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ISSN : 1229-6457(Print)
ISSN : 2466-040X(Online)

The Korean Journal of Vision Science Vol.27 No.3 pp.167-181
DOI : https://doi.org/10.17337/JMBI.2025.27.3.167

Investigation of Chromatic Aberration Induced by Decentered Myopia Correction Lenses

Bon-Yeop Koo¹⁾

, Myoung-Hee Lee²⁾

, Young-Chul Kim³⁾

¹⁾Dept. of Optometry, Shinsung University, Professor, Dangjin
²⁾Dept. of Optometry, Baekseok Culture University, Professor, Cheonan
³⁾Dept. of Optometry, Eulji University, Professor, Seongnam

^* Address reprint requests to Young-Chul Kim (https://orcid.org/0000-0001-5103-900X) Dept. of Optometry, Eulji University, Seongnam TEL: +82-31-740-7201, E-mail: yckim@eulji.ac.kr

Received June 15, 2025 Review September 19, 2025 Accepted September 22, 2025

Abstract

Purpose : This study investigates the chromatic aberration induced by decentered corrective lenses for myopia.

Methods : Using the exact law of refraction without paraxial approximation, ray tracing simulations were performed to evaluate the focal lengths and optical powers corresponding to wavelengths of 486.1 nm, 589.3 nm, and 656.3 nm. Furthermore, the 3D Gullstrand schematic eye model was employed to simulate the retinal image formation of the Snellen letter E, at different wavelengths, allowing for a comprehensive comparison of the wavelength-dependent image shifts and distortions.

Results : As the decentration from the on-axis ray increases, the focal length decreases. This is mainly due to the increase in the prism diopter at the periphery of the corrective lens. In addition, as the decentration increases, the lateral decentration distance also increases. The off-axis ray shows a relatively complex pattern because it has a prismatic effect itself, and the prismatic effect due to decentration occurs simulatneously. In the case of the off-axis ray, the focal length increases, and the refractive power shows the opposite trend, while the lateral decentration distance increases with the focal length. The resolution of the retinal image was high on the retina, due to the corrective lens, and it was confirmed to be the highest in the yellow wavelength. There was a slight decrease in resolution when decentration occurred.

Conclusion : Our findings provide insights into the impact of lens decentration on chromatic aberration and its implications for visual performance.

Key Words : Chromatic aberration , Gullstrand schematic eye model , Myopia correction , Optical simulation , Retinal image

근시 교정 렌즈 편심에 따른 색수차 연구

구본엽¹⁾, 이명희²⁾, 김영철³⁾

¹⁾신성대학교 안경광학과, 교수, 당진
²⁾백석문화대학교 안경광학과, 교수, 천안
³⁾을지대학교 안경광학과, 교수, 성남

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Ⅰ. Introduction

The optical correction of myopia is generally based on the principle of aligning the image focal point of the corrective lens with the far point to form a clear image on the retina¹⁾. Corrective lenses require precision design and manufacturing processes to optimize optical performance. They are dispensed to suit the wearer's visual requirements. However, decentration can occur due to lens manufacturing tolerances, prism prescription lenses, errors in spectacle compounding processing, and spectacle wearing habits²⁾. Previous studies have suggested that the decentering of corrective lenses can cause changes in refractive power, reduced resolution, increased chromatic aberration, and peripheral distortion, as the expected focal length changes due to alterations in the ray path³⁾. In particular, even slight decentration has been reported to significantly reduce visual performance in cases of high myopia and astigmatism. These issues may lead to visual fatigue and long-term effects such as heterophoria, highlighting the need to minimize decentration in corrective lenses⁵⁾.

The decentration of the corrective lens was also found to affect the occurrence of chromatic aberration, which was more prominent when the refractive index was high⁶⁾. Chromatic aberration occurs when the refractive index changes with wavelength and the focal length of a ray passing through the corrective lens changes, and among these, transverse chromatic aberration has been shown to cause color spreading⁷⁾. Decentration of corrective lenses can cause coma and astigmatism aberration, increase visual fatigue in the wearer due to changes in corrective refractive power, and reduce the corrective effect⁸⁾. Recently, in clinical practice, personalized designs that take into account the frame and wearing conditions through free-form processing are actively being applied to minimize the effects of corrective lens decentration, and efforts are being made to improve optical performance by combining lowdispersion materials for chromatic aberration correction and multi-coating technology⁹⁾.

