U.S. patent application number 10/987095 was filed with the patent office on 2005-04-28 for wavefront characterization of corneas.
Invention is credited to Erry, Gavin R. G., Harrison, Paul, Otten, Leonard John III, Woods, Simon S..
Application Number | 20050088618 10/987095 |
Document ID | / |
Family ID | 25404312 |
Filed Date | 2005-04-28 |
United States Patent
Application |
20050088618 |
Kind Code |
A1 |
Otten, Leonard John III ; et
al. |
April 28, 2005 |
Wavefront characterization of corneas
Abstract
Apparatus for determining if a cornea (whether in vitro or in
vivo) has been modified (either surgically or otherwise). The
method includes the steps of: passing a beam of collimated light a
(either coherent or incoherent) through the cornea to produce a
distorted wavefront; determining the characteristics of the
distorted wavefront; and analyzing the distorted wavefront for
characteristics that identify the presence of a modification. The
analysis of the distorted wavefront can be for the presence of
higher order aberrations, or Gausian characteristics which are
indicative of modifications. More particularly, the method includes
the steps of providing an optical system that has a pupil plane and
an image plane at a detector; positioning the cornea in the pupil
plane; passing a collimated beam of light through the cornea to
produce at least two images in the image plane; determining the
characteristics of the distorted wavefront; and analyzing the
distorted wavefront for characteristics that identify the presence
of a modification. The apparatus includes: a source of collimated
light: an optical system including a distorted grating and an
imaging lens (which have a pupil plane, first and second virtual
planes, and an image plane); structure for positioning the cornea
in the pupil plane; and a computer. The structure for positioning
the cornea (which is immersed in a suitable storage fluid) includes
first and second plano/plano lenses. The first and second plano
lens, which are substantially and perpendicular to and centered
with respect to the axis, have less than .lambda./10 total
distortions.
Inventors: |
Otten, Leonard John III;
(Placitas, NM) ; Erry, Gavin R. G.; (Malvern,
GB) ; Woods, Simon S.; (Cheltenham, GB) ;
Harrison, Paul; (Wellington Heath, GB) |
Correspondence
Address: |
RODEY, DICKASON, SLOAN, AKIN & ROBB, PA
P.O. BOX 1888
ALBUQUERQUE
NM
87103
US
|
Family ID: |
25404312 |
Appl. No.: |
10/987095 |
Filed: |
November 12, 2004 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
10987095 |
Nov 12, 2004 |
|
|
|
10115355 |
Apr 2, 2002 |
|
|
|
10115355 |
Apr 2, 2002 |
|
|
|
09895309 |
Jun 29, 2001 |
|
|
|
6464357 |
|
|
|
|
09895309 |
Jun 29, 2001 |
|
|
|
09693076 |
Oct 20, 2000 |
|
|
|
6286959 |
|
|
|
|
Current U.S.
Class: |
351/212 |
Current CPC
Class: |
G01J 9/00 20130101; A61B
3/107 20130101; A61B 3/1015 20130101; A61F 2/142 20130101 |
Class at
Publication: |
351/212 |
International
Class: |
A61B 003/10 |
Claims
1. A method of determining whether an in-vivo cornea has been
surgically modified, said method including the steps of: a. passing
a beam of collimated light through said in-vivo cornea twice to
produce a wavefront modified by said cornea; b. measuring said
modified wavefront; and c. analyzing said measured, modified
wavefront for features that identify the presence of a cornea
indicative of surgical modification.
2. The method of claim 1, wherein said analysis is for the presence
of higher order optical aberrations.
3. The method of claim 2, wherein said analysis is for the presence
of residual grating-like optical aberrations, said optical
aberrations being indicative of surgical modification.
4. The method of claim 1, wherein said analysis is for the presence
of Gausian characteristics which are indicative of surgical
modification.
5. The method of claim 1, wherein said step for passing said beam
of collimated light is accomplished with coherent light.
6. The method of claim 1, wherein said step for passing said beam
of collimated light is accomplished with incoherent light.
7. (canceled)
8. (canceled)
9. The method of claim 1, wherein said step of measuring includes
mathematically producing a representation of said modified
wavefront.
10. The method of claim 9, wherein measuring includes use of the
Intensity Transport Equation and a Green's Function.
11. The method of claim 1 wherein said analysis includes comparing
said modified wavefront to a stored wavefront.
