Corneal corrective laser surgery procedures like PTK and LASIK have made
dramatic improvements in the last decade, yet a large number of patients
cannot achieve targeted correction. Many machines, especially of early
generations, are excessively rigid, not allowing adaptation to the intricacies
of the corneal changes (Gualini et al., 2000). Use of corneal topographic
devices like videokeratometers has proven insufficient since these devices
operate at resolution of around 100 microns, while ablation depth is less
than few microns in total and single-shot removal is in sub-micron range.
White light interferometers have better resolution of around 10 micron
but it is still not sufficient.
In fact, a wave-front analysis does not give any information about the
critical parameter of corneal elasticity. But the corneal surface reconstruction
process after ablation depends greatly on the corneal tissue elasticity,
as confirmed by the results obtained by using steroids to modify the intra-ocular
pressure or IOP during the post-op period. Thus a real improvement in
PTK procedures would be to combine wave-front analysis with an effective
method that takes tissue elasticity into consideration (Drescher et
al., 1999; Kasprzak et al., 1994; Matsuda et al., 1982).
The use of a Twymann-Green Interferometer (TGI) (Gualini et al.,
2000; Licznerski et al., 1999) for mapping of corneal surfaces
and to also measure their variations due to intrinsic elasticity coefficients
is proposed. Such system can go to sub-micron resolution and should prove
to be an attractive alternative.
For mapping the behaviour of cornea under dynamic stresses, a very innovative
laser device, i.e., a PulsESPI camera, is being used. PulsESPI is very
good candidate for this purpose as its resolution goes to sub-micron ranges.
Through this study, the resonance frequency and the corresponding corneal
deformations are determined in real time, probably for the first time.
MATERIALS AND METHODS
An experiment was conceived in order to evaluate the use of a PulsESPI
camera to measure the animal corneal deformations in real time. This research
should pave way to in vivo experiments on human cornea. A normal
bovine cornea was used for the study, which is probably not the best choice
to emulate a human cornea, since other smaller animals (e.g., goat, sheep,
pig) may be more comparable. Along with the reasons of availability and
the drawback of having low reflection coefficient to visible light, it
does offer quite a wide surface so that fringes can be conveniently displayed
and the tip of a shaker could easily be applied without significantly
disturbing the field of view. The experiments were conducted at Steinbichler
Optotechnik GmbH in Neubeuren, Germany few years back. The authors jointly
took the responsibility of experimentation and analysis, which took few
weeks for completion.
A PulsESPI device is being chosen for the study because of the many advantages
offered by this technique in real-time deformation analysis. PulsESPI
is becoming increasingly popular as a reliable and accurate investigation
method compared to conventional Double Pulse Holography (Kasprzak et
al., 1994; Bally, 1979; Friedlander et al., 1991; Ohzu and
Kawara, 1982). Here, instead of using photographic films, PulsESPI can
directly record images in the PC through a CCD camera. PulsESPI images
can be obtained with very short light pulses at high repetition rates,
which make the method insensitive to mechanical vibrations. Pulse widths
and repetition rates can be adjusted conveniently to cover quite a wide
range of applications. Due to the short recording time (few nanoseconds)
PulsESPI is insensitive to disruptive factors like low frequency vibrations
or shocks transmitted to the apparatus. Presently PulsESPI is probably
the best investigational method to study transient and dynamic behaviour
of objects under excitation. It largely combines the advantages of both
conventional Double Pulsed Holography (DPH) and ESPI. Figure
1 shows a basic layout of a Twymann-Green Interferometer. Figure
2 shows the basic layout of a PulsESPI system.
In these experiments, data was acquired and processed by the powerful
software FRAMESplus release 5.0, developed by Steinbichler Optotechnik
GmBH. The equipment used for this experiment has a resolution ranging
between λ/30 and λ/10 at 20 pixels fringe width. The camera
resolution is 1280x1024 pixels. The ruby laser pulse separation ranges
from 2 to 800 μsec. Polytec Laser Vibrometer was used to determine
the resonance frequency.
For inducing strain to the bovine cornea a mechanical vibrator in the
shape of a rod connected with a motor was used. When the motor was electrically
driven, the tip of rod would poke the sample with its tip moving back
and forth with a displacement of a fraction of millimeter. The oscillating
frequency of the tip was variable over wide range and Polytec laser vibrometer
was used to measure its frequency. The bovine cornea was supported by
aluminum film and polystyrene.
In the PulsESPI experiment, the ruby laser light was widely diffused,
thus the back-scattered signal was found to be very poor due to the high
transparency of the bovine cornea. This problem was overcome by spraying
the corneal surface with white powder film in order to ensure high reflectivity
and uniformity of the back-scattered signal. This may appear a limitation
for an in vivo application on human cornea, but in that case a
comparatively better reflectivity to the ruby laser (632.8 nm) is expected,
as already reported by other authors (Kasprzak et al., 1994; Bally,
1979; Friedlander et al., 1991; Ohzu and Kawara, 1982).
|| Layout of a basic TGI setup
|| Layout of a basic PulsESPI setup
Initially, some static measurements were performed using a TGI setup
in order to map the static condition of bovine cornea. The setup of the
TGI experiment is visible in Fig. 3, while Fig.
