effects of error in radius of curvature on the corneal power measurement before and after laser...

$: Effects of error in radius of curvature on the corneal power measurement before and after laser refractive surgery for myopia$
TECHNICAL NOTE

Effects of error in radius of curvature on the corneal powermeasurement before and after laser refractive surgery formyopiaYongji Liu1, Yan Wang2, Zhaoqi Wang1 and Tong Zuo2

1Institute of Modern Optics, Key Laboratory of Optical Information Science and Technology, Ministry of Education, Nankai University, Tianjin, and2Refractive Surgery Center, Tianjin Eye Hospital, Tianjin, China

Citation information: Liu Y, Wang Y, Wang Z & Zuo T. Effects of error in radius of curvature on the corneal power measurement before and

after laser refractive surgery for myopia. Ophthalmic Physiol Opt 2012, 32, 355–361. doi: 10.1111/j.1475-1313.2012.00921.x

Keywords: corneal power, intraocular lens,

measurement error, refractive surgery

Correspondence: Yongji Liu

E-mail address: [email protected]

Received: 21 December 2011; Accepted: 14

May 2012

Abstract

Purpose: To investigate the sources of error in corneal power measurement

before and after corneal refractive surgery for myopia.

Methods: The study comprised 28 eyes of six males and eight females with a

mean age of 26 (range 18–39 years). The radius of curvature of anterior and

posterior corneal surface, Q-Values of anterior and posterior corneal surface

and corneal central thickness were measured by rotating Scheimpflug imaging

(Pentacam). The true net power Fg, back vertex power Fv, and keratometric

power SimK, were calculated respectively at the apex and at a paracentral area

on the 3 mm ring.

Results: For virgin eyes, the overestimation (0.53 ± 0.11 D) of the corneal

power by using a keratometric index of 1.3375 was balanced by the underesti-

mation ()0.21 ± 0.09 D) of the corneal power by the error in the radius of

curvature, resulting in a relatively small corneal power error with a mean value

of 0.33 ± 0.11 D. With the Q-value changing from )0.09 to )0.41, the percent-

age balanced by the error in radius of curvature increased from 16% to 73%.

However, for eyes after laser refractive surgery, the radius of curvature error

lead to an overestimation (0.54 ± 0.16 D) of the corneal power and the kerato-

metric index of 1.3375 again overestimated (1.59 ± 0.26 D) the corneal power,

resulting in a large measurement error with a mean value of 2.12 ± 0.40 D.

With the Q-value changing from 0.35 to 1.89, the percentage added by the

error in radius of curvature increased from 14% to 32%.

Conclusions: For virgin eyes, the overestimation of the corneal power by using a

keratometric index of 1.3375 is balanced by the underestimation of the corneal

power by the error in the radius of curvature, resulting in a relatively small cor-

neal power error. However, for eyes after laser refractive surgery, the flatter

anterior corneal surface means that the use of a keratometric index of 1.3375

significantly overestimates the corneal power and the radius of curvature error

now adds to this overestimation and results in a large measurement error.

Introduction

Due to the difficulty of measuring the posterior corneal

radius of curvature, the corneal power is conventionally

determined by the anterior corneal radius with the for-

mula (n)1)/r, where n is taken as 1.3375 for most kera-

tometers and corneal topography systems and r is the

corneal anterior radius. There are two prior assumptions

behind this formula: The first assumption is a constant

posterior/anterior curvature ratio, resulting in the anterior

and posterior corneal surfaces being considered as one

surface with a fictitious single refractive index of 1.3375.

The second assumption is that the corneal anterior sur-

face is considered to be spherical with a zero Q-value

Ophthalmic & Physiological Optics ISSN 0275-5408

Ophthalmic & Physiological Optics 32 (2012) 355–361 ª 2012 The College of Optometrists 355

(which is a factor that describes the shape of the surface)

over the paracentral zone of 2 mm or 3 mm, resulting in

a uniform corneal power in this zone.

It is well known that after laser refractive surgery the

posterior/anterior curvature ratio is not a constant and

the anterior corneal surface is changed from prolate to

oblate.1 However the validity of the assumptions made

using keratometers did not draw much attention until

hyperopic refractions2,3 were observed in patients who

had phacoemulsification with intraocular lens (IOL)

implantation after previously having laser refractive sur-

gery for myopia. After this observation was made, the

first assumption has been been extensively studied4 and

the general conclusion is that the index of 1.3375 tends to

overestimate the corneal power, which helps to explain

the hyperopic surprise after IOL exchange surgery. Since

the role of the second assumption on the corneal mea-

surement for eyes with previous laser refractive surgery

has received little attention, the focus of this research is

try to address this issue.

