ELP stands for Effective Lens Position, i.e., the distance between the
corneal vertex and the principal plane of the intraocular lens.
It represents the optical separation used in all thin-lens equations.
In pseudophakic eyes, this distance can be directly measured postoperatively
using anterior-segment OCT or optical biometers, which provide precise imaging
of the IOL location. Since the ELP strongly influences the relationship between IOL power and
ocular refraction, it is a key parameter in both the vergence-based conversion and the
Gatinel Q-ratio method.
Using the true measured ELP rather than an estimated one allows
a more accurate conversion of toric IOL cylinder from the implant plane to
the corneal plane (see Gatinel conversion method – Q ratio).
Ps and Pc refer respectively to the spherical power
and the cylindrical power of the intraocular lens, both defined at the IOL plane.
The spherical component Ps should be understood as the
equivalent sphere (or mean optical power) of the implant,
not as the “sphere” term used in spectacle refraction notation
(which belongs to a sphero-cylindrical prescription at the spectacle plane).
The Pc term corresponds to the toric or cylindrical component
of the IOL, whose effective contribution at the corneal plane depends on the
cornea–IOL distance (ELP) and on the selected conversion model
(e.g. vergence method or Gatinel Q-ratio).
Q is the local ratio Q = ∂P/∂R linking a change in IOL power
dP to the induced change in ocular refraction at the corneal plane
dR (signs are opposite: increasing IOL power makes refraction more myopic).
In the paraxial pseudophakic-eye model:
Q = − 1 / [ 1 − (E / na) · (K + R) ]2,
with E the cornea–IOL distance (meters),
na=1.336, K the keratometric power, and
R the refraction at the corneal vertex.
Hence dR = (1/Q)·dP.
Toric conversion. Compute Q on the two principal meridians
(K1, K2) and average:
Pc,eff ≈ ½ · ( |1/Q(K1)| + |1/Q(K2)| ) · Pc.
This is what the solver uses to convert a toric IOL cylinder at the IOL plane to its
effective cylinder at the corneal plane.
Versus classic “vergence” translation. The thin‑lens translation
Feff = F / (1 + (E/na)·F) ignores corneal power.
The Q‑based approach explicitly includes K (via K+R) and ELP,
so it better captures extremes (flat/steep corneas, anterior/posterior ELP).
Typical magnitudes (R=0): for K≈43 D and
ELP≈3.5–5.0 mm, |Q|≈1.3–1.5 so
|1/Q|≈0.65–0.77 per diopter. See the tables for a full grid of
values.
Reference : Gatinel D, Debellemanière G, Saad A, Malet J. Relationship between intraocular lens power and ocular refraction variations. J Cataract Refract Surg. 2025 Jun 1;51(6):488-495.