SYSTEM AND METHOD FOR OPHTHALMIC SURFACE MEASUREMENTS BASED ON SEQUENTIAL ESTIMATES

• US 20130138094A1
• Filed: 11/30/2012
• Published: 05/30/2013
• Est. Priority Date: 11/30/2011
• Status: Abandoned Application

• Current Assignee: AMO Development LLC (Johnson & Johnson)
• Original Assignee: AMO Development LLC (Johnson & Johnson)
• Inventors: Fabrikant, Anatoly
• Application Number:
  US13/690,979
• Publication Number:
  US 20130138094A1
• Time in Patent Office: Days
• US Class Current: 606/5
• CPC Class Codes: A61B 3/107 for determining the shape or measuring the curvature of the cornea
• CPC Class Codes: A61B 5/725 using specific filters therefor, e.g. Kalman or adaptive filters A61B5/316 take precedence
• CPC Class Codes: A61F 2009/00872 Cornea
• CPC Class Codes: A61F 2009/0088 based on wavefront
• CPC Class Codes: A61F 2009/00882 based on topography
• CPC Class Codes: A61F 9/00804 Refractive treatments
• CPC Class Codes: A61F 9/00806 Correction of higher orders
• CPC Class Codes: F04C 2270/041 Controlled or regulated

Abstract

Systems and methods for measuring a topography of an optical tissue surface of an eye are provided by combining measured elevations of the surface with a priori information of the surface to provide an estimate of mean and covariance of post-measurement orthogonal polynomial sequence amplitudes associated with the surface, determining a variance of elevation of the surface from the estimate, and constructing the topography from the estimate of mean and covariance of post-measurement amplitudes based on a comparison of the variance of elevation of the surface with a pre-determined threshold. The a priori information includes an estimate of mean and covariance of pre-measurement orthogonal polynomial sequence amplitudes associated with the surface.

Claims

1. A method of measuring a topography of a corneal surface, the method comprising:

measuring a plurality of elevations for a corneal surface;

combining the measured elevations with a priori information of the corneal surface to provide an estimate of mean and covariance of post-measurement Zernike amplitudes associated with the corneal surface, the a priori information comprising a plurality of mean and covariance of pre-measurement Zernike amplitudes associated with the corneal surface known prior to the measuring step;

determining a variance of elevation of the corneal surface from the estimate; and

constructing the topography of the corneal surface from the estimate based on a comparison of the variance with a pre-determined threshold.

2. The method according to claim 1, further comprising estimating the plurality of mean and covariance of Zernike amplitudes associated with the corneal surface prior to the measuring step.

3. The method of claim 1, further comprising decomposing each of the measured elevations into a Zernike series representation.

4. The method of claim 1, further comprising:

acquiring topography elevation fields measured of human eyes;

decomposing each of the topography elevation fields into a Zernike series;

evaluating a mean and a variance of each amplitude of the Zernike series; and

preparing the a priori information from the mean and the variance of each amplitude of the Zernike series.

5. The method of claim 1, wherein the combining step comprises inputting the a priori information into a Kalman-Bucy filter together with the measured elevations.

6. The method of claim 5, wherein the inputting step comprises applying the Kalman-Bucy filter according to

A_k⁺=A_k⁻

+{circumflex over (K)}·

{{right arrow over (H)}−

Ĝ

·

A_k⁻

}, M_k⁺={circumflex over (K)}·

{Î

−

{circumflex over (K)}Ĝ

}·

M_k⁻

{circumflex over (K)}={circumflex over (M)}<sup>−

1</sup>Ĝ

^T{circumflex over (F)}

{circumflex over (F)}={Ĝ

M⁻

−

Ĝ

^T+{circumflex over (N)}}<sup>−

1</sup>

where A_k⁻

represents Zernike amplitudes prior to assimilation of measurement data, M_k⁻

is a covariance matrix of A_k⁻

, A_k⁺ represents Zernike amplitudes after assimilation of measurement data, M_k⁺ is a covariance matrix of A_k⁺, {right arrow over (H)} is a vector of the measured elevations, Ĝ

is an operator of surface reconstruction from the Zernike amplitudes, {circumflex over (K)} is a Kalman-Bucy gain, {circumflex over (F)} is a D×

D matrix, {circumflex over (N)} is a data noise covariance matrix, {circumflex over (M)} is covariance matrix of the measured amplitudes, and Î

is a unitary matrix.

