup i.e.
reflection from the mirror and the subsequent second pass through the IOL did not have to
be modelled.
The mirror and second IOL surfaces were thus removed. As before, the objective-IOL
distance was optimised to minimise image plane RMS spot size when focussing using the
second paraxial lens. The method was again qualitatively checked by temporarily ignoring
the paraxial lens; the emergent light was indeed collimated. This time, however, the second
paraxial lens remained in place to focus the collimated emergent light onto the image plane,
with the single pass wave aberration errors viewed there; see Figure 4.7 below.
Figure 4.7. 2D side-view of the Zemax single pass model.
The objective beam (left) enters the IOL at the confocal position and emerges collimated. It is then
focussed onto the image plane (right) by a paraxial lens placed directly after the IOL. Note
that the posterior surface is facing to the left, with the anterior surface facing to the right.
19
5. Results
5.1 Characterisation of the Retro-Reflective Return Mirror
The sixteen measurement values for the retro-reflective mirror were found to be highly
consistent. The surface peak-to-valley and root mean square (RMS) values are quoted as a
fraction of the wavelength of the laser light ( =632.8nm). The errors were calculated as the
standard error of the mean.
5.2 Characterisation of the Water Meniscus Lensing Effect
Characterisation of the water meniscus lensing effect was found to be problematic. The
water meniscus was found to fluctuate constantly, even after extended periods with no noise
or movement in the laboratory. Figure 5.1 is an example interferogram of the water
meniscus.
Figure 5.1. Interferogram of the water meniscus.
Note the false ripples on the map due to movement of the water meniscus.
5.3 Metrology of Bausch & Lomb 21.5D IOL in Water
A series of measurements were taken for the Bausch & Lomb IOL in the confocal position.
The IOL was oriented with the anterior surface facing the collimated light (toward the mirror).
For each measurement, the corresponding surface deviation map and Zernike polynomials
were saved to disk. At the end of the measurement trial, the surface deviation maps were
studied to see which gave the most complete coverage, or which were missing the least data
points, if any. Data points were missed in the interferogram if the image intensity at that point
20
was not high enough and occurred, for example, if a dust particle was present. Figure 5.2
below represents the best map obtained.
Figure 5.2. Confocal interferogram of Bausch & Lomb 21D IOL in water.
The image on the left is the interferogram as seen on the CCD camera. The image
on the right is the interferogram as interpreted by µShape®.
As already stated, the water meniscus caused divergence of the objective beam at the
autocollimated position and hence the beam was slower in the water. The autocollimated
measurement maps were accordingly small. They therefore only represent a small portion of
the surface near the centre and do not represent the surface as a whole. Consequently, they
are deemed useless and are not included here.
5.4 Metrology of Pharmacia (AMO) 17D IOL in Air
The same procedure was carried out for the dry as for the wet measurements, whereby
several measurements were taken for each of the positions of interest. In this case, two
different sets of maps were obtained for the IOL in the autocollimated position, one set for
each lens surface facing the mirror. As previously outlined, it was reasoned that the anterior
surface should be facing the collimated light (the mirror) when the maps exhibited the least
spherical aberration. Subsequent analysis of the Zernike coefficients indicated that one of
the orientations did indeed exhibit less spherical aberration; thus, it was decided to use
those maps as the wave aberration of the lens, with the surface facing the mirror deemed
the anterior surface. Figure 5.3 is the best obtained confocal interferogram for that lens
orientation. To the left of the software map is the interferogram as seen on the CCD camera,
shown here again for completeness.
21
Figure 5.3. Confocal interferogram of Pharmacia 17D IOL in air.
The image on the left is the interferogram as seen on the CCD camera. The image
on the right is the interferogram as interpreted by µShape®.
The anterior and posterior surfaces were completely filled by the objective beam at
the autocollimated position, in strong contrast to the same position in the wet measurements.
Several measurements of both surfaces were again taken, with the fullest map chosen as
the representative measurement; they are shown in Figure 5.4 and Figure 5.5 below. The
interferograms as seen on the CCD are not shown here, since they do not contribute
anything in particular to the discussion.
Figure 5.4. Autocollimated interferogram of Pharmacia 17D IOL anterior surface in air.