12. Method of determining whether or not an in-vivo cornea has been
altered, said method including the steps of: a. positioning a
person's head such that said in-vivo cornea is in the pupil plane
of an optical system; b. passing a collimated beam of light through
said in-vivo cornea twice and a distorted grating to produce, in
the image plane of said optical system, an image of said pupil
plane and two virtual image planes located on either side of said
pupil plane; c. determining from said image, the wavefront of said
light after it has passed twice through, and been modified by, said
in-vivo cornea; and d. analyzing said modified wavefront for
features that identify an altered in-vivo cornea.
13. The method as set forth in claim 12, of wherein said intensity
maps are the zero, +1 and -1 diffraction orders produced by said
distorted grating.
14. The method as set forth in claim 13, wherein said analysis
includes the step of comparing said modified wavefront with a
stored norm.
15. The method as set forth in claim 13, wherein said modified
wavefront is determined from said image, the Intensity Transport
Equation and a Green's function.
16. The method of claim 15, wherein said analysis of said modified
wavefront is to determine the presence of higher order
aberrations.
17. The method of claim 16, wherein said analysis of said modified
wavefront is to determine the presence of grating like features
which are indicative of a particular type of surgical
modification.
18. The method of claim 15, wherein said analysis of said modified
wavefront is to determine the presence of Gausian characteristics
which are indicative of modifications.
19. The method of claim 12, further including the step of
introducing predetermined modifications into said collimated beam
of light prior to said beam of light passing through said in-vivo
cornea to increase the dynamic range of said determination.
20. Apparatus for determining whether an in-vivo cornea has an
abnormality, said apparatus comprising: a. a source of collimated
light having known wavefront characteristics; b. an optical system
including an optical path, a distorted grating and lens means, said
optical system also including pupil plane, first and second virtual
planes, and an image plane, said first and second virtual planes
being on opposite sides of and equally spaced from said pupil
plane; c. means for positioning a person's head such that said
in-vivo cornea is in said pupil plane; d. means for focusing said
virtual planes in said image plane, and means for recording the
images of said first and second virtual planes; e. means for
determining from said images of said first and second virtual
planes the wavefront of said source after it has passed twice
through and been modified by said in-vivo cornea; and f. means for
analyzing said modified wavefront for features indicative of an
in-vivo cornea with an abnormality.
21. (canceled)
22. (canceled)
23. The apparatus of claim 20, wherein said means for positioning
said in-vivo cornea includes apparatus for positioning a patient's
head such that his/her in-vivo cornea is in said pupil plane.
24. The apparatus of claim 20, wherein said means for determining
said modified wavefront includes means for producing a mathematical
representation of said modified wavefront.
25. The apparatus of claim 24, wherein said means for producing
said mathematical representation includes a computer, the Intensity
Transport Equation and a Green's Function.
26. The apparatus of claim 25, wherein said means for analyzing
said modified wavefront also includes means for storing said
images.
27. The apparatus of claim 26, wherein said means for analyzing
includes a stored norm.
28. The method as set forth in claim 13, wherein said virtual image
planes are equally spaced from said pupil plane.
Description
FIELD OF THE INVENTION
[0001] This invention relates to the use of wavefront sensing to
determine whether or not a cornea has been altered (due to
corrective surgery, or accident). More specifically, the present
invention relates to the use of wavefront sensing using a distorted
defraction grating to identify corneas (whether in vitro or in
vivo) that have been surgically modified (e.g., radical keratotomy
(RK), excimer laser photorefractive keratectomy (PRK),
laser-assisted in situ keratomileusis (LASIK) and automated
lamellar keratoplasty (ALK)).
BACKGROUND OF THE INVENTION
[0002] In the United States about 40,000 corneal transplant
operations are performed each year. While success of such surgery
may depend upon a number of other factors, one factor that always
has an effect on the outcome is the condition of the donor cornea.
In the United States, a donor cornea must be transplanted within 7
days of harvesting. Outside the United States donor corneas may be
used up to 14 days after harvesting. Additionally, it is essential
to use only corneas which have not been modified (e.g., the subject
of photorefractive surgery).
[0003] The growth of refractive surgery over the last five years
has been dramatic. In the August 2000 issue of Archives of
Ophthalmology, P. J. McDonnell, M.D. states that this year alone
over 1,500,000 refractive procedures will be performed. As
beneficial as these procedures are, the individual corneas are
permanently altered, which makes them unsuitable for corneal
transplanting.
[0004] The increase in refraction surgery increases the likelihood
that a modified cornea will be harvested for transplant purposes.
