MEASURING METHOD FOR DETERMINING AN ASTIGMATISM OF AN EYE

A measuring method for determining an astigmatism of an eye with a confocal refractometer providing a measurement beam path, in which an optical arrangement having an adaptive optical component with a variable cylinder power and a variable cylindrical axis position is arranged to compensate for an astigmatism of the eye in the wavefront of the measurement beam path. In a first measurement, the cylinder power of the adaptive optical component for a first fixed cylindrical axis position of the adaptive optical component is varied until the measured intensity becomes maximal. In a second measurement, the cylinder power of the adaptive optical component for a second fixed axis position—different than the first—of the adaptive optical component is varied until the measured intensity is maximal. The power and axis position of the astigmatism of the eye are determined from first and second measurement values.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority to German patent application DE 10 2019 101 618.5, filed Jan. 23, 2019, the entire content of which is incorporated herein by reference.

TECHNICAL FIELD

The disclosure relates to a measuring method for determining an astigmatism of an eye with the aid of a confocal refractometer providing a measurement beam path, in which is arranged an optical arrangement having an adaptive optical component having a variable cylinder power and a variable cylindrical axis position in order to compensate for an astigmatism of the eye in the wavefront of the measurement beam path.

BACKGROUND

Such a measuring method is generally known from the subsequently published document DE 10 2017 117 925 A1. Said document also describes a confocal refractometer that can be used to carry out the measuring method. A further confocal refractometer is known from the document US 2015/0109580 A1.

Such a confocal refractometer can be used to measure the spherical equivalent SE of the ametropia of a patient's eye, an astigmatism of the patient's eye including the axis position of the astigmatism of the patient's eye. Both the spherical equivalent SE and the astigmatism C are usually specified in diopters (D). Typically, eyes with the spherical equivalent of SE<0 D are referred to as nearsighted or myopic, while eyes with SE>0 D are referred to as farsighted or hyperopic. Patients' eyes with SE≈0 D are referred to as having spherically perfect vision or as emmetropic. The astigmatism C specifies the difference between the refractive powers of the eye in two mutually perpendicular principal meridians. The axis position φ specifies the position of these principal meridians, represents an angle and is specified in the unit of degrees (°).

The following convention is used in the description of the present disclosure: The astigmatism C is always positive and satisfies C>0 D. In the two principal meridians, the defective vision of the patient's eye is described by SE±(1/2) C. The axis position φ describes the position of that principal meridian with the defective vision SE +(1/2) C. For known values SE, C, and φ, it is possible to produce a spectacle lens that corrects the defective vision of the patient's eye. It is also possible to use other conventions for describing defective vision, but they can always be converted into the convention indicated above.

In the context of the present disclosure, “confocal” is understood to mean an optical system that enables “point-to-point” imaging. A pinhole stop illuminated with measurement light by a light source of the refractometer is imaged onto the retina of the patient's eye as a measurement light beam, with the result that a light spot is produced on the retina. For this purpose, the measurement light beam is focused onto the retina by a focusing device of the optical arrangement of the refractometer, with the result that the light spot on the retina can be chosen to be as small as possible. Measurement light incident in the region of the light spot is partly scattered or reflected by the retina, with the result that light energy emerges from the eye as measurement light reflected back. A confocal stop is positioned in a plane conjugate to the retina, said stop at least partly transmitting the measurement light reflected back from the eye, wherein the intensity of the back-reflected measurement light transmitted by the stop is measured by a measuring module with a light detector. Instead of physical stops, it is also possible to use the end of an optical fiber as a confocal stop on the light source side and as a confocal stop on the light detector side.

In the case of the measuring method for determining an astigmatism of a patient's eye with the aid of a confocal refractometer as known from the document cited in the introduction, after the spherical equivalent of the ametropia of the patient's eye has been measured, firstly the axis position of the astigmatism of the patient's eye (with compensated spherical equivalent) is measured. For this purpose, either a known cylinder power or a small cylinder power is set at the adaptive optical component. Afterward, the axis position of the adaptive optical component is varied, and the intensity of the measurement light reflected back is determined. The sought axis position of the astigmatism is found at maximum intensity of the measurement light reflected back. In a further step, for the axis position determined, the cylinder power of the adaptive optical component is then varied until the intensity of the measurement light reflected back becomes maximal again, from which the power of the astigmatism can then be determined.

In the case of the known measuring method, the astigmatism is thus determined by firstly carrying out an axis measurement and then a cylinder measurement.

Measurements carried out on subjects in accordance with the known measuring method have shown that measurement signals that cannot be evaluated often occur during the axis measurement with the known measuring method. As a result, the power of the astigmatism and the axis position thereof cannot be determined reliably.

SUMMARY

Therefore, it is an object of the disclosure to provide a measuring method for determining an astigmatism of an eye with the aid of a confocal refractometer with which the power of the astigmatism and the axis position thereof can be determined reliably.

According to a first aspect of the disclosure, the object is achieved by a measuring method for determining an astigmatism of an eye with the aid of a confocal refractometer providing a measurement beam path, in which is arranged an optical arrangement having an adaptive optical component having a variable cylinder power and a variable cylindrical axis position in order to compensate for an astigmatism of the eye in the wavefront of the measurement beam path, including the following steps: directing a measurement light beam onto the eye such that a light spot is produced on the retina of the eye, measuring an intensity of measurement light reflected back from the retina, wherein in a first measurement the cylinder power of the adaptive optical component for a first fixed cylindrical axis position of the adaptive optical component is varied until the measured intensity becomes maximal in order to obtain a first measurement value, and in a second measurement the cylinder power of the adaptive optical component for a second fixed axis position—different than the first—of the adaptive optical component is varied until the measured intensity is maximal in order to obtain a second measurement value, determining the power and axis position of the astigmatism of the eye at least from the first and second measurement values.

