Refractive Vergence Formula.
When both patient and surgeon are unhappy with the postoperative
refraction following cataract surgery, removing the original intraocular
lens may not always be the best approach. When the first IOL is
within the capsular bag, an ideal solution may be to place another
IOL in the ciliary sulcus. This second lens has come to be known
as a "piggyback" IOL.
According to Holladay, there are several reasons why this approach
may be better than a lens exchange. First, removing the original
lens may rupture the capsule and/or loosen zonules. Second, inserting
a piggyback lens is technically much easier than attempting a lens
exchange. And third, the true cause of the refractive error is
usually unknown. If the original lens was mislabeled, then a lens
exchange may further compound the refractive problem.
Piggyback IOL
In 1993, Holladay elegantly described a method for pseudophakic
and aphakic intraocular lens power calculations, independent of
axial length.
Holladay JT: Refractive Power Calculations for Intraocular Lenses in the
Phakic Eye. AJO 1993; 116: 6366 
When significant refractive deviations are seen, the Refractive Vergence
Formula is very helpful in understanding how much optical power must be added
to, or subtracted from, an eye at the level of the anterior chamber, ciliary
sulcus, or capsular bag. This formula also works well for the phakic and
aphakic eye.
The power of the IOL to be implanted is determined by the following:

ELP
o = effective lens position.
K
o = net corneal power.
IOL
e = IOL power.
V = vertex distance.
PreRx = preop refraction.
DPostRx = desired postop refraction. 
The Effective Lens Position (ELPo) is the distance from the secondary principal plane of the cornea to the principal plane of the thinIOL equivalent. The keratometric power of the cornea (Kk) is converted to the net optical power of the cornea (Ko) as follows: Ko = Kk * 0.98765431
If the keratometric power (Kk) is 44.50 D, then...
Ko = 44.50 D * 0.98765431 = 43.95 D
The net optical power of the cornea (Ko) would then be 43.95 D
The following
links will take you to our Physician Downloads,
for an Excel spreadsheet used for calculating the Refractive
Vergence Formula.
Example:
Let's say that during cataract surgery, the operating room
staff mistakenly handed you a +22.00 D posterior chamber lens when the
calculations called for a +18.00 D lens to be placed in the capsular bag (ELPo
= 5.55 mm).
Not a surprise, the patient is now 3.25 D more myopic than planned.
In spite of aniseikonic bases curves, the smallest eyesize possible and a
very close vertex distance, the image disparity cannot be tolerated and she
is requesting that you find some other solution.
With postoperative keratometry
of 44.25/44.75 x 090, the Refractive Vergence Formula would tell you that a
4.00 D posterior chamber lens, placed in the ciliary sulcus (ELPo = 4.80),
will achieve a postoperative refraction close to 0.25 D.
Another example. If an aphakic patient had a refraction of +12.50 D sphere
(vertex distance of 10 mm) and keratometry of 45.00/45.00 x 090, it would take
a +19.50 D anterior chamber IOL (ELPo = 3.50 mm) to achieve a postoperative
refraction of approximately 0.25 D.
In our practice, we typically use the Refractive Vergence Formula for this
type of IOL calculation.
The Holladay
IOL Consultant has a much more sophisticated form of the Refractive
Vergence Formula (known as Holladay R), which is highly recommended.
