Purkinje images and reflections
Study of eye reflections
These images, described by the Czech anatomist Jan Evangelista Purkinje (19th century), are formed by the reflections of the light incident on the surfaces of the optical elements of the eye : the cornea and the lens. They can be used to study the curvature and the relative shift of the optical surfaces, or identify some areas as the optical axis, and the pupil axis. The anterior corneal reflection is the largest clinical.
Indeed, the study of the reflection of an image on the cornea allows to calculate its curvature and deduce its central optical power)keratometry). The specular reflection of a composed image of a disc of Placido is the basis for the completion of the review of corneal topography specular.
Their study further requires a few laws of geometrical optics to the specular reflection on curved surfaces (convex and concave mirrors).
All of the light that enters the eye does not participate in the training of the retinal image; part of it is broadcast (imperfect related to the transparent luminous eye tissue dispersion), another is absorbed, and finally - this is what interests us in the context of the study of Purkinje images. a small percentage of incident light undergoes a reflection. It is this small proportion of reflected light that form the images of the reflections that an observer can see.
The 'specular' of this reflection character is linked to the fact cornea, covered of the tear film, is a smooth surface, as well as, to a lesser extent, the back side of the cornea, the front and back of the lens faces.
Characterization of Purkinje images
Purkinje images are induced by light reflections: the eye surface act as mirrors. The number of images of Purkinje is equal to)four) surface facing the light, each providing a reflection: anterior surface of the cornea, posterior side of the cornea, anterior side of the lens of the eye. The images obtained by these successive reflections are called: PI, PII, PIII, PIV. The easiest to observe picture is PI, because the brightness of this corneal reflection dominates that of the other three images. In certain clinical circumstances, one can also observe PIV (after cataract surgery, thanks to the reflection induced by the posterior side of the artificial lens).
If the corneal reflection is superimposed with the geometric center of the pupil, it materializes then l‘pupillary axis. In general, and particularly at the hypermetropia and astigmatic, the corneal reflection is projected in nasal pupillary area. The gap between the Visual axis (which perforated the corneal dome in a supposed region close to the vertex) and pupillary axis is quantified as an angle: thekappa angle.
In corneal topography, the specular reflection of the center of the focus of fixation (the central ring of the disc of Placido) to locate the k axis that connects this reflection in the crosshairs, and contains the local center of curvature of the cornea.
For a same incident light source, located at a given distance of the eye:
THEintensity These four Purkinje images depends on of the difference index between the incident and the reflective middle.
Them size depends of the curvature of the reflecting surface
Them position also depends on of the curvature reflective surfaces.
Cristallinienne accommodation changes the curvature of the front and back of the lens faces; During accommodation, there is logically a variation of the position of PIII and PIV.
The following figure shows schematically the axial location of plans where form these Purkinje images.
Intensity of Purkinje images
(The apparent brightness) image obtained by reflection intensity depends on the proportion of reflected light (R) to the transmitted light (T): it is given by the Fresnel equations:
R = (no - n) 2 / (no + n) ^ 2 where n is the index of refraction of the incident medium and not the reflective middle one (ex: n = 1 for air and n = 1336: tear film / image ft).
With R + T = 1 and T = 4nn of fact ' / (no + n) 2
These equations neglect the possibility of light absorption by the crossed structures.
Intensity R is therefore all the more important that the index difference is great. Thus,. the brilliance of PI is about 100 times higher than that of the other images, because the index difference between the stroma and the aqueous crystalline and glass is much lower.
A light source of 1 candels (near apparent brightness of a candle) will provide corneal reflection (PI) an image that the shine will be equal to:
I = 1 x (0.336) 2 / (1336) x 2 = 0.063 candela.
The anterior surface of the cornea thinks about 6% the intensity of the incident light.
Using the values of index of refraction of the eye circles, we can calculate that with respect to IP, the relative brightness of PII is ≈ 0.009%, PIII = 0.01%, and PIV = 0.01%.
Size and axial position of Purkinje images
The position of a Purkinje image matches the "apparent" position of the image formed by reflection from a surface. The simplest case is the first image of Purkinje (PI), because it is the fruit of the reflection of light rays unless they have undergone prior refractive.
The calculation of the size and the position of the following images is more complex, as should then take into account the effect of the refraction of the dioptres previous reflection.
The observation of the corneal reflection tends to induce the intuitive perception that this image is formed 'on' the corneal dome. The position of the image should be understood here as the "apparent position" of the reflected image, which corresponds to the position in space the plan where the points of the image formed by reflection of the incident rays from sources on a convex mirror points virtually (the surface of the cornea). In the case of a convex mirror for a distant source located close to the optical axis, the reflection image formed in a plan which located behind the surface of the mirror (and therefore ' the eye', behind the cornea).
A calculation using the formula of conjugation, likening the cornea to a spherical mirror convex with apical curvature radius of 8 mm is used to calculate the position of the PI of a source image to infinity is 4 mm from the corneal Summit (home of the mirror is located at a distance equal to half of the radius of curvature towards the top). If this source is approached to 40 cm, the apparent image moves slightly in front of the home (to the corneal vertex).
The following image was obtained by performing a macro of the eye of a subject near a window. Where the plan of the image formed by reflection on the cornea corneal Summit, and what is his height?
In this calculation, we use the conjugation of mirrors formula, which applies in principle only in conditions paraxiales (which strictly speaking is not the case here), and for convenience and despite the absence of real refraction, the inverse of the distances with the top of the considered mirror will be called "vergence.