Another issue in question is how accurate both

assumptions are for virgin eyes. Studies5,6 have shown

that the standard keratometric index of 1.3375 tends to

overestimate the true corneal power for virgin eyes. In

addition, studies7 have reported that the normal anterior

corneal surface is prolate with a negative Q-value, so that

the second assumption is also questionable. However,

both assumptions work surprisingly well for virgin eyes in

terms of IOL power calculation which has been generally

explained8,9 by the formulae for calculating IOL power

having built-in compensations for the bias introduced by

the conventional keratometric index of 1.3375.

Methods

Subjects

Both eyes of 14 patients were randomly selected from the

Refractive surgery Center of the Tianjin Eye Hospital of

the Tanjin Medical University. The study followed the

tenets of the Declaration of Helsinki. Informed consent

was obtained from all subjects after the nature and possible

consequences of the study had been explained. Those who

had corneal or retinal disease or had previous ocular sur-

gery were excluded. Subjects who had worn contact lens at

any time 2 weeks before the examination were excluded as

well. All subjects had a full ophthalmic examination.

Corneal topography was performed with the rotating

Scheimppflug imaging system (Pentacam; http://www.

pentacam.com) preoperatively and about 1 month after

laser refractive surgery. Values recorded from the topog-

raphy included mean radius of corneal anterior surface

(R1), mean radius of posterior surface (R2) and Q-values

for anterior and posterior corneal surface. According to

the Pentacam instruction manual, the mean radius of cur-

vature represents the average of the radius of curvature in

the central 3.0 mm zone. A diameter of 8.0 mm (corre-

sponding to 30�) was chosen to obtain the corneal shape

factor Q-value because in most eyes the ablation zone is

about 8.0 mm. The laser in situ keratomileusis (LASIK)

was performed under topical anesthesia, with the Moria

M2 microkeratome (http://www.moria-surgical.com) being

used to create a superior hinged 110-lm flap measuring

9.0 mm in diameter. The flap was superiorly reflected,

and the stromal bed was ablated using the VISX STAR S4

excimer laser system (http://www.visx.com).

Mathematical method to calculate measurement errors in

corneal power

We suppose the anterior corneal surface is a rotationally

symmetric conicoid surface and for simplicity, the corneal

surface is represented in the x–z plane by the following

formula:

y2 þ ð1þ QÞz2 � 2zR ¼ 0 ð1Þ

where the origin is chosen at the anterior corneal surface

apex, y is the vertical meridian, z is the axis of revolution,

R is the apical radius and Q is the aspheric parameter

that specifies the type of conicoid. Clinical data10 showed

that the cornea anterior surface could be represented by

an ellipse, corresponding to )1 < Q < 0, representing a

prolate, and Q > 0, representing an oblate.

With the measured anterior and posterior corneal radii

and the cornea central thickness, a cornea model was

constructed. In the present paper, we used a corneal

model to study the errors in measuring eyes with and

without laser refractive surgery using keratometry. Since

the keratometry gives the axial radius11 of points on the

3.0 mm ring, then the axial radius of the cornea model

was selected and was calculated using the formula12:

Ra ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR� Qy2

pð2Þ

In addition, the back vertex power of the cornea at the

posterior surface was calculated by:

Fv ¼Fg

1� dnc� Fa

ð3Þ

where the back vertex power of the cornea, the true net

power obtained from Gaussian formula, the actual power

of anterior corneal surface, the corneal central thickness

and the index of cornea (1.376) are represented by Fv, Fg,

Fa, d, nc respectively.

Using the cornea model, the measurement errors

caused by using an index of 1.3375 (corresponding to the

first assumption) and by error in radius of curvature

Effects of error in radius for the corneal power measurement Y Liu et al.

356 Ophthalmic & Physiological Optics 32 (2012) 355–361 ª 2012 The College of Optometrists

(corresponding to the second assumption) are calculated

by the following steps:

1 At the apex, the true net power Fg, back vertex power

Fv by Equation (4), and keratometric power obtained by

(1.3375)1)/R, SimKapex, were calculated respectively.

2 At the paracentral area on the 3.0 mm ring, kerato-

metric power obtained by (1.3375)1)/Ra SimKmanual was

calculated, where SimKmanaul corresponds to the reading

from the keratometery.