Unfortunately, it is generally not possible to conclusively tell,
either visually or under a microscope, whether such a donor cornea
has been subjected to a surgical procedure or otherwise
altered.
[0005] Even when properly stored in a container (e.g., a Chiron
Ophtholmics cornea container) filled with Optisol.RTM. or another
appropriate solution, a donated cornea changes optically in the 14
day time period referenced above. The interior starts to develop
optical scatter sources and the optical power of the cornea
changes. The scatter resources manifest themselves as randomly
distributed optical aberrations which increase over time. It is
believed that this is caused by the cells of the harvested cornea
not being able to reject waste material. The change in optical
power is believed to be caused by an overall relaxation of the
tissue. Regardless of the cause, the net result is that these
aberrations produce scintillation and static aberrations when a
beam of light is passed through a donated cornea.
[0006] PCT/GB99/00658 (International Publication No. WO 99/467768),
based on applications filed in Great Britain on Mar. 10, 1998 and
Dec. 23, 1998, discloses a three dimensional imaging system
including a lens and a distorted diffraction grating which images
objects located at different distances from the grating
simultaneously and spatially separated in a single image plane. The
grating is distorted according to a quadratic function so as to
cause the images to be formed under different focus conditions. It
is stated that the system is useful for simultaneously imaging
multiple layers within a three dimensional object field, and has
applicability in a number of fields including optical information
storage, imaging short-time scale phenomena, microscopy, imaging
three dimensional object structures, passive ranging, laser beam
profiling, wavefront analysis, and millimeter wave optics. The
ability to make wavefront measurements is not disclosed or
claimed.
[0007] P. M. Blanchard et al., "Multi-Plane Imaging With a
Distorted Grating," Proceedings of the 2nd International Workshop
on Adaptive Optics for Industry and Medicine, World Scientific, pp.
296-301, 12-16 Jul. 1999, describe a technique for simultaneously
imaging multiple layers within an object field onto the detector
plane of a single detector. The authors, who are the named
inventors in PCT/GB99/00658, state that the imaging of multiple
layers within an object field is "useful in many applications
including microscopy, medical imaging and data storage." (See page
296.) The apparatus includes the use of a binary diffraction
grating in which the lines are distorted such at each different
level of defocus is associated with each diffraction order. When
such a grating is placed in close proximity to a lens, the grating
creates multiple foci of the image. This multi-foci effect enables
the imaging of multiple object planes onto a single image
plane.
[0008] L. J. Otten et al. "3-D Cataract Imaging System,"
Proceedings of the 2nd International Workshop in Adaptive Optics
for Industry and Medicine, World Scientific, pp. 51-56, describe
optics and an associated diagnostic system for volumetric, in vivo
imaging of the human lens to characterize or grade cataracts. The
described method and apparatus are based on the use of a distorted
grating (of the type disclosed in PCT/GB99/00658 and the Blanchard
et al. paper, supra) in conjunction with a focusing lens and a
re-imaging lens. (See FIG. 1 of this reference.) The quadratic
phase shift, introduced by the grating, leads to a different degree
of defocus in all diffraction orders, which produces a series of
images of different layers of the cataract, each with different
defocus conditions, simultaneously and side-by-side on the
detector. Thus, in-focus images of different object planes are
produced.
[0009] Analysis of the optical images referenced above requires the
use of the Intensity Transport Equation (I.T.E.) and the employment
of a Green's function to produce a wavefront map. S. Woods, P. M.
Blanchard and A. H. Greenaway, "Laser Wavefront Sensing Using the
Intensity Transport Equation," Proceedings of the 2nd International
Workshop on Adaptive Optics for Industry and Medicine, World
Scientific, pp. 260-265, 12-16 Jul. 1999, describe both the I.T.E.
and a Green's function solution thereto in conjunction with laser
wavefront sensing.
OBJECTS OF THE INVENTION
[0010] It is an object of the present invention to determine, with
wavefront sensing, whether or not a cornea has been altered (either
deliberately or accidentally).
[0011] It is another object of the present invention to determine,
with the use of wavefront sensing using a distorted grating, those
donor corneas that have been modified by surgery or other
methods.
[0012] It is another object of the present invention to provide a
simple optical system (particularly including a light source, an
imaging lens, a distorted grating and a data camera) to form, in
the detector plane, images from which wavefront aberrations in the
cornea can be derived. The beam of light that passes through a
cornea (located in the pupil plane) and two virtual planes on
opposite sides of and equidistant from such pupil plane.