4 shows the bovine cornea surface mapped by the TGI fringes. Fringes
generated on the surface of the bovine cornea were processed by FRAMESplus
release 5.0/1, which generates results within few seconds (Licznerski
et al., 1999).
|| Setup of the TGI experiment
|| Bovine cornea mapped with TGI
Once the cornea was mapped without deformation, a specific static stress
(controllable in intensity and direction) was induced to the bovine corneal
surface as visible in Fig. 5. The resulting corneal
deformation mapped by the TGI device and obtained after the fringe analysis
from the software is shown in Fig. 6.
Preliminarily, a HeNe laser is used to align the optical system in eye
safe conditions for the operator, before the actual use of the high power
ruby laser. Part of the beam is injected into a single-mode, polarization-maintaining
optical fiber, which carries the reference beam signal directly onto the
CCD camera surface.
|| Sample fitted in TGI experiment
|| Static deformation mapped with TGI
|| Vibration frequency spectrum for the cornea
|| Dynamic stressing setup for the cornea
|| Deformation of cornea at resonance
|| No deformation of cornea outside resonance
Figure 7 shows the amplitude response versus the frequency
spectrum of the bovine cornea surface shacked with the tip synchronized
to the Laser Vibrometer. Figure 8 shows the measurement
setup. The graph of the amplitude versus frequency spectrum is directly
obtained from the vibrometer. The resonance frequency is clearly visible
at 175 Hz. Thus, the tip vibration frequency was fixed at resonance conditions
and the surface deformation at this resonance frequency was detected using
PulsESPI setup. As is visible from Fig. 9, the cornea
looks evidently deformed. Quite interestingly there are no apparent measurable
deformations at frequencies slightly offset from the resonance, as visible
in Fig. 10. The bumpy surface is due to unfiltered
calculation noise generated by the software, which is shown in the original
Firstly, the fast and direct but static mapping of cornea with the help
of modified Twymann-Green Interferometer were obtained. Though it gives
impressive output, the target here was to obtain the mapping of the cornea
under dynamic stress applications which is necessary to obtain the elastic
behaviour of the sample. PulsESPI was able to provide this important information
to us. This technique can be used for the systematic studies and investigations
on the elastic behaviour of cornea. Information of the cornea elasticity
can be very well utilized for fine-tuning the final surgical ablation
It was found out that the cornea surface as used in this experiment exhibits
a resonance frequency which can very well give information about its elastic
parameters. This information of having a specific resonance frequency
can be characteristic to a specific cornea or the eye. Also evident is
that PulsESPI is a dependable and promising method for the conduction
of stress-related investigations on a biological sample (Reiss, 2003;
Looking at the earlier researches for the development of topographers
and videokeratormaters, it is found that the corneal elasticity is generally
neglected parameter in these studies. Using PulsESPI to extend the studies
in this direction opens up another avenue which will pave way for other
stress-related studies on biological samples with this technique.
Preliminary studies on animals can be useful to determine all the process
parameters and functions needed for elasticity determination. As an implementation,
treating patients with excimer laser and then monitoring the corneal evolution
during the post-op time can be compared with the calculated figures of
forecasted cornea surface. This procedure will enable us to refine a mathematical
model so that it can be used in vivo conditions for humans (Garcia
et al., 1998, 1999).
It is suggested that normal optical methods like TGI or wave front analysis
are not sufficient for completely establishing the Targeted Correction,
unless corneal elastic properties and coefficients are duly taken into
account. Thus stress analysis should help to predict the post-op time
evolution of the corneal tissue.
In an attempt to demonstrate findings, the bovine cornea was mapped at rest
and under static and dynamic stress conditions. The optical measurement methods
are used that involve data acquisition without contact with the sample.
To map the cornea at rest and under static stress conditions, a modified
Twymann-Green interferometer is used. Then for the first time ever PulsESPI
is utilized to measure and map the deformations of the bovine cornea to
a dynamic stress and to find the intrinsic resonance frequency of the
bovine cornea. It was finally noticed that outside resonance condition
the bovine cornea is practically not deformed.
The technique can then be adapted and developed for in vivo experiments
on animals and humans. This would yield a very accurate definition of
corneal mathematical model, so that a prediction curve of the cornea evolution
with time can be visualized. It is also proposed that PulsESPI can be
used in combination with a wave front analysis device to achieve much
better results compared to their isolated use.
The authors are particularly grateful to Mr. Sun who has helped in setting
up the optical experiments and then to all the staff of Steinbichler Optotechnik
GmbH for their support, specifically in handling biological specimen.