3 DFapex¼SimKapex� Fv;DSimK¼ SimKmanual � SimKapex;

DF ¼SimKmanual�Fvwere calculated respectively. DFapex =

SimKapex ) F reflects the error solely caused by using an

index of 1.3375. DSimK = SimKmanual ) SimKapex reflects

the error solely caused by the error in the radius of cur-

vature. DF = SimKmanual ) Fv reflects the corneal error

caused by using both an index of 1.3375 and the error in

corneal radius measurement, because 1.3375 and the

radius of curvature on the 3 mm ring are used to get

SimKmanual.

The above calculations were conducted in Matlab (Ver-

sion 7.0, http://www.mathworks.com) and the statistics

analysis was conducted with SPSS (Version 11.5; http://

www.ibm.com/SPSS_statistics).

Results

Subjects

The study comprised of 28 eyes from six males and eight

females with a mean age of 26 (range 18–39 years). The

mean manifest refraction spherical equivalent before sur-

gery was )7.12 ± 1.72 D (range )4.00 to )10.50 D). After

surgery, the mean manifest refraction spherical equivalent

was )0.26 ± 0.71 D (range )1.69 to 1.44 D).

The mean radius of the anterior cornea surface was sig-

nificantly changed from 7.75 to 9.02 mm after laser

refractive surgery, with the radius of the posterior cornea

surface almost unchanged. The average Q-value of the

anterior corneal surface was prolate with a negative

Q-value of )0.25 (range )0.09 to )0.41). After surgery,

the average anterior corneal surface was oblate with a

positive Q-value of 1.05 (range 0.35–1.89), whereas the

posterior cornea surface remained prolate.

The effects of error in the radius for virgin eyes

In Figure 1, for virgin eyes, the error due to using a cor-

neal refractive index of 1.3375 is shown by the solid tri-

angles, the error in the measured radius of curvature is

shown by the solid squares and the resultant error is

shown by the open circles. The corneal power measure-

ment error caused by the error in the measured radius

of curvature increased negatively with the Q-value. With

the Q-value changing from )0.10 to )0.40, the error

changed from )0.08 to )0.35 D with a mean value of

)0.21 ± 0.09 D.

As shown in Figure 1, the error due to using a corneal

refractive index of 1.3375 overestimates the true corneal

power. The average overestimation is 0.53 ± 0.11 D, rang-

ing from 0.33 to 0.74 D. However, the total corneal

power measurement error caused by using an index of

1.3375 and the error in radius of curvature, was relatively

small with a mean value of 0.33 ± 0.11 D, ranging from

0.12 to 0.53 D.

The effects of the error in the radius for eyes with laser

refractive surgery

For the eyes after laser refractive surgery, the corneal

power measurement error due to using an index of

1.3375, the error in radius of curvature and the resultant

total corneal power measurement error are shown in

Figure 2. In contrast with the results for virgin eyes, the

error in the radius of curvature lead to an overestimation

of the corneal power for eyes after laser refractive surgery.

The overestimation increased as the Q-value increased.

With the Q-value ranging from 0.35 to 1.89, the overesti-

mation increased from 0.2 to 0.78 D with a mean value

of 0.54 ± 0.16 D. The corneal power measurement error

caused solely by using an index of 1.3375 shows an over-

estimation of the corneal power with a mean value of

1.59 ± 0.26 D (range 1.04 to 2.03 D). However, the mag-

nitude of the overestimation increased statistically signifi-

cantly (t27 = 32.41 p < 0.001) in the laser refractive

Figure 1. For eyes before refractive surgery, with prolate corneas,

the error due to using a corneal refractive index of 1.3375 is shown

by the solid triangles and has an average of +0.53 D. The error in the

measured radius of curvature is shown by the solid squares. It

increases negatively with Q-value, helps neutralize the error caused by

using the 1.3375 refractive index, and has an average of )0.21 D.

The resultant error is shown by the open circles and has an average

of +0.33 D.

Y Liu et al. Effects of error in radius for the corneal power measurement


surgery eyes compared to that for virgin eyes, which had

a mean value of 0.53 ± 0.11 D (range 0.33 to 0.74 D).

Discussion

Because the physical meaning of keratometric power

obtained from the keratometric index of 1.3375 is of vital

importance to the discussion, it is first explained. The

keratometric index was proposed13 based on the Gull-

strand eye model, in which the radius of the anterior cor-

neal surface, the radius of the posterior corneal surface

and the thickness of the central cornea are 7.7, 6.8 and

0.5 mm respectively.