[0013] It is an additional object of the present invention to
provide a holder for a donor cornea which does not mask optical
data from such cornea.
[0014] It is yet another object of the present invention to provide
a holder for a donor cornea that has optical windows that are
substantially free of distortion which would mask corneal optical
data.
[0015] It is yet still another object of the present invention in
which the optical windows have less than .lambda./10
distortions.
[0016] These and other objects will be apparent from the
description which follows.
SUMMARY OF THE INVENTION
[0017] A method of determining if a cornea (whether in vitro or in
vivo) has been modified (either surgically or otherwise). The
method includes the steps of: passing a beam of collimated light a
(either coherent or incoherent) through the cornea to produce a
distorted wavefront; determining the characteristics of the
distorted wavefront; and analyzing the distorted wavefront for
characteristics that identify the presence of a modification. The
analysis of the distorted wavefront can be for the presence of
higher order aberrations, or Gausian characteristics which are
indicative of modifications. More particularly, the method includes
the steps of providing an optical system that has a pupil plane and
an image plane at a detector; positioning the cornea in the pupil
plane; passing a collimated beam of light through the cornea to
produce at least two images in the image plane; determining the
characteristics of the distorted wavefront; and analyzing the
distorted wavefront for characteristics that identify the presence
of a modification.
[0018] The apparatus for determining whether a cornea has been
surgically modified includes: a source of collimated light, an
optical system including a distorted grating and an imaging lens
(which have a pupil plane, first and second virtual planes, and an
image plane); structure for positioning the cornea in the pupil
plane; means for recording the images of the first and second
virtual planes; means for determining from the first and second
images the distorted wavefront; and means for analyzing said
wavefront for characteristics indicative of modified corneas. The
first and second virtual planes are on opposite sides of and
equally spaced from said pupil plane.
[0019] The structure for positioning the cornea (which is immersed
in a suitable storage fluid) is a container which includes: a
housing having first and second ends; structure positioned within
the housing for supporting the perimeter of the cornea; a first
plano/plano lens for closing the first end of the housing; and a
cap for closing the second end of the housing. The cornea support
is substantially symmetrical with respect to an optical axis. The
first plano/plano lens is substantially perpendicular to the
optical axis. Finally, the cap includes a second plano/plano lens
which is substantially parallel to the first piano lens. The first
and second plano/plano lens, which are substantially centered with
respect to the axis, have less than .lambda./10 total distortions.
The support structure includes a cage and a pedestal with the cage
being supported by the pedestal. Preferably, the cage and pedestal
are integrally formed with the housing. Finally, the cap has a top
portion and a skirt which axially inwardly spaces the second lens
from the top portion to create an annular area where air will
collect when the container is holding a cornea and fluid, so that
air will not interfere with a beam of light passing through the
first and second piano/piano lenses and cornea.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] FIG. 1 is a schematic of the optical system of the
instrument to characterize donor corneas;
[0021] FIG. 1A is the front view of the distorted grating used in
the instrumentation to characterize corneas;
[0022] FIG. 1B is the front view of the detector plane of the
detector of the instrumentation to characterize corneas, and the
images in such plane;
[0023] FIG. 2 is a cross-section view of an optical cornea
container of the present invention;
[0024] FIG. 3 is a cross-sectional, perspective view of an improved
cornea container of the present invention;
[0025] FIG. 4 is a cross-sectional view of the improved optical
cornea container of FIG. 3 in the open position;
[0026] FIG. 4A is a cross sectional view of the improved optical
cornea container of FIG. 3 in the closed position.
[0027] FIG. 5 is a diagram showing the baseline date of the system
of FIG. 1, with no cornea or container;
[0028] FIG. 6 is a diagram showing the baseline date of the system
of FIG. 1, with the container of FIG. 2 filled with Optisol.RTM.,
but with no cornea;
[0029] FIG. 7 is a diagram showing the data from an unmodified
cornea L, held in the container of FIG. 2, positioned in the pupil
plane of FIG. 1, and exposed to coherent and collimated light;
[0030] FIG. 8 is a diagram showing the data from a an unmodified
cornea R, held in the container of FIG. 2, positioned in the pupil
plane of FIG. 1, and exposed to coherent and collimated light;
[0031] FIG. 9 is a diagram showing the data from cornea L after it
has been surgically modified, again held in the container of FIG.