7. A method of planning a refractive correction treatment for an eye, the method comprising:

measuring a plurality of elevations for a corneal surface of the eye;

combining the measured elevations with a priori information of the corneal surface to provide an estimate of mean and covariance of post-measurement Zernike amplitudes associated with the corneal surface, the a priori information comprising a plurality of mean and covariance of pre-measurement Zernike amplitudes associated with the corneal surface known prior to the measuring step;

determining a variance of elevation of the corneal surface from the estimate;

constructing the topography of the corneal surface from the estimate based on a comparison of the variance with a pre-determined threshold;

determining ablation properties locally across the corneal surface based on the topography; and

formulating a treatment plan using the ablation properties by adjusting a first virtual ablation shape to form a second virtual ablation shape, the first virtual shape representing a depth of material to be removed from the treatment area to form a desired shape, the second virtual shape being formed from the first virtual shape in response to the topography.

8. A method of treating a cornea of a patient'"'"'s eye with a laser beam, the method comprising:

measuring a plurality of elevations for a surface of the cornea;

combining the measured elevations with a priori information of the surface to provide an estimate of mean and covariance of post-measurement Zernike amplitudes associated with the surface, the a priori information comprising a plurality of mean and covariance of pre-measurement Zernike amplitudes associated with the surface known prior to the measuring step;

determining a variance of elevation of the corneal surface from the estimate;

constructing the topography of the corneal surface from the estimate based on a comparison of the variance with a pre-determined threshold;

mapping angles between the surface and the laser beam over a treatment area;

determining ablation properties locally across the treatment area in response to the mapped angles;

formulating a treatment plan using the ablation properties by adjusting a first virtual ablation shape to form a second virtual ablation shape, the first virtual shape representing a depth of material to be removed from the treatment area to form a desired shape, the second virtual shape being formed from the first virtual shape in response to the mapped angles; and

ablating the treatment area according to the treatment plan to form the desired shape in the surface.

9. The method according to claim 8 wherein the desired shape is based at least in part on a result of a measurement selected from the group consisting of an aberration measurement of the eye, a refractive measurement of the eye and a topography measurement of the eye.

10. A system for treating a corneal surface of a patient'"'"'s eye with a laser beam, the eye having a refractive defect, wherein a desired refractive correcting shape mitigates the refractive defect, the system comprising:

a laser emitting a beam of an ablative light energy; and

at least one processor coupled to the laser beam and having a computer program, the computer program embodying instructions for;

combining measured elevations of the corneal surface with a priori information of the corneal surface to provide an estimate of mean and covariance of post-measurement Zernike amplitudes associated with the corneal surface, the a priori information comprising a plurality of mean and covariance of pre-measurement Zernike amplitudes associated with the corneal surface known prior to the measuring step;

determining a variance of elevation of the corneal surface from the estimate;

constructing the topography of the corneal surface from the estimate based on a comparison of the variance with a pre-determined threshold

determining ablation properties locally across the corneal surface based on the topography;

formulating a treatment plan using the ablation properties by adjusting a first virtual ablation shape to form a second virtual ablation shape, the first virtual shape representing a depth of material to be removed from the treatment area to form a desired shape, the second virtual shape being formed from the first virtual shape in response to the topography; and

controlling an ablative treatment using the treatment plan from the second virtual shape so that the treatment forms the desired refractive correcting shape in the surface.

11. A method of measuring a topography of an optical tissue surface of an eye, the method comprising:

combining measured elevations of the surface with a priori information of the surface to provide an estimate of mean and covariance of post-measurement orthogonal polynomial sequence amplitudes associated with the surface, the a priori information comprising an estimate of mean and covariance of pre-measurement orthogonal polynomial sequence amplitudes associated with the surface;

determining a variance of elevation of the surface from the estimate of mean and covariance of post-measurement amplitudes associated with the surface, the variance representing a measure of measurement quality; and

constructing the topography from the estimate of mean and covariance of post-measurement amplitudes based on a comparison of the variance of elevation of the surface with a pre-determined threshold.

12. The method according to claim 11, wherein the optical tissue surface is selected from a group consisting of a corneal surface of the eye and a wavefront of the eye.