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Schematic description of a pseudophakic eye (left) and definition of geometrical parameters for the paraxial principal and marginal rays (right).
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This manuscript reports on a closed-form solution determining the personalized required shape of a new intraocular lens able to remove spherical aberration and coma of a pseudophakic eye. The proposed analytical method, within the framework of the Seidel theory of third-order optical aberrations, considers corneal conicities, fourth-order aspheric...
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Introduction:
Intraocular lenses (IOLs) may lose their optical quality if they are not correctly placed inside the capsular bag once implanted. One possible malpositioning of the IOL could be the implantation in an upside-down position. In this work, three aspheric IOLs with different spherical aberration (SA) have been designed and numerically te...
Citations
... However, seeking exact analytical solutions is important as they could be used as a baseline performance estimator and benchmark [22]. These exact solutions can perform quick optical design over a few free parameters giving insights into important design parameters [23,24] or can be applied to obtain exact predetermined coefficients in a design [25]. As such, finding exact solutions for the phase gradient of the metasurface is relevant for the field of metasurface design and could help refine the existing optimization processes. ...
We propose a method to design the exact phase profile of at least one metasurface in a stigmatic singlet that can be made to implement a desired ray mapping. Following the generalized vector law of refraction and Fermat’s principle, we can obtain exact solutions for the required lens shape and phase profile of a phase gradient metasurface to respect particular ray conditions (e.g., Abbe sine) as if it were a freeform refractive element. To do so, the method requires solving an implicit ordinary differential equation. We present comparisons with Zemax simulations of illustrative designed lenses to confirm the anticipated optical behaviour.
... By using ZEMAX optical design software [17], and based on the Liou-Brennan model (LBME) [18], which is shown in table 1 The intraocular lens (SofPort AO) [19], shown in table 2 [20], is implanted instead of the crystalline lens represented by the 5th and 6th surfaces of LBME. Then the IOL was decentered with values (0, ±0.4, ...
The popular treatment of cloudy eyes (cataracts) replaces the cloudy natural lens with an artificial intraocular lens (IOL). The spherical and chromatic aberration are the main factors that affect the IOL image quality. This paper uses hybrid (refractive-diffractive) intraocular lenses with an aspherical surface to minimize chromatic and spherical aberrations. Three types of hybrid IOLs are selected to replace the eye crystal lens, and their performances are evaluated and compared with the healthy eye, based on the results estimated from Liou and Brennan eye model (LBEM). The vision is assessed by calculating the polychromatic modulation transfer function (MTF), the point spread function (PSF), the longitudinal chromatic aberration (LchC), and the encircled energy (EE) using the ray-tracing Zemax program. The results indicate that the polychromatic vision with PMMA hybrid IOL gives the best optical performance compared with other hybrid IOLs and provides a magnitude of (LchC) comparable with a healthy eye.
... By using ZEMAX optical design software [17], and based on the Liou-Brennan model (LBME) [18], which is shown in table 1 The intraocular lens (SofPort AO) [19], shown in table 2 [20], is implanted instead of the crystalline lens represented by the 5th and 6th surfaces of LBME. Then the IOL was decentered with values (0, ±0.4, ...
The implanted lens inside the eye may be exposed to a decenter during or after cataract surgery, by exposure to a specific accident that leads to a change of the lens position, which leads to a vision deterioration. This paper provides a detailed study about the intraocular lens decentering effect, which was implanted instead of the Liou & Brennan eye model (LBME) crystalline lens. Based on ZEMAX optical design software, the lens was shifted towards the (X and Y) axes by (0, ±0.4, ±1) mm, with pupil diameter values (2.5, 4, and 5) mm. The basic criteria to measure the vision quality as, the modulation transfer function (MTF), spot size (RMS), wave aberration coefficients, and RMS wavefront errors were used. It was found that the image is destroyed as the decenter increases. This effect worsened as the pupil diameter increases due to the increasing aberration, especially spherical and coma aberration. Finally, compression between the IOL effect decentering and the natural crystal lens of the healthy eye was done.
