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Kappa angle

Kappa angle is conventionally defined as the angle formed between thepupillary axis (of pupillary Center to the corneal surface, according to a direction perpendicular to the tangent to the cornea at this point) and theVisual axiswhich connects the attachment with the first point nodal point. Among all the lines passing through the center of the pupil and who cut the anterior surface of the cornea, only one is locally perpendicular to the cornea: she embodies thepupillary axis.

We find a different definition some authors where the Kappa angle corresponds to the angle formed by the pupil axis and the 'line of sight' ('line of sight' in English), while this angle is defined by other authors as Lambda terms. These differences are rather academic in nature, because in practice, values between these well defined angles are minimal.

Know the notion of angle Kappa helps to better understand the position of the reflection (corneal)image of Purkinje), and optimize the corrections laser centering in refractive surgery.

Schematic representation of the main eye. The eye represented in schematic Cup is a look right, cut horizontally. The upper part of the globe is removed (the eye is seen from above). The cornea, the pupil and the lens are not aligned on a common axis; It is possible to define a centerline, or "Best Fit Axis" (BFA), from the respective axes of symmetry of these surfaces. This axis is sometimes likened to the 'optical axis' of the eye and is represented in gray dots. F is the set target point (ex: the central point of the mires of Placido), which the image is formed on the fovea. Point E is located at the center of the entrance pupil (Pe), which is the image formed by the IRIS pupil cornea. The FE segment is the central Ray ("chief ray") of the bunch of rays which contributes to the formation of the Foveal image. Point E' in the middle of the output pupil (Ps), which is the image formed by the lens of the IRIS pupil. The line that connects the attachment point to the center of the IRIS pupil is defined as the line of sight (line of sight). The reflection of F (its projection on the cornea, it's the first Purkinje image) allows you to set the axis k (in red), called 'fixing' normal English. This axis contains the local center of curvature of the cornea, and it is locally perpendicular to the corneal surface. The Visual axis (in blue) connects the point of fixation to the first node, and the second nodal point to the fovea. The nodal points of an optical system are two points in the rated optical axis N don't, combined to the other, i.e. image and one of the other, for which bank angles of rays from the centerline, passing n and out in are identical. Is called nodal point of emergence. The distance between the fovea and is and is close to 17 mm for an Emmetropic eye. This distance is useful to calculate the angular size of the retinal image of an object source. The pupillary axis (in green) corresponds to the normal (perpendicular) to the surface corneal and passing right through the center of the pupil. The pupillary (AP) axis is a angle with the line of sight with the Visual axis the angle kappa and lambda. In practice, the proximity of the Visual axis to the line of sight allows to consider these angles as equivalent.

Some topographers as the Orbscan provide an estimate of the angle Kappa, from a joint measure of the plan and the location of the IRIS pupil (topography of elevation by scanning). The positive angle Kappa value (positive because the pupillary axis is usually temporal to the line of sight and the Visual axis) is included in the normal population between 4 ° and 6 °. Its value tends to increase at the hypermetropia and astigmatic (up to 10 °, sometimes more).


Topographic map elevation and (Orbscan Quad Map view) curvature of the cornea of a farsighted and astigmatic strongly left eye including the position of the corneal reflection is shown in Figure 9. Kappa angle is estimated to be more than 10 °, and this guidance explains the high score of irregularity, as well as moving in temporal of the physiological area of central corneal thinning (yellow area on the map of thickness in bottom right). Strongly farsighted or astigmatic eyes often present an important Kappa angle. To be strictly rigorous, the Orbscan angle is actually the Lambda, because it measures the angle between the line of sight and the pupil axis).

The existence of the Kappa angle thus reflects the absence of common optical axis for different refractive structures of the human eye, and the fact that the Visual axis is usually located in nasal pupillary axis. Like any angle, its measurement must be in degrees. Sometimes, the Kappa angle is expressed in millimetres; These correspond to the distance between the center of the pupil of the vertex (Center of the mires of Placido). It is a assumption, because the precise location of the Visual axis is not easy in a clinic, and the pupil axis is not equal to the direction perpendicular to the plane of the pupil passing through its Center, such registered topographic examination. Some studies suggest that the Visual axis would be located near the vertex (corneal reflection, first Purkinje image). In practice, the surveyors expressing angle kappa in millimeters are based on these simplifications. Clinically, we can consider that a pronounced kappa angle translated a tendency to "external rotation" greater of the eyeball at the Central fixation.


The realization of an ocular biometry with the biometer IOLMaster 700 (Zeiss) allows you to view the effect of this rotation of the globe during the fixation.

kappa nasal vertex angle

The external rotation of the globe over the Foveal fixation target fixation explains the nasal projection of the reflection of Purkinje. The Center hard reflection of hexagonal fixing target corresponds to the projection of the corneal vertex. The camera being coaxial with this focus, the location of it is always located in the center of the picture taken by the camera.

The image in OCT swept source provided by the biometer (upper part of the previous image) can be interpreted roughly as follows:

angle kappa vertex biometrics fixation

Schematic representation of the alignment of the eyeball in setting for a biometric measure. This horizontal cut with a left eye is observed by 'below. The fovea is located in temporal with respect to the optical axis (which is an 'average' axis between the different refractive eye interfaces). This causes a slight external rotation of the globe to its centerline to ensure the central focus Foveal fixation. A reflection of the focus of attachment appears projected in nasal of the lamina and the pupil.


A particular interesting case is provided by the eye aphakedevoid of lens; the only refractive surface of this eye is the cornea, and the Visual axis is then confused with the k axis.

pupillary axis axis Visual kappa aphake

For an aphake eye, the Visual axis and axis k are confused, the corneal surface is the only refractive surface. The lack of symmetry of revolution of the ocular structures, and the rotation of the eye to ensure the Foveal fixation, the pupillary and Visual axes are disjoint.

The following image is obtained Cup OCT through the biometer IOLmaster 700 (Zeiss) for an aphake look. We note the absence of the lens behind the iris plan. The corneal reflection is located in nasal of the pupil; it materializes in this case (aphakia) the intersection of the cornea with the Visual axis.

iolmaster700 eye aphake

Biometric a (initially nearsighted) aphake eye examination. Note the nasal localization of the corneal reflection, while the cornea is the only refractive surface.

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