In previous studies, we tried to analyze optical performance according to corrective lens decentration have analyzed the effects of aberrations occurring in the corrective lens and the optical system inside the eye, but it was confirmed that there was insufficient analysis on the occurrence of chromatic aberration by major visible ray wavelengths¹⁰⁾. Therefore, it was expected that if we could clearly understand phenomena such as the influence of chromatic aberration at each visible ray wavelength according to corrective lens decentration, it would be helpful in the development of corrective lens design to improve optical performance.

In this study, we performed ray tracing simulations based on the exact law of refraction without paraxial approximation to accurately calculate the propagation of rays passing through corrective lenses. We confirmed longitudinal chromatic aberrations occurring in the main visible ray spectrums of 486.1 nm (blue), 589.3 nm (yellow), and 656.3 nm (red), and compared the distortions on the retina using a 3D Gullstrand schematic eye model. In addition, we investigated the effects of decentration of corrective lenses on focal length, image resolution, refractive power, and chromatic aberration, and discussed the necessity of optimizing lens design and visual performance.

Through this, we aimed to deepen the understanding of chromatic aberration caused by corrective lens decentration and to propose strategies for reducing its optical effects, thereby providing foundational data for advanced optical design. In addition, we employed a ray tracing method based on the exact law of refraction and a 3D Gullstrand schematic eye model to quantitatively analyze wavelength-dependent chromatic aberration, aiming to more precisely evaluate the degradation of visual performance caused by lens decentration.

Ⅱ. Methods

1. Design in the schematic eye model

The 3D Gullstrand schematic eye model was designed using the 3D optical simulation program SPEOS (ANSYS Inc., USA) based on the data values of the ocular media presented in a previous study¹¹⁾. At this time, the curvature radii of the anterior and posterior cornea were 7.70 mm and 6.80 mm, and the refractive index was 1.376. The curvature radii of the anterior and posterior lens cortex were 10.00 mm and -6.00 mm, and the refractive index was 1.386. The curvature radii of the anterior and posterior lens nucleus were 7.91 mm and –5.76 mm, and the refractive index was 1.406. The refractive indices of the aqueous humor and the vitreous were 1.336, respectively.

2. Design of refractive error in the schematic eye model

In order to confirm the change in optical characteristics according to the decentration of the corrective lens, the refractive error was artificially set. At this time, the corneal anterior curvature radius of the model eye was changed to become myopic S-4.00 D for the wavelength of 589.3 nm (yellow).

That is, when the anterior and posterior curvature radii of the corrective lens are 100.00 mm and 337.65 mm, respectively, and the refractive power of the corrective lens is -4.20 D at the vertex distance of 12.99 mm, the anterior corneal curvature radius and refractive power of –4.00 D myopia

r_{1} = 7.11717 m m

(1)

{D_{1}}^{'} = \frac{1.37611 - 1.00000}{7.11717} = + 52.845 D

(2)

were calculated by equations (1) and (2), which shows that the myopia state increases by approximately +4.00 D compared to the anterior refractive power of +48.33 D (radius of curvature 7.70 mm) of the schematic eye model.

3. Design of corrective lenses

The refractive index of the corrective lenses used in this study for the 589.3 nm (yellow) wavelength was 1.600, and the refractive power, radius of curvature, and Abbe number by wavelength are as shown in Table 1.

In addition, the refractive index according to wavelength in the schematic eye model

n (λ) = A + B λ^{- 2} + C λ^{- 4} + D λ^{- 6}

(3)

was calculated using equation (3) and is shown in Table 2.

4. Design of the corrective lens decentration and fixation target

In order to verify the effect of the corrective lens decentration on the retina, the Snellen E letter was implemented as a fixation target using a 3D simulation program, as shown in Fig. 1, and the size and resolution of the retinal image were verified. Here, Fig. 1(a) is a model eye viewed from the front and the Snellen E fixation target in front of it, and Fig. 1(b) shows the eye (orange sphere) and the corrective lens (white circle), respectively, when the optical axes are aligned (left) and when they are eccentric (δ) (right).