From Gaussian Optics, the refractive power of the cor-

nea, which is considered as a thick lens, is calculated by:

Fg ¼ Fa þ Fp �d

nc� Fa � Fp ð4Þ

where Fg is the corneal power, Fa is the power of the

anterior surface, Fp is the power of the posterior surface,

d is the thickness of the central cornea, nc is the index of

the cornea. With the data of Gullstrand eye model, we

obtained:

Fa ¼nc � 1

Ra¼ ð1:376� 1Þ � 1000

7:7¼ 48:83D ð4:1Þ

Fp¼ na � nc

Rp¼ ð1:336� 1:376Þ � 1000

6:8¼ �5:88D ð4:2Þ

d

nc� Fa � Fp ¼

0:5

1:376� 1000� 48:83� ð�5:88Þ ¼ �0:1D

ð4:3Þ

Fg¼ 48:83þ ð�5:88Þ � ð�0:1Þ ¼ 43:05D ð4:4Þ

The cornea back vertex power at the cornea posterior

surface is:

Fv ¼Fg

1� dnc� nc�1

Ra

¼ 43:05

1� 0:51:376� 1:376�1

7:7

¼ 43:83D ð5Þ

If we apply a refractive index to the front surface that

would produce the same result as the thick lens calcula-

tion, the index can be calculated from Fg by:

ng ¼ Fg � Ra þ 1 ¼ 43:05� 7:7� 10�3 þ 1 ¼ 1:3315

ð6Þ

If we use the cornea back vertex power at the posterior

corneal surface Fv to get the index, we obtained:

nv ¼ Fv � Ra þ 1 ¼ 43:83� 7:7� 10�3 þ 1 ¼ 1:3375

ð7Þ

From the above calculations, it is quite clear that if

1.3315 is chosen as the constant index to calculate the

corneal power with the radius of anterior corneal sur-

face by (n)1)/R, the resulting corneal power can be

regarded as the power from Gaussian Optics, which is

usually called the true net corneal power. If 1.3375 is

used to calculate corneal power, the result reflects the

back vertex power at the posterior corneal surface. Con-

sequently, the keratometric corneal power obtained from

most clinical instruments, including keratometers or

topography systems can be considered as the cornea

back vertex power at the posterior corneal surface.

Therefore, the corneal power used to calculate IOL

power for virgin eyes is also the back vertex power of

the cornea, rather than the true net corneal power (This

can explain why true net power cannot be entered into

IOL power formulae even for virgin eyes6). Drawing

form this conclusion, in terms of the IOL power calcu-

lation, the error in the back vertex power measurement

before and after laser refractive surgery is our major

focus of the discussion.

Figure 2. For eyes after refractive surgery, with oblate corneas, the

error due to using a corneal refractive index of 1.3375 is shown by

the solid triangles and has an average of +1.59 D. The error in the

measured radius of curvature is shown by the solid squares. It

increases positively with Q-value, adds to the error caused by using

the 1.3375 refractive index, and has an average of +0.54 D. The

resultant error is shown by the open circles and has an average of

+2.12 D.



The effects of error in the radius for virgin eyes

Because the corneal power is actually measured on a ring

with 3 mm diameter and the corneal anterior surface is

not spherical, there is a measurement error, which stems

from the error in radius of curvature. The effects of the

error in radius of curvature on the corneal power mea-

surement were studied in this paper. As expected for a

prolate corneal anterior surface, the error in the radius

of curvature underestimates the apical corneal power for

virgin eyes.

It is well known5,6 that the index of 1.3375 overesti-

mates the true net power. The back vertex power, which

is the main focus of our study, is higher than the true net

power. Therefore, our first question is whether an index

of 1.3375 continues to overestimate the back vertex

power? Our results have shown that the apical keratometric

power is higher than the apical back vertex power, which

confirms that the keratometric index of 1.3375 continues

to show an overestimation of the corneal back vertex

power.

An important finding of the present study is that the

overestimation by using the index of 1.3375 is balanced

by the adius of curvature error, resulting in a relatively

small corneal power measurement error for virgin eyes.

To get a more detailed look, we calculated the percentage

of the error due to using an index of 1.3375 that is bal-

anced by the error in measuring the radius of curvature

and the results are shown in Figure 3. When the Q-value

is around )0.4, almost 70% of the error introduced by

using an index of 1.3375 was balanced by the negative

error in the radius of curvature. Around a Q-value of

)0.25, which is the mean Q-value for normal eyes7,

about 30–40% of the error caused by using the index of

1.3375 is balanced. The balance leads to a relatively small

corneal power measurement error with a mean value of

0.33 ± 0.11 D.

