USRE38839EExpiredUtility
Methods and devices to design and fabricate surfaces on contact lenses and on corneal tissue that correct the eye's optical aberrations
Est. expirySep 20, 2019(expired)· nominal 20-yr term from priority
Inventors:Peter C. Magnante
A61B 3/1015
65
PatentIndex Score
42
Cited by
17
References
26
Claims
Abstract
Methods and devices are described that are needed to design and fabricate modified surfaces on contact lenses or on corneal tissue that correct the eye's optical aberrations beyond defocus and astigmatism. The invention provides the means for: 1) measuring the eye's optical aberrations either with or without a contact lens in place on the cornea, 2) performing a mathematical analysis on the eye's optical aberrations in order to design a modified surface shape for the original contact lens or cornea that will correct the optical aberrations, 3) fabricating the aberration-correcting surface on a contact lens by diamond point turning, three dimensional contour cutting, laser ablation, thermal molding, photolithography, thin film deposition, or surface chemistry alteration, and 4) fabricating the aberration-correcting surface on a cornea by laser ablation.
Claims
exact text as granted — not AI-modified1. A method for correcting the optical aberrations beyond defocus and astigmatism of an eye fitted with an original contact lens having a known anterior surface shape by providing a modified or new contact lens which has its anterior surface reshaped from said original contact lens's anterior surface, comprising the steps of:
a) measuring said optical aberrations of an eye fitted with an original contact lens,
b) performing a mathematical analysis of said eye's optical aberrations when fitted with original contact lens to determine said modified anterior contact lens surface shape, and
c) fabricating said modified anterior contact lens surface by methods that remove, add or compress material or alter the surface chemistry.
2. A method as claimed in claim 1 wherein said measuring of the eye's optical aberrations comprises the sub-steps of:
i) optically projecting the image of a small point of incoherent light onto the macular region of the eye's retina,
ii) optically conveying the image of the eye's pupil, through which light scattered back from the macular region emerges, onto a microlens array,
iii) optically conveying the multiple spot images formed by said microlens array onto the image plane of a photo-electronic imaging device,
iv) transforming by means of the photo-electronic imaging device the multiple spot images formed by said microlens array to an electronic signal which represents the images,
v) conveying said electronic signal to a computer for data processing,
vi) processing first the electronic signal with said computer in order to obtain the coordinate locations of the centroids of said multiple spot images formed by said microlens array, and
vii) processing next said coordinate locations with said computer in order to obtain the slopes of optical rays emerging from the subject's pupil at said coordinate locations.
3. A method as claimed in claim 1 wherein said mathematical analysis comprises the sub-steps of:
i) determining mathematically the normal vectors of said original contact lens's anterior surface,
ii) determining mathematically the directional derivatives of said modified or new contact lens's anterior surface using data of said normal vectors of original contact lens's anterior surface and data of said eye's optical aberrations, and
iii) fitting mathematically by the method of least squares said directional derivatives to the corresponding directional derivatives of a polynomial expression that represents said modified or new contact lens's anterior surface.
4. A method as claimed in claim 1 wherein said step of fabricating said modified or new contact lens's anterior surface is chosen from the group of methods comprising diamond point machining, laser ablation, thermal molding, photo-lithographic etching, thin film deposition, and surface chemistry alteration.
5. A method for correcting the optical aberrations beyond defocus and astigmatism of an eye with an original anterior corneal surface of known shape by providing a modified anterior corneal surface shape, comprising the steps of:
a) measuring said eye's optical aberrations,
b) performing a mathematical analysis of said eye's optical aberrations to determine said modified anterior corneal surface shape,
c) fabricating said modified anterior corneal surface by laser ablation.
6. A method as claimed in claim 5 wherein said measuring of the eye's optical aberrations comprises the sub-steps of:
i) optically projecting the image of a small point of incoherent light onto the macular region of the eye's retina,
ii) optically conveying the image of the eye's pupil, through which light scattered back from the macular region emerges, onto a microlens array,
iii) optically conveying the multiple spot images formed by said microlens array onto the image plane of a photo-electronic imaging device,
iv) transforming by means of the photo-electronic imaging device the multiple spot images formed by said microlens array to an electronic signal which represents the images,
v) conveying said electronic signal to a computer for data processmg,
vi) processing first the electronic signal with said computer in order to obtain the coordinate locations of the centroids of said multiple spot images formed by said microlens array, and
vii) processing next said coordinate locations with said computer in order to obtain the slopes of optical rays emerging from the subject's pupil at said coordinate locations.