... In ophthalmology systems, due to the limitations of the design space, diffraction substrates are designed as spheres to provide more diopters. There currently is a move toward aspheric substrates to carry functions such as eliminating aberrations [13,14]. In this approach, DOEs are designed on the aspheric lenses surface, and the change of substrates from plane to aspheric surface leads to a reduction in the diffraction performance, which causes a deterioration in the visual quality. ...
... where r j −1 , r j can be obtained by Eq. (13). Therefore, according to the relationship in Fig. 4, the true phase delay under the influence of the surface can be expressed as ...
... where r j is obtained by Eq. (13), and r is the overall DOE period radius. The evaluation of the diffraction efficiency of the system is usually based on the overall waveband. ...
Diffractive optical elements (DOEs), which can produce arbitrary light distribution, are widely applied in ophthalmic lens design with spheric substrates. However, diffraction substrates tend to be designed as aspheric surfaces to eliminate aberrations. In this case, the diffraction theory of plane substrates is no longer accurate, which affects the diffraction performance. Therefore, a diffraction theory of aspheric diffraction substrates is proposed in this paper. Using the range of common parameters for aspheric substrates in ophthalmology, the influence of the substrate diopter and the aspheric surface parameters on the period radius and phase delay is analyzed. Then, through a design example of a diffraction intraocular lens (IOL), an optimization equation is proposed and discussed. The results show that the diffraction theory of aspheric substrates and the optimization equation model can analyze and reduce the effect of aspheric diffraction substrates. This research can be used in DOE design with aspheric substrates in ophthalmology.
... So any deviation of the lens causes a change in the light direction and thus a decrease in vision [10] due to the optical aberration appearance (spherical, coma, astigmatism, and defocus) [11]. There is a very close relationship between the tilt effect and the lens design and the amount of its aberration [12]. Many clinical studies [13,14,15] and engineering [16] were presented to study the tilt effect on many optical elements such as contact lenses [17], implantable lenses [18], and the pupil as well [18]. ...
... Likewise, the astigmatic and aspherical surface was on the anterior surface of the IOLs and the aspherical lenses were designed with a pure biconical surface. Further studies may involve other aspherical designs [41,42], with an anterior and posterior aspheric surface and with the cylinder distributed on both. ...
Toric intraocular lenses (T-IOLs) may lose their optical quality if they are not correctly positioned inside the capsular bag once implanted. In this work, T-IOLs with cylinder powers of +1.50, +4.50 and +7.50 D and differing degrees of spherical aberration have been designed, manufactured and tested in vitro using a commercial optical bench that complies with the requirements of standard ISO 11979-2. Moreover, the effect of tilt and rotation on optical quality was assessed by means of numerical ray tracing on an astigmatic eye model, while the effect of decentration was evaluated numerically and experimentally.
... Due to their consequently asymmetric 3D-PSF, the application of the new algorithm will produce inaccurate CSIs leading to misinterpretations and wrong conclusions about the investigated IOLs. Recent IOL-designs compensating the aberrations induced by imaging at the kappa angle [47] are not rotationally asymmetric, however, their 3D-PSF should be symmetric, if the model eye is appropriately rotated around the nodal point. Hence, such IOLs could be evaluated using the newly developed method. ...
Cross-sectional images of three-dimensional point spread functions of intraocular lenses are used to study their image formation. To obtain those, light sheet-based methods are established. Due to the non-negligible thicknesses of the light sheets, the image quality of the cross-sectional images is constrained. To overcome this hurdle, we present a dedicated evaluation algorithm to increase image quality in the post-processing step. Additionally, we compare the developed- with the light sheet method based on our own investigations of a multifocal diffractive intraocular lens conducted in an in-house designed optical bench. The comparative study showed the clear superiority of the newly developed method in terms of image quality, fine structure visibility, and signal-to-noise ratio compared to the light sheet based method. However, since the algorithm assumes a rotationally symmetrical point spread function, it is only suitable for all rotationally symmetrical lenses.