Fig. 2 shows the detailed settings of the Snellen letter E of the fixation target. The fixation target was installed 250.0 mm in front of the cornea of the eye model and was set to 1.50 mm × 2.50 mm. The small picture in Fig. 2 shows the image formed by a 0.50 mm × 0.50 mm detector installed at the retinal position (z = 24.38 mm).

Ⅲ. Results

1. Ray Tracing

Parallel rays from a distant fixation target are refracted by the front and back surfaces of the corrective lens and the eye, ultimately reaching the retina where the photoreceptor cells reside. When there is no decentration, rays entering along the optical axis pass through the optical center without deviation. However, decentration causes the rays to refract due to prism effects, altering their expected paths. These rays often enter the eye in an oblique direction, are refracted at each surface, and form an image at a certain point. Therefore, in this study, the paths of rays that enter along the optical axis (center rays) and rays that enter off the optical axis (off-axis rays) were traced to analyze the effect of decentration of the corrective lens.

1) On-axis ray tracing

Fig. 3 shows the changes in focal length (a), refractive power (b), and transverse decentration distance (c) by the decentration of the corrective lens for the on-axis ray.

Fig. 3(a) shows the change in focal length according to the decentration of the corrective lens, and the absolute value of the focal length decreases as the decentration increases. This is because the prism effect increases as the distance from the optical center of the corrective lens increases. In other words, it is the same reason that the absolute value of the refractive power increases as the distance from the optical center of the corrective lens increases in Fig. 3(b). Fig. 3(c) shows the transverse decentration distance at the retinal location (z = 24.38 mm) of the on-axis ray (height = 0.00 mm). Here, since the results for (+) and (-) decentration for the onaxis ray are symmetrical, only the (+) decentration is presented. The transverse decentration distance at the retinal location changed one-dimensionally, and as the decentration increased, the transverse decentration distance also increased proportionally. The transverse decentration distance at the decentration of 3.00 mm was approximately 0.21 mm, which was confirmed by the 3D simulation results, and the effect on the retina could be analyzed through this.

2) Off-axis ray tracing

The effect of decentration on off-axis rays is relatively complex. This is because the prism effect of the off-axis ray itself and the prism effect due to decentration occur simultaneously.

Fig. 4 shows the result of refracting a 589.3 nm (yellow) ray as it passes through the corrective lens and the optical system of the eye in sequence. At this time, the height means the vertical distance of the incident ray from the optical axis. At this time, the two points on the left represent the contact points at the front and back of the corrective lens. The next six points are the contact points at the front and back of the cornea, the front of the lens cortex, the front and back of the lens nucleus, and the back of the lens cortex. The last point is the point where the refracted ray from the optical system of the eye meets the optical axis, which is the focus of the incident ray. It can be seen that the focus changes depending on the decentration of the corrective lens.

Fig. 5 shows the ray paths of 486.1 nm (blue), 589.3 nm (yellow), and 656.3 nm (red) according to decentration. In Fig. 5(a), the ray path distinction seems unclear because the change in refractive index for the wavelength is small, but the difference is revealed when the focus part is enlarged as in Fig. 5(b). Here, it can be seen that the focus is formed at a point farther from the cornea in the order of blue, yellow, and red. In other words, as the wavelength increases, the refractive index decreases, so that the focus is formed at a farther point.

Fig. 6 shows the focal length (a), refractive power (b), and lateral decentration (c) according to the amount of decentration. That is, the distance from the front surface of the cornea in Fig. 4 to the focus is shown according to the amount of decentration. As in Fig. 6(a), it was confirmed that the focal length becomes longer as the amount of decentration increases. When the incident ray height is 3.00 mm and the amount of decentration is -3.00 mm, the incident ray passes through the optical center point of the corrective lens. That is, the trend of the focal length was linear and changed more rapidly when the amount of decentration became –3.00 mm. In Fig. 6(b), it was confirmed that the refractive power is inversely proportional to the focal length, so it is the opposite. Fig. 6(c) shows the lateral decentration at the retinal position (z = 24.38 mm), and since this value is proportional to the focal length, it shows a change very similar to the focal length distribution.