22
Figure 5.5. Autocollimated interferogram of Pharmacia 17D IOL posterior surface in air.
The micrometer reading was recorded for each of the confocal, top and bottom cat’s
eyes and the autocollimated positions for each IOL orientation. The procedure was carried
out four times, with the values subsequently used to calculate back focal lengths, radii of
curvature and apparent apical thicknesses. All values are included in Table 5.1 below. Note
that the error values were calculated as the standard error of the mean.
It was deemed necessary to only determine the real apical thickness for one lens
orientation and so only that thickness is included; see Section 6.6 for a discussion on its
error. Its value was calculated as:
Anterior surface
Posterior Surface
Trial # Back Focal Length Radius Apical Thickness Back Focal Length Radius Apical Thickness
1 18.020 15.530 0.580 17.950 21.865 0.575
2 18.020 15.545 0.570 17.990 21.905 0.570
3 17.975 15.575 0.575 17.960 21.890 0.570
4 17.965 15.625 0.580 17.970 21.870 0.570
Average 17.995 15.569 0.576 17.968 21.883 0.571
Error 0.015 0.021 0.002 0.009 0.009 0.001
Table 5.1. Experimentally measured physical parameters of the 17D IOL.
5.5 Zemax Ray-Tracing Analysis
The rearranged and normalised Zernike coefficients obtained from the µShape® software for
the anterior and posterior surfaces were entered into Zemax, as outlined above. The
resultant surfaces are shown below beside the experimental maps, for comparison, in Figure
5.6 and Figure 5.7.
23
Figure 5.6. Comparison of modelled and experimental anterior 17D IOL surface.
The experimental map is shown on the left, with the resultant Zemax model on the right.
Figure 5.7. Comparison of modelled and experimental posterior 17D IOL surface.
Again, the experimental map is shown on the left, with the resultant Zemax model on the right.
After definition of the anterior and posterior surfaces, the wave aberration in transmission
through the IOL was modelled. The simulated interferogram is compared to the experimental
interferogram in Figure 5.8 below.
Figure 5.8. Comparison of modelled and experimental 17D IOL wave aberration.
24
The values and percentage differences for the respective experimental and modelled peak-
to-valley and root mean square errors are listed in Table 5.1 below. The wavefront errors are
quoted as a fraction of . ( =632.8nm)
Peak-to-valley Root mean square
Experimental 1.99 0.39
Modelled 1.62 0.40
% Difference 18.6% 2.5%
Table 5.1. List of experimental vs modelled total wavefront errors, including % difference.
Figure 5.9 and Figure 5.10 below are screenshots of the final Zemax user interface showing
lens editor fields, and total wave aberration and 2D layout, respectively. The lens editors are
those in which the lens data parameters were entered.
Figure 5.9. Final Zemax user-interface showing lens editor fields.
Figure 5.10. Final Zemax user-interface showing total wave aberration and 2D layout.
25
6. Discussion.
6.1 Design and Construction of the IOL Stage
The design and construction of the IOL stage required a considerable amount of effort and
time. The particular difficulty arose in allowing independent tip, tilt and translation controls for
both the IOL and the mirror. The choice of potentiometer-type screws for the bath tip/tilt table
may seem trivial, or even ridiculous; however it was only through the use of such random
components that said table could have been built.
The initial Linos stage was discarded since the rod suspending the platform entered
the water too close to where the IOL would be located. Moreover, the rod was not symmetric
about the IOL location, so the meniscus would not only have been highly curved, but it would
also have been anti-symmetric; this anti-symmetric meniscus would have been exceedingly
difficult to measure and account for in the Zemax model. Thus, it was decided to opt for the
Meccano model, since the platform supports entered the water symmetrically much farther
from the IOL location. The Meccano stage also allowed greater customisation possibilities.
Furthermore, the IOL stage had to be designed such that it could be removed and
replaced without disturbing the mirror. This was useful for example when pre-aligning the
mirror with the interferometer. In the end, a satisfactory prototype was designed which
allowed all of the above and also minimised the IOL-mirror distance. Minimum IOL-mirror
distance was necessary to reduce errors due to mirror misalignment in the light re-tracing its
path back through the IOL.
