Patent Description:
The invention relates also to a method for calculating an ophthalmic lens using this method.

In order to customize the ophthalmic lens for a specific subject, geometrical, postural and behavioral parameters of the subject and/or of the subject with his/her eyeglasses need to be determined.

Among these parameters, the position of a center of rotation of at least one of the eyes is determined.

Movements of each eye of a subject can generally be considered as being a combination of rotations about a particular point that is referred to as the center of rotation of the eye or "eye rotation center", hereinafter also referred to as ERC.

It is desirable to determine the position of this particular point, for example to perform calculations of a personalized optical design by ray tracing for the corrective lens that is to be fitted properly to a frame chosen by the subject.

In present practice, the position of the ERC may be deduced approximately from the position of the cornea by assuming a mean value for the radius of the eye, typically a value of about <NUM> millimeters (mm). Unfortunately, the radius of the eye varies significantly from one subject to another, such that this approximation leads to significant errors that are highly penalizing for the pertinence of the personalized optical design calculation.

In order to determine the position of the ERC, it is also known a method based on image processing, wherein one captures, by means of an image capture apparatus, at least two facial images of the subject equipped with a reference accessory while the subject looks at this image capture apparatus.

These images are treated in order to determine the ERC. The reference accessory gives information on the relative position of the head of the subject and the image capture device.

However, such method takes time to be carried out and is not particularly well suited to be performed rapidly in the shop of an eye-care practitioner.

Moreover, such method is very precise, whereas a lower level of precision is required, for example to discriminate those patients having an ERC with a position situated outside of the normal range.

<CIT> discloses to determine the position of the centre of rotation of the eye by evaluating the ellipses formed by the iris and the corresponding optical axes in a plurality of images, then intersecting said optical axes. The Gullstrand eye model can be used. <CIT> discloses to determine the position of the centre of rotation of the eye by first determining the apex of the cornea from an image of the eye, then adding a quantity based on the Gullstrand eye model along the optical axis. <CIT> discloses to determine the distance of the center of rotation of the eye from a camera capturing images of the eye using the iris contours.

Therefore one object of the invention is to provide an easy-to-implement method to determine quickly an approximate value of the position of the ERC of a subject, in particular without the need of using a reference accessory.

The above object is achieved according to the invention by the method defined in claim <NUM>.

By "geometric model" of the eye, one understands any physical model adapted to summarize both the optical path of the light through a human eye, and also the movements of this eye.

As the physiological structure of a human eye is very complicated, a complete geometric model of an eye is very hard to elaborate, taking into account all the optical surfaces and physical media involved in the optical path of the light through the eye.

Advantageously, a simple geometric model may be used wherein the geometry of the eye is partially modeled with only two spheres nested one in the other (see <NPL>). A first part of one sphere can be contemplated as the sclera of the eye: the eye rotation center is positioned at the center of this sphere. A second part of the other sphere can be contemplated as the cornea of the eye.

Another possible geometric model may be used wherein the geometry of the eye is modeled with one sphere for the sclera of the eye and one ellipsoid for the cornea of the eye. In this model, the position of the eye rotation may be determined as a function of:.

The eccentricity of the cornea may be found by a measurement using an apparatus called an auto kerato-refractometer (also known as "AKR"), for example the VX120 Multi-Diagnostic Unit from the US company Visionix.

With this apparatus, one gets easily the 3D profile of the cornea and one can then find the ellipsoid which models the cornea in the best way.

Other advantageous and non-limiting features of the method according to the invention include:.

The invention also relates to a method for calculating a personalized ophthalmic lens for a subject comprising:.

The invention finally relates to the device defined in claim <NUM>.

The following description, enriched with joint drawings that should be taken as non limitative examples, will help understand the invention and figure out how it can be realized.

We represent on <FIG> a section view of a simplified physiological structure of a human eye <NUM> (one the two eyes of a subject, who is not represented on <FIG>). This structure is basically, with a quite good approximation, a shape of revolution around an optical axis <NUM>, said optical axis <NUM> passing by the eye rotation center <NUM> (hereinafter noted ERC) of the eye <NUM>.

It is well-known that the eye <NUM> comprises mainly a cornea <NUM>, an intra-ocular lens <NUM> (hereinafter referred to as lens <NUM>) of variable optical power, and a sclera <NUM>.

