EYE MEASUREMENT

Abstract

In a method for interferometrically capturing measurement points of a region of an eye, a plurality of measurement points are captured by a measurement beam along a trajectory, wherein the same trajectory is passed over by the measurement beam in the region during at least a first iteration and a second iteration. The trajectory of the first iteration is rotated through an angle and/or displaced by a distance in relation to the trajectory of the second iteration in order to obtain a more homogeneous measurement point distribution.

Claims

1. Method for interferometrically capturing measurement points of a region of an eye, wherein a plurality of measurement points are captured by a measurement beam along a trajectory, wherein the same trajectory is passed over by the measurement beam in the region during at least a first iteration and a second iteration, characterized in that the trajectory of the first iteration is rotated through an angle and/or displaced by a distance in relation to the trajectory of the second iteration in order to obtain a more homogeneous measurement point distribution.

2. Method according to claim 1, characterized in that any straight line extending within the trajectory intersects the trajectory at at least two spaced apart points.

3. Method according to claim 1, characterized in that an initial point of the second trajectory corresponds to the endpoint of the first trajectory.

4. Method according to claim 1, characterized in that the trajectory covers the region.

5. Method according to claim 1, characterized in that the trajectory is continuously rotated through an angle and/or displaced by a distance.

6. Method according to claim 1, characterized in that the trajectory of the second iteration is rotated through an angle and/or displaced by a distance in relation to the trajectory of the first iteration only on account of a movement of the eye, as a result of which a more homogeneous measurement point distribution is obtained.

7. Method according to claim 1, characterized in that the trajectory is rotated through an angle of m*360°/n after each iteration, where m, n≧2 and m≠n.

8. Method according to claim 7, characterized in that the trajectory after the second iteration in relation to the first iteration is rotated through an angle between $360\star 0.9\star \left(\frac{3.Math.\sqrt{5}}{2}\right).Math..Math.\mathrm{and}.Math..Math.360\star 1.1\star \left(\frac{3.Math.\sqrt{5}}{2}\right),$ preferably between $360\star 0.95\star \left(\frac{3.Math.\sqrt{5}}{2}\right).Math..Math.\mathrm{and}.Math..Math.360\star 1.05\star \left(\frac{3.Math.\sqrt{5}}{2}\right),$ particularly preferably between $360\star 0.99\star \left(\frac{3.Math.\sqrt{5}}{2}\right).Math..Math.\mathrm{and}.Math..Math.360\star 1.01\star \left(\frac{3.Math.\sqrt{5}}{2}\right),$ in particular through an angle of approximately $360\star \left(\frac{3.Math.\sqrt{5}}{2}\right).$

9. Method according to claim 1, characterized in that, at least a first model of the region is calculated on the basis of the measurement points of the first iteration and a second model of the region is calculated on the basis of the measurement points of the second iteration.

10. Method according to claim 9, characterized in that a spatial curve, which represents the movement of the eye, is calculated on the basis of the at least first model and the second model.

11. Method according to claim 10, characterized in that symmetry vectors are determined for the first model and the second model, the spatial curve representing the movement of the eye being calculated on the basis of said symmetry vectors.

12. Method according to claim 11, characterized in that the movement comprises translational and rotating movement components.

13. Method according to claim 9, characterized in that a mean model is calculated from the models.

14. Method according to claim 9, characterized in that, for the purposes of reducing movement artifacts, measurement points are corrected to corrected measurement points on account of the first model and of the second model.

15. Method according to claim 9, characterized in that the at least first model and the second model are interpolated for the purposes of correcting the measurement points.

16. Method according to claim 15, characterized in that the corrected measurement points of the first iteration and of the second iteration are combined to form a cumulative model.

17. Method according to claim 1, characterized in that the trajectory is passed over in m iterations, where m is selected in such a way that a mean measurement point distance is less than a predetermined expected lateral movement of the eye.

18. Method according to claim 1, characterized in that the trajectory has the form of a. a spiral, in particular a Fermat's spiral; b. a hypotrochoid; c. a grid, in particular parallel lines; or of d. radially arranged loops with a common point of intersection.

