SYSTEM AND METHOD FOR OPHTHALMIC SURFACE MEASUREMENTS BASED ON SEQUENTIAL ESTIMATES

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)} −1 Ĝ T {circumflex over (F)}

{circumflex over (F)}={ĜM − −Ĝ T +{circumflex over (N)}} −1

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.