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Paraxial power of the IOL - Docteur Damien Gatinel + +

Paraxial power of the IOL

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

The paraxial optical power or vergence of an intraocular lens depends on the curvature of its front (anterior) and back (posterior) surfaces, as well as on its thickness.

This power is also a function of the environment in which the implant is located. After insertion into the eye during cataract surgery, the anterior surface of the implant is in contact with aqueous humor, and the posterior surface in contact with the vitreous cavity.

The refractive indices of these compartments differ slightly from an isotonic solution (BSS) which is generally used as a reference for measurements of the paraxial power of an intraocular implant in vitro.

The optical design of monofocal IOLs varies from model to model. For the same paraxial optical power, one can for example choose to distribute the power equally on the front face and the back surface (the curvatures are identical and the implant is symmetrical). One can also choose to give more power to the posterior surface of the implant (the radius of curvature of the posterior face will then be shorter than that of the anterior face). These choices generally result from non-paraxial considerations (control of spherical aberration), but have paraxial consequences as they influence the position of the principal planes).

The Coddington shape factor is a variable that is calculated from the values of the anterior radius of curvature and the posterior radius of curvature of a thick lens. Hence, if we know the value of the paraxial power of the implant and the Coddington factor, we can deduce the geometry of the implant for a given thickness.

 

Paraxial formulas

The following figure makes it possible to calculate for the anterior surface, the posterior surface, and the IOL assimilated to a thick lens inserted in the eye:

-the total paraxial power,

-the object focal length,

-the image focal length,

– the position of the principal planes of the IOL

 

IOL paraxial power formulas

 

Numerical example

 

In this model:

-the radius of curvature of the anterior face is Ria is 20.00 mm

– the radius of curvature of the posterior face Rip is -16.00 mm

-the lens thickness is di = 1.00 mm

-the refractive index of the lens is ni = 1.52

-the refractive index of aqueous humor is na = 1.337

-the refractive index of the vitreous is nv = 1.336

Power of the anterior surface of the IOL

The power of the anterior surface of the lens Dia is given by:

Dia = (ns – na) / Ria = (1.52 – 1.337) /0.02000 = 9.15 D

 

Power of the posterior surface of the IOL

The power of the posterior surface of the lens Dip is given by

Dip = (nv – ni) / Rip = (1.337 – 1.52) /0.01150 = 11.50 D

 

Focal distances from the anterior surface

We can now calculate the focal object and image distances :

The object focal length is fia = -1.337 / 9.15 = – 146.12 mm

The image focal length is f’ia = 1.52 / 9.15 = 166.12 mm

 

 Focal distances from the posterior surface

The object focal length is fip = -1.52 / 11.50 = – 132.174 mm

The image focal length is f’ip = 1.336 / 11.50 = 116.174 mm

 

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

We use Gullstrand’s formula, which takes into account the distance between the vertexes of IOL’s refractive surfaces (i.e. the thickness of the lens). It allows to calculate of the power of the overall system (Di), made up of the anterior and posterior surface of the IOL:

Di = Dia + Dip – di x (Dia x Dip) / ni = 20.58 D

 

Focal distances of the whole lens

These distances are established with respect to the respective positions of the principal object and image planes of the lens (which will be determined below)

The object focal length is given by:

fi = -1.337/ Di = -1.52/ 20.58 = – 64.964 mm

 

The image focal length is given by:

f’i = 1.336 / Di = 1.336 / 20.58 = 64.915 mm

 

 

Position of the principal planes of the lens

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

 

 

Principal  object plane:

The distance from the top of the anterior face of the lens is given by:

S3Hi = di x fi / fip = 0.492 mm

 

Principal image plane

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

S4H’i = di x f’i / f’ia = = -0.391 mm

 

Interactive calculator for IOL design and principal plane positions

 

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