With the measuring method according to an aspect of the disclosure, the astigmatism is determined by carrying out a first and a second measurement, which in each case are also referred to as cylinder measurements in the present description. In the case of the measuring method for determining the astigmatism of a patient's eye, a measurement of the axis position of the astigmatism becomes superfluous. Rather, the axis position of the astigmatism of the patient's eye is determined computationally from the two cylinder measurements. Inaccurate measurement signals or measurement signals that cannot be evaluated are thus avoided. The measuring method in accordance with the first aspect of the disclosure is distinguished by its high robustness and accuracy.

In the case of the first cylinder measurement, a first fixed cylindrical axis position is set at the adaptive optical component. The first fixed cylindrical axis position is arbitrary, but known on account of the setting. For this first fixed cylindrical axis position, the cylinder power of the adaptive optical component is varied until the measured intensity becomes maximal. A first measurement value is yielded as the measurement result, which first measurement value is also referred to as cylinder measurement value in the present description. After the first cylinder measurement, a second cylinder measurement is carried out, in the case of which a second fixed axis position is set at the adaptive optical component, said second fixed axis position being different from the first axis position. For this second axis position of the adaptive optical component, the cylinder power of the adaptive optical component is varied until the measured intensity is maximal again. A second measurement value or cylinder measurement value is obtained as the result.

The first cylinder measurement value and the second cylinder measurement value are accordingly obtained by an intensity measurement of the measurement light reflected back. Both in the case of the first cylinder measurement and in the case of the second cylinder measurement, the cylinder power of the adaptive optical component is varied until the measured intensity of the measurement light reflected back is maximal. The two cylinder measurement values can be gleaned from the setting of the respective cylinder power of the adaptive optical component. The astigmatism and the axis position of the patient's eye are then determined by calculation from the first and second cylinder measurement values, and optionally the first axis position and the second axis position of the adaptive optical component. The first and second axis positions of the adaptive optical component, as already mentioned, are arbitrary, but known on account of the setting of the adaptive optical component.

Typically, the spherical equivalent of the patient's eye is measured before the first cylinder measurement. For this purpose, the optical arrangement of the confocal refractometer is furthermore designed to vary a focus position of the measurement beam path in order to compensate for a spherical equivalent of the ametropia of the eye in the wavefront of the measurement beam path, wherein before the first measurement (cylinder measurement) with the aid of the optical arrangement the focus position of the measurement beam path is varied until the measured intensity of the measurement light reflected back from the retina is maximal.

The advantage of this measure is that the two cylinder measurements are carried out with a compensated spherical equivalent of the ametropia, and the cylinder measurements are thus independent of the spherical equivalent.

The cylinder power of the adaptive optical component can be set to zero or neutral during the variation of the focus position. As a result, the spherical equivalent of the ametropia can be optimally compensated for by varying the focus position of the optical arrangement.

With further preference, the spherical equivalent of the ametropia of the eye is determined from the setting of the optical arrangement in which the spherical equivalent of the ametropia is compensated for.

In this configuration, the measuring method thus allows not only the measurement of the astigmatism, but also the measurement of the spherical equivalent of the ametropia of the patient's eye. In this configuration, the measuring method in accordance with the first aspect requires a total of just three measuring steps, specifically one measuring step for measuring the spherical equivalent of the ametropia and two measuring steps for measuring the astigmatism including the axis position thereof.

The first measurement value a and the second measurement value b can be linked with the power of the astigmatism Ceyeof the eye and the axis position φ in a simple manner by: a=−Ceye·cos(2β1), b=−Ceye·cos(2β2), where β1=φ−φ1and β2=φ−φ2, wherein φ1is the axis position of the adaptive optical component in the first measurement and φ2is the axis position of the adaptive optical component in the second measurement.

The axis position φ of the astigmatism of the eye can thus be determined in a simple manner by calculation from the first measurement value a, the second measurement value b, the first axis position φ1of the adaptive optical component and the angle Δη between the first axis position and the second axis position of the adaptive optical component in accordance with the following equation:

Typically, the second axis position of the adaptive optical component (AOE) differs from the first axis position of the adaptive optical component (AOE) by an angle in the range of 30° to 45°.

The calculation of the power and the axis position of the astigmatism of the eye from the first and second measurement values is simplified even further if the first axis position of the adaptive optical component is set to 0° with respect to the horizontal axis of the eye (12) and the second axis position is altered by 45° relative to the first axis position, as is provided in one exemplary embodiment.

By means of the measure mentioned above, the power of the astigmatism Ceyeof the eye can be determined just from the first measurement value a and the second measurement value b in accordance with the following equation:

The axis position φ of the astigmatism of the eye can likewise be determined in a simple manner just from the first measurement value (a) and the second measurement value (b) in accordance with the following equation:

In this calculation method, the power of the astigmatism of the eye can be calculated independently of and before the determination of the axis position of the astigmatism of the eye, and vice versa.

According to a second aspect of the disclosure, the object is achieved by a measuring method for determining an astigmatism of an eye with the aid of a confocal refractometer providing a measurement beam path, in which is arranged an optical arrangement having an adaptive optical component having a variable cylinder power and a variable cylindrical axis position in order to compensate for an astigmatism of the eye in the wavefront of the measurement beam path, and wherein the optical arrangement is furthermore configured to vary a focus position of the measurement beam path to compensate for a spherical equivalent of the ametropia of the eye in the wavefront of the measurement beam path, the method including the following steps: directing a measurement light beam onto the eye such that a light spot is produced on the retina of the eye, measuring an intensity of measurement light reflected back from the retina, wherein in a first measurement the focus position of the measurement beam path for a fixed first cylinder power of the adaptive optical component and a fixed axis position of the adaptive optical component is varied until the measured intensity of the measurement light reflected back from the retina is maximal in order to obtain a first measurement value, and in a second measurement the focus position of the measurement beam path for the first cylinder power and a second axis position—different than the first—of the adaptive optical component is varied until the measured intensity of the measurement light reflected back from the retina is maximal in order to obtain a second measurement value, and determining the power of the astigmatism of the eye and the axis position thereof at least from the first and second measurement values.