The cornea <NUM> is formed by two surfaces <NUM>, <NUM>: a front (anterior) face <NUM> and a rear (posterior) face <NUM>. Geometrically, those surfaces are in reality very complex, e.g. aspherical, yet in practice, and in the framework of this application, one will assume that the front face <NUM> and the rear face <NUM> are substantially spherical surfaces having said optical axis <NUM> as an axis of revolution (the respective centers of the two spheres are on this optical axis), said optical axis <NUM> intersecting said surfaces <NUM>, <NUM> at points <NUM>, <NUM> (see <FIG>). In the following, the intersection point <NUM> will be referred to as the "apex" of the cornea <NUM>. Optically, the front and back faces <NUM>, <NUM> of the cornea <NUM> form two optical spherical (concave) diopters of radius RC,<NUM> and RC,<NUM> which have here positive values with the geometrical convention chosen for <FIG> (see arrow at the top of this figure indicating the direction of propagating light).

Right behind the cornea <NUM> is the anterior chamber <NUM> of the eye <NUM> which contains a liquid, the "aqueous humor", which is an optically transparent medium with a refractive index nAH around <NUM>. This anterior chamber <NUM> hence extends from the rear face <NUM> to the front face <NUM> of the lens <NUM>, said front face <NUM> being pressed against the iris <NUM> of the eye <NUM> (although in <FIG> it is not the case for the sake of clarity), so that the front face <NUM> of the lens <NUM> is approximately coplanar with the pupil <NUM> of the eye <NUM>. The "anterior chamber depth" (hereinafter also referred to as "ACD") is the distance dAC from the rear apex <NUM> of the cornea <NUM> to the front apex <NUM> of the lens <NUM>. This distance dAC is generally comprised between <NUM> and <NUM>, and decreases with the age of the subject (see below). The iris <NUM> of the eye <NUM> clings to the cornea <NUM> and the sclera <NUM> at two transitional regions <NUM>, <NUM> also known as the "corneal limbi" of the eye <NUM>.

Like the cornea <NUM>, the lens <NUM> is formed by two surfaces <NUM>, <NUM> of revolution around the optical axis <NUM>: the front face <NUM> and the rear face <NUM> of the lens <NUM>. Those lens surfaces <NUM>, <NUM> are not only of very complex shape - typically aspherical - but also change of shape with accommodation of the eye <NUM> (increase of the optical power of the eye <NUM> by modifying the front and/or the shapes of the front and rear surfaces <NUM>, <NUM>). For the sake of simplicity, we will consider in the following description that the eye <NUM> is here at rest, namely without accommodation and with lowest optical power. In this configuration, the base thickness tL of the lens <NUM> between the front apex <NUM> and the rear apex <NUM> of the lens <NUM> is comprised between <NUM> and <NUM> (the thickness tL of the lens <NUM> vary also as a function of accommodation). Optically, the front and back faces <NUM>, <NUM> of the lens <NUM> form two optical spherical diopters of radius RL,<NUM> (concave, positive) and RL,<NUM> (concave, negative) separated by the base thickness tL of the lens <NUM>.

The rest of the eye <NUM> is formed by the sclera <NUM> which takes around <NUM>/<NUM>th of circumference of the eye <NUM>, and by the vitreous body <NUM>, which is basically a transparent aqueous liquid contained in the eye <NUM>, filling the space comprised between the rear face <NUM> of the lens <NUM> and the retina <NUM> which partially covers the internal surface of the sclera <NUM>. The optical axis <NUM> of the eye <NUM> intersects the retina <NUM> at the foveal zone <NUM>, also known as the fovea, which is the area of the retina <NUM> with the highest visual acuity (highest concentration of sensitive photo-receptors) where the images of objects or persons seen by the subject are formed optically.

On the optical axis <NUM> is the ERC <NUM> which is aligned with the apex <NUM> of the cornea <NUM> and with the fovea <NUM> of the sclera <NUM>. The distance LE from the apex <NUM> to the fovea <NUM> (see <FIG>) is referred to as the "length"of the eye <NUM> and is typically comprised between <NUM> and <NUM>, more often between <NUM> and <NUM>. The position of the ERC <NUM> may be determined for example by the raw data of the distance dERC (see <FIG>) between the apex <NUM> of the cornea <NUM> and the ERC <NUM>.