7. A method as claimed in claim 5 wherein said mathematical analysis comprises the sub-steps of:
i) determining mathematically the normal vectors of said original anterior corneal surface,
ii) determining mathematically the directional derivatives of said modified anterior corneal surface using data of said normal vectors of original anterior corneal surface and data of said eye's optical aberrations, and
iii) fitting mathematically by the method of least squares said directional derivatives to the corresponding directional derivatives of a polynomial expression that represents said modified anterior corneal surface.
8. An ophthalmic device for measuring the eye's optical aberrations either with or without a contact lens in place on the cornea, including;
a) an optical projection system for imaging a small point of light onto the macular region of the eye's retina with an improvement provided by use of an incoherent light source chosen from the group comprising laser diodes operated below threshold, light emitting diodes, arc and plasma sources, and incandescent filament lamps,
b) an optical image acquisition system for conveying the image of the eye's pupil, through which light scattered back from the macular region emerges, onto a microlens array,
c) a microlens array to form multiple spot images onto the image plane of a photo-electronic imaging device,
d) a photo-electronic imaging device for transforming said multiple spot images formed by said microlens array to an electronic signal which represents the images,
e) a computer for processing the electronic signal in order, first, to obtain the coordinate locations of the centroids of said multiple spot images formed by said microlens array and, second, to obtain the slopes of optical rays emerging from the subject's pupil at said coordinate locations, and
f) an optical alignment system allowing the entering beam to be accurately centered with respect to the subject's pupil.
9. An ophthalmic device as claimed in claim 8 wherein said optical projection system includes an optical isolator consisting of a quarter-wave plate and polarizer.
10. An ophthalmic device as claimed in claim 8 wherein said optical projection system includes a field stop placed at a location that is optically conjugate to the eye's retina.
11. An ophthalmic device as claimed in claim 8 wherein said optical projection system includes both an optical isolator consisting of a quarter-wave plate and polarizer, and a field stop placed at a location that is optically conjugate to the eye's retina.
12. An ophthalmic device as claimed in claim 8 wherein said photo-electronic imaging device is chosen from the group comprising vidicons, charge-coupled devices, and charge-injection devices.
13. A device for thermally forming surfaces on thermoplastic contact lens blanks that correct eyes' optical aberrations beyond defocus and astigmatism consisting of a die with an adjustable surface shape (either continuous or discontinuous) formed by computer-controlled electromechanical actuators or electromechanical fingers which are known in the field of adaptive optics.
14. A lathe device for machining surfaces on contact lens blanks that correct eyes' optical aberrations beyond defocus and astigmatism consisting of a rotating spindle onto which a contact lens blank is fastened, translation slides for precisely positioning a diamond point cutting tool with respect to the surface of the contact lens blank, and a programmed computer that controls the movement of the translation slides synchronously with the rotational location of the spindle.
15. A contour cutting device for machining surfaces on contact lens blanks that correct eyes'optical aberrations beyond defocus and astigmatism consisting of a means for supporting and holding stationary a contact lens blank, translation slides for precisely positioning in three dimensions a diamond point cutting tool with respect to the surface of the contact lens blank, and a programmed computer that controls the movement of the translation slides.
16. A method for correcting optical aberrations beyond defocus and astigmatism of an eye comprising:
a ) fitting the eye with a first contact lens having a known anterior surface shape that is corrected for at least focus, b ) measuring the optical aberrations of the eye fitted with the first contact lens, c ) performing a mathematical analysis of the eye's optical aberrations when fitted with the first contact lens to determine a modified anterior contact lens surface shape, and d ) fabricating a second contact lens having the modified anterior contact lens surface.
17. A method as claimed in claim 16 performing the mathematical analysis to at least the eye's 4 th order optical aberrations of the eye when fitted with the first contact lens to determine the second contact lens surface shape, and the anterior surface of the second contact lens to have the modified anterior surface that corrects the eye to at least the 4 th order aberration.