In the case of the measuring method in accordance with the second aspect of the disclosure, an astigmatism of a patient's eye is determined by carrying out two measurements based in each case on an intensity measurement for measuring the spherical equivalent of the ametropia of the patient's eye. In the present description, the two measurements are also referred to as SE measurements, wherein SE stands for the spherical equivalent of the ametropia of the patient's eye.

As in the measuring method in accordance with the first aspect of the disclosure, the intensity of measurement light reflected back from the retina is measured in each case. In the first SE measurement, a fixed first cylinder power is set at the adaptive optical component, which cylinder power can in particular be not equal to 0 D. In this case, the first cylinder power is arbitrary and known on the basis of the setting of the adaptive optical arrangement. Furthermore, a fixed axis position of the cylinder of the adaptive optical component is set at the adaptive optical component, which axis position is correspondingly known and can be arbitrary. For a set first cylinder power and first axis position of the adaptive optical component, the focus position of the optical arrangement is varied until the measured intensity of the measurement light reflected back from the retina is maximal. A first measurement value is obtained as the result, said first measurement value also being referred to as the SE measurement value in the present description.

In the second SE measurement, a second fixed axis position different than the first axis position is set at the adaptive optical component. The first cylinder power of the adaptive optical arrangement set in the first SE measurement is maintained in this case. Afterward, the focus position of the optical arrangement is varied again until the measured intensity of the measurement light reflected back from the retina is maximal. A second SE measurement value is obtained as a result of the measurement. In the subsequent step, the power of the astigmatism of the eye and the axis position thereof can be determined from the first and second SE measurement values and optionally the set first cylinder power and axis position of the adaptive optical component.

An advantage of the measuring method in accordance with the second aspect is that the astigmatism of the patient's eye and the axis position thereof can be determined with a total of just two measuring steps.

In the case of a patient's eye afflicted with astigmatism, two intensity maxima usually occur during the variation of the focus position of the measurement beam path. Accordingly, in one configuration of the measuring method in accordance with the second aspect of the disclosure, in the first and second measurements the focus position is varied until the measured intensity of the measurement light reflected back in each measurement has respectively a first and a second intensity maximum, wherein the first and second measurement values are respectively determined from that setting of the optical arrangement which is associated with the first and second intensity maxima. If, e.g., the optical arrangement of the confocal refractometer for varying the focus position of the measurement beam path has one or more movable optical elements, the first and respectively the second SE measurement value can be obtained from the displacement distance of the optical element(s) between the two respective intensity maxima.

However, it may happen that the astigmatism of the patient's eye was randomly compensated for or almost compensated for as a result of the setting of the first cylinder power of the adaptive optical component, and so only one intensity maximum occurs during the variation of the focus position of the measurement beam path in the first measurement. In this case, if the first cylinder power of the adaptive optical component is altered, two well-separated intensity maxima can be detected.

As in the case of the measuring method in accordance with the first aspect of the disclosure, a simple algorithm is provided for the calculation of the power of the astigmatism of the patient's eye and the axis position of the astigmatism of the patient's eye. In this regard, the first measurement value A1and the second measurement value A2are linked with the power of the astigmatism Ceyeof the eye by:

where CAOEis the set first cylinder power of the adaptive optical component, β1is the angle between the principal meridians of the cylinders of the adaptive optical component and of the eye in the first measurement, and β2is the angle between the principal meridians of the cylinders of the adaptive optical component and of the eye in the second measurement.

The abovementioned relationship between the first and second measurement values A1,2and the power of the astigmatism can be simplified further if the axis position of the adaptive optical component in the second SE measurement is rotated by 90° relative to the axis position of the adaptive optical component in the first SE measurement. The power of the astigmatism Ceyecan then be determined in a simple manner from the first and second measurement values A1,2and the set cylinder power CAOEof the adaptive optical component:

Likewise, the angle β1between the principal meridians of the cylinders of the adaptive optical component and of the eye in the first measurement can be calculated in a simple manner by:

The axis position φ of the astigmatism of the eye then results from the relationship φ=φ1+β1, wherein φ1 is the axis position of the adaptive optical component in the first SE measurement.

The measuring method in accordance with the second aspect of the disclosure enables faster measurements of the astigmatism since only two measuring steps are required.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Further advantages and features are evident from the following description and the attached drawing. It goes without saying that the aforementioned features and those yet to be explained below can be used not only in the respectively specified combination but also in other combinations or on their own, without departing from the scope of the present disclosure.

Before one exemplary embodiment of a measuring method for determining an astigmatism of a patient's eye is described, firstly the construction of a confocal refractometer is described by way of example. It goes without saying that such a confocal refractometer can be integrated into an ophthalmic surgical microscope. For reasons of simpler illustration, however, an illustration of an integration of the refractometer into a surgical microscope is dispensed with here.

FIG. 1shows a confocal refractometer10. The confocal refractometer10can generally be used for determining the refraction of a patient's eye12. The confocal refractometer10includes a measurement light source14for generating a measurement light beam16. The measurement light beam is indicated by dashed lines inFIG. 1. The confocal refractometer10furthermore includes a measuring module18including a light detector20for measuring an intensity of reflected-back measurement light24, which is indicated by solid lines inFIG. 1.

