Refraction of the pseudophakic eye
This page is devoted to the calculation of the theoretical refraction in the spectacle plane of a pseudophakic eye when we know the effective position of the implant as well as its optical power and the main biometric parameters (anatomical axial length, total corneal power).
We will use a simple method, which consists of calculating the total corneal power allowing to induce emmetropia. The refraction of the eye considered is then equal to the difference between this value and that of the real corneal power.
Calculation of the emmetropizing corneal power
We have established a formula to relate the main biometric dimensions of the emmetropic pseudophakic eye using thick lenses paraxial modeling:
- ALT is equal to the anatomical axial length of the emmetropic eye (ALA) reduced by the distance between the principal planes of the implant (HiH’i) and the distance between the anterior surface of the cornea and the secondary principal plane of the cornea (S1H’c).
- ELPT is referred to here as the effective lens position of a thick IOL, i.e. the distance separating the principal image plane of the cornea from the principal object plane of the IOL (H’cHi).
- na is the refractive index of the aqueous humor
- nv is the refractive index of the vitreous
- Dc is the total power of the cornea
- Di is the total power of the IOL
Using the previous formula, we could calculate the distance from the theoretical image focus (F’e) of the couple cornea + IOL (it provides the value corresponding to the axial length making that thick lens pseudophakic eye emmetropic). If this distance is shorter than ALT, then the eye is nearsighted. If it is longer, the eye is hyperopic. If it coincides with ALT, the eye is emmetropic.
Rather than comparing these distances, it is more convenient to calculate the value of the total corneal power of the eye considered which would give it emmetropia. If this value is equal to that of the measured corneal power, then the eye is emmetropic. If it is lower, the eye is farsighted, and if it is higher, the eye is nearsighted. The advantage is that it suffices simply to subtract these powers in the corneal plane to obtain the theoretical value of the spherical equivalent of the pseudophakic eye considered. It is then easy to convert it into the plane of the spectacle lenses.
Solving this equation for Dc provides the expected total corneal power Dce for which the considered eye is emmetropic when an IOL of power Di is positioned so that its object principal plane Hi is located at distance ELPT from the image principal plane H’c of the cornea:
Refraction of the pseudophakic eye in the spectacle plane
The refraction in the spectacle plane of a given pseudophakic eye is a function of the difference between Dc and Dce in the corneal plane:
where d is the distance to the spectacle plane.
Computing the refraction of the pseudophakic eye
The following spreadsheet makes it possible to calculate the theoretical spherical equivalent of a pseudophakic eye of which we know the biometric parameters, the power, and the anatomical position of the implant (distance between the corneal vertex and the vertex of the IOL).