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Power the lens paraxial optics

Calculation of the power optical paraxial (vergence) of the lens


Optical power paraxial or vergence of the lens depends on the curvature of its front and rear faces of its index, as well as its thickness.  The lens is an elastic and flexible structure (this allows the)accommodation(, until the installation of presbyopia). It has an index that varies between the Center (core) and the periphery (cortex). At the front, its anterior surface is in contact with the aqueous, aft, in contact with the glass.

The following calculations will be made on numerical values used by the simplified model of theoretical eye of the great. The anterior side of the lens is the 3e interface light meet during his trip intraocular; the back 4.

In this model:

-the radius of curvature of the anterior surface is R3 East of 10.2 mm

-the radius of curvature of the face after R4 East of-6 mm

-l' thickness of the lens is eCR= 4mm

-l' refractive index of the lens is nCR=1.42

-l' refractive index of the lens is nHaq=1.3374

-l' refractive index of the glass is nlives=1.3360

lens optical power

Representation of the anatomical and physical constants to calculate the paraxial of crystalline power


Determination of the power of the side front of the lens

The power of the side front of the crystalline D3 is given by

D3 (n =CR -nHaq) / R3   = (1.42 - 1.337)/0.0102 = 8.14 D)

We can now calculate the focal object and image because we know the indices of refraction of environments that separates the dioptre represented by the face front of the lens of the eye (aqueous and cortex of the lens).

The focal length f is3= - 1,337 / 8.14 =-0.16425 m

The focal image is f'3= - 1.42 / 8.14 = - 0.17445 m


Determination of the power of the back side of the lens

The dioptre formed by the rear of the lens separates the posterior cortex of the vitreous.

D4 (n =lives -nCR) / R4   = (1.36 - 1.42)/-0.006 = 14 D

The focal length f is4= - 1.42 / 14 =-0.10143 m

The focal image is f'4= - 1336 / 14 =-0.09543 m


Determination of the power of a centered system equivalent to the lens

Using the formula of Gullstrand, which takes into account the distance between the vertices of the refractive surfaces (i.e. the thickness of the lens). It allows to calculate the power of the overall system (DCR), consisting of the front and rear of the lens

DCR = D3 + D4 -eCR (D x3x D4) / nCR = 8.14 + 14 - 0.004 x 8.14×14/1.42 = 21.82 D

The focus distance object is given by:

fCR= - 1,337 / DCR=-1.337/21.82 = - 0.06127 m

The focal image is given by:

f'CR= 1.42 / DCR=1.42/21.82 = - 0.06123 m


It remains now to determine the position of the principal planes of the lens, all elements required for this calculation are available.


Determination of the principal planes of the lens

(see for more background explanations the pages dedicated to the)paraxial optics and main plans, and the page dedicated to the plans and main points of a system paraxial optics)

Plan main purpose:

The distance from the top of the front of the lens is given by:

S3HCRe =CR x fCR / f4 = 4 x - 61.27 /-101.43 = 2.42 mm

Plan main image:

The distance from the top of the posterior side of the lens is given by:

S4H'CR=  -eCR x fCR / f3 = 4 x - 61.23 /-174.45 = - 1.4 mm

Representation of the position of the principal planes of the lens

Representation of the position of the principal planes of the lens


The optical power of the lens (vergence) not accommodating is close to 22D (in the eye). The biometric calculationwhich aims to calculate the power of an implant to replace the lens, provides generally an average close to 22D in population of the candidates eyes cataract surgery.

It is likely that the power of the natural lens not accommodated varies less from one eye to the other than the power of the cornea. This is related to the fact that unlike index between the lens and the circles in which he bathes is eniton 4 times less pronounced than for the cornea, which is the contact air (air/cornea = 0.376, unlike crystalline index index difference aqueous = 0.09). However, the deformation of the lens during accommodation (the previous RADIUS reduction), is able to provide a significant increase in its power. For example, using the same model of the lens including the anterior curvature would be now to 7 mm (thickness, increased due to the more spherical shape of the lens, 5 mm, it does not change the geometry of the rear face) and obtain a greater power of about 5 diopters.

The purpose of the biometric calculation is not to calculate the power of the lens 'in situ' to replace it with an implant of the same power, but predict what value should have the replacement implant for an eye to get the desired vision (refraction). With strong myopic, the replacement of the natural lens by an artificial lens less powerful (ex: 10 d) allows to correct partially or totally myopia. In hypermetropia, the artificial lens has a power greater than 22 D (between 23D and 34 D depending on the emmetropia).

The biometric calculation is based on specific measures that take into account the optical power of the cornea, axial length, and other anatomical parameters, depending on the chosen formula. The position of the implant in the eye after the surgery can however only be predicted, and this introduced a certain "margin of error" in the biometric calculation. Depending on the geometry of the implant, the capsular bag, etc., uncertainty about 1 mm are.

The actual position of the implant is the distance between the main image of the cornea (see power and plan of the cornea), and the plan main purpose of the artificial lens.

The knowledge of these elements is essential for the calculation of the Optical power of an entire eye model.





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