2. Chromatic aberration

Generally, chromatic aberration is a value

chromatic aberration = {D_{F}}^{'} - {D_{C}}^{'}

(4)

defined by the equation (4) of the difference in refractive power between blue and red wavelengths. To confirm the change in chromatic aberration according to decentration, chromatic aberration was investigated for the on-axis ray and the parallel ray incident at a height of +3.00 mm from the optical axis. At this time, the decentration was set to +6.00 mm to -6.00 mm, and the optical axis was set to pass through the eye model.

Fig. 7 shows the chromatic aberration caused by the amount of decentration of the corrective lens. It was found that as the amount of decentration increases, the chromatic aberration also increases. At this time, the chromatic aberration trend according to the amount of decentration was symmetrical for the on-axis ray (h = 0.00 mm), but an asymmetric change was confirmed for the off-axis ray (h = 1.00 ~ 3.00 mm).

3. Retinal image

1) Clarity of retinal image

To investigate the characteristics of the image formed before and after the retinal position in the eye, some detectors that act as retinas were installed at various locations in the model eye. Through this, changes in the retinal image according to decentration could be confirmed.

Fig. 8 shows the results of retinal images by wavelength when there is no decentration of the corrective lens (δ = 0.00). Since there is no decentration, it can be seen that Snellen E is focused at the center of the detector. For all wavelengths, the retinal images are mostly clear. Here, if we look at the apparent images in more detail, we can see that they are clear in the order of yellow, red, and blue.

Fig. 9 shows the results of retinal images by wavelength when the corrective lens decentration is δ = 3.00. It can be seen that there is a transverse decentration of the retinal image due to the corrective lens decentration. The transverse decentration distances on the retina according to the red, yellow, and blue wavelengths are 0.191746 mm, 0.193147 mm, and 0.196648 mm, respectively, which do not differ greatly from each other, but they can be seen to increase very slightly as the wavelength increases. This result is an investigation of the transverse decentration distance for the on-axis ray from the center of the fixation target, and it can be seen that it is similar to the values of 0.19995 mm (red), 0.19477 mm (yellow), and 0.18328 mm (blue) according to the decentration at the point where the dotted lines meet in Fig. 3(c).

The height of the ray incident on the corrective lens from the upper center of the Snellen E letter is +1.00 mm, and the changes in the focal length and the transverse decentration distance when this ray passes through the corrective lens and the eye are presented in Fig. 10. At this time, since the longitudinal focal length and the transverse decentration distance are proportional to each other, it can be seen that the change trends are similar. It was confirmed that the slope of the graph changed starting from the incident height h = 1.00 mm, and it was confirmed that the focal length and the transverse decentration distance increased linearly as the amount of decentration increased.

In Fig. 10(a), when there is no decentration, the focal length for blue is 24.0277 mm, and when the decentration is +3.00 mm, the focal length for blue is 28.3371 mm. In other words, it can be seen that a decentration of 3.00 mm increases the focal length by approximately 4.30 mm. It can be seen that the focal length moves further behind the retina as the decentration increases. Fig. 10(b) is the transverse decentration distance at the retina position. Since the transverse decentration distance is proportional to the focal length, the graph trends are similar. When there is no decentration, the transverse decentration distance for blue is 0.01619 mm, and it is 0.18328 mm for a decentration of 3.00 mm. In other words, the transverse decentration on the retina due to a decentration of 3.00 mm was confirmed to be 0.19947 mm.

In addition, the refractive power and chromatic aberration changes acting on these rays are presented in Fig. 11. As the amount of decentration increases, the refractive power and chromatic aberration decrease. In particular, it can be seen that the refractive power and chromatic aberration changes are very large when the amount of decentration is a minus value. When these results are summarized, it can be confirmed that the refractive power change and chromatic aberration according to the amount of decentration show similar trends, confirming that they are closely related to each other.

2) Magnification of the retinal image

The size of the image formed on the retina with the unaided eye is smaller than the original size of the object being viewed. The transverse magnification (ｍ_β) is the ratio of the transverse size of the image to the transverse size of the object.