18. A method as claimed in claim 17 wherein the measuring of the eye's optical aberrations comprises the sub- steps of: i ) optically projecting the image of a small point of incoherent light onto the macular region of the eye's retina, ii ) optically conveying the image of the eye's pupil, through which light scattered back from the macular region emerges, onto a microlens array, iii ) optically conveying the multiple spot images formed by the microlens array onto the image plane of a photo - electronic imaging device, iv ) transforming by means of the photo - electronic imaging device the multiple spot images formed by the microlens array to an electronic signal which represents the images, v ) conveying the electronic signal to a computer for data processing, vi ) processing first the electronic signal with the computer in order to obtain the coordinate locations of the centroids of the multiple spot images formed by the microlens array, and vii ) processing next the coordinate locations with the computer in order to obtain the slopes of optical rays emerging from the subject's pupil at the coordinate locations.
19. A method as claimed in claim 17 wherein the mathematical analysis comprises the sub- steps of: i ) determining mathematically the normal vectors of the first contact lens's anterior surface, ii ) determining mathematically the directional derivatives of the second contact lens's anterior surface using data of the normal vectors of the first contact lens's surface and data of the eye's optical aberrations, and iii ) fitting mathematically by the method of least squares the directional derivatives to the corresponding directional derivatives of a polynomial expression that represents the second contact lens's anterior surface.
20. A method as claimed in claim 1 wherein the original contact lens's anterior surface contour function z ( x,y ) and the eye's optical aberrations, represented by optical rays emerging from the pupil given by vector function B ( x,y ), are used to find the surface contour function z′ ( x,y ) of the modified or new contact lens by the following mathematical procedures: a ) z′ ( x,y ) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, a j ·g j ( x,y ), consists of an unknown constant coefficient a j and a known function g j ( x,y ) as shown in following Equation ( 1 )
z
′
(
x
,
y
)
≡
∑
j
a
j
·
g
j
(
x
,
y
)
(
1
)
b ) following Equation ( 2 ) is obtained by taking vector gradients of both sides of Equation ( 1 ) where grad z′ ( x,y ) is a two - dimensional vector having components [ δ z ′ ( x , y ) / δ x , δ z ′ ( x , y ) / δ y ] grad z ′ ( x , y ) = ∑ j a j · grad g j ( x , y ) ( 2 )
c ) the normal vectors of the original contact lens's anterior surface, given by vector function N ( x,y ), are found by taking the vector gradient of z ( x,y ) and normalizing it to unity as shown in the following Equations ( 3 A ) to ( 3 D )
Nx ≡ 1 MAG · - δ z ( x , y ) δ x , ( 3 A ) Ny ≡ 1 MAG · - δ z ( x , y ) δ y , ( 3 B ) Nz ≡ 1 MAG ( 3 C )
MAG≡[ 1 + (δ z ( x,y ) /δx ) 2 +(δ z ( x,y )/δ y ) 2 ] 1/2 ( 3 D )
d ) the rays incident on the original contact lens coming from within the eye are given by vector function A ( x,y ) which is found by applying Snell's law of refraction at the air/lens interface which relates A ( x,y ) to known vector function B ( x,y ) representing the emerging rays, and vector function N ( x,y ) given by Equations ( 3 A )-( 3 D ),
e ) the normal vectors of the modified or new contact len's anterior surface, given by the vector function N′, are found from the following Equation ( 4 ) where vector function B′ is represented by unit vectors pointed along the positive z - axis, and n is the lens's refractive index N ′ ≡ ( n · A - B ′ ) n · A - B ‵ ( 4 )
f ) the directional derivatives of the modified or new contact lens's anterior surface are obtained from the following Equation ( 5 ) using the components of vector function N′=[N′ x , N′ y , N′ z ] found from Equation ( 4 )
δ z ′ δ x ≡ - N x ‵ N z ‵ and δ z ′ δ y ≡ - N y ‵ N z ‵ ( 5 )
g ) apply the method of least squares to minimize the square the difference between the component values of grad z′ ( x,y ) found from Equation ( 5 ) and the component values of grad z′ ( x,y ) given by the approximation series, Equa . ( 2 ), in order to obtain matrix Equation ( 6 )
M·a≡b ( 6 )
where
M
(
i
,
j
)
≡
∑
x
,
y
(
grad
g
i
·
grad
g
j
)
and
b
i
≡
∑
x
,
y
(
grad
g
i
·
grad
z
‵
)
(
7
)
h ) obtain the inverse of matrix M, and then find the a - coefficients from matrix Equation ( 8 )
a≡M −1 ·b ( 8 )
i ) the a - coefficients determined from Equation ( 8 ) are used in Equation ( 1 ) which defines the modified or new contact lens's anterior surface, z′ ( x,y ) when it is represented, for example, by a 5 th order Taylor series.