19. Apparatus for carrying out a method according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0079] In the drawings used to explain the exemplary embodiment:

[0080] FIG. 1 shows a first cycle of the Fermat's spiral;

[0081] FIG. 2 shows a complete scan with the Fermat's spiral, with eight cycles;

[0082] FIG. 3 shows a second embodiment of a possible trajectory; and

[0083] FIG. 4 shows a third embodiment of a possible trajectory.

[0084] In principle, the same parts are provided with the same reference signs in the figures.

WAYS OF IMPLEMENTING THE INVENTION

[0085] In a first preferred embodiment, the trajectory has the form of a Fermat's spiral and it is defined as follows:

r=±θ.sup.1/2

where r is the radius and θ is the angle of the spiral points in polar coordinates. The spiral may be expanded by the following parameters and properties: [0086] R: maximum radius, from which the spiral runs back to the center point. [0087] M: number of rotations for a sweep (denoted by “s” in the index in the following formulae). This number defines how often the spiral runs around the center point before the maximum radius is reached. [0088] θ.sub.G: angle through which the pattern is rotated during an iteration.

[0089] Sweep denotes the trajectory from the center point to the reversal point at the edge, and vice versa. Cycle denotes a sweep (respectively abbreviated by s in the index) toward the outside and the subsequent sweep toward the inside. The term “iteration” means the same as the term “cycle”.

[0090] From this, the following auxiliary parameters emerge for defining the trajectory:

[00007]${\theta }_s=M\star 2.Math.\pi -\frac{\pi }{2}+\frac{{\theta }_G}{2}$$a={\left(\frac{R^2}{{\theta }_s}\right)}^{1/2}$

[0091] Hence, the following emerges for the Fermat's spiral:

[00008]$r=\{\begin{array}{cc}{a\left(\theta .Math..Math.\mathrm{mod}.Math..Math.{\theta }_s\right)}^{1/2}& \mathrm{for}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.2.Math.{\theta }_s\le {\theta }_s.Math..Math.\mathrm{and}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.4.Math.{\theta }_s\le 2.Math.{\theta }_s\\ {a\left({\theta }_s.Math.-\left(\theta .Math..Math.\mathrm{mod}.Math..Math.{\theta }_s\right)\right)}^{1/2}& \mathrm{for}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.2.Math.{\theta }_s>{\theta }_s.Math..Math.\mathrm{and}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.4.Math.{\theta }_s\le 2.Math.{\theta }_s\\ -{a\left(\theta .Math..Math.\mathrm{mod}.Math..Math.{\theta }_s\right)}^{1/2}& \mathrm{for}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.2.Math.{\theta }_s\le {\theta }_s.Math..Math.\mathrm{and}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.4.Math.{\theta }_s>2.Math.{\theta }_s\\ -{a\left({\theta }_s-\left(\theta .Math..Math.\mathrm{mod}.Math..Math.{\theta }_s\right)\right)}^{1/2}& \mathrm{for}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.2.Math.{\theta }_s>{\theta }_s.Math..Math.\mathrm{and}.Math..Math.\theta .Math..Math.\mathrm{mod}.Math..Math.4.Math.{\theta }_s>2.Math.{\theta }_s\end{array}$

[0092] The scanning pattern now emerges from the temporal sequence of measurement points or scanning points on the trajectory. A uniform distribution of the points in the area may be achieved by virtue of the scanning points being distributed regularly in θ. If N.sub.cycle denotes the number of points per cycle and N denotes the number of measurement points, the following emerges for θ:

[00009]$\theta =\frac{n\star 2\star {\theta }_s}{N_{\mathrm{cycle}}}.Math..Math.\mathrm{for}.Math..Math.n=0,1,2,\mathrm{.Math.}.Math.,N.$

[0093] The golden angle is inserted for θ in the ideal case with a theoretically infinite increase in the measurement point density (see above). However, it is usually sufficient in practice for the trajectory to repeat after a finite number of sweeps or cycles or iterations. To this end, e.g. θ.sub.G=0.375*2π; M=8; N.sub.cycle=4096; N=8*4096=32768 could be selected instead of the golden angle. In the case of an A-scan rate of 10 kHz, a measurement would take e.g. 3.28 seconds. The radius of the region of the eye which is measured is typically 3.75 mm, but may also deviate therefrom. As already explained above, it is also possible to select a different number of iterations, measurement points, etc. Likewise, it is possible to use other trajectories than Fermat's trajectory.