2, positioned in the pupil plane of the system of FIG. 1, and
exposed to the same coherent and collimated light;
[0032] FIG. 10 is a diagram showing the data from the cornea R
after it has been surgically modified, again held in the container
of FIG. 2, positioned in the pupil plane of FIG. 1, and exposed to
the same coherent and collimated light;
[0033] FIG. 11 is a three dimensional presentation of the data set
forth in FIG. 7;
[0034] FIG. 12 is a three dimensional presentation of the data set
forth in FIG. 8;
[0035] FIG. 13 is a three dimensional presentation of the data set
forth in FIG. 9;
[0036] FIG. 14 is a three dimensional presentation of the data set
forth in FIG. 10;
[0037] FIG. 15 is a three dimensional presentation of the wavefront
of cornea LL which was modified by a LASIK procedure (prior to the
death of the donor), held in the container of FIG. 2, positioned in
the pupil plane of FIG. 1, and exposed to coherent, illuminated
light;
[0038] FIG. 16 is a three dimensional presentation of the wavefront
of cornea LR which was modified by a LASIK procedure (prior to the
death of the donor), held in the container of FIG. 2, positioned in
the pupil plane of FIG. 1, and exposed to coherent, illuminated
light; and
[0039] FIG. 17 is a schematic of the optical system used to
characterize in vivo corneas.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0040] With reference to FIG. 1, the apparatus 11 for determining
whether an in vitro cornea has been modified (either surgically or
otherwise) includes a source of collimated coherent light 13, a
cornea container 15, a distorted diffraction grating 17, a high
quality imaging lens (or lens set) 19, and a detector 21 (either
film or electronic) having a detector plane 23. (Grating 17, lens
19 and detector 21 are sometimes referred to as wavefront sensor
24.) Apparatus 11 also includes a beam path 25, a pupil plane 27,
first virtual plane 29, second virtual plane 31, and a computer 33.
Computer 33 is connected to detector 21, via a data acquisition
device such as a frame grabber (located within the computer
housing). Computer 33 stores the images form detector 21,
determines the wavefront from the stored images, and the analyzes
the wavefront for the characteristics that identify an altered
cornea (e.g. compares the wavefronts to a stored norm). The
representation of the virtual planes between source 13 and sensor
24 is for convenience only. In the preferred embodiment they are 73
cm on either side of pupil plane 27. Source 13 is a coherent laser
such as a 633 nm HeNe laser. As those skilled in the art will
appreciate non-coherent sources, such as spectrally band filtered
white light, could also be used.
[0041] With grating 17 in close proximity to lens 19 (typically
these two elements would, in fact, be in contact with each other
along beam path 25), the 0, +1 and -1 diffraction orders of grating
17 image pupil plane 27, virtual object plane 29 and virtual object
plane 31 onto detector plane 23. The higher order diffraction
orders are cut off by an appropriately placed field stop so as not
to contaminate the image of the 0 and +1 and -1 orders. Further,
with the zero order being an image of the pupil plane 27, the
images in the +1 and -1 diffraction orders correspond to virtual
image planes equidistant from and an opposite sides of pupil plane
27. The grating is distorted according to, 1 x ( x , y ) = W 20 d R
2 ( x 2 + y 2 )
[0042] where .lambda. is the optical wavelength, x and y are
Cartesian co-ordinates with an origin on the optical axis and R is
the radius of the grating aperture which is centered on the optical
axis. The parameter W.sub.20, defines the defocusing power of the
gratings, and is the standard coefficient of the defocus equivalent
on the extra pathlength introduced at the edge of the aperature, in
this case for the wavefront diffracted into the +1 order. The phase
change (.O slashed..sub.m) imposed on the wavefront diffracted into
each order m is given by, 2 m ( x , y ) = m 2 W 20 R 2 ( x 2 + y 2
)
[0043] The various containers in which donor corneas are stored are
unusable for optical diagnostics. The aberrations produced by the
walls of such containers mask the aberrations exhibited by corneas
both unaltered and altered. With reference to FIG. 2, optical
cornea container 15 includes cylindrical housing 41, first optical
window 43, second optical window 45, and fluid containment ring 47.
Housing 41 and ring 47 are concentric rings, both bonded to optical
window 43. Window 43 is a plano/plano lens having surfaces 49, 51
which are substantially concentric with respect to beam path 25 and
substantially perpendicular thereto. Similarly, window 45 is a
piano/plano lens having surfaces 53, 55 which are also
substantially concentric with and substantially perpendicular to
beam path 25. Collectively, windows 43 and 45, including surfaces
49, 51 and 53, 55 have total aberrations of less than .lambda./10.