6.2 Characterisation of the Retro-Reflective Return Mirror
Measurements of the retro-reflective mirror were found to be highly consistent, evidenced in
the values for the standard error of the mean. The mirror was measured as having zero RMS
surface error. However, it is non-physical to assume that the RMS surface error was exactly
zero; it was simply zero within the specified number of decimal places in the µShape®
software. It seemed reasonable to assume that the mirror could be so flat, since it had a
relatively large diameter and ample thickness. It was noted that the manufacture of optical
flats is far easier for those which are relatively large; thus, that sizeable mirror could be
manufactured to a high degree of flatness.
As previously stated, it was not possible to simultaneously calibrate the
interferometer for measurement of plane and spherical surfaces. It was therefore necessary
to include the mirror surface error in an error budget for the double pass wave aberration
errors. Owing to the mirror RMS surface error figure of zero, it was decided to simply ignore
any mirror surface error, since the aberrations introduced in double pass through the IOL
would be an order of magnitude greater in any case.
6.3 Characterisation of the Water Meniscus Lensing Effect
As previously stated, characterisation of the water meniscus was found to be highly
problematic. The appeal of interferometry as a measurement technique is in its ability to
resolve extremely small distances. However, without the use of sophisticated self-correcting
interferometers, this sensitive technique is highly susceptible to mechanical vibration. Thus,
26
the sensitivity is self perpetuating. It was observed that the movement of cars outside the
building and the closing of doors in the corridor caused turbulent meniscus motion. It is
important to note that the meniscus appeared perfectly still to the eye. However, a single
fringe on the interferogram represented surface error of one wavelength of light. Accordingly,
surface motion of just ~700nm would cause a fringe to continuously drift across the
interferogram, rendering it unreadable.
The effects of meniscus motion can be seen in Figure 5.1. The µShape® software
phase-unwrapping algorithm can be seen to have broken down in regions where motion was
excessive. In regions where the interferogram was successfully captured, the measurement
map is characterised by a rippling effect incorrectly introduced by the meniscus motion. This
rippling effect erroneously introduces large amounts of higher-order Zernike terms in the
map and so the map is deemed futile. Furthermore, as with the mirror surface error, the
small peak-to-valley and RMS values of 0.26 and 0.02 (expressed as a fraction of
=632.8nm) would be an order of magnitude less than the IOL wave aberration errors in any
instance.
6.4 Metrology of Bausch & Lomb 21.5D IOL in Water
The high-quality double pass interferogram of the 21.5D IOL in water is shown in Figure 5.2.
It represents a breakthrough in IOL metrology which was previously thought impossible, due
to the inherent complications in measurement at the confocal position. A very slight amount
of shading is barely visible in the CCD interferogram on the left-hand side. This shading,
which is characteristic of an astigmatic wavefront, was clearly resolved by the µShape®
software in the image to the right. Thus, the phase-shifting interferometric technique is highly
accurate and is capable of resolving features that are scarcely visible to the human eye.
The choice of water as the submersion liquid is a contentious issue. It is important to
note that this project was concerned in particular with the proof of the concept of double
pass IOL metrology in water. The main focus was not in obtaining quantitative results for the
exact determination of IOL aberration, but was in qualitatively confirming a metrology that
was previously thought impossible. However, the choice of water is still reasonable [2].
Water is readily available, its index of refraction has been well characterised for a range of
wavelengths and temperatures and it is physicochemically representative of the in situ
environment [13-15]. It was noted that the use of balanced salt solution (BSS) would have
been preferable since it would better mimic the in situ environment; however, lack thereof
rendered its employment impossible.
The main limiting factor to the wet measurement technique was the small size of the
obtained autocollimated maps, due to diversion of the objective beam at the air/water
interface. According to Snell’s law [16], light bends toward the normal at the point of
incidence when passing from a rarer to denser medium. With the interferometer at the
autocollimated position, the objective beam is converging at the air/water interface, thus the
water meniscus serves to bend the light rays away from the optical axis. With the
interferometer at the confocal position, the objective beam is diverging and so the meniscus
serves to bend the light rays toward the optical axis. An illustration of the effect is shown in
Figure 6.1 below. Thus, at the autocollimated position, the objective beam was accordingly
slower and hence poor coverage of the IOL surface resulted.