[0094] FIG. 1 shows, in the XY-plane, a first cycle of the Fermat's spiral in accordance with the example above, with only every tenth measurement point being imaged. The initial point and endpoint of the cycle lie at the apex or in the center. At the center, the end of the cycle coincides with the start of the cycle at an acute angle, which may be traced back to the continuous rotation through the angle of θ.sub.G=0.375*2π.

[0095] FIG. 2 finally shows the complete scan after eight cycles in the XY-plane. Here, it is possible to see that a very good measurement point distribution has been achieved.

[0096] What can be seen particularly well in this exemplary embodiment is that the requirements on the dynamic properties of the OCT scanner are kept relatively low as the radii of curvature of the trajectory are comparatively large over the entire iteration or cycle. In the region of the apex, the trajectory is aligned almost tangentially in relation to the gradient of the cornea. Hence, the ratio between the signal and noise is improved in relation to a conventional grid.

[0097] FIGS. 3 and 4, below, depict further possible trajectories of the general form:

x(t)=r.sub.0 sin(ω.sub.Bt)*cos(ω.sub.Tt)

y(t)=r.sub.0 sin(ω.sub.Bt)*sin(ω.sub.Tt).

[0098] Here: [0099] r.sub.0: radius of the circumference of the scanning pattern

[00010]${\omega }_B.Math.\text{:}.Math..Math.{\omega }_B=2.Math.\pi .Math.\frac{B}{2.Math.t_{{\mathrm{pattern}}^{\prime }}}$${\omega }_T.Math.\text{:}.Math..Math.{\omega }_T=2.Math.\pi .Math.\frac{T}{t_{\mathrm{pattern}}}.$

[0100] For the following examples, the measurement duration t.sub.pattern is 200 ms (milliseconds). It is clear to a person skilled in the art that, as a matter of principle, a measurement duration which is as short as possible is sought after. However, this depends, firstly, on the employed measurement appliance and, secondly, on the number of measurement points.

[0101] In the present case, the number of measurement points equals 3200; the measurement frequency (i.e. the rate at which measurement points are captured) is f=16 kHz. Here, an equilibrium in which the measurement duration is sufficiently small and, at the same time, the number of measurement points and hence, in the case of a constant area to be measured, the resolution are sufficiently high, is sought after.

[0102] Furthermore, the measurement frequency is, however, only so large that a sufficient signal strength still emerges for each measurement point as said signal strength decreases with increasing measurement frequency.

[0103] FIG. 3 shows an embodiment of a possible trajectory in a particularly preferred form, with B=8 and T=7. From the graph of the function, it can readily be identified that the radius of curvature in each case increases from the edge region toward the center. Moreover, eight points of intersection always lie on a circle concentric with the center of the circumference in each case and the center point is passed through multiple times. Furthermore, it can be seen from the figure that both the edge region and the region near the center may be measured with a high resolution. The scanning pattern has 48 single points of intersection and one eight-fold point of intersection in the center. It is possible to detect and eliminate the eye movement, in particular using the points of intersection away from the center. The high number of points of intersection allows a detection of the eye movement with a correspondingly high frequency (measurement time/number of points of intersection=mean updating time). In the present case, the rotation after each cycle is θ.sub.G=0.4375*2π, and so the trajectory is once again present in the original orientation after 16 cycles.

