Download Optical zone diameters for photorefractive corneal surgery.

Optical Zone Diameters for Photorefractive
Corneal Surgery
Calvin W. Roberts* and Charles J. Koesterf
Purpose. To examine the physiological optics of photorefractive corneal surgery and to study
the effect on glare production of the optical zone diameter.
Methods. An optical analysis computer program was used to generate rays that define the edge
of the optical zone for any given pupil size and glare-free field.
Results. The optical zone diameter must be based on the postoperative corneal curvature
because that determines magnification of the pupil. The minimal optical zone diameter of
uniform optical power was determined both for myopic and hyperopic surgery and for two
values of anterior chamber depth.
Conclusions. Optical zone diameters must be at least as large as the entrance pupil diameter to
preclude glare at the fovea, and larger than the entrance pupil to preclude parafoveal glare.
Invest Ophthalmol Vis Sci 1993;34:2275-2281.
Hixcimer laser photorefractive keratectomy alters the
refractive power of the cornea by ablating a central
disc of the superficial stroma so as to induce a new
corneal profile. The required depth of the keratectomy is a function of the amount of ametropia to be
corrected and the diameter of the optical zone selected.1 Greater refractive errors or larger optical
zones require deeper keratectomies. Recent studies
have demonstrated better healing with less stromal
haze when more superficial keratectomies are performed.2"5 Therefore, the smallest diameter optical
zone should be used compatible with normal physiologic optics of the cornea.
One optical concern in photorefractive keratectomy is the glare induced by beams of light entering
From *Comell University Me.dic.ul College, and ^Columbia University College of
Physicians and Surgeons, New York, New York.
Supported by grants to Dr. Roberts from Michael and Gina Ricciardi foundation,
Oebra and Leon Mack, Leonard and Sylvia Marx, and the Leonard and Adele
lUock Foundation, ami to The Department of Ophthalmology, Columbia University
from Research to Prevent Hlindmss.
Submitted for publication: August 30, 1991; accepted August 20, 1992.
Proprietary interest category: Dr. Robert, N; Dr. Koester, I.
Reprint requests: Calvin W. Roberts, Department of Ophthalmology, Cornell
University Medical College, 520 East 70th Street, New York, NY 10021.
the pupil through the cornea outside the area of ablation. As the pupil dilates, more of these rays will reach
the retina and degrade the image, either in the fovea
or in the parafoveal region.
Glare, in the sense used here, can arise when light
from a bright source is incident on an interface or
irregularity that reflects, refracts, or scatters light to
the fovea or the parafovea area of the retina. Such an
interface or irregularity can, in principle, be on any
surface or region between the object and the retina. In
this study we consider just irregularities on the cornea.
The type of glare arising from postoperative stromal
haze in the optical zone is not within the scope of this
study.
Uozato and Guyton6 were the first to calculate the
optical zone area needed to obtain glare-free distance
vision in emmetropia. They stated that, "for a patient
to have a zone of glare-free vision centered on the
point of fixation, the optical zone of the cornea must
be larger than the entrance pupil (apparent diameter
of the pupil)." Not only must this optical zone be without scarring and irregularity, but it must also be of
uniform refractive power.
Investigative Ophthalmology & Visual Science, June 1993, Vol. 34, No. 7
Copyright © Association for Research in Vision and Ophthalmology
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Investigative Ophthalmology & Visual Science, June 1993, Vol. 34, No. 7
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We extend their findings to include the effect of
different anterior chamber depths and the effect of a
postoperative corneal curvature that is (intentionally)
different from the preoperative value.
In a related topic, Uozato et al7 dealt with the required optical zone diameters of contact lenses for
various glare-free field sizes.
Maloney8 described the consequences of a decentered optical zone and discussed methods to ensure
centering.