21. A methdo as claimed in claim 19 wherein the first Contact lens's anterior surface contour function z( x,y ) and the eye's optical aberrations, represented by optical rays emerging from the pupil given by vector function B ( x,y ), are used to find the surface contour function z′ ( x−y ) of the second contact lens by the following mathematical procedures: a ) z′ ( x,y ) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, a j ·g j ( x,y ), consists of an unknown constant coefficient a j and a known function g j ( x,y ) as shown in following Equation ( 1 )
z ′ ( x , y ) ≡ ∑ j a j · g j ( x , y ) ( 1 ) b ) following Equation ( 2 ) is obtained by taking vector gradients of both sides of Equation ( 1 ) where grad z′ ( x,y ) is a two - dimensional vector having components [ δ z ′ ( x , y ) / δ x , δ z ′ ( x , y ) / δ y ] grad z ′ ( x , y ) = ∑ j a j · grad g j ( x , y ) ( 2 ) c ) the normal vectors of the first contact lens's anterior surface, given by vector function N ( x,y ), are found by taking the vector gradient of z ( x,y ) and normalizing it to unity as shown in the following Equations ( 3 A ) to ( 3 D )
Nx ≡ 1 MAG · - δ z ( x , y ) δ x , ( 3 A ) Ny ≡ 1 MAG · - δ z ( x , y ) δ y , ( 3 B ) Nz ≡ 1 MAG ( 3 C )
MAG≡[ 1 + (δ z ( x,y )/δ x ) 2 +(δ z ( x,y )/δ y ) 2 ] 1/2 ( 3 D ) d ) the rays incident on the first contact lens coming from within the eye are given by vector function A ( x,y ) which is found by applying Snell's law of refraction at the air/lens interface which relates A ( x,y ) to known vector function B ( x,y ) representing the emerging rays, and vector function N ( x,y ) given by Equations ( 3 A )-( 3 B ), e ) the normal vectors of the second contact lens's anterior surface, given by the vector function N′, are found from the following Equation ( 4 ) where vector function B′ is represented by unit vectors pointing along the positive z - axis, and n is the lens's refractive index N ′ = ( n · A - B ′ ) n · A - B ‵ ( 4 ) f ) the directional derivatives of the second contact lens's anterior surface are obtained from the following Equation ( 5 ) using the components of vector function N′=[N′ x ,N′ y ,N′ z ] found from Equation ( 4 )
δ z ′ δ x ≡ - N x ‵ N z ‵ and δ z ′ δ y ≡ - N y ‵ N z ‵ ( 5 ) g ) apply the method of at least squares to minimize the square the difference between the component values of grad z′ ( x,y ) found from Equation ( 5 ) and the component values of grad z′ ( x,y ) given by the approximation series, Equa . ( 2 ), in order to obtain matrix Equation ( 6 )
M·a≡b ( 6 )
where
M
(
i
,
j
)
≡
∑
x
,
y
(
grad
g
i
·
grad
g
j
)
and
b
i
=
∑
x
,
y
(
grad
g
i
·
grad
z
‵
)
(
7
)
h ) obtain the inverse of matrix M, and then find the a - coefficient from matrix Equation ( 8 )
a≡M −1 ·b (8)
i ) the a - coefficients determined from Equation ( 8 ) are used in Equation ( 1 ) which defines the second contact lens's anterior surface, z′ ( x,y ) when it is represented, for example, by a 5 th order Taylor series.