An interesting fact is that though the two assumptions

are questionable, both work surprisingly well for virgin

eyes in terms of the IOL power calculation. The phenom-

enon is explained by a built-in compensation8,9 in the

formulae for calculation of the IOL power. If only the

error due to using the keratometric index of 1.3375 is

taken into account, an error of 0.53 D in keratometry

caused by using 1.3375, translates into about 0.78 D

refractive error14 after an IOL implantation. As it is

reported that the mean absolute refractive error after

modern optimized phacoemulsification is approximately

0.40 to 0.50 D,15,16 which is lower than 0.78 D, it is rea-

sonable to use the built-in compensation to explain the

discrepancy. However if the error in the radius of curva-

ture is also taken into account, the total error in keratom-

etry declines to 0.33 D, corresponding to a refractive

error of 0.40 D after an IOL implantation, which is

within the range of clinical results of 0.40 to 0.50 D.

Two reasons may lead to the discrepancy between our

results and the results in previous studies. First, in the

previous studies, only the effect of keratometric index of

1.3375 on the corneal power calculation was considered.

However, in our study, besides the corneal power mea-

surement error caused by 1.3375, the corneal power mea-

surement error caused by error in the radius of curvature

is also considered causing the neutralization between the

error in keratometric index and the error in the radius of

curvature to be observed. Secondly, it is the back vertex

power, rather than the vertex power at the corneal ante-

rior surface that was used in our study.

The effects of the error in the radius of eyes with laser

refractive surgery

After laser refractive surgery, a distinct change is that the

corneal power measurement error caused by the error in

the radius of curvature is positive, which is the result of

the oblated anterior surface. In addition, the absolute

value of measurement error caused by error in radius of

curvature increases in comparison with that for virgin

eyes (0.54 D vs )0.21 D).

After laser refractive surgery, the corneal power mea-

surement error caused by using an index of 1.3375

remains positive. However, the magnitude is significantly

increased from a mean value of 0.53 D for virgin eyes to

a mean value of 1.59 D for eyes with laser refractive sur-

gery, because the ratio between the anterior and the pos-

terior radius of curvature has increased. The calculated

percentage of the corneal power error caused by the error

in the radius of curvature as a function of the Q-value in

eyes after laser refractive surgery is shown in Figure 4. ForFigure 3. For virgin eyes, the relationship between the contribution

of the error in the radius of curvature and Q-value.



eyes with laser refractive surgery, the error caused by the

index of 1.3375 plays a dominant role in the corneal

power measurement error. However, the additional effect

of the radius of curvature error should not be neglected

especially for eyes with large Q-values.

There are few studies on this issue. A recent study by

Savini et al.17 found no statistically significant difference

between the corneal curvature measurement in both the

paracentral area and over the entrance pupil for eyes with

excimer laser surgery. It concluded that the radius error

had limited relevance in the context of corneal power

measurements after myopic excimer laser surgery, at least

when a large optical zone (6.5 mm) is used. The discrep-

ancy between our results and Savini’s results can be

explained as follows: In our study, the difference between

the corneal power measurement at the apex and at a

position on the 3 mm ring is used, which is more suitable

to reflect the effects of the error in the radius in compari-

son to the mean central value used in Savini’s study. In

another study, Roberts18 has shown that the error in the

radius of curvature plays an important role in the corneal

power measurement even for virgin eyes. In her study, it

is the instantaneous radius that is used to evaluate the

effects of the error in the radius of curvature. In our

study, it is the axial radius that is used to evaluate the

effects of the error in the radius of curvature on corneal

power measurement, as the reading from the keratometry

is the axial corneal power.10

One limitation in our study is that both eyes from sub-

jects were used in the analyses. It is known that two eyes

of one subject are typically similar so that measurements

such as corneal power are correlated. Therefore, in terms

of statistical analysis, more accurate results will be

obtained if data from one eye of a subject are used.

Another limitation of our study is the relatively small

sample size. However, the main focus of the present study

is to investigate the sources of error in corneal power

measurement before and after corneal refractive surgery,

therefore the tendency of the contributions of different

errors seems to be the same with a larger data base. Cer-

tainly, a larger data base is needed for a better quantifica-

tion of the contributions of different errors.