In operation, cavity 57 is filled with Optisol.RTM., or another
solution suitable for the storage of donor corneas, to the top of
housing 41 so that the meniscus causes such fluid to slightly over
fill cavity 57. Window 45 is then slid over housing 41 without
trapping any air in cavity 57. Excess fluid is collected between
housing 41 and ring 47.
[0044] With reference to FIGS. 3 and 4, improved cornea container
15.sup.1 includes a cylindrical body portion 61, a cornea support
cage portion 63, and a cap portion 65. Body portion includes a
bottom surface 67, an upper skirt portion 69 having a groove 71
therein for supporting an o-ring seal 73 and threads (not shown),
and a cavity 74. Body portion 61 also includes a conical shaped
skirt 75 integral with bottom surface 67 for centrally positioning
cage portion 63 within body portion 61 as illustrated in FIGS. 3
and 4. Cage portion 63 includes a plurality of fingers 77, which
are supported by ring portion 79 of skirt 75 in a cylindrical
pattern concentric with axis 81. As best illustrated in FIG. 4, the
free ends of fingers 77 include, inter alia, an inwardly sloping
bevel 83 and notch 84 for supporting a donor cornea, such as
illustrated at 85. Finally, body portion 61 includes a plano/plano
lens 87 secured to ring portion 79. Lens 87 has parallel piano
surfaces 89 and 91 which are substantially centered with respect to
axis 81 and substantially perpendicular thereto. Cap portion 65
includes a skirt portion 93, a shoulder 95 which seats against 73,
a top portion 96, and an inner skirt portion 97 having a
circumferential lip 99. Inner surface 100 includes threads (not
shown) which mate with the threads (also not shown) on skirt 69.
Secured to lip 99 is a second plano/plano lens 101 having plano
parallel surfaces 103 and 105. When cornea container 15.sup.1 is
closed, with seal 73 received in circumferential recess 95,
surfaces 103 and 105 are substantially centered with respect to
axis 81 and substantially perpendicular thereto. Collectively, the
aberrations in lenses 87 and 101, including surfaces 89, 91, 103
and 105, have a total aberration of less than .lambda./10.
[0045] In operation, donor cornea 85 is placed in cage 63, with a
portion of the convex surface thereof in contact with bevels 83 and
the perimeter received within notches 84. In this position, donor
cornea is substantially centered about axis 81. Cavity 74 is then
filled with a suitable storage fluid and capped by screwing on cap
65. As can be seen from FIG. 4A, because inner skirt portion 97
projects inwardly, closure of cap 65 will force excess fluid out of
cavity 74. In the event that there is any under filling of cavity
74, any air which might be trapped in cavity 74 is collected in
annular area 107 (outside of the beam path).
[0046] With nothing in pupil plane 27 of apparatus 11 (e.g., cornea
container 15 removed) and source 13 present, the images recorded on
detector plane 23 are as illustrated in FIG. 1B. Data was collected
without any disturbances (i.e., no cornea container, cornea storage
solution, or cornea) to determine the residual errors in the optics
and, thus, establish the base line for instrument 11. With
reference to FIG. 5, the raw images as recorded by detector 21 are
shown along with the reduced Zernike terms, annotated to show where
the various types of data are located in the figure. All the data
are taken using a 633 nanometer HeNe laser as the illumination
source. Most of the error is tip and tilt, which is the result of
not accurately aligning wavefront sensor 24 and for not accurately
accounting for where the distorted grating images were actually
placed on detector plane 23. These two terms can be made equal to
zero by: (1) subtracting them in the analysis of the wavefront to
accommodate images that are not exactly centered on the same line;
or (2) a more precise alignment of wavefront sensor 24. The other
aberrations (e.g. focus) are seen to be small, on the order of or
less than 0.1 .lambda.. All the baseline aberrations, including tip
and tilt, can be subtracted from the cornea data.
[0047] Next, a baseline for optical system 11, with cornea
container 15 located in pupil plane 27 and cavity 57 filled with
Optisol.RTM. solution, but without a cornea, was established. The
baseline data is set forth in FIG. 6. Again, all aberrations can be
compensated for or eliminated using the criteria set forth above
with regard to FIG. 5.