The refractometer10includes an optical unit22, through which a measurement beam path passes, in order to direct the measurement light beam16onto the retina23of the eye12and to feed measurement light24reflected back at the retina23to the light detector20. The measurement beam path should be understood to mean the totality of the measurement light beam16and the reflected-back measurement light24.

Overall, the measurement beam path is confocal. In the case of the refractometer10, “confocal” should be understood to mean that the measurement light source14, to put it more prec3isely a confocal opening26provided as an opening in a pinhole stop27, is imaged onto the retina23, with the result that a light spot28that is as small as possible is produced on the retina, and light that impinges in the region of the light spot28is partly scattered by the retina23, with the result that light energy emerges from the eye12as measurement light reflected back. A confocal opening30provided as an opening in a pinhole stop31is located in a plane conjugate to the retina23and to the opening26and at least partly transmits the reflected-back measurement light emerging from the eye12. The intensity of the reflected-back measurement light24downstream of the confocal opening30is measured by the light detector20. The opening26assigned to the measurement light source is focused onto the retina23by the optical unit22, with the result that the light spot28on the retina23can be chosen to be as small as possible.

As shown inFIG. 1, the optical unit22further includes a lens group32, by which the measurement light beam coming from the opening26is approximately collimated. The measurement light beam16thus collimated is guided via two beam splitters34and36into an optical arrangement AOM. The optical arrangement AOM contains, as will be described in even greater detail further below, one or more adaptive optical components AOE, as shown inFIG. 3. The optical arrangement AOM can generally contain optical components such as lenses, diffractive-optical elements, mirrors, beam splitters, etc., which can also be arranged in a displaceable manner.

In the context of the present description, a “lens group” is understood to mean either a single lens or, as shown inFIG. 1, an arrangement composed of a plurality of lenses, which can also have an air clearance between the individual lenses.

The optical arrangement AOM is settable by way of a control unit38. The wavefront of the measurement light beam16incident in the optical arrangement AOM is altered depending on the setting of the optical arrangement AOM. The measurement light beam16entering the eye12generates a light spot28of greater or lesser size on the retina23of the eye12. The impinging measurement light is scattered in the region of the light spot28on the retina23. Part of the scattered light leaves the eye12as measurement light24reflected back. The measurement light24reflected back passes through the optical arrangement AOM in the opposite direction and is guided as an approximately collimated light beam via the beam splitter36and the beam splitter34to the confocal opening30. A further lens group33focuses the measurement light24reflected back onto the opening30.

The light detector20downstream of the opening30measures the intensity or the power of the reflected-back measurement light24that passes through the opening30. The control unit38contains an arithmetic unit, for example, which can set the optical arrangement AOM by a suitable algorithm such that a maximum power is measured at the light detector20. On the basis of the setting of the optical arrangement AOM for which the measured intensity of the measurement light24reflected back has a maximum, the measuring module18can then determine the refraction of the eye12, in particular the spherical equivalent of the ametropia, the astigmatism and the axis position of the astigmatism, as will be described in greater detail later. The measuring module18and the control unit38can be embodied as a functional unit, wherein the function of the measuring module18can also be performed by the control unit38, and vice versa.

It goes without saying that further optical components can be positioned between the eye12and the optical arrangement AOM.

The optionally provided beam splitter36can be followed by a display and/or an image sensor40, wherein the display40and/or the image sensor40are/is arranged on an optical axis OA passing through the eye12and the optical arrangement AOM. A converging lens group42is arranged between the beam splitter36and the display and/or image sensor40. The display40can be used to give the patient a stimulus for aligning the axis of the eye along the optical axis OA of the refractometer10, or to give the patient a stimulus for accommodation. The display40can equally well also be used for subjective refraction measurement with the optical arrangement AOM being used as a phoropter. The image sensor40can serve to record an image of the front region of the eye12and to monitor whether the eye12is located in a suitable position relative to the refractometer10.

FIG. 2shows a modification of the confocal refractometer10. For the confocal refractometer10shown inFIG. 2, the same reference signs as inFIG. 1are used for elements which are identical, similar or comparable to elements of the refractometer10inFIG. 1.

In the case of the refractometer10inFIG. 2, the measurement light source14is connected to a first optical fiber44and the light detector20is connected to a second optical fiber46. The first optical fiber44and the second optical fiber46are connected to a third optical fiber50via a fiber coupler48, or merge into said third optical fiber. A free end52of the third optical fiber50forms an exit end for the measurement light beam16and an entrance end for the back-reflected measurement light24. In this configuration, the confocality of the confocal refractometer10is achieved by virtue of the fact that the free end52of the optical fiber50simultaneously acts as a confocal opening and thus replaces the two confocal openings30and26of the confocal refractometer10shown inFIG. 1. In this configuration, moreover, the beam splitter34shown inFIG. 1can be omitted, as is shown inFIG. 2. For the rest, reference can be made to the description of the refractometer10inFIG. 1.

The optical arrangement AOM of the refractometer10both shown inFIG. 1and inFIG. 2is configured to compensate for instances of spherical defective vision of the eye12, e.g., by altering air clearances in the optical arrangement AOM or air clearances of the optical arrangement AOM with respect to other optical elements of the optical unit22, with the result that different curvatures of the wavefront of the measurement light beam incident in the eye12can be produced at the pupil P of the eye12. Furthermore, the optical arrangement AOM is configured to compensate for not only the spherical equivalent of the ametropia of the eye12but also an astigmatism for an arbitrary axis position of the astigmatism. For this purpose, the optical arrangement AOM includes one or more adaptive optical components AOE configured to compensate for the astigmatism in the wavefront of the measurement light by the setting of the adaptive optical component. The measuring module18can be configured to determine the astigmatism of the eye and the axis position of the astigmatism from a setting of the optical arrangement AOM and/or of the adaptive optical component(s) AOE for which the measured intensity of the back-reflected measurement light24, as is measured by the light detector20, has a maximum, as will also be described later.