[0104] FIG. 4 finally shows, as a further example, a hypotrochoid trajectory as a possible embodiment. The hypotrochoid trajectory has the following general form:

[00011]$x\left(t\right)=\left(a-b\right).Math..Math.\cos .Math..Math.\left(s\right)+c\star \cos .Math..Math.\left(\left(\frac{a-b}{b}\right)\star s\right);$$y\left(t\right)=\left(a-b\right).Math..Math.\sin .Math..Math.\left(s\right)+c\star \sin .Math..Math.\left(\left(\frac{a-b}{b}\right)\star s\right).$

[0105] For the purposes of ascertaining measurement values in ophthalmology, the values may be selected in such a way that, once again, a radius of approximately 4 mm is achieved. As an example, a=2, b=0.1 and c=2.1 have been selected in FIG. 4. Using this parameterization, a free circle may be identified in the center of the circumference, said free circle having a radius of approximately 0.2 mm. Therefore, this free area satisfies the 0.5 mm criterion specified at the outset.

[0106] In the present case, the rotation after each cycle is θ.sub.G=0.56*2π, and so the trajectory is once again present in the original orientation after 25 cycles.

[0107] In a further exemplary embodiment, use is made of a grid of parallel lines as a trajectory, with the grid being displaced by e.g. 10% of the line spacing in the XY-plane at right angles to a line direction after each iteration. In a further embodiment, there is in each case a displacement by half of the last line spacing, as a result of which it is possible to obtain a continuous refinement of the measurement point distribution. In a further embodiment, the grid is rotated through an angle at each iteration, as explained at the outset. Finally, the grid is both rotated and displaced after each iteration in a further embodiment.

[0108] While the trajectory is continuously rotated and/or displaced in each case during the iteration in the exemplary embodiments above, the trajectory may also be rotated and/or displaced between the iterations in each case. However, a consequence of this is that, as a rule, the measurement beam must pass through a relatively large directional change between the iterations, as a result of which, once again, the measurement method is slowed down.

[0109] In each of the exemplary embodiments listed above, a model of the region of the eye is advantageously created for the purposes of correcting the movement artifacts after each iteration or after each sweep. A symmetry vector is determined on the basis of the model, by means of which it is also possible to determine the orientation of the eye in respect of a rotation about the symmetry vector and in the XY-plane. A movement trajectory of the eye is preferably obtained subsequently using the plurality of symmetry vectors. Finally, each model of the region of the eye ascertained in advance may be aligned by means of the movement trajectory of the eye. The aligned regions of the eye may once again be combined by calculation in an advantageous manner to form a mean model of the region of the eye. A person skilled in the art knows of any variants for the present correction of the movement artifacts. Thus, the movement trajectory may be used to correct the individual points, etc.

[0110] The measurement duration and the number of measurement points may also be smaller or larger, depending on the employed measurement appliance. Depending on the measurement arrangement, it may be advantageous if the measurement duration is shortened, with the smaller resolution being accepted. On the other hand, it is also possible to increase the number of measurement points to the detriment of the measurement duration.

[0111] In the present case, the radius of the area to be measured is between 3 and 4 mm. However, this likewise depends on the specific requirements and may, in principle, be selected as required, e.g. 10 mm, 3.5 mm, 1.5 mm and all regions lying therebetween and outside thereof.

[0112] In the present case, the axial system resolution of the measurement appliance lies at approximately 4.6 μm, but it may also be higher or lower.

[0113] It is clear to a person skilled in the art that the diameter, the number of measurement points and the measurement time may lie in different ranges.

[0114] Depending on the measurement system, the measurement frequency may range from a few kHz to several MHz. Measurement frequencies in the range from 10 to 200 kHz were found to be worth pursuing.

[0115] Finally, it is also clear to a person skilled in the art that the trajectory is not restricted to exactly observing the graphs formed by the specified mathematical formulae. A trajectory or scanning pattern may also deviate from the mathematically exact form. By way of example, the family of points ascertained with the measurement beam may merely approximately correspond to such a function as an interpolation.

[0116] In conclusion, it should be noted that, according to the invention, a method is developed for interferometrically capturing measurement points of a region of an eye, said method permitting a particularly precise capture of the topographies of the region. Further, this achieves a movement correction of the eye in an advantageous manner.