Next, the postoperative corneal radius was calculated. We assume that only the anterior surface curvature is altered by the excimer laser procedure, so we
first need to calculate the initial power, PS1, of the
anterior corneal surface:
PS1 = (1.376- 1)/R1
If the desired change in corneal power is -AP, the
postoperative anterior surface power is
PS2 =PS1 - AP
METHODS
The edge of the optical zone was determined by exact
ray tracing using the corneal model as given by Helmholz:9 Radius of posterior surface, 6.8 mm; refractive
index of cornea, 1.376; refractive index of aqueous
humor, 1.336; thickness of cornea, 0.5 mm. Figure 1
illustrates the rays used to determine the diameter of
the anatomic pupil and the diameter of the optical
zone. For a given preoperative corneal power, K, the
anterior corneal radius Rl was calculated using the
keratometer equation:
Rl = 0.3375/K
where Rl is in meters, and K is the corneal power
determined by an ophthalmometer. The corneal surfaces were assumed to be spherical.
The entrance pupil diameter was then selected,
and a ray (LR1) parallel to the axis was traced to determine the diameter of the anatomic pupil (AP). The
edge of the pupil is the point of intersection (AP) of
the ray and the pupil plane, 3.6 mm posterior to the
corneal surface.
FIGURE l. Tracing the rays thatjust clear the pupil and reach
the fovea. These limiting rays, LR1 and LR2, are parallel to
the line of sight outside the eye, and are aimed toward the
edge of the entrance pupil, EP, which is the virtual image of
the anatomic pupil, AP. The optical zone diameter (OZ) for
the zero degree field (fovea only) is then the distance OZ
between the limiting rays.
and the post-op anterior surface radius is given by
R2 = (1.376-1)/PS2.
The anterior radius was next changed to R2, and
in the case of myopic correction the thickness of the
cornea was reduced to account for the tissue that was
removed centrally, as described by Munnerlyn et al.1
The starting data were the power of the preoperative cornea, the anterior chamber depth, and the anticipated entrance pupil diameter. The latter is the maximum entrance pupil that is anticipated when the patient will be engaged in activities where glare-free
vision is important. Because this is a clinical decision
involving many factors, our calculations were done for
the range of anticipated entrance pupil diameters
from 2 to 8 mm. These entrance pupil diameters are
based on the preoperative corneal curvature, because
that curvature determines the pupil size seen during
preoperative examination. The computer calculates
the postoperative entrance pupil diameter based on
the planned postoperative corneal curvature.
Optical design software (SuperOSLO, Sinclair
Optics, Fairport, NY) was used to perform the following steps:
1. For the 43D (preoperative) cornea, a ray was
traced parallel to the axis at a distance equal to
the radius of the entrance pupil (EP) (Fig. 1). At
the plane of the pupil the point of intersection,
AP, was located.
2. The radius of the cornea was then changed to
correspond to the postoperative dioptric power,
based on the corneal index 1.376.
3. A "reference" ray was traced from infinity at the
desired angle relative to the axis, aimed so it
would pass through point P in the pupil plane
(Fig. 2). (The reference ray tracing routine in the
software program automatically finds the ray
that passes through the specified point P.)
4. The intersection of this reference ray with the
corneal surface was then determined (C in Fig.
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Optical Zone for Photorefractive Corneal Surgery
FIGURE 2. Tracing the limiting ray at the angle 6. Three rays
are shown, all of which focus to point H on the retina. The
ray that determines the radius of the optical zone is the uppermost ray, labeled LR, which just passes the edge of the
pupil at P. The point C at which the ray intersects the cornea
determines the radius R of the optical zone for the glarefree field of half-angle 6.
2). The distance R from C to the axis is the radius
of the optical zone.
