Optical Perspective of Polycarbonate Material
JP Wei, Ph. D.
November 2011 Introduction
Among the materials developed for eyeglasses, polycarbonate is one that has a number of very unique properties and provides real benefits to eyeglass wearers. Polycarbonate lenses are not only cosmetically thinner, lighter, and provide superior impact-resistance, but also produce sharp optical clarity for both central and peripheral vision.
It is well-known that as the index of refraction increases dispersion also increases. In other words, the higher the refractive index, the low the ABBE value. An increase in dispersion will cause an increase in chromatic aberration. Therefore, one of the concerns in the use of lens materials such as polycarbonate is: will chromatic aberration negatively affect patient adaption?
MID 1.70 LENS MATERIAL CR39 TRIVEX INDEX POLYCARBONATE 1.67 INDEX INDEX REFRACTIVE INDEX 1.499 1.529 1.558 1.586 1.661 1.700 ABBE VALUES 58 45 37 30 32 36
The refractive index of a material is often abbreviated “n.” Except for air, which has a refractive index of approximately 1, the refractive index of most substances is greater than 1 (n > 1). Water, for instance, has a refractive index of 1.333. The higher the refractive index of a lens material, the slower the light will travel through it.
While it is commonly recognized that high index materials will have greater chromatic aberration than CR-39 or low refractive index lenses, there has been no quantification of the amount of visual acuity loss that results from chromatic aberration.
The purpose of this paper is to review the optical properties of polycarbonate material, its advantages over other lens materials, and the impact of chromatic aberration caused by the relative low ABBE value of the material on vision and clinical significance.
Refraction Index and Lens Design
The refraction index of a material is simply the ratio of the speed that light passes through a vacuum to the speed that light passes through a given material. It is well known that the speed at which a ray of light will pass through a material varies with the wavelength of light. Therefore, the index of refraction of a material will vary with the wavelength of light. This necessitates that when specifying the index of refraction, the wavelength of light used is also specified. Therefore, refractive index is the measure of the bending of a ray of light when passing from one medium into another.
Like polycarbonate lenses, lenses made of Trivex are thin, lightweight and more impact- resistant than regular plastic. However, polycarbonate has a higher index of refraction than Trivex (1.586 vs. 1.529), therefore polycarbonate lenses are about 10 percent thinner than Trivex lenses. The benefit for the wearer are lenses that are less conspicuous.
2 For a given lens power and the same base curve, lens material with higher refractive index will result in a flatter back curve, therefore a significantly thinner ET for minus lenses at minimal CT.
For plus lenses, to achieve the same lens power with the same front base curve, higher refractive index material gives steeper back curve. With the same minimal ET, the lens will have a significantly thinner CT, especially for high plus lenses.
Index of Refraction and Chromatic Dispersion
Dispersion is the difference in the index of refraction at different wavelengths.
The refractive index of any material also varies slightly as a function of the wavelength. Colors of light will each actually have a slightly different refractive index in the same lens material. This phenomenon is responsible for chromatic dispersion, or the breaking
3 up of white light into its component colors by prisms and lenses. Blue light, which has a higher refractive index than red light, is therefore refracted—or bent—more than red light as it passes through a lens or prism.
Chromatic dispersion is a result of the fact that colors of light with shorter wavelengths, like blue, travel more slowly through most transparent materials than colors with longer wavelengths, like red.
Dispersion is defined as:
Relative Dispersion = (F - C) / (d - 1) . . . 1)
In the equation 1 F is the index of refraction at the Fraunhofer F-line (486.13 nm), C is the index of refraction at the Fraunhofer C-line (656.27nm) and d is the index of refraction at the helium d-line (587.6 nm). These particular wavelengths are used because they encompass over 90% of the photopic efficiency of the human eye.
The Constringence of a material is the reciprocal (inverse) of Relative Dispersion. Constringence is also called the Abbe number and is defined as:
Abbe Number = d = (d - 1) / (F - C) . . . 2)
The degree to which a given lens material will disperse light is described by a measure of its refractive efficiency or, more commonly, its Abbe value after Ernst Abbe.
The following table gives the index of refraction and Abbe number for some common lens materials.