One can see that the above described structure of the human eye <NUM> is quite complicated. The position of the ERC <NUM> may be difficult to determine directly not only because the ERC <NUM> is internal to the eye <NUM> but also because its actual position depends on many other parameters, most of them, like the anterior chamber depth dAC, lens thickness tL, eye length LE being difficult to measure directly. By direct measurement, it is meant a simple geometrical measurement, e.g. with a simple graduated ruler.

Therefore, it is one object of the invention to allow determining the position of the ERC <NUM> indirectly by measuring directly at least one geometric dimension of the eye <NUM> of the subject.

More precisely, according to the invention, we propose a method for determining a distance between an eye rotation center of an eye of a subject and an apex of a cornea of the eye, the method being carried out using calculation means and comprising:.

We represented on <FIG> a possible geometric model of the eye <NUM> of <FIG>. This geometric model is built on the assumption that the sclera <NUM> and the cornea <NUM> are respectively a part of a first and a second spheres.

More precisely, this geometric model is a model of the sclera <NUM> and of the cornea <NUM> of the eye <NUM>, said sclera <NUM> being modeled (see <FIG>) by a first sphere (see first circle C<NUM> drawn on <FIG>) having a first radius R<NUM> and said cornea <NUM> being modeled by a second sphere (see second circle C<NUM> drawn on <FIG>) having a second radius R<NUM> smaller than the first radius R<NUM> (R<NUM> < R<NUM>), said first sphere and said second sphere having a first center P<NUM> and a second center P<NUM> respectively, said first center P<NUM> and said second center P<NUM> being aligned on a straight line A defining the optical axis <NUM> of the eye <NUM>.

As obviously shown on <FIG>, the distance P<NUM>P<NUM> between the two centers P<NUM> and P<NUM> is such that P<NUM>P<NUM> < (R<NUM><NUM> - R<NUM><NUM>)½. Note also that on <FIG>, these two spheres are represented by two circles C<NUM>, C<NUM>, whose part drawn with a solid line (---) corresponds respectively to the cornea <NUM> and to the sclera <NUM>. The parts of the circles C<NUM>, C<NUM> drawn with a dashed line (- -) on <FIG> have no physical reality and have been represented here only of the sake of understanding.

In this simple geometric model, the ERC <NUM> is positioned at the center P<NUM> of the first circle C<NUM>. With this geometric model, we consider that the corneal limbi <NUM>, <NUM> of the eye <NUM> in <FIG> correspond to the intersection points P<NUM>, P<NUM> of the first circle C<NUM> with the second circle C<NUM>. The segment [P<NUM>P<NUM>] joining the intersection points P<NUM>, P<NUM> may be considered to be in the same plane as the pupil <NUM> and the iris <NUM> of the eye <NUM>: it crosses perpendicularly the straight line A (i.e. the optical axis <NUM>) at point P<NUM>.

One easily understands that there are only three degrees of liberty in this simple geometric model:.

Nevertheless, those three geometric dimensions R<NUM>, R<NUM>, d<NUM> are not directly measurable in a simple manner on the subject. Then, we prefer to rebuild the geometric model of the eye <NUM> of <FIG> around the three following geometric dimensions, namely (see <FIG>):.

Working out the trigonometry in <FIG>, one can show the following relation (referred to as equation (<NUM>)) between the three geometric dimensions LE, dAC, DI and the position of the ERC <NUM> (geometrically at the center P<NUM> of the first circle C<NUM>), e.g. the distance dERC from the apex <NUM> of the cornea <NUM> to the ERC <NUM>: <MAT>.

Hence the problem of determining the position of the ERC <NUM> is equivalent to the problem of determining the three geometric dimensions LE, dAC, DI of the rebuilt geometrical model.

Among the selected geometric dimensions LE, dAC, DI, the outer diameter DI of the iris <NUM> may be easily measured geometrically. One thus may choose the outer diameter DI of the iris <NUM> as the first geometric dimension of the eye <NUM> of the subject to be included in the geometric model.

In a preferred embodiment, the step of measuring a first value of the outer diameter DI of the iris <NUM> comprises:.

To implement this method, the invention also provides a device for determining a distance between an eye rotation center of an eye of a subject and an apex of a cornea of the eye, said device comprising:.