5. Steps 3 and 4 were then repeated for each desired field angle, 0-60°.
6. Steps 1 through 5 were repeated for each entrance pupil diameter.
RESULTS
2277
FIGURE 4. Point A is at the edge of the optical zone. The solid
ray starting at A just grazes the iris and is refracted by the
lens to the fovea. Point B is outside the optical zone. No rays
originating at B can arrive at the fovea, as denoted by the
dashed lines.
have no glare at 30° from the fovea with a 6.69 mm
optical zone. As illustrated in Table 2, if the anterior
chamber is increased to 4.1 mm (the long end of the
distribution of anterior chamber depths, as reported
by Sorsby10), a 4 mm round pupil will require a 7.13
mm optical zone at 30°.
In Tables 3, 4, and 5, the value in parenthesis below each optical zone diameter is the thickness of tissue removed by an ablation of that diameter. An asterisk denotes an ablation depth exceeding 0.5 mm.
The minimum optical zones of uniform optical power
necessary to preclude glare from the fovea and from
the peripheral cornea are shown in Tables 1-5. Comparison of Tables 1 and 2 indicates that for a greater
anterior chamber depth, a larger optical zone is required to protect the extrafoveal region from glare.
For example, Table 1 shows that for an eye with 3.6
mm anterior chamber depth, a 4 mm round pupil will
FIGURE 3. Hypothetical corneal contour (exaggerated) to illustrate that refraction at an inclined surface can produce
glare light at the fovea.
FIGURE 5. Computer-generated ray traces, illustrating the
sleps in calculating optical zone diameters. I: iris diaphram,
AP: edge of anatomic pupil, A: optical axis of the cornea, C:
intercept of the reference ray (2) at the cornea.
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Investigative Ophthalmology & Visual Science, June 1993, Vol. 34, No. 7
TABLE l.
Optical Zone Diameters for a 43D Cornea, Anterior Chamber Depth of 3.6 mm
Glare-free
Anticipated Entrance Pupil Diameter (mm)
angle, degrees)
2
3
4
5
6
7
8
0
10
20
30
40
50
60
2.00
3.02
4.03
5.04
6.05
7.08
8.15
3.00
3.98
4.94
5.88
6.82
7.76
8.72
4.00
4.93
5.83
6.69
7.55
8.40
9.26
5.00
5.87
6.69
7.48
8.25
9.01
9.77
6.00
6.79
7.54
8.24
8.92
9.58
10.25
7.00
7.71
8.36
8.98
9.56
10.13
10.70
8.00
8.61
9.17
9.69
10.18
10.66
11.13
The second variable studied was the effect of flattening or steepening of the cornea on the requisite
optical zone. Table 3 indicates that a myopic patient
with a preoperative cornea of 43 diopters and a preoperative entrance pupil of 4 mm, whose cornea was to
be flattened to 38 diopters, would require an optical
zone of 3.59 mm to be glare-free at the fovea. Table 4
gives the corresponding optical zone diameters for a
ten diopter myopia correction. In each case the required optical zone is slightly smaller than for the 5D
myopic correction illustrated in Table 3. However, the
ablation depths are approximately twice as great as for
the 5D case, and in several situations would exceed the
(assumed) corneal thickness, 0.5 mm.
In Table 5 it is seen that an aphakic patient with a
preoperative entrance pupil of 4 mm whose cornea
was to be steepened from 43 diopters to 59 diopters
would require a 4.11 mm optical zone for glare-free
vision at the fovea.
DISCUSSION
Irregularities on the cornea could be of two types:
scattering and refractive. Scattering could occur, for
example, from a radial keratotomy incision. A refractive glare source is one in which there is a local change
of slope of the corneal surface, particularly if the
change in slope is sufficient to refract light from a
strong source so that it strikes the fovea (Figure 3).
TABLE
Both the untreated cornea and the transition zone are
sources of refractive glare, because they produce outof-focus images on the retina.
For a given eye, and particularly for a given pupil
diameter, there is an optical zone such that an irregularity outside this circular zone is incapable of scattering or refracting light to the fovea. This is illustrated in
Figure 4. Point A is at the edge of the optical zone
because there is one ray from A that can strike the
fovea. Point B, located outside the optical zone, is incapable of scattering or refracting any ray to reach the
fovea, as indicated by the fan of rays.