[0048] After establishing the baseline, an unmodified donor cornea
L was placed in cornea container 15, centered as illustrated in
FIG. 2, filled with Optisol.RTM. solution, and then closed with
optical window 45 in the manner set forth above. Container 15 was
then placed in instrument 11, in optical beam path 25 and with
cornea L in pupil plane 27, as illustrated in FIG. 1. If necessary,
predetermined aberrations can be introduced into the beam path
prior to the beam reaching the pupil plane and subsequently
accommodated in the analysis of the data. The measured errors are
illustrated in FIG. 7. In this figure the tip and tilt terms are
irrelevant since they are associated with cornea container 15 and,
the orientation of cornea L therein. Cornea L is seen to have focus
and astigmatism errors.
[0049] As with cornea L, cornea R was placed in container 15, and
centered as set forth above. Cavity 57 as was then filled with
Optisol.RTM. and closed with optical window 45. Cornea container 15
was then placed in the pupil plane of instrument 11. The measured
errors are illustrated in FIG. 8. As with cornea L, the tip and
tilt terms for cornea R are irrelevant since they are associated
with container 15 and the specific orientation of cornea R therein,
both of which are not controlled. As is evident from FIG. 8, cornea
R has focus, astigmatism and coma errors.
[0050] The data illustrated in FIGS. 7 and 8 were collected using a
12 mm diameter collimated beam. The measurements were repeated with
an 8 mm, and 5 mm collimated beams to see if the measured
aberrations were being effected by the irregular outer edge of the
corneas. The effect of reducing the beam size was to improve the
quality of the images but at the expense of brightness and the area
examined. All data were collected with the beam centered on the
cornea.
[0051] To demonstrate the ability of apparatus 11 to detect
surgically modified corneas, cornea L was then modified using a PRK
procedure to add 4 diopters of focus change. Cornea R was also
subjected to the same procedure to add 8 diopters of focus change.
After modification each cornea was, in turn, again centered in
cavity 57, which was filled with Optisol.RTM. and closed, and
container 15 placed in apparatus 11 with the modified cornea again
in pupil plane 27.
[0052] The measured errors for cornea L (modified) are illustrated
in FIG. 9. Again, tip and tilt are irrelevant since they are
associated with cornea container 15 and the orientation of cornea L
(modified) therein. Cornea L (modified) is seen to have
considerably larger focus and astymatism errors then cornea L. The
higher order errors (coma 1, coma 2, trifoil 1, trifoil 2 and
spherical) are also considerably larger and provide one of the
basis for the determination that the cornea has been altered.
[0053] The measured errors for cornea R (modified) are illustrated
in FIG. 10. As before, tip and tilt are irrelevant. Cornea R
(modified) is seen to have considerably larger focus and astymatism
errors than cornea R. As with cornea L (modified) the higher order
aberrations have also increased (again indicating that the cornea
has been modified). A summary of the results is shown in Table 1.
Note that the measured difference (in waves) between the two
corneas is a factor of 2, the same amount of focus difference
introduced by the PRK procedure.
1TABLE 1 Focus Term Before Focus Term After Difference Cornea
Modification (waves) Modification (waves) (waves) L 1.77 3.23 1.46
R 1.024 4.132 3.108
[0054] An alternative way of illustrating the data set forth in
conjunction with FIGS. 7-10 is to present the distorted wavefronts
produced by the respective unaltered and altered corneas as three
dimensional images. This type of presentation is illustrated in
FIGS. 11-14, wherein: FIG. 11 corresponds to FIG. 7; FIG. 12, to
FIG. 8; FIG. 13, to FIG. 9; and FIG. 14, to FIG. 10. In FIGS.
11-16, the grey scale on the right is a representation of the
distortion. Note the similarities of the Gaussian-like slope of the
wavefront aberrations measured for the modified corneas, which
provides another basis for determining whether a cornea has been
modified.
[0055] Right (RL) and left (LL) corneas from a donor who had the
LASIK corrective surgery prior to death were measured in the same
manner as the unmodified corneas L and R (FIGS. 7 and 8) and the
PRK modified corneas (FIGS. 9 and 10). FIG. 15 is the left (LL)
LASIK modified cornea. FIG. 16 is the right (RL) LASIK modified
cornea. The characteristics Gausian-like shape of the wavefront
produced by the laser surgery is clearly present in both corneas.
As with the PRK modified corneas (FIGS. 9 and 10), the hier order
aberrations are considerably larger than those aberrations in the
unmodified corneas (FIGS. 7 and 8).