... Lenses are a basic component of various optical systems. Despite a very long history dating back to the ancient Egyptians and Mesopotamians, the design of aspherical lenses with specified optical properties remains an urgent scientific and practical problem [1][2][3][4][5][6][7][8][9][10][11][12]. In particular, in [1,2], analytical calculation of stigmatic lenses is considered, for which the first surface is given, and the second is calculated from the condition of a constant optical path length of the rays for two conjugate points. ...
... For the selected pair of points, such a lens does not have spherical aberration, i.e., converts a spherical wavefront from a point of the object into a converging spherical wavefront with the center at a point of the paraxial image. In [3][4][5][6][7][8][9], the calculation of aplanatic lenses with two aspherical surfaces is considered. In aplanatic lenses, in addition to the stigmatic condition (the condition of a constant optical path length for two conjugate points), the Abbe sine condition [13] is fulfilled, which ensures the absence of coma. ...
This erratum includes a necessary additional reference for the article [J. Opt. Soc. Am. A 38, 855 (2021)JOAOD60740-323210.1364/JOSAA.425379].
... Lenses are a basic component of various optical systems. Despite the fact that lenses were invented before the Common Era, the calculation of aspherical lenses with specified optical properties remains a relevant scientific and practical problem [1][2][3][4][5][6][7][8][9][10][11][12][13]. In particular, in works [1][2][3], analytical calculation of stigmatic lenses is considered, for which the first surface is given, and the second is calculated from the condition of a constant optical path length of the rays for two conjugate points. ...
... The "freedom" in choosing one of the surfaces of the stigmatic lens [1][2][3] shows that, in the general case, a lens with two aspherical surfaces makes it possible not only to eliminate the spherical aberration but also to additionally ensure the fulfillment of one more specified condition. In particular, in [4][5][6][7][8][9][10][11][12][13], the calculation of aplanatic lenses with two aspherical surfaces is considered. In aplanatic lenses, in addition to the stigmatic condition (the condition of a constant optical path length of the rays for two conjugate points), the Abbe sine condition is additionally fulfilled [13,14]. ...
We consider a method for designing stigmatic lenses implementing required ray mappings. A ray mapping relates the angular coordinates of the rays at the image points with the angular coordinates of the rays coming from the object. The calculation of a stigmatic lens with a required ray mapping is reduced to solving an explicit ordinary differential equation. As examples, we design stigmatic lenses satisfying the Abbe sine condition, the Herschel's condition, and the constant angular magnification condition.
... However, the influence of misalignment on the optical performance of pseudophakic eyes with aspheric IOLs is more serious than that with spherical IOL. It is essential that the ability of IOL aspheric surface design to reduce optical aberrations is not only on-axis but also off-axis [2]. Decentration and tilt of IOLs, which are one of the most common postoperative complications, have a negative impact on the optical performance of pseudophakic eyes by causing asymmetric off-axis aberrations, especially coma aberration (CA) [3]. ...
Intraocular lens (IOL) misalignment and angle $\kappa$ κ have had significant negative impact on post-operative quality of vision. ZEMAX software has been used to imitate the optical performance of pseudophakic eyes with different IOL surface designs at different orientations of IOL misalignment (decentration of 0.4 mm and tilt of 7°, and with the existence of 0.5 mm angle $\kappa$ κ ). We found that an aspheric balanced curve optic surface maintained better optical performance via inducing less coma aberration. Coma aberration played an unexpectedly important role in the optical performance. With angle $\kappa$ κ , the impact of IOL misalignment on visual quality was associated with the orientation of decentration and tilt, indicating that the coma compensation also took effect in pseudophakic eyes. Due to the high incidence of post-operative IOL misalignment, our results provide evidence of the importance of considering personalized angle $\kappa$ κ before cataract surgery for patients.