The height of the window is 60 cm, it is located in 8 m of the cornea with the apical curvature radius of R = 8 mm.
The vergence of the st object equal to V = 1 /-8 m = - 0.125 D (the negative sign is related to the convention which made measuring algebraic distances in the positive to the right, negative to the left). The home of the mirror is located at half of the radius of curvature (4 mm behind the corneal Summit). The power of the mirror is 1 /-0.004 = 250 D. Deduces the vergence of the image:-250 D + - 0.125D =-250.125 D. The position of the image is given by the inverse of the vergence:-1 /-250.125 = 0.00399 = 3.99 mm. This distance is to the right of the corneal Summit, "in the eye". The magnification is equal to the object/image vergences report:-0.125 /-250.16 −soit 0.5%. The size of the window in the image formed is close to 3 mm.
What a closer source, as that of a Placido disc ?
Imagine a Placido disk which has a total diameter of 25 cm, in 10 cm of the cornea, which the apical curvature RADIUS is R = 7.8 mm.
The vergence of the V drive is equal to V = 1 / - 0.10 m = - 10 D (the negative sign is related to the convention which made measuring algebraic distances in the positive to the right, negative to the left).
Home to the corneal convex mirror is located at ½ R 3.9 mm. The corresponding vergence is 1 /-0.0039 = - 256.4 D. The vergence of the Vi image is equal to-256.4 + -10 D = - 266.4 D. The position of the image reflected towards the Summit is-1 /-266.4 = 0.0037 m = 3.7 mm.
The magnification of the image is equal to the report of the vergences between object and image, either-10/-266.4=+0.0375 or approximately 4%.
The image of Placido will drive a close apparent size of 25 cm x 0.0375 = 0.9375 cm: This allows "covering" almost all of the corneal surface (whose diameter is close to 1 cm). The dimension of the domes of Placido and the distance to which they must be positioned towards the focal length of the digital camera that in photography reflect respectively are close to 25 m and 10 cm with most of the topographic systems specular.
Reflections of Purkinje II and III have a relative importance in the clinic. The reflection II is very difficult to observe (small difference in index of refraction between endothelium and aqueous). The reflection III is also required, and it is formed in a relatively later plan. If one observes the reflections of the eye of coaxial way with a point light source, can be defined theoptical axis like the one which minimizes the distance between the PI, PII, PIII and PIV reflections.
The IV reflection is interesting because from the reflection on a concave surface (the back of the lens); his image is formed in a close enough plan of the corneal reflection (Purkinje I). However, it is also very difficult to observe in standard conditions of observation for a phakic eye.
Calculate its approximate theoretical position. To simplify this calculation, it is considered the incident rays are derived from a source located at infinity, and reflection is done as in the air.
To calculate the power of the mirror represents the back side of the lens, it is necessary to know its curvature. The measure of the curvature of the posterior side of the lens is quite difficult with the conventional means of observation: it is precisely some conducted the study of Purkinje IV image sizes for estimating this RADIUS (ex: Rabbets in Bennett and Rabbets' Clinical Visual Optics, 3rd edition, Butterworth - Heinemann). A value of 6 mm can be regarded as realistic for a not accommodating lens (the anterior side of the lens is flatter, its RADIUS estimated close to 10 mm - out of accommodation).
The home of the later cristallinien mirror is located at-3 mm from the posterior pole of the lens. The power of the considered mirror is + 333.33 D. For parallel incident rays, the image of reflection with the posterior side of the lens is formed so 3 mm in front of the top of it, in neighboring image of Purkinje I plan, that it appears approximately 3.8 mm behind the corneal dome. Indeed, the distance between the corneal vertex and the posterior pole of the lens is close to 7 mm. Notable fact, chis image PIV is reversed (the power is positive), and in fact the magnification coefficient is negative.
In a model eye of Gullstrand, the distances of each of the Purkinje images with the corneal vertex are (Atchinson DA, Smith G, Optics of the human eye, Butterworh Heinemann, 2000):
PI: 3,850 mm
PII: 3,765 mm
PIII: 10.620 mm
PIV: 3.979 mm
Clinical observation of a reflection IV is more easily observed in the pseudophakes eyes, surgery of cataract, because there is a difference in index of refraction between the implant and him vitreous considerably higher than that separates the cristallinien cortex of the vitreous, and increased the transparency of the eye circles. The radius of curvature of the implants is significantly larger than the posterior lens (close to 12 mm, depending on the power and the geometry of the implant). This closer images PI and PIV on the axial plan, the latter then that might appear in a more anterior than the PI image plan. In a frontal plan, these images appear right aligned; PI is usually slightly offset in nasal towards the geometric center of the cornea. PIV moves in a way opposite with PI, and appears in the temporal.
The surgeon informed, this image is clearly visible during the cataract surgery, once the implant has been placed. She is brilliant as outcome of the reflection of the coaxial lighting bulbs to the surgical microscopic sighting system, and moves in opposition to PI during eye movements.
After cataract surgery, the fourth reflection of Purkinje (posterior face of the implant) is also visible. The following image allows d ' observe a horizontal cut of the left eye image after cataract surgery and to a trifocal Diffractive implant. Due to the presence of a relatively pronounced Kappa corner, external rotation of the eye laying down the center of the coxiale of the IOL Master 700 biometer keratometry target causes a displacement nasal of the image I of Purkinke (vertex) and temporal IV of Purkinje image (posterior face of the implant).