22. A method as claimed in claim 5 wherein the original cornea's anterior surface contour function z( x,y ) and the eye's optical aberrations, represented by optical rays emerging from the pupil given by vector function B ( x,y ), are used to find the surface contour function z′ ( x,y ) of the modified cornea by the following mathematical procedures: a ) z′ ( x,y ) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, a j ·g j ( x,y ), consists of an unknown constant coefficient a j and a known function g j ( x,y ) as shown in following Equation ( 1 )
z ′ ( x , y ) ≡ ∑ j a j · g j ( x , y ) ( 1 ) b ) following Equation ( 2 ) is obtained by taking vector gradients of both sides of Equation ( 1 ) where grad z′ ( x,y ) is a two-dimensional vector having components [ δ z ′ ( x , y ) / δ x , δ z ′ ( x , y ) / δ y ] grad z ′ ( x , y ) = ∑ j a j · grad g j ( x , y ) ( 2 ) c ) the normal vectors of the original cornea's anterior surface, given by vector function N ( x,y ), are found by taking the vector gradient of z ( x,y ) and normalizing it to unity as shown in the following Equations ( 3 A ) to ( 3 D )
Nx ≡ 1 MAG · - δ z ( x , y ) δ x , ( 3 A ) Ny ≡ 1 MAG · - δ z ( x , y ) δ y , ( 3 B ) Nz ≡ 1 MAG ( 3 C )
MAG≡[ 1 + (δ z ( x,y ) /δx ) 2 +( δz ( x,y ) /δy ) 2 ] 1/2 ( 30 ) d ) the rays incident on the original cornea coming from within the eye are given by vector function A ( x,y ) which is found by applying Snell's law of reflection at the air/cornea interface which relates A ( x,y ) to known vector function B ( x,y ) representing the emerging rays, and vector function N ( x,y ) given by Equations ( 3 A )-( 3 B ), e ) the normal vectors of the modified cornea's anterior surface, given by the vector function N′, are found from the following Equation ( 4 ) where vector function B′ is represented by unit vectors pointing along the positive z - axis, and n is the cornea's refractive index N ′ ≡ ( n · A - B ′ ) n · A - B ‵ ( 4 ) f ) the directional derivatives of the modified cornea's anterior surface are obtained from the following Equation ( 5 ) using the components of vector function N′=[N′ x , N′ y , N′ z ] found from Equation ( 4 )
δ z ′ δ x ≡ - N x ‵ N z ‵ and δ z ′ δ y ≡ - N y ‵ N z ‵ ( 5 ) g ) apply the method of least squares to minimize the square the difference between the component values of grad z′ ( x,y ) found the Equation ( 5 ) and the component values of grad z′ ( x,y ) given by the approximation series, Equa . ( 2 ), in order to obtain matrix Equation ( 6 )
M·a≡b ( 6 )
where
M
(
i
,
j
)
≡
∑
x
,
y
(
grad
g
i
·
grad
g
j
)
and
b
i
=
∑
x
,
y
(
grad
g
i
·
grad
z
‵
)
(
7
)
h ) obtain the inverse of matrix M, and then find the a - coefficients from matrix Equation ( 8 )
a≡M −1 ·b
i ) the a - coefficient determined from Equation ( 8 ) are used in Equation ( 1 ) which defines the modified cornea's anterior surface, z′ ( x,y ) when it is represented, for example, by a 5 th order Taylor series.
23. A contact lens comprising an anterior surface which is fabricated to correct the optical aberration to at least 4 th order of a person's eye.
24. The contact lens of claim 23 wherein the measuring of the eye's optical aberrations is by steps of:
( i ) optically projecting the image of a small point of incoherent light onto the macular region of the eye's retina, ( ii ) optically conveying the image of the eye's pupil, through which light scattered back from the macular region emerges onto a microlens array, ( iii ) optically conveying the multiple spot images formed by the microlens array onto the image plane of a photo - electronic imaging device, ( iv ) transforming by means of the photo - electronic imaging device the multiple spot images formed by the microlens array to an electronic signal which represents the images; ( v ) conveying the electronic signal to a computer for data processing, ( vi ) processing first the electronic signal with the computer in order to obtain the coordinate locations of the centroids of the multiple spot images formed by the microlens array, and ( vii ) processing next the coordinate locations with the computer in order to obtain the slopes of optical rays emerging from the subject's pupil at the coordinate locations.