In surgery the optical zone should be centered on
the line of sight, for reasons discussed by Walsh and
Guyton,11 by Uozato and Guyton,6 and by Maloney.8
The principal reason is that the line of sight passes
through the center of the entrance pupil, by definition. If the optical zone were centered at another
point, say the corneal light reflex, then the optical
zone would be off center with respect to the pupil and
an optical zone of a given diameter would not produce
as large a glare-free field in all directions as that shown
in Tables 1-5.
We use the term "optical zone" to describe that
part of the ablated central cornea that has the desired
optical correction. After surgery there is also a transition zone, a small peripheral ring around the optical
zone that connects the optical zone to the nonablated
cornea. The optical zone therefore is generally smaller
than the ablated area. The optical zone reported by
2. Optical Zone Diameters for a 43D Cornea, Anterior Chamber Depth of 4.1 mm
Glare-free
Anticipated Entrance Pupil Diameter (mm)
angle, degrees)
2
3
4
5
6
7
8
0
10
20
30
40
50
60
2.00
3.19
4,35
5.51
6.66
7.81
8.98
3.00
4.15
5.25
6.33
7.39
8.45
9.51
4.00
5.09
6.13
7.13
8.10
9.05
10.00
5.00
6.02
6.98
7.89
8.77
9.62
10.46
6.00
6.94
7.82
8.63
9.41
10.16
10.90
7.00
7.85
8.63
9.35
10.03
10.68
11.31
8.00
8.75
9.42
10.04
10.62
11.17
11.70
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Optical Zone for Photorefractive Corneal Surgery
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3. Optical Zone Diameters for a Postoperative Cornea power of 38D, Anterior
Chamber Depth of 3.6 mm
TABLE
Glare-free
Field (half
angle,
degrees)
0
10
20
30
40
50
60
Anticipated Entrance Pupil Diameter (mm)
2
3
4
5
6
7
8
1.97
(.006)
2.97
(.015)
3.96
(.028)
4.95
(.045)
5.93
(.067)
6.93
(.097)
7.93
(.137)
2.95
(.015)
3.92
(.027)
4.86
(.043)
5.78
(.063)
6.69
(.088)
7.60
(.121)
8.51
(.164)
3.94
(.027)
4.86
(.042)
5.74
(.061)
6.59
(.085)
7.42
(.113)
8.24
(.149)
9.05
(.195)
4.92
(.043)
5.79
(.062)
6.60
(.084)
7.37
(.110)
8.12
(.142)
8.85
(.180)
9.57
(.228)
5.91
(.065)
6.70
(.087)
7.44
(.112)
8.13
(.141)
8.79
(.175)
9.43
(.215)
10.05
(.265)
6.90
(.092)
7.61
(.117)
8.26
(.145)
8.87
(.176)
9.44
(.212)
9.99
(.255)
10.51
(.305)
7.89
(.127)
8.51
(.155)
9.07
(.185)
9.58
(.219)
10.06
(.256)
10.51
(.300)
10.94
(.350)
Entrance pupil diameters are based on a preoperative corneal power oF43D. Central ablation depths (mm) are given in parentheses.
many investigators is really the ablation area and therefore overstates the true optical zone in their patients.
If the optical zone is smaller than the entrance
pupil, there will be an out-of-focus image of the object
formed on the retina in addition to the in-focus image,
resulting in degradation of the in-focus image. The
figures in the first rows of Table 3 and 4 indicate that
for myopic correction the optical zone could in principle be slightly less than the diameter of the anticipated
entrance pupil. However, it has been shown12 that the
diameter of the optical zone should not be smaller
than the entrance pupil as seen through the unoperated
cornea. The reason is that light that passes through the
annulus of untreated cornea will focus either in front
of or behind the retina. If the subject is fixating on a
bright object, the out-of-focus light will form a halo
around the image of the object. In this case the cornea
is functioning as a bifocal optical element.