[0056] The basis for extracting the wavefront from the data
collected from detector 21 is to solve the Intensity Transport
Equation (I.T.E.). The I.T.E. is derived by expressing the
parabolic wave equation for complex amplitude in terms of intensity
(I) and phase (.O slashed.), and relates to the rate of change of
intensity in the direction of the propagation to the transverse
gradient and La Placian of the phase: 3 - 2 I z = I 2 + I
[0057] For a uniformly illuminate aperture, R, with perimeter P,
the ITE simplifies to 4 2 I I o I z = W R 2 - P
[0058] where W.sub.R is the aperture function (=1 inside R, =0
outside R), .delta..sub.p is a delta-function around P, and
.differential..phi./.diff- erential..eta. is the normal derivative
of .O slashed. on P.
[0059] Consider the problem of finding the phase at a particular
point r. We can express this in terms of an integral involving a
delta-function as follows:
.phi.(r)=.intg..sub.R.phi.(r').delta.(r-r')
[0060] If we have a Green's function satisfying 5 2 G ( r , r ' ) =
( r - r ' ) , G ( r - r ' ) | P = 0
[0061] then we can say
.phi.(r)=.intg..sub.R.phi.(r').gradient..sup.2G(r,r')
[0062] Applying Green's 2.sup.nd identify; 6 ( r ) = R G ( r , r '
) 2 ( r ' ) + P ( r ' ) G ( r - r ' ) - P G ( r , r ' ) ( r ' )
[0063] and the boundary condition on the Green's function; 7 ( r )
= R G ( r , r ' ) 2 ( r ' ) - P G ( r , r ' ) ( r ' ) = R G ( r , r
' ) ( 2 ( r ' ) - P ( r ' ) )
[0064] we get the solution. The term in parenthesis is the right
hand side of the ITE. The wavefront phase is thus obtained by
measuring the intensity derivative (the left hand side of the ITE),
multiplying by the Green's function and integrating; 8 ( r ) = - 2
1 Io R G ( r , r ' ) I ( r ' ) z
[0065] The intensity derivative, 9 I ( r ' ) z
[0066] is obtained by the subtraction of two pixellated images. The
Green's function is be pre-calculated on the appropriate grid and
the solution obtained by the matrix multiplication: 10 = - 2 1 I o
J Gi j ( I z ) j
[0067] The particular solution will vary, depending on the
specifics of the optical design, the detector and the distorted
grating used.
[0068] While the foregoing has dealt with donor corneas, the same
basic procedure can also be used on in vivo corneas. With reference
to FIG. 17, system 111 includes a source of collimated coherent
light 113, a beam splitter 115, a distorted diffraction grating
117, a high quality imaging lens or lens set 119, and a detector
121 (either film or electronic) having a detector plane 123. As
with instrument 11, grating 117, lens 119 and detector 121
constitute wavefront sensor 124. System 111 also includes a beam
light 125, a pupil plane 127, a first virtual plane 129, a second
virtual plane 131, and a computer 133 connected to detector 121 by
a data acquisition device, such as a frame grabber located within
the computer housing. As with the first embodiment, source 113 is a
coherent laser whose energy, when projected into the eye meets FDA
approved eye safe levels. Grating 117, which is also distorted
according to the grating equation set forth above, is in close
proximity with or touching lens 119. System 111 also includes
apparatus, not shown, for positioning the patient's head such that
his/her cornea is in pupil plane 127.
[0069] In operation the beam from source 113 is directed through
beam splitter 115, through the cornea 125 and of eye 127, onto the
retina 129 where it is reflected back through the cornea and then
directed, by beam splitter 115 to wavefront sensor 124. As with
instrument 11, the 0, +1 and --I diffraction orders of grating 117
image pupil plane 127, virtual object plane 129 and virtual object
plane 131 onto detector plane 123. Again, the higher order
diffraction orders are cut off by an appropriately placed field
stop so as not to contaminate the image of the 0 and +1 and -1
orders. Further, with zero order being an image of the pupil plane
127, the images in the +1 and -1 diffraction orders correspond to
virtual image planes equidistant from and opposite sides of pupil
plane 127. Computer 133 stores the images from detector 121,
determines the wavefront from the stored images in the manner set
forth above with the I.T.E. and a Green's function, and then
analyzes the wavefront for the characteristics that identify an
altered cornea (e.g., compares the wavefront to a stored norm).
[0070] Whereas the drawings and accompanying description have shown
and described the preferred embodiment of the present invention, it
should be apparent to those skilled in the art that various changes
may be made in the form of the invention without affecting the
scope thereof.
* * * * *