At this time, the transverse magnification changes when wearing a corrective lens. In other words, it can be expressed as the product of the magnification by the spectacle lens (ｍ_eye) and the magnification by the eye (m_len).

m_{β} = m_{e y e} m_{l e n s}

(5)

-4.00D myopia, and the vertex power of the spectacle lens at the vertex distance of 12.00mm is -4.25D, so the transverse magnification of the retinal image is equation (6).

m_{β} = (\frac{l_{i m a g e}}{l_{o b j e c t}}) (\frac{1}{1 - c {D_{1}}^{'}} \frac{1}{1 - d {D_{υ}}^{'}}) \approx 0.06206

(6)

Here, c is the thickness at the center of the spectacle lens, and d is the vertex distance. In addition, l_image and l_object are the image distance and the object distance, respectively.

\begin{matrix} l_{i m a g e} = N_{1} A_{7} = A_{1} A_{7} - A_{1} N_{1} \\ = (24.38 - 7.66) = 16.72 m m \end{matrix}

(7)

\begin{matrix} l_{o b j e c t} = N_{1} A_{1} + A_{1} M \\ = - (250.00 + 7.66) = - 257.66 m m \end{matrix}

(8)

Here, A₁, A₇, and N₁ represent the anterior cornea, retina, and nodal point, respectively. Also, M is the objective point. Therefore, the transverse magnifications of the eye and lens are calculated as m_eye ≈ 0.0649 and m_lens ≈ 0.956, respectively, and the transverse magnification (m_β) on the retina by the yellow wavelength is

m_{β} = \frac{i m a g e s i z e}{o b j e c t s i z e} = \frac{0.1688 m m}{2.500 m m} = 0.06752

(9)

That is, the simulation-based image magnification result equation (9) is found to be slightly larger than the theoretical result equation (6). This is believed to be due to the increase in spreading as the resolution decreases, causing the overall size to increase.

3) Resolution of retinal image

The resolution of the image formed on the retina was investigated using the method defined in a previous study¹²⁾. The intensity distribution of the retinal image based on the central line crossing the Snellen E in Fig. 8 is as shown in Fig. 12. Visibility and clarity were calculated using the central peak, and the resolution was calculated by multiplying these two values.

Fig. 13 shows the results of comparing the resolution measured directly behind the fixation target, when wearing the corrective lens, and the resolution according to the corrective lens decentration (δ = 3.00). High resolution was observed mostly at the retinal location due to the corrective lens. The resolution appeared to be highest in the yellow wavelength, with lower resolution trends observed for red and blue, which were focused behind and in front of the retina, respectively. A similar trend may be suggested under lens decentration conditions, with a slight decrease in resolution; however, no statistically significant difference was identified.

Ⅳ. Discussion

In clinical practice, decentration of corrective lenses can commonly occur due to errors in preparation and processing or prism prescriptions, and can have negative effects such as decreased resolution on the retina due to increased chromatic aberration¹³⁾. Decentration of the corrective lens changes the light path, which changes the expected focal length¹⁴⁾.

In this study, the optical paths of the central and off-axis rays were analyzed through ray tracing without approximation, and the focal length, refractive power, and transverse decentration distance were confirmed.

In the case of the on-axis ray, the focal length tended to decrease as the corrective lens decentration increased. This is mainly due to the increase in prisms in the periphery of the corrective lens as it moves away from the optical center of the corrective lens, and is interpreted for the same reason that the refractive power increases as it moves away from the optical center. For the same reason, it was confirmed that the transverse decentration distance also increases proportionally as the decentration increases.

In the case of the off-axis ray, a relatively complex pattern was observed, which is interpreted as the prism effect of the off-axis ray itself and the prism effect due to decentration occurring together. In the off-axis ray, the change in the wavelength-specific light path due to decentration seemed to be unclear because the change in refractive index due to wavelength was insignificant, but when the focus was enlarged, it was confirmed that the focus was formed at a point farther from the cornea in the order of blue, yellow, and red. In other words, it is interpreted that as the wavelength increases, the refractive index decreases, focusing at a farther point and affecting the resolution of the retina image analyzed later. In the off-axis ray, the change in the focal length, refractive power, and transverse decentration distance due to decentration showed that the focal length increased as the decentration increased, and the refractive power showed an opposite trend in proportion to the inverse of the focal length, and the transverse decentration distance showed the same variation in proportion to the focal length. At this time, the focal length in the central light showed a linear change overall, while in the off-axis ray, the focal length was linear and changed more steeply based on the decentration of –3.00 mm.