Examples of adaptive optical components AOE which can be used to compensate for an astigmatism and the axis position thereof are Stokes lenses, Alvarez lenses, liquid-filled lenses, etc., will be described below.

Stokes lenses have two cylindrical lenses, which are rotatable relative to one another and of which one cylindrical lens has a positive refractive power Ccyland a second cylindrical lens has an opposite negative refractive power −Ccylof equal magnitude. If one of the cylindrical lenses is rotated by an angle θ and the other by the angle −θ, then the resulting cylindrical refractive power CSLof the Stokes lens is given by CSL=2Ccyl·sin(2θ). Consequently, a Stokes lens allows the production of a continuously adjustable cylindrical refractive power CSL. It is possible to vary the axis position if both cylindrical lenses are rotated together. Stokes lenses of this type can be used in the optical arrangement AOM of the refractometer10.

An Alvarez lens can compensate for not only an astigmatism but also a spherical equivalent of the ametropia. It includes two or more plates each having a surface contour, wherein the two surface contours are mutually complementary, and wherein the plates are translationally displaceable and/or rotatable relative to one another. The refractive power and/or the astigmatism of an Alvarez lens can be altered in a continuously variable manner by the plates being positioned accordingly with respect to one another.

In the case of liquid-filled lenses, the spherical and/or astigmatic refractive power is likewise variable. By way of example, it is possible to use two liquid-filled cylindrical lenses in the optical arrangement AOM, which lenses each have a variable refractive power and are crossed with respect to one another by an angle of not equal to 0°, e.g., of 45°. The cylindrical lenses are positionally fixed with respect to one another, wherein the astigmatism and the axis position of this combination of cylindrical lenses can be varied in a continuously adjustable manner by the astigmatic refractive powers of the two individual cylindrical lenses being set in a suitable manner. In this configuration, the adaptive optical component of the optical arrangement AOM is variable with regard to its astigmatic power including axis position, without the adaptive optical component having to be moved mechanically.

Typically, the adaptive optical component is settable into a neutral setting independently of its specific configuration, the adaptive optical component having no astigmatic power in said neutral setting. Such a neutral setting is provided in the case of the above-described examples of a Stokes lens, an Alvarez plate or liquid-filled lenses.

The confocal refractometers10shown inFIGS. 1 and 2can be used to determine the spherical equivalent SE, the astigmatism Ceyeand the axis position φ of the astigmatism of the examined eye12. The spherical equivalent SE is a statistic for the ametropia. Both the spherical equivalent SE and the astigmatism Ceyeare usually specified in dioptres (D). Usually, eyes with the spherical equivalent of SE<0 D are referred to as nearsighted or myopic, while eyes with SE>0 D are referred to as farsighted or hyperopic. Patients' eyes with SE≈0 D are referred to as having spherically perfect vision or as emmetropic. The astigmatism Ceyespecifies the difference between the refractive powers of the eye12in two mutually perpendicular principal meridians. The axis position φ specifies the position of these principal meridians, represents an angle and is specified in the unit of degrees (°).

The following convention is used in the present description. The astigmatism Ceyeis always positive and satisfies Ceye>0 D. In the two principal meridians, the defective vision of the patient's eye is described by SE±(1/2)C. The axis position φ describes the position of that principal meridian with the defective vision SE+(1/2) C. For known values SE, Ceye, and φ, it is possible to produce a spectacle lens that corrects instances of defective vision of the patient's eye. It goes without saying that it is also possible to use other conventions for describing defective vision, but they can always be converted into the convention indicated above.

An exemplary more detailed configuration of an optical arrangement AOM is described below with reference toFIG. 3.FIG. 3shows an optical unit22having an optical arrangement AOM, wherein the optical unit22can be used in particular in the refractometer10in accordance withFIG. 2.FIG. 3shows only the confocal optical unit22of the refractometer, while the other components such as measurement light source, light detector, measuring module and control unit have been omitted for reasons of clarity. The reference signs which are used inFIG. 3and are identical to reference signs inFIG. 2refer to the elements described with reference toFIG. 2.

InFIG. 3, ellipses at the right-hand edge of the figure show schematic patients' eyes having spherical equivalents of from SE=−10 D (bottom) to SE=+10 D (top).

The optical arrangement AOM includes a first lens group72, an adaptive optical component AOE and a further lens group76. The end52of the optical fiber50is located near a focal plane of the first lens group72, which collimates the measurement light beam emerging from the end52of the optical fiber50. The focal length of the lens group72is 40 mm, for example. The adaptive optical component AOE can be embodied, e.g., as a Stokes lens including cylindrical lenses, e.g., having a cylindrical refractive power Ccyl=+1 D. The adaptive optical component AOE is arranged near a focal plane of the second lens group76. The second lens group76has, e.g., a focal length f76of 150 mm. A third lens group78is arranged such that the pupil P of the eye12is located near the focal plane of the third lens group78. The third lens group78has, e.g., a focal length f78of 60 mm. The lens groups76and78form, e.g., a Kepler telescope.

The optical arrangement AOM is suitable for compensating for spherical defective vision, astigmatism and the axis position thereof. The optical arrangement AOM is movable as a whole along the optical axis in accordance with a double-headed arrow80, e.g., by virtue of the optical arrangement AOM being mounted on a slide, with the result that the distance between the optical arrangement AOM and the third lens group78can be varied. The respectively set position of the optical arrangement AOM can be specified by a distance d between the two lens groups76and78.