27
Figure 6.1. Examples of the lensing effect of the water meniscus.
Shown is a converging beam (left) and
diverging beam (right). The water was modelled as having a refractive index of 1.33.
Due to time constraints, it was not possible to obtain a faster objective of such quality
as the µLens 15/43. Without availability of a faster beam, measurements of IOL surface
deviation were limited to only a small portion in the central region of the surface. It is
important to note that the Zernike polynomials are orthogonal on the unit circle. Hence, when
describing particular surfaces, they are meaningful only when used across the same
physical size across all surfaces i.e. they cannot be extrapolated to account for larger
diameters. The particular problem associated with the small autocollimated measurement
maps was that their Zernike coefficients were useful only for those small sizes. This
therefore also rendered useless the larger high-quality double pass measurement maps.
Moreover, the obtainment of high-quality measurement maps was hindered by
distinctively low-contrast CCD interferograms. This lack in contrast was attributable to the
low-intensity reflection from the water/IOL interface due to the small refractive index
differential there. The amount of light reflected from the interface between two media can be
calculated using the fresnel reflection coefficients for s and p polarised light, respectively
[17]. It was attempted to improve the map acquisition performance by increasing the
integration (or exposure) time of the CCD camera. However, increasing the exposure made
the system more susceptible to error due to mechanical vibration.
Note that these adverse effects also plagued the previously performed experimental
measurements of surface deviation [18]. Consequently, it was decided to measure a dry IOL
in air.
6.5 Metrology of Pharmacia (AMO) 17D IOL in Air
Initially, it was decided to attempt the wet measurements since it was anticipated that they
would be hardest to perform, and indeed they were. Furthermore, as previously outlined, the
Bausch & Lomb 21.5D IOL best matched the most commonly implanted 21D.
However, measurement of an IOL submerged in water was not pivotal to the success
of the experiment; measurement of a dry IOL would prove just as useful. The downside of
dry IOL measurements in this case, however, was the fact that the best matched 17D did not
very closely match the most commonly implanted 21D. This minor disadvantage could easily
be overcome by simply acquiring a 21D IOL. However, such an IOL was not available at
time of experimentation.
Air
Water Meniscus
Air
Water Meniscus
Water Water
28
The high-quality measurement maps obtained, visible in Figure 5.3, Figure 5.4 and
Figure 5.5, owe to the relatively large refractive index differential at the air/IOL interface.
Prior to measurement of the IOL, it was anticipated that a large amount of spherical
aberration would be present in the confocal position. This would result in a possibly
indeterminate exact null fringe condition, since spherical aberration serves to elongate the
focal region into a paraxial and marginal focus. i.e. there is no single definite focal point.
Thus, there would be a relatively large distance over which the confocal position could be
defined. Fortunately, excessive spherical aberration was not observed and so the confocal
position was relatively well-defined.
It can also be argued that measurement of the dry IOL in air is not representative of
the in situ environment. The IOL material may absorb some of the ocular fluid and in doing
so, change its physical characteristics. However, an experiment previously performed by the
author indicated that the IOL’s physics characteristics did not change when submerged in
water, even for extended periods. The minimal error values of all measured physical
parameters also indicate that the technique was highly consistent, even for just four
measurement trials. Thus, measurement in air was accordingly acceptable.
6.6 Zemax Ray-Tracing Analysis
It is clear from Figure 5.6 and Figure 5.7 that the Zemax models faithfully recreated both the
anterior and posterior IOL surface deviations.
It is worth noting that the real apical thickness calculated in Zemax is not quoted with
any error. This does not mean that the value was calculated with infinite uncertainty. Instead,
the analysis of its error was simply omitted, since it was deemed unnecessary in this proof-
of-concept model. Its calculation would be performed by taking the error of the experimental
apparent thickness and using Zemax to compute the corresponding error of the real
thickness.