If the optical zone diameter is larger than the entrance pupil then the fovea will receive only the in-focus image. In the latter case, the parafoveal region
beyond a certain distance will receive both in-focus
4. Optical Zone Diameters for a Postoperative Corneal Power of 33D, Anterior
Chamber Depth, 3.6 mm
TABLE
Glare-free
Field (half
angle,
degrees)
0
10
20
30
40
50
60
Anticipated E ntrance Pupil Diameter (mm)
2
1.94
(.013)
2.93
(.029)
3.90
(.054)
4.87
(.087)
5.83
(.131)
6.78
(.190)
7.71
(.270)
3
2.91
™ (.029)
3.87
(.052)
4.79
(.083)
5.70
(.123)
6.58
(.174)
7.45
(.240)
8.29
(.327)
4
5
6
7
8
3.88
(.052)
4.79
(.082)
5.66
(.120)
6.50
(.166)
7.31
(.223)
8.09
(.296)
8.83
(.389)
4.85
(.084)
5.71
(.121)
6.52
(.164)
7.28
(.217)
8.00
(.280)
8.69
(.359)
9.33
(.459)
5.83
(125)
6.62
(.168)
7.35
(.218)
8.03
(.277)
8.67
(.346)
9.26
(.431)
*
6.81
(.177)
7.52
(.227)
8.17
(.283)
8.76
(.348)
9.31
(.423)
*
7.79
(.243)
8.42
(.299)
8.97
(.362)
9.47
(.432)
*
*
*
Entrance pupil diameters are based on a preoperative corneal power of 43D. Central ablation depths (mm) are given in parentheses.
* Indicates that this combination of field and pupil cannot be achieved because the ablation depth would exceed 0.5 mm.
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*
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Investigative Ophthalmology & Visual Science, June 1993, Vol. 34, No. 7
5. Optical Zone Diameters and Edge Depths for a Postoperative Cornea Power of
59D, Anterior Chamber Depth of 3.6 mm
TABLE
Glare-free
field (half
angle
degrees)
0
10
20
30
40
50
60
Anticipated Entrance Pupil, Diameter (mm)
2
3
4
5
6
7
8
2.11
(.028)
3.16
(.064)
4.16
(.111)
5.11
(.169)
6.03
(.237)
6.92
(.316)
7.78
(.403)
3.17
(.064)
4.14
(.110)
5.05
(.165)
5.91
(.227)
6.71
(.296)
7.48
(.371)
8.20
(.451)
4.11
(.114)
5.10
(.168)
5.91
(.227)
6.65
(.290)
7.34
(.356)
7.98
(.426)
8.58
(.497)
5.25
(.178)
6.02
(.236)
6.72
(.296)
7.34
(.357)
7.91
(.418)
8.44
(.479)
*
6.26
(.256)
6.91
(.314)
7.48
(.371)
7.98
(.426)
8.44
(.480)
*
7.25
(.347)
7.75
(.400)
8.19
(.450)
8.58
(.496)
*
8.18
(.449)
8.54
(.492)
*
*
*
*
*
*
*
*
Entrance pupil diameters are based on a prcoperalive corneal power of 43D. Edge depths are shown in parentheses.
* Indicates that this combination of field and pupil cannot be achieved because the ablation depth would exceed 0.5 mm.
and out-of-focus images. The tables of optical zone
cal zone should include the entire area of the entrance
diameter give the apparent angle at which the out-ofpupil.
focus image will begin to overlap the in-focus image.