In summary, for virgin eyes, the overestimation of the

corneal power by using a keratometric index of 1.3375 is

reasonably balanced by the underestimation of the corneal

power by the error in the radius of curvature, resulting in

a relatively small corneal power error. However, for eyes

after laser refractive surgery, the flatter anterior corneal

surface means that the use of a keratometric index of

1.3375 further overestimates the corneal power and the

radius of curvature error now adds to this overestimation

and results in a large measurement error.

Acknowledgements

This research is supported by National Science Founda-

tion of China (NO. 60978068, NO. 11104149), by the

Science and Technology Project of Tianjin city (No.

10ZCKFGX18800) and by the Fundamental Research

Funds for the Central Universities.

References

1. Tuan K & Chernyak D. Corneal asphericity and visual

function after wavefront-guided LASIK.pdf. Optom Vis Sci

2006; 83: 605–610.

2. Seitz B, Langenbucher A, Nguyen NX, Kus MM & Kuchle

M. Underestimation of intraocular lens power for cataract

surgery after myopic photorefractive keratectomy. Oph-

thalmology 1999; 106: 693–702.

3. Gimbel HV, Sun R, Furlong MT, van Westenbrugge JA &

Kassab J. Accuracy and predictability of intraocular lens

power calculation after photorefractive keratectomy. J

Cataract Refr Surg 2000; 26: 1147–1151.

4. Shammas HJ, Shammas MC, Garabet A, Kim JH, Sham-

mas A & Labree L. Correcting the corneal power measure-

ments for intraocular lens power calculations after myopic

laser in situ keratomileusis. Am J Ophthal 2003; 136: 426–

432.

5. Olsen T. Calculation of intraocular lens power: a review.

Acta Ophthalmol Scand 2007; 85: 472–485.

6. Savini G, Barboni P, Carbonelli M & Hoffer KJ. Agree-

ment between pentacam and videokeratography in corneal

power assessment. J Refract Surg 2009; 25: 534–538.

7. Gonzalez-Meijome JM, Villa-Collar C, Montes-Mico R &

Gomes A. Asphericity of the anterior human cornea with

different corneal diameters. J Refract Surg 2007; 33: 465–

473.

Figure 4. For the eyes after laser surgery, the relationship between

the contribution of the error in the radius of curvature and Q-value.



8. Tang ML, Li Y, Avila M & Huang D. Measuring total cor-

neal power before and after laser in situ keratomileusis

with high-speed optical coherence tomography. J Cataract

Refract Surg 2006; 32: 1843–1850.

9. Ho J, Tsai C, Tsai R, Kuo L, Tsai I & Liou S. Validity of

the keratometric index: evaluation by the Pentacam rotat-

ing Scheimpflug camera. J Cataract Refract Surg 2008; 34:

137–145.

10. Anera R, Jime¢nez J, Barco LG, Bermu¢dez J & Hita E.

Changes in corneal asphericity after laser in situ keratomi-

leusis. J Cataract Refract Surg 2003; 29: 762–768.

11. Mandel RB. Corneal power correction factor for photo-

refractive keratectomy. J Refract Corneal Surg 1994; 10:

125–128.

12. Salmon THD. Comparison of elevation, curvature, and

power descriptors for corneal topographic mapping.

Optom Vis Sci 1995; 72: 800–808.

13. Cheng ACK, Rao SSK, Lau S, Wong A & Lam DSC. Com-

parison of techniques for corneal power assessment after

myopic LASIK without the use of preoperative data. J

Refract Surg 2008; 24: 539–543.

14. Liu YJ, Wang ZQ & Mu GG. Effects of measurement

errors on refractive outcomes for pseudophakic eye based

on eye model. Optik 2010; 121: 1347–1354.

15. Norrby S, Lydahl E, Koranyi G et al. Clinical application

of the lens haptic plane concept with transformed axial

lengths. J Cataract Refract Surg 2005; 31: 1338–1344.

16. Feiz V, Mannis MJ, Garcia-Ferrer F et al. Intraocular lens

power calculation after laser in situ keratomileusis for

myopia and hyperopia – a standardized approach. Cornea

2001; 20: 792–797.

17. Savini G, Carbonelli M, Barboni P & Hoffer KJ. Clinical

relevance of radius of curvature error in corneal power

measurements after excimer laser surgery. J Cataract

Refract Surg 2010; 36: 82–86.

18. Roberts C. Characterization of the inherent error in a spheri-

cally-biased corneal topography system in mapping a radially

aspheric surface. J Cataract Refract Surg 1994; 10: 103–111.



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