As the amount of decentration increases, chromatic aberration also increases. In contrast to the symmetrical trend in the on-axis ray, an asymmetrical change was confirmed in the off-axis ray. This is because the center of the ray and the corrective lens change depending on whether the decentration is in the same direction as the incident ray or in the opposite direction. In the results of this study, chromatic aberration increased rapidly as the amount of decentration increased, and it was found that chromatic aberration increased when the decentration was a negative value, that is, when the decentration occurred in the same direction as the incident ray. In addition, it was confirmed that the amount of chromatic aberration was very large for a ray with an incident height of 1.00 mm. However, it was confirmed that the chromatic aberration according to the amount of decentration decreased again when the incident height of the ray increased excessively. In terms of the resolution on the retina, the myopic model eye showed high resolution at the retinal location due to the corrective lens, and it was confirmed that the highest resolution was confirmed in yellow. There was a slight decrease in resolution when there was decentration, but no significant difference was found.

Ⅴ. Conclusion

In this study, we investigated the change in optical performance according to decentration of the corrective lens using the ray tracing method based on the law of refraction without approximation in a 3D Gullstrand schematic eye model using a simulation program.

We confirmed the focal length and refractive power of the corrective lens for the main wavelengths of visible light, the change in the transverse decentration distance, and the occurrence of chromatic aberration. In addition, we identified the formation of the retinal image, the change in wavelength, and the distortion through the Snellen E letter, which is the main fixation target of focus, and evaluated the resolution. The results of this study may offer useful insights into how lens decentration influences chromatic aberration and retinal image quality, and can be used as reference data for clinical spectacle lens design. However, due to the complexity of human visual perception and individual variability, further clinical studies are needed to validate these findings.

Figure

Fig. 1.

The design concept of simulations in this study. (a) 3D Gullstrand schematic eye model, fixation target(Snellen E), and (b) corrective lens decentration.

Fig. 2.

The design concept of fixation target, Snellen E letter, in this study.

Fig. 3.

Changes in the on-axis ray path with (a) focal length, (b) refractive power, and (c) lateral decentration distance.

Fig. 4.

Changes in the off-axis ray path with the yellow wavelength for an incident height of 3.00mm.

Fig. 5.

Changes in the off-axis ray path with (a) at incident height 0.00mm, and (b) zoomed in at the focal point.

Fig. 6.

Changes in the off-axis ray path with (a) focal length, (b) refractive power, and (c) lateral decentration distance.

Fig. 7.

Changes in chromatic aberration with on-axis and off-axis rays.

Fig. 8.

Results of the retinal image investigation with each wavelength (δ = 0.00, and z = 24.38 mm). (a) Red, (b) yellow, and (c) blue.

Fig. 9.

Results of the retinal image investigation with each wavelength (δ = 3.00, and z = 24.38 mm). (a) Red, (b) yellow, and (c) blue.

Fig. 10.

Changes in the ray path with (a) focal length, (b) refractive power, and (c) lateral decentration distance at the incident height of 1.00 mm.

Fig. 11.

Changes in the chromatic aberration at the incident height of 1.00 mm.

Fig. 12.

Results of retinal image Intensity investigation with yellow wavelength.

Fig. 13.

Results of retinal image resolution investigation with the right behind the corrective lens, the corrective lens, and the corrective lens decentration location.

Table

Table 1.

Optical parameters of the correction lens used in this study

Wave length (nm)	Refractive index (n)	Curvature radius (mm) of	Abbe number (V)
486.1	1.607
589.3	1.600	100.000	337.649	66.667
656.3	1.598

Table 2.

Refractive index of the 3D Gullstrand schematic eye model in accordance with wave length

Wave length (nm)	Refractive index (n)
486.1		1.38080	1.33970	1.38983	1.41013	1.38983	1.33893
589.3	1.0000	1.37611	1.33509	1.38391	1.40412	1.38391	1.33439
656.3		1.37405	1.33306	1.38141	1.40158	1.38141	1.33240

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Wave length (nm)	Refractive index (n)	Curvature radius (mm) of		Abbe number (V)

		Anterior	Posterior

486.1	1.607
589.3	1.600	100.000	337.649	66.667
656.3	1.598