25. The contact lens of claim 23 wherein the mathematical analysis comprises the sub- steps of: ( a ) determining mathematically the normal vectors of a first contact lens anterior surface; ( b ) determining mathematically the directional derivatives of the a second contact lens anterior surface using data of the normal vectors of the first contact lens anterior surface and data of the eye's optical aberrations; and ( c ) fitting mathematically by the method of least squares the directional derivatives to the corresponding directional derivatives of a polynomial expression that represents the second contact lens anterior surface.
26. The contact lens of claim 23 wherein the first contact lens anterior surface contour function z( x,y ) and the eye's optical aberrations, represented by optical rays emerging from the pupil given by vector function B ( x,y ), are used to find the surface contour function z′ ( x,y ) of the second contact lens by the following mathematical procedures: ( a ) z′ ( x,y ) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, a j ·g j ( x,y ), consists of an unknown constant coefficient a j and a known function g j ( x,y ) as shown in following Equation ( 1 )
z ′ ( x , y ) ≡ ∑ j a j · g j ( x , y ) ( 1 )
b ) following Equation ( 2 ) is obtained by taking vector gradients of both sides of Equation ( 1 ) where grad z′ ( x,y ) is a two - dimensional vector having components [δ z′ ( x,y ) /δx, δz′ ( x,y )/ δy] grad z ′ ( x , y ) = ∑ j a j · grad g j ( x , y ) ( 2 ) c ) the normal vectors of the first contact lens's anterior surface, given by vector function N ( x,y ), are found by taking the vector gradient of z ( x,y ) and normalizing it to unity as shown in the following Equations ( 3 A ) to ( 3 D )
Nx ≡ 1 MAG · - δ z ( x , y ) δ x , ( 3 A ) Ny ≡ 1 MAG · - δ z ( x , y ) δ y , ( 3 B ) Nz ≡ 1 MAG ( 3 C )
MAG≡[ 1 + ( δz ( x,y ) /δx ) 2 +( δz ( x,y ) /δy ) 2 ] ½ ( 3 D ) d ) the rays incident on the first contact lens coming from within the eye are given by vector function A ( x,y ) which is found by applying Snell's law of refraction at the air/lens interface which relates A ( x,y ) to known vector function B ( x,y ) representing the emerging rays, and vector function N ( x,y ) given by Equations ( 3 A )−( 3 B ), e ) the normal vectors of the second contact lens's anterior surface, given by the vector function N′, are found from the following Equation ( 4 ) where vector function B′ is represented by unit vectors pointing along the positive z - axis, and n is the lens's ( or cornea's ) refractive index N ′ ≡ ( n · A - B ′ ) n · A - B ‵ ( 4 ) f ) the directional derivatives of the second contact lens's anterior surface are obtained from the following Equation ( 5 ) using the components of vector function N′=[N′ x , N′ y , N′ z ] found from Equation ( 4 )
δ z ′ δ x ≡ - N x ‵ N z ‵ and δ z ′ δ y ≡ - N y ‵ N z ‵ ( 5 ) g ) apply the method of least squares to minimize the square the difference between the component values of grad z′ ( x,y ) found from Equation ( 5 ) and the component values of grad z′ ( x,y ) given by the approximation series, Equa . ( 2 ), in order to obtain matrix Equation ( 6 )
M·a≡b ( 6 )
where
M
(
i
,
j
)
≡
∑
x
,
y
(
grad
g
i
·
grad
g
j
)
and
b
i
≡
∑
x
,
y
(
grad
g
i
·
grad
z
‵
)
(
7
)
h ) obtain the inverse of matrix M, and then find the a - coefficients from matrix Equation ( 8 )
a≡M − ·b ( 8 )
i ) the a - coefficients determined from Equation ( 8 ) are used in Equation ( 1 ) which defines the second contact lens's anterior surface, z′ ( x,y ) when it is represented, for example, by a 5 th order Taylor series.Cited by (0)
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