The end52of the optical fiber50, the lens group72, the adaptive optical component AOE and the lens group76are positionally fixed with respect to one another in the direction of the optical axis (arrow80). In the exemplary case of the configuration of the adaptive optical component AOE as a Stokes lens, the two associated cylindrical lenses are rotatable relative to one another about the optical axis in order to vary the cylinder power of the Stokes lens, and rotatable jointly in order to vary the axis position of the Stokes lens.

The measurement light beam emerging from the end52of the optical fiber50is collimated by the lens group72, passes through the adaptive optical component AOE and also the lens groups76and78and enters the patient's eye12through the pupil P, where it produces a light spot28on the retina23. The light scattered at the light spot28partly leaves the eye12again as reflected-back measurement light, passes through the optical unit22in the opposite order and is focused by the first lens group72onto the end52of the optical fiber50, where it is partly coupled into the optical fiber50, and passes through the fiber coupler48(seeFIG. 2). The intensity of the reflected-back measurement light reaching the light detector20is measured by the light detector20(seeFIG. 2). During the measurement of the intensity of the reflected-back measurement light, the optical arrangement AOM including the adaptive optical component AOE can be set until the intensity measured at the light detector20becomes maximal, wherein a maximal intensity of the reflected-back measurement light means that the spherical equivalent of the ametropia and the astigmatism and also the axis position thereof for the patient's eye are compensated for.

A description is given below of exemplary embodiments of measuring methods for determining an astigmatism of a patient's eye with the aid of a confocal refractometer, e.g., the refractometer10inFIG. 2having the optical unit22inFIG. 3.

FIG. 6shows a flowchart of a first exemplary embodiment of a measuring method of this type.

As already described above, in the measuring method, a measurement light beam16is directed onto the eye12, with the result that a light spot is produced on the retina23of the eye12. An intensity of measurement light24reflected back from the retina23is measured.

A step100in accordance withFIG. 6involves firstly performing a measurement and/or compensation of the spherical equivalent of the ametropia. In step102, a first cylinder measurement is carried out. In a step104, a second cylinder measurement is carried out. In a step106, the power and axis position of the astigmatism are determined from the cylinder measurement values resulting from the first cylinder measurement and the second cylinder measurement.

Firstly, a description is given of the measurement and/or compensation of the spherical equivalent SE of the ametropia of the eye12by way of example with reference toFIG. 3. While the intensity of the measurement light reflected back from the retina23is measured by the light detector20(seeFIG. 2), the optical arrangement AOM is displaced in accordance with the arrow80until a maximum intensity is measured at the light detector20. In this case, the adaptive optical component AOE is typically set in its neutral position, with the result that it does not exhibit any astigmatic power. In a position of the optical arrangement AOM in which the focal points of the lens groups76and78coincide, the associated distance d between the lens groups76and78is referred to hereinafter as dafoc. For the distance dafocit holds true approximately that dafoc≈f76+f78. In the abovementioned example for the focal lengths f76and f78of 150 mm and 60 mm a value of approximately 210 mm results for the distance dafoc. A more accurate determination of dafocfor given lens groups76and78is possible both computationally and experimentally.

The optical unit22inFIG. 3can be configured in particular such that the adaptive optical component AOE is arranged approximately in the focal plane of the lens group76, and the pupil P of the eye12is located near the focal plane of the lens group78. In this arrangement, the adaptive and optical component AOE and the pupil P are located in mutually conjugate planes.

FIG. 4shows exemplary measurements of the intensity I for various patients' eyes free of astigmatism and having a different spherical equivalent SE. The difference between the set distance d and the distance dafocis plotted on the abscissa of the diagram inFIG. 4, and the associated intensity on the ordinate.

From the distance d for which the measured intensity I assumes its maximum, in this case the spherical equivalent SE can be determined computationally by the equation

when the exemplary value mentioned above for the focal length f78is used.

In step100, by displacing the optical arrangement AOM inFIG. 3, the focus position of the measurement beam path is thus varied until the measured intensity of the measurement light24reflected back from the retina23is maximal. The spherical equivalent of the ametropia can then be determined from the displacement distance d−dafoc.

After the measurement of the spherical equivalent of the ametropia has been carried out and in order that the spherical equivalent of the ametropia is compensated for in the measurement beam path, the first cylinder measurement102is carried out. During the first cylinder measurement, the measurement light beam16is still directed onto the eye12, and the intensity of the measurement light24reflected back from the retina23is still measured.

FIG. 7shows a flow diagram illustrating individual steps of the first cylinder measurement102. In a step1021, a fixed cylindrical axis position of the adaptive optical component AOE is set. In a step1022, the intensity of the measurement light24reflected back from the retina23is measured. In this case, the cylinder power of the adaptive optical component AOE is varied until the measured intensity becomes maximal. A first cylinder measurement value is obtained from this in a step1023, said first cylinder measurement value resulting from the cylinder power of the component AOE for which the measured intensity is maximal.

After the first cylinder measurement102, the second cylinder measurement104is carried out.FIG. 8shows a flow diagram of individual steps of the second cylinder measurement104. In a step1041, a second fixed axis position is set at the adaptive optical component AOE, said second fixed axis position being different than the first axis position in the first cylinder measurement102. In a step1042, once again the intensity of the measurement light24reflected back from the retina23is measured. In this case, the cylinder power of the adaptive optical component AOE is varied until the measured intensity is maximal again. In a step1043, a second cylinder measurement value b is obtained, which then corresponds to the cylinder power which is set at the component and for which the measured intensity is once again maximal.

In the step106inFIG. 6, the power of the astigmatism Ceyeand the axis position φ thereof are then determined by calculation from the first measurement value a, the second measurement value b, the first axis position φ1 and the second axis position φ2=φ1+Δβ of the adaptive optical component AOE. A description is given below of how the power of the astigmatism Ceyeand the axis position φ thereof are calculated.

