Optical Performance of Aspherical Monofocal Intraocular Lenses in Misaligned States

Intraocular Lens （IOL） is a medical device implanted into the eye， commonly utilized in the treatment of ophthalmic conditions such as cataracts. In clinical practice， implanted IOLs frequently exhibit varying degrees of decentration and tilt. These positional deviations from the ideal alignment can significantly compromise the eye's optical performance. Among the widely adopted monofocal IOLs， which are primarily designed to restore distance vision， two main categories exist： spherical and aspherical monofocal IOLs. Aspherical monofocal IOLs can be further subdivided into two types： Aberration-correcting Intraocular Lens （ACIOL） and Aberration-free Intraocular Lens （AFIOL）. ACIOL is specifically designed to neutralize the cornea's inherent positive spherical aberration， thereby enhancing the quality of distance vision. Under perfect centration conditions， these lenses are capable of delivering optimal optical outcomes. In contrast， AFIOL， while not altering the overall spherical aberration of the eye， demonstrate superior performance in the presence of decentration or tilt. Under such non-ideal positional conditions， they are usually superior to ACIOL. However， while numerous studies have evaluated the optical performance of misaligned IOLs， the underlying causes of performance variations among different aspherical monofocal IOL types remain inadequately explored—a challenge that persists in the field. Some investigations have focused on compensating for refractive errors resulting from IOL tilt or axial shift， whereas others have derived analytical expressions to estimate the specific aberration terms that require correction under given decentration conditions. Despite these valuable efforts， a critical gap remains： the absence of a comprehensive theoretical model capable of simultaneously characterizing the aberrations of the human eye's optical system in the presence of both decentration and tilt. This limitation ultimately hinders a systematic analysis of the factors responsible for optical performance differences among misaligned IOLs.To address these challenges， this study introduces several key improvements. First， the computational model incorporates the thickness of both the cornea and the IOL. Under realistic implantation conditions， the anterior surface of the IOL may not be perfectly aligned with the iris and can exhibit a measurable offset. This misalignment significantly increases the complexity of aberration calculations， requiring repeated application of the pupil-shift law to both optical surfaces. To enable efficient computation and analysis， the wave aberration coefficients corresponding to primary spherical aberration and primary coma in the pseudophakic eye are explicitly derived. Then， based on functional differences， different axial lengths， and functional principles， three types of ACIOL and three types of AFIOL were designed respectively. The validity of both ACIOL and AFIOL is confirmed through a comprehensive analysis of their Modulation Transfer Function （MTF）， spot diagrams， simulated imaging， and aberration characteristics. The accuracy of these aberration coefficients is subsequently verified using numerical software. During the development of the misaligned pseudophakic eye model， we clarify why the primary spherical aberration field remains invariant under lateral misalignments. Subsequently， we establish the relationship between the primary coma field and the aberration field decenter vector. A mathematical formula for determining the coordinates of the primary coma field center is derived， revealing that under misaligned conditions， the pseudophakic eye possesses only one nodal point for primary coma—a position that is demonstrably influenced by lateral misalignments. Moreover， a comparison was made between the designed IOL and a commercial ACIOL， which showed similar MTF， thus demonstrating the universality of the conclusions drawn in this study.Based on the misaligned pseudophakic eye model， this study investigates the primary coma field centers of both ACIOL and AFIOL under misaligned conditions. Analytical results indicate that a larger shift in the primary coma field center is associated with a lower MTF. Under decentered conditions， the primary coma field center shift of ACIOL is significantly greater than that of AFIOL. Since the posterior surface spherical aberration is consistent between the two types of IOLs， and the absolute value of the anterior surface spherical aberration in ACIOL is significantly higher than that of the posterior surface， reducing the anterior surface spherical aberration becomes necessary to achieve zero overall spherical aberration. However， as both IOL types share the same dioptric power， their spherical contributions to anterior surface spherical aberration are comparable. Consequently， the reduction of anterior surface spherical aberration must be achieved by decreasing its aspherical contribution， specifically by reducing the conic constant of the anterior surface. This adjustment ensures that the total spherical aberration of the IOL is zero for AFIOL. Once the conic constant of the IOL anterior surface is reduced， the aspherical contribution of the primary coma coefficient of the anterior surface decreases. Given that the aspherical contribution of the posterior surface's primary coma coefficient is zero， this reduction leads to a diminished aspherical contribution to the primary coma field center under decentered conditions. Then， the accuracy of calculating the center of the aberration field is verified through numerical software. Furthermore， by discussing the differences in refractive index between corneal and intraocular structures at different wavelengths and their impact on aberration calculation， the rationality of eye model selection can be enhanced. Finally， by discussing the potential impact of a single parameter such as corneal aberration and thickness， the applicability of the conclusions drawn in this study is demonstrated.By integrating nodal aberration theory with primary aberration theory， we establish a mathematical model that systematically relates IOL misalignments to the primary aberrations of the entire eye. This analytical framework offers a clear advantage over purely numerical approaches， allowing for a principled evaluation of how IOL decentration and tilt influence overall ocular aberrations. Consequently， the model provides a theoretical basis for explaining the performance differences between the two types of aspherical monofocal IOLs under misaligned conditions. The following conclusion can be drawn： 1） Decentration and tilt of an IOL cause displacement of the primary coma field center from the field center. This displacement is collectively influenced by factors such as the magnitude of IOL misalignment， geometry of lens surface， and refractive index. Moreover， the magnitude of the primary coma field center shift demonstrates a negative correlation with the system's MTF； 2） In the design of aspherical monofocal IOLs， appropriately reducing the conic constant can significantly diminish the primary coma field center shift induced by decentration， thereby enhancing optical performance under misaligned conditions. When the primary coma field center shift is sufficiently minimized， the system's MTF can be maintained nearly unchanged. In summary， the misaligned pseudophakic eye model provides a comprehensive framework for understanding how decentration and tilt influence the performance of aspherical IOLs. This approach offers valuable theoretical guidance for future IOL design and evaluation criteria.