Index of Refraction for Different Materials
Material Refractive Index ABBE CR-39 1.498 57.8 Crown Glass 1.523 58.5 Trivex 1.529 47.0 1.56 Plastic 1.555 36.0 Polycarbonate 1.586 30.0 1.60 Plastic 1.594 37.0 1.66 Plastic 1.660 32.0 1.70 Plastic 1.70 36.0 1.70 Glass 1.701 32.0 1.80 Glass 1.805 25.4
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Chromatic Aberration
Ideally, a spectacle lens should bring all of the component colors of white light to a single point focus at the focal length of the lens. This means that the lens will refract all of the colors of white light equally, so they all intersect each other at the same location (or focus).
There are two types of chromatic aberration; Longitudinal (Axial) Chromatic Aberration (LCA) and Transverse Chromatic Aberration (TCA).
1. Longitudinal Chromatic Aberration (LCA) LCA occurs when viewing on the optical axis of the lens. LCA creates multiple images along the optical axis as shown in the following figure.
Longitudinal Chromatic Aberration
Because the index of refraction varies with wavelength, the focal length of a lens will vary for each wavelength of light. As seen in the above figure, the blue image is focused at the shortest distance while the red image is focused at the longest distance.
Longitudinal chromatic aberration is a measure of the difference in focus between the blue and red ends of the color spectrum caused by chromatic dispersion.
5 LCA can be quantified as:
LCA = F / d . . . 3) where :
F is the lens power in Diopters d is the Abbe number.
From this equation, it is apparent that there is no LCA for a plano power lens and that LCA increases in direct proportion to lens power.
The table below shows LCA values for some different lens powers (either plus or minus powers) and for some different lens materials.
Longitudinal Chromatic Aberration (D) Versus Lens Power (D)
Lens Power (D) CR-39 Trivex Poly 1.60 Index 1.70 Index 20.00 0.350 0.426 0.670 0.540 0.556 15.00 0.260 0.319 0.500 0.410 0.417 10.00 0.170 0.213 0.330 0.270 0.278 5.00 0.090 0.106 0.170 0.140 0.139 4.00 0.070 0.085 0.130 0.110 0.111 3.00 0.050 0.064 0.100 0.080 0.083 2.00 0.030 0.043 0.070 0.050 0.056 1.00 0.020 0.021 0.030 0.030 0.028
The human eye has a significant amount of LCA. Gullstrand estimated the Abbe number of the eye to be about 43 - 45. Various studies have determined the LCA of the eye to be over 2.50 D. Additionally, LCA of the eye decreases with age, particularly in the waveband of 440 - 560 nm. This is presumably due to yellowing of the crystalline lens.
The graph below shows the spectral longitudinal chromatic aberration of the eye determined in the Lewis, Katz and Oehrlein study.
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Longitudinal Chromatic Aberration of the Eye
1
0.5
0 350 400 450 500 550 600 650 700
-0.5
rs te p io -1 D
-1.5
-2
-2.5
-3 Wavelength (nm)
The conclusion reached is that longitudinal chromatic aberration of the lens is not significant because it is small in comparison to that of the human eye. For example, a 20.00 diopter polycarbonate lens has 0.67 D of LCA compared to 2.50 D for the eye. the visual response curve is centered on yellow and falls rapidly toward the red and blue.
2. Transverse Chromatic Aberration The second type of chromatic aberration is Transverse Chromatic Aberration (TCA). It is the off-axis equivalent of longitudinal chromatic aberration and creates multiple images displaced laterally.
Transverse Chromatic Aberration
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The following equation expresses TCA as a difference in prismatic effect:
TCA = (Lens Power * Decentration) / Abbe Number . . . 4)
TCA therefore depends only on lens power, eccentricity of gaze and the dispersion of the lens material.
3. Peripheral Vision There have been numerous studies of eye movements from the primary fixation point. Clinical studies indicated that 80% of eye movements are within 200 of the point of fixation and 100% are within 300. Beyond 300 the individual will turn their head rather than rotate their eyes.
Decentration as a function of the angle of gaze is found by ray tracing various lens powers for different angles of gaze. While decentration as a function of the angle of gaze varies with lens power, in general, a decentration for a 200 gaze angle is approximately 10 mm and the decentration for a 300 angle of gaze is approximately 15 mm.
Using equation 4, Transverse Chromatic Aberration can be calculated for various lens materials and powers. The table below shows TCA in prism diopters for several materials.
TCA () Versus Lens Power (15 mm decentration, 300 angle of gaze)
Power CR-39 Trivex Poly 1.60 index
20.00 0.520 0.638 1.000 0.810 15.00 0.390 0.479 0.750 0.610 10.00 0.260 0.319 0.500 0.410 5.00 0.130 0.160 0.250 0.200
1.00 0.030 0.050 0.040 0.032
Acuity loss due to TCA can also be compared to other aberrations. The following two graphs, one for CR-39 and one for polycarbonate, compare TCA to spherical aberration, marginal astigmatism and power error. Each of the errors was computed at a 15mm decentration (300 angle of gaze) using spherical front curves.