Hence, the calculation means comprise a geometric model of the eye of the subject such as, for example, the one described above (<NUM>-spheres model).

The image-processing means and calculation means may be a computer receiving the facial image from the image-capture apparatus.

In another embodiment, the device for determining a position of the eye rotation center of an eye of a subject comprises:.

Such device is described in the document <CIT> in the name of the applicant.

In a variant of the method, the step of measuring a first value of the outer diameter DI of the iris <NUM> may comprise:.

Then, in the method according to the invention, one assesses the remaining values of the remaining geometric dimensions of the geometric model, that is the eye length LE; and the anterior chamber depth dAC (the distance between point P<NUM> and P<NUM> in <FIG>).

In the preferred embodiment of the invention described here, one evaluates the anterior chamber depth dAC based on tabulated data gathered among a large number of subjects. The anterior chamber depth can be measured using an apparatus called an auto kerato-refractometer (also known as "AKR"), for example the VX120 Multi-Diagnostic Unit from the US company Visionix.

Advantageously, one may sort out the measured values of the anterior chamber depth based on age, gender, and/or ethnicity of the subject, so that one can interpolate and/or extrapolate a mathematical rule to assess the value of the anterior chamber depth dAC as a function of these personal parameters of the subject.

According to Eq. <NUM> above, a value of the eye length LE shall be now assessed in order to determine the position (here the distance dERC, see <FIG>) of the ERC <NUM> of the eye <NUM> of the subject.

Like the anterior chamber depth dAC, one could estimate the eye length LE based on other tabulated data, eventually depending on personal parameters of the subject.

Yet, in the preferred embodiment described here, one evaluates the eye length LE using an optical model which allows determining said eye length LE based on the objective optical power PE of said eye <NUM> and a subjective need K of visual correction for said subject (both optical power PE and need K of visual correction are expressed in diopters).

Again, the optical power PE of said eye <NUM> may be either measured (using for example the same apparatus VX110) directly or evaluated directly using tabulated data, eventually depending on personal parameters of the subject.

Here, one prefers using a complete optical model of the eye <NUM>, wherein the eye length LE, which is the geometric distance between the apex <NUM> of the cornea <NUM> and the fovea <NUM> of the sclera <NUM>, can be calculated, in the paraxial approximation, as a function of geometric and optical parameters of the eye <NUM>.

We have represented in <FIG> a schematic optical drawing, in the paraxial approximation, of the eye <NUM> of the subject, here with a corrective ophthalmic lens <NUM> corresponding to the need K of visual correction for the subject.

The different references in this <FIG> are the following:.

From <FIG>, it is clear that the eye length LE is the distance from the apex SC,<NUM> (apex <NUM> of <FIG>) of the cornea <NUM> to the image focal length F'SYS (fovea <NUM> of <FIG>): LE = |SC,<NUM>F'SYS| = SC,<NUM>F'SYS > <NUM>.

The cornea <NUM>, with its two apex SC,<NUM> and SC,<NUM>, may be, in the optical paraxial approximation, modeled by a centered system having an optical power PC given by the well-known Gullstrand's formula: <MAT> <MAT> <MAT> and principal points HC (object) and H'C (image) given by <MAT> <MAT>.

In the same way, the lens <NUM>, with its two apex SL,<NUM> and SL,<NUM>, may be, in the paraxial approximation, modeled by a centered system having an optical power PL given by the Gullstrand's formula: <MAT> <MAT> <MAT> and where principal points HL (object) and H'L (image) are such that: <MAT> <MAT>.

Using Equations (<NUM>) and (<NUM>), one gets: <MAT> and the objective optical power PE of the eye <NUM> by the following equation: <MAT>.

Again, using Gullstrand's formulas, one derives the principal points HE (object) and H'E (image) of the eye <NUM> (made up by association of cornea <NUM> and lens <NUM>) as: <MAT> <MAT>.

By definition, the object focal length fE and the image focal length f'E of the eye are given by: <MAT> <MAT>so that:<MAT> <MAT>.

Now, one considers the whole optical system formed by:.

and one calculates the total optical power PSYS of this system as: <MAT> <MAT>.

Moreover, again using Gullstrand's formula, one got: <MAT> <MAT>.