After calculation of the real apical IOL thickness, the anterior and posterior surfaces
were modelled to qualitatively determine the total wave aberration in transmission through
this modelled IOL. Figure 5.8 illustrates the agreement of the experimental and modelled
total wavefront errors. In comparing the two sets of data, some unexpected results were
observed. In particular, the peak-to-valley (PV), root mean square (RMS) and spherical
aberration errors of the modelled wavefront were considerably larger than the experimental
wavefront errors. The following are proposed as the reasons for this discrepancy.
Firstly, at the confocal position, it was initially assumed that light passed through the
entire optic region to be retro-reflected from the mirror. However, it is assessed that this
assumption is not correct. Edge effects at the optic periphery will cause any light rays
passing through there to be diverted largely and so these rays will not be retro-reflected by
the mirror; consequently, they do not form part of the interferogram. Thus, only a smaller
region of the optic is represented by the confocal interferogram. When the diameters of the
IOL surfaces were reduced in the Zemax model, the resultant PV, RMS and spherical
aberration values were found to decrease accordingly, in closer agreement with the
experimental wavefront.
Secondly, the posterior IOL surface was found to be slightly aspheric. It was aspheric
in the sense that it was difficult to obtain an exact null fringe condition at the autocollimated
position. The observed effect was similar to a spherically aberrated wavefront focussing on
an image plane, where the definite focal point is elongated between a paraxial and marginal
focus. In this case, the null fringe condition was found to be elongated between a focal
region for the paraxial rays and a focal region for the marginal rays. Therefore, a certain
29
error was present in the determination of the posterior radius of curvature. When the
posterior radius of curvature was increased slightly to a value of 23.5mm, the modelled
wavefront errors were found to more closely agree with the experimental values.
Furthermore, as previously stated, the IOL was observed to exhibit less spherical
aberration in double pass than was anticipated. Therefore, perhaps the IOL is designed for
minimal induction of spherical aberration, with the internal lens material and aspheric surface
acting to cancel it out. With the reduction in modelled lens diameter and increase in posterior
radius of curvature, the modelled RMS surface error is within just 2.5% of the experimental
value; thus the two are in relatively close agreement.
At this initial proof-of-concept stage with many undetermined variables, it is impossible to
ascertain as to what is causing the discrepancy between experiment and theory. If all
variables were removed, then the discrepancy could in fact be directly attributed to internal
lens inhomogeneities. However, without such removal of inherent variables, it is not possible
to confidently determine the source of discrepancy.
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7. Conclusion
In conclusion, the concept of measuring double pass wave aberration in transmission
through an IOL has been proven. This previously deemed impossible measurement is not
only repeatable, but results obtained can be subsequently confirmed with software ray-
tracing analysis. The particular success of this project was in the design and development of
individual tip and tilt controls for the IOL and retro-reflective mirror.
A whole gamut of IOL types can be characterised through measurement in the wet or
dry. Measurement with the IOL submerged in water is not pivotal to experimental success;
however, it is more representative of the in situ environment. With this in mind, further work
performed in this area would employ balanced salt solution (BSS) as the submersion liquid.
The software confirmation of dry experimental measurements has been performed.
Particular care must be taken in future work to better determine the extent to which the
objective beam covers the IOL in both confocal and autocollimated measurements. It was
observed that incorrectly large coverage assumptions are highly erroneous. As for wet
measurements, it is clear that future success will necessitate the use of a faster high-quality
objective beam. Only then will the surfaces of higher-powered IOLs be completely covered
at the autocollimated position.
Finally, with future successful elimination of variables, the discrepancy between
experimentally and theoretically determined wavefront errrors can be attributed to internal
IOL material inhomogeneity.
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8. Acknowledgements
The author wishes to acknowledge the expert advice and consultation of Dr. Alexander Goncharov and the consultation of Matt Sheehan. Worthy of acknowledgement also is the time spent bouncing physics trivia off my good friends Adam Beatty, Colm Lynch, Marieke van der Putten and other classmates over the occasional pint of Guinness. In addition, to my brother Brian who tirelessly proof reads all my documents. Without them, I would scarcely have survived.
9. References
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[13] Thormählen, I., Straub, J. And Grigull, U. (1985) “Refractive index of water and its
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[18] Sheehan, M. (2012). Private communication.