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CR-39 Aberrations
8.5 8 7.5
7 Chromatic 6.5 Spherical Astigmatism 6 Power Error 5.5 5 4.5 4 3.5 Defocus(D) 3 2.5 2 1.5 1 0.5 0 -0.5 1 3 5 7 9 11 13 15 17 19 Lens Power (D)
Polycarbonate Aberrations
6.25
5.75
5.25
4.75
4.25 Chromatic Spherical 3.75 Astigmatism Power Error 3.25
2.75 Defocus (D) Defocus 2.25
1.75
1.25
0.75
0.25
-0.25 1 6 11 16 Lens Power (D)
It is readily apparent that Transverse Chromatic Aberration is a minor contributor to defocus. At low powers TCA is comparable to other aberrations. At high powers, even for dispersive materials like polycarbonate, marginal astigmatism and power error contribute much more to defocus.
9 Clinical Studies on Transverse Chromatic Aberration
Transverse Chromatic Aberration is manifest as the appearance of colored fringes. However, it has been determined that the perception of colored fringes does not occur simultaneously with loss of visual acuity.
Acuity Loss (After Meslin) 30 degree Angle of Gaze 65.00
60.00 CR-39 (58) 55.00 1.6 Glass (42) 1.6 Plastic (37) 50.00 1.66 Plastic (32) Polycarbonate (30) 45.00
40.00
35.00 Snellen Denominator
30.00
25.00
20.00 1 2 3 4 5 6 7 8 9 10 Lens Power (D)
It is seen that, allowing for variation in the data and depicted with the error bars, polycarbonate and CR-39 follow the same acuity loss. The relation that Hampton et al found can be extended to other materials as shown on the following graph.
Visual Acuity at 30 degree Angle of Gaze (after Hampton et al)
40
38 CR-39 (58) 36 1.6 Glass (42) 1.6 Plastic (37) 34 1.66 Plastic (32) Polycarbonate (30) 32
30
28
26 Snellen Denominator Snellen
24
22
20 1 2 3 4 5 6 7 8 9 10 Lens Power (D)
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Clinical data has shown that an acuity loss of 1 line (20/25) at a 300 angle of gaze is not reached for polycarbonate until the lens power reaches 4.00 D. At a 200 angle of gaze a loss of 1 line of acuity is not reached for polycarbonate until the lens power is about 6.00 D. For reference, 96.9% of all prescriptions are within -6.00 D to +5.00 D and 91.6% are within + 4.00 D.
Anatomically, the retina contains two types of photoreceptors, rods and cones. The rods are more numerous, some 120 million, and are more sensitive than the cones. However, they are not sensitive to color. The 6 to 7 million cones provide the eye's color sensitivity and they are much more concentrated in the central fovea.
Both color vision and visual acuity are mediated by the cones. At 200 gaze angle, color discrimination sensitivity is very low. Any colored fringes caused by TCA are perceptually not noticeable. Visual acuity is determined primarily by the cone size and density. Because cones are concentrated in fovea, visual acuity reduces quickly as cone size increases and density decreases dramatically from central fovea toward periphery. Therefore, the impact of TCA on peripheral vision is negotiable.
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TCA is an off-axis aberration and therefore will be minimized with accurate optical center placement relative to the line of sight. As noted before, lenses with a smaller corneal vertex distance have lesser decentration for the same angle of gaze. The lenses should be fit as close as practical taking into consideration the anatomical constraints of the wearer.
Summary
The review of the effect of chromatic aberration on visual acuity can be summarized as follows:
1. Longitudinal Chromatic Aberration caused by the lens is not a concern because it is less than one-quarter that of the human eye.
12 2. Transverse Chromatic Aberration measured in all clinical studies shows that for even the most dispersive of materials (polycarbonate and 1.66 Plastic), acuity loss is less than 1 line of acuity (20/25) at a 300 angle of gaze only for lens powers within + 4.00 D. This power range covers nearly 92% of prescriptions. 3. For powers greater than + 4.00 D, 1line of acuity will be lost for dispersive materials. However, the loss of acuity due to chromatic aberration is typically less than for other lens aberrations. 4. Acuity loss due to chromatic aberration is small compared to other off-axis aberrations.
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