And, at the end, one obtains the final equation giving the eye length LE of the subject based on all the optical parameters of <FIG>: <MAT>.

From those calculations, one can make the following remarks:.

<FIG> shows an example of result for the calculation of the eye length LE as a function of the outer diameter DI of the iris <NUM> of the eye <NUM> of the subject. This result has been obtained using the data tabulated for the above-mentioned variables from<NPL>.

The tabulation has been made as a function of both AGE of the subject and need K of visual correction for the subject. Below are the expressions of the different variables used for the calculation of <FIG>:.

For <FIG>, one assumes that H'KSC,<NUM> = <NUM> mm , which is a common value used with standard auto-refractometer. One then traced the curve <NUM> of the length of the eye LE for a subject being <NUM> years old (AGE = <NUM>).

On this figure, one can see that the eye length LE is comprised between around <NUM> and <NUM>.

Moreover, one can see that the curve <NUM> is a quasi straight line, showing that the eye length LE varies linearly with the need K in visual correction.

Finally, from this <FIG>, one recovers the fact that, on one hand, a nearsighted eye (needing a negative power of correction, i.e. a divergent ophthalmic lens) is longer than the "normal" eye (needing no power of correction, K = <NUM>), and, on the other end, a farsighted eye (needing a positive power of correction, i.e. a convergent ophthalmic lens) is shorter than the "normal" eye.

<FIG> shows a 3D plot of the position dERC of the ERC <NUM> of the eye <NUM> of the subject as a function of age and need K (in diopters) of visual correction.

On this figure, one rediscovers that a myopic eye, needing negative correction (K < <NUM>, divergent ophthalmic lens), is longer than a "normal" eye without such need (K = <NUM>). The same is true for a hypermetropic eye (need K > <NUM>; convergent ophthalmic lens) which is too short. For an age of <NUM> years, one sees that:.

Preferably, after having determined a first approximate value of the position dERC of the ERC <NUM> performing the different steps above, one then compares said first approximate value with a reference value dERC,ref, e.g. found in a geometrical database which stores an huge amount of measured values of the position dERC as function of age, need in visual correction, gender, and/or ethnicity, etc.. ; and one determines a second approximate value of said position of the eye rotation center based on the result of said comparison.

In practice, when the result of the comparison shows that the difference ΔdERC = |dERC - dERC,ref| between the approximate value dERC and the reference value dERC,ref is smaller than a predetermined threshold equal to <NUM> millimeter, preferably equal to <NUM>, the step of determining the second approximate value of the position of said eye comprises:.

On the contrary, when the result of the comparison shows that the difference between the approximate value dERC and the reference value dERC,ref is larger than the predetermined threshold, determining the second approximate value of the position of said eye rotation center comprises:.

Claim 1:
Method for determining a distance (dERC) between an eye rotation center (<NUM>) of an eye (<NUM>) of a subject and an apex (<NUM>) of a cornea (<NUM>) of the eye (<NUM>), the method being carried out using calculation means and comprising:
- providing a geometric model of an eye (<NUM>), whereby the eye (<NUM>) is modeled with a first sphere (C1) for the sclera (<NUM>) of the eye (<NUM>) and a second sphere (C2) for the cornea (<NUM>) of the eye (<NUM>), the first sphere (C1) having a first radius (R1) and a first center (P1), the second sphere (C2) having a second radius (R2) smaller than the first radius (R1) and a second center (P2), the first center (P1) and the second center (P2) being aligned on an optical axis (<NUM>) of the eye (<NUM>), another distance "P1P2" between first center (P1) and the second center (P2) being such that P1P2 < (R<NUM><NUM> - R2<NUM>)½, "R1" referring to the first radius (R1) and "R2" referring to the second radius (R2), the eye rotation center (<NUM>) of this eye (<NUM>) being positioned at the center (P1) of the first sphere (C1), said distance (dERC) being determined based on a set of personal parameters (LE, dAC, DI, AGE, K) including at least a first geometric dimension (DI) of the eye (<NUM>), each personal parameter (LE, dAC, DI, AGE, K) being distinct from said distance (dERc) ;
- determining a value of each personal parameter (LE, dAC, DI, AGE, K) for the subject; and
- determining a first approximate value of said distance (dERC) in accordance with said geometric model based on the values of the personal parameters (LE, dAC, DI, AGE, K).