If the spherical equivalent of the ametropia is compensated for in the measurement beam path, there is located on the retina23either a focus point if the patient's eye12is not afflicted with astigmatism, or a “circle of least confusion” if the patient's eye is afflicted with astigmatism. A change in the power of the cylinder of the adaptive optical component AOE does not influence the spherical equivalent. As a result of the imaging of the adaptive optical component AOE into the vicinity of the pupil P of the patient's eye12, the astigmatism of the adaptive optical component AOE and the astigmatism of the eye are superimposed. The astigmatism of the adaptive optical component and the astigmatism of the eye can be described by the Zernike polynomials since the slightly elliptical pupil P of the patient can be assumed to be approximately round.FIG. 9shows a coordinate system101in relation to the patient's eye12, whereinFIG. 9shows a front view, such as is seen by a physician, both for the right and for the left eye. The z-axis points out of the plane of the drawing inFIG. 9. The x-axis is the horizontal axis of the eye. Both the angle θ of the Zernike polynomials and the angle φ of the axis position of the astigmatism are measured with respect to the x-axis. The radius R is measured in the xy-plane with respect to the coordinate origin.

The vertical astigmatism is described by the Zernike polynomial Z5=R2cos(2θ) and the 45° astigmatism is described by the Zernike polynomial Z6=R2sin(2θ). The power of the astigmatism is described by an additional coefficient in the respective polynomial. Any arbitrary astigmatism Ast can be described as a superimposition of the two polynomials Z5and Z6:

The superimposition of the two polynomials can also be combined into one polynomial:

With the aid of the addition theorem sin(x+y)=sin(x)cos(y)+cos(x)sin(y), it is possible to rearrange the sin term:

For the coefficients c5and c6it additionally holds true that:

The coefficient cAstis thus calculated with:

If the power of two cylindrical lenses C1and C2is superimposed, this superimposition can likewise be described by an addition of the Zernike polynomials. If both cylindrical lenses are oriented identically and the axes are in each case oriented in such a way that both cylindrical lenses produce a 45° astigmatism, then the resulting astigmatism can be described as follows:

If one cylindrical lens is rotated by the angle +α in the xy-plane, and the other cylindrical lens by the angle −α, the following results:

This in turn corresponds to an addition of the polynomials Z5and Z6, with coefficients that are dependent on the angle α of rotation. In order to deduce the power of the astigmatism, the coefficients of Z5and Z6can be summed as described above to form a coefficient A(α):

This yields with cos2x−sin2x−cos(2x), the general case for the superimposition of two cylindrical lenses:

The principal meridians or axes of the two cylindrical lenses here form the angle 2α.

The Zernike coefficients can be converted to obtain the customary spherocylindrical representation in diopters. In this case, there is a linear relationship between the refractive power and the associated Zernike coefficient (see Wesemann, W. “Mathematical note: What relationship is there between the normal spherocylindrical notation of corrective lenses and the Zernike polynomials?” in DOZ, issue 3/2005, pages 40-44). The same formula can thus be applied to the notation with refractive powers in diopters.

As a result of the imaging of the adaptive optical component AOE into the vicinity of the pupil of the eye, the system including adaptive optical component AOE and eye can likewise be regarded as a superimposition of two cylindrical lenses, where

The power of the cylinder of the adaptive optical component AOE is settable in a variable manner, as is the angle 2α. However, since the axis position of the cylinder of the eye is initially unknown, 2α is also unknown. The astigmatism that arises from the superimposition of the two cylinders (AOE and eye) is intended to become as small as possible in order to measure a high intensity of the measurement light 24 reflected back from the retina23, that is to say:

The zero of the first derivative of A with respect to CAOE is thus calculated:

In the case of the measuring method in accordance with the present exemplary embodiment, with a compensated spherical equivalent SE and an arbitrary, but known, first axis position of the adaptive optical component AOE, with the result that the axis of the adaptive optical component AOE and the axis of the cylinder of the eye form the angle β1, the power of the astigmatism CAOEis varied until a maximal intensity of the measurement light24reflected back from the retina23is measured (step102).

The measurement value a is thus obtained:

The first measurement value a is that cylinder power CAOEset at the adaptive optical component for which the measured intensity is maximal, and C=Ceye.

The first axis position of the adaptive optical component AOE is then altered by an arbitrary, but known, angle Δβ into a second axis position. The angle between the axis positions of the cylinder of the eye and of the cylinder of the adaptive optical component AOE is then β2=β1+Δβ. The power of the astigmatism CAOEis once again varied until a maximal intensity of the measurement light24reflected back from the retina23is measured (step104). The second measurement value b results:

Both equations (14) and (15) can be solved with respect to (−C) and then equated:

After application of the addition theorem:

and rearrangement, the following is obtained:

The tangent of the angle 2β1can thus be calculated:

The sought power of the astigmatism C=Ceyeof the eye is then:

For the angle β1it holds true that:

wherein φ is the axis position of the astigmatism of the eye and φ1is the axis position of the adaptive optical component AOE in the first measurement102.

For simplification, it is appropriate to choose φ1=0° and Δβ=45°. This results in:

The following then results for the axis position φ of the astigmatism of the eye:

The spherical equivalent SE of the ametropia of the patient's eye12is known from step100of the measurement. The first cylinder measurement102and the second cylinder measurement104yield the measurement values a and b, and the latter and the known first and second axis positions of the adaptive optical component AOE in the measurements102and104yield the axis position φ of the patient's eye12with the formulae (19) and (21) or with the formula (24) (for Δβ=45° and φ1=0°) and also the power of the astigmatism Ceyeof the patient's eye with the formula (20) or (22) (for Δβ=45° and φ1=0°.