In the correction of myopia by photorefractive
In Table 1, for example, a central zone of 4.94 mm
keratectomy, a distinct trade-off exists for the surtogether with an entrance pupil diameter of 3 mm
geon. To prevent glare, high myopes require large opwould give a field of 20° half-angle in which there is
tical zones, which means ablating deeper into the cenonly one image.
tral stroma.1 Surgeons must weigh the disadvantages
of deeper surgery with the advantage of glare prevenIt should be emphasized thai while the decision on
the optical zone diameter must be made preoperatively, tion. In addition, careful preoperative evaluation requires an assessment of the anticipated variation in
the choice should be based on the best estimate of the
postoperative entrance pupil. The latter should take ac- pupil size in differing ambient light. Those patients
who do extensive night driving or who engage in other
count for both the anticipated change in corneal
activities in which glare could be a problem should be
power (as has been done in the current calculations),
considered for larger optical zones.
and the expected postoperative pupil size of the patient.
The presence of an out-of-focus second image in
Key Words
the parafoveal region may or may not be a matter of
concern, considering the rapid decrease in visual
refractive surgei"y, glare, optical zone, cornea, photorefracacuity at retinal points away from the fovea. However,
tive keratectomy
in the parafoveal region where both images are present, there may be a sensation of diplopia or of image
Acknowledgment
swimming whenever the eye moves to a new fixation
point. This region will be annular in shape, and located
The authors acknowledge numerous helpful discussions
just outside the visual field angle given by the table, ie,
with Stephen Trokel.
20° in the example cited. It would appear desirable to
keep this annular zone at as great a distance from cenReferences
tral vision as is feasible.
A useful rule of thumb is that the optical zone of
1. Munnerlyu CR, Koons SJ, Marshall J: Photorefractive
uniform optical power should never be less than the
keratectomy: a technique for laser refractive surgery.
largest expected postoperative entrance pupil diameter.
J Cataract Refract Surg. 1988; 14:46-52
Care should be taken to allow for pupillary dilation in
2. Marshall J, Trokel S, Rothery S, Krueger RR: Longterm healing of the central cornea after photorefraclow light. If the pupil has an irregular shape, the opti-
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2281
Optical Zone for Photorefractive Corneal Surgery
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5.
6.
7.
8.
9.
10.
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12.
live keratectomy using an excimer laser. Ophthalmology. 1988;95:1411-1421
Tuft S, Marshall J, Rothery S: Stromal remodeling following photorefractive keratectomy. Lasers Ophthalmol 1987;1:177-185
Taylor DM, L'Esperance FA, DelPero RA, et al: Human excimer laser lamellar keratectomy. Ophthalmology. 1989; 96:654-664
Mandel ER, Krueger RR, et al. Excimer laser large
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procedures. Am J Ophthalmol. 1987; 103:264-275
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Duane TD, ed. Clinical Ophthalmology. Vol. 1. Philadelphia: JB Lippincott; 1989:6.
Walsh PM, Guyton DL. Comparison of two methods
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Invest Ophthalmol Vis'Sci. 1990;31:481. Supplement.
Appendix
Details of the ray tracing are illustrated in Fig. 5. The
iris is shown at I, and the axis of the cornea is at A. The
following step numbers correspond to those in the
Methods section.
1. First the entrance pupil diameter was selected.
Ray 1 was then traced parallel to the axis, at a
distance equal to the radius of the entrance pupil. The point, AP, where the ray crossed the
plane of the iris was thereby located, and was
used to determine the radius of the anatomic pupil for the selected entrance pupil diameter.
2. The radius of the anterior corneal surface was
then changed in the program, using the equation
for determining the postoperative anterior surface. For ease of illustration the anterior radius
in Figure 5 is not changed. (This diagram corresponds to the ray tracing done for Tables 1 and
2, where the cornea was not changed.)
3. A "reference" ray (2) was traced from infinity at
the desired angle, 30° in this figure. The program automatically finds the ray at 30° that
passes through the designated point, which in
this case is the point AP.
4. The intersection of the reference ray with the
anterior corneal surface at point C was determined. The distance from C to the axis is then
the radius of the optical zone.
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