The difference Δβ between the first and second axis positions of the adaptive optical component AOE (74) can be in an angular range of 30° to 45°.

A further exemplary embodiment of a measuring method for determining an astigmatism of an eye with the aid of a confocal refractometer is described with reference toFIG. 10 to 12. For example, as in the previous exemplary embodiment, the confocal refractometer can be the refractometer10inFIG. 2having the optical unit22inFIG. 3. In the measuring method in accordance with the present exemplary embodiment, a measurement light beam16is directed onto the eye12, with the result that a light spot is produced on the retina23of the eye. An intensity of measurement light24reflected back from the retina23is measured. In accordance with a step110a first measurement of the spherical equivalent of the ametropia is carried out. In a step112, a second measurement of the spherical equivalent of the ametropia of the eye12is carried out. A step114involves determining or calculating the power and axis position of the astigmatism of the patient's eye from the first and second measurements of the spherical equivalent of the ametropia.

FIG. 11shows individual steps of the first measurement of the spherical equivalent SE. In the case of the first SE measurement, in a step1101, a fixed cylinder power, which can be not equal to 0 D, and a fixed first cylindrical axis position are set during the first SE measurement at the adaptive optical component. In a step1102, the intensity is measured and in this case the focus position of the optical arrangement AOM (FIG. 3) is varied until the measured intensity of the measurement light24reflected back from the retina23is maximal twice. In a step1103, a first SE measurement value is obtained as the result of the first SE measurement.

FIG. 12shows individual steps of the second SE measurement112. A step1121involves setting a second fixed axis position at the adaptive optical component74, said second fixed axis position being different than the first fixed axis position of the adaptive optical component74. The cylinder power of the adaptive optical component AOE set in step1101is maintained. In a step1122, the intensity of the measurement light24reflected back from the retina23is measured and in this case the focus position of the optical arrangement AOM is varied until the intensity is once again maximal twice. A second SE measurement value is obtained as the result in step1123.

The occurrence of two intensity maxima is explained below with reference toFIG. 5.FIG. 5shows by way of example the measured intensity I when eyes are characterized by astigmatisms C having different powers for one respectively identical spherical equivalent SE=+5 D. While the measurement curve has only one maximum in the astigmatism-free case where C=0 D, two maxima occur in the case of C>0 D. These two maxima of the intensity I arise if, in the example of the refractometer10inFIG. 2having the optical unit22inFIG. 3, the end52of the optical fiber50is imaged onto the retina23in a focused manner in one of the two principal meridians. Specifically, since an eye with astigmatism in both principal meridians has a different refractive power, there are two distances d inFIG. 3for which the intensity I becomes maximal, specifically d1and d2with d1<d2. If the eye12has only a small astigmatism, it may happen that both maxima merge together and only one widened maximum is resolvable. In this case, the two distances d1and d2are identical. If such a case occurs, it is advantageous to alter the cylinder power of the adaptive optical component AOE in the first SE measurement. The distance Δ=d2−d1between the intensity maxima is approximately related to the astigmatism of the eye (for the abovementioned exemplary value of the focal length f78) by way of the equation Δ=C·f278=(C/D)·3.6 mm. The spherical equivalent SE of an eye afflicted with astigmatism results from d1and d2in accordance with the relationship (d1+d2)/2−dafoc=SEZ·f278=(SE/D)·3.6 mm.

From the displacement distance of the optical arrangement AOM inFIG. 3and the resultant distance between the two intensity maxima as a function of the displacement distance, it is thus possible to determine the first SE measurement value and the second SE measurement value in diopters. The first SE measurement value is designated hereinafter by A1and the second SE measurement value is designated hereinafter by A2.

The way in which the power of the astigmatism of the patient's eye and the axis position thereof can be determined from the two SE measurement values A1and A2is described below.

In the case of eyes having astigmatism, as described above, two maxima usually occur during the measurement of the spherical equivalent of the ametropia. If an astigmatism is set at the adaptive optical component AOE, it is imaged onto the eye12. As a result, two maxima likewise occur during the measurement of the spherical equivalent. If two cylindrical lenses having cylinder powers C1and C2, in this case the cylindrical lens given by the adaptive optical component AOE and the cylindrical lens given by the eye12, are superimposed with one another, and the principal meridians of the two cylindrical lenses C1and C2together form the angle β, the resulting cylindrical refractive power is:

The two measurement values A1and A2are:

where β2=β1+δ, wherein β1is the angle between the principal meridians of the two cylindrical lenses CAOEand C=Ceyein the first SE measurement and δ is the difference between the axis positions of the adaptive optical component in the first and second SE measurements. C is the cylinder power or the power of the astigmatism Ceyeof the eye12. If δ=90° is advantageously chosen, the following results from the two equations above:

In order to determine the axis position φ of the astigmatism of the eye12, firstly the angle β1is calculated:

The angle β1is the angle between the principal meridians of the cylinder of the eye and of the cylinder of the adaptive optical component AOE. For a known axis position φ1of the adaptive optical component AOE, the axis position φ of the eye12can thus be calculated:

Since an astigmatism of the adaptive optical component AOE does not influence the spherical equivalent of the ametropia of the patient's eye, with the first SE measurement and the second SE measurement, from the position of the intensity maxima, as described above, it is possible to determine the sought spherical equivalent of the patient's eye (see above). With the SE measurement values A1and A2and also the known value of the set cylinder power CAOE, the power of the astigmatism Ceyeof the patient's eye can be calculated using formula (28). With the calculated value Ceyeand the measurement values A1and A2and also the set known cylinder power CAOEof the adaptive optical component, the axis position φ of the astigmatism of the eye12can in turn be determined using formulae (30) and (31).