The Fourier hybrid circular Airy vortex beam (FHCAVB) is synthesized in the Fourier domain by preserving the intrinsic phase profile from the Fourier transform of the circular Airy vortex beam (CAVB), while substituting its amplitude with a Gaussian distribution. Despite these modifications, the FHCAVB retains key properties of the original CAVB, offering enhanced autofocusing contrast and maintaining controllability through the same set of parameters. This beam can be efficiently generated using pure-phase devices via a Fourier transform setup. In our experiments, the FHCAVB was successfully produced using a phase-only spatial light modulator (SLM) in a Fourier transform configuration, with results aligning well with simulations. As a high-fidelity approximation of the CAVB, this method for generating autofocusing Airy (AAF) vortex beams shows significant potential for applications in optical trapping, tweezing, communications, and related fields.
{"title":"Fourier hybrid circular Airy vortex beam.","authors":"Bingsong Cao, Zhangrong Mei, Yonghua Mao, Peizhen Qiu, Kaikai Huang","doi":"10.1364/JOSAA.577504","DOIUrl":"https://doi.org/10.1364/JOSAA.577504","url":null,"abstract":"<p><p>The Fourier hybrid circular Airy vortex beam (FHCAVB) is synthesized in the Fourier domain by preserving the intrinsic phase profile from the Fourier transform of the circular Airy vortex beam (CAVB), while substituting its amplitude with a Gaussian distribution. Despite these modifications, the FHCAVB retains key properties of the original CAVB, offering enhanced autofocusing contrast and maintaining controllability through the same set of parameters. This beam can be efficiently generated using pure-phase devices via a Fourier transform setup. In our experiments, the FHCAVB was successfully produced using a phase-only spatial light modulator (SLM) in a Fourier transform configuration, with results aligning well with simulations. As a high-fidelity approximation of the CAVB, this method for generating autofocusing Airy (AAF) vortex beams shows significant potential for applications in optical trapping, tweezing, communications, and related fields.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1864-1870"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
While in traditional methods object detection is based on the handcrafted definition of relevant visual features and rules, in machine/deep learning methods this task is achieved by learning both features and rules from a training set. The traditional and machine/deep learning object detection workflows are often described as opposite because in the traditional framework, the visual features and rules to detect the object of interest are provided as input, while in the machine/deep learning-based framework they are automatically learned from the data depending on the task considered and constitute the final trained model. In this work, we analyze the object detection recipe, and we show that these two approaches actually present three common issues that require human supervision and ad hoc procedures to be addressed: the design of an object model suitable for the context, devices, and task at hand; the achievement of detection robustness against several factors like noise, image quality, changes in geometry, and light variations; and the definition of an appropriate matching function. We also briefly review some common metrics for evaluating object detection performance, proving that human intervention is crucial in this task as well. Our analysis aims at fostering a more aware use of the object detection approaches and stimulating new research for automating-where possible-the tasks that humans are still in charge of.
{"title":"Common issues and human intervention in object detection from handcrafted features to deep learning: discussion.","authors":"Michela Lecca, Simone Bianco","doi":"10.1364/JOSAA.569685","DOIUrl":"https://doi.org/10.1364/JOSAA.569685","url":null,"abstract":"<p><p>While in traditional methods object detection is based on the handcrafted definition of relevant visual features and rules, in machine/deep learning methods this task is achieved by learning both features and rules from a training set. The traditional and machine/deep learning object detection workflows are often described as opposite because in the traditional framework, the visual features and rules to detect the object of interest are provided as input, while in the machine/deep learning-based framework they are automatically learned from the data depending on the task considered and constitute the final trained model. In this work, we analyze the object detection recipe, and we show that these two approaches actually present three common issues that require human supervision and ad hoc procedures to be addressed: the design of an object model suitable for the context, devices, and task at hand; the achievement of detection robustness against several factors like noise, image quality, changes in geometry, and light variations; and the definition of an appropriate matching function. We also briefly review some common metrics for evaluating object detection performance, proving that human intervention is crucial in this task as well. Our analysis aims at fostering a more aware use of the object detection approaches and stimulating new research for automating-where possible-the tasks that humans are still in charge of.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1977-1987"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Valery A Loiko, Alexander A Miskevich, Natalia A Loiko
The influence of disorder in the spatial arrangement of identical, homogeneous spherical particles of an infinite two-dimensional (2D) array on the energy density spectra of the electric and magnetic fields on their surfaces under normal incidence of a plane electromagnetic wave is studied. The consideration is based on a semi-analytical statistical method (SASM) developed by us. Radial distribution functions based on the hard-disk model are used to simulate particle arrangements in arrays. We wrote a formula for this function describing the perfect azimuthally averaged lattice and analyzed in detail the energy densities for different deviations of particle centers from the nodes of the perfect lattice. The calculation results for a partially ordered array and imperfect and perfect lattices of silver (Ag), crystalline silicon (c-Si), and titanium oxide (TiO2) particles with sizes of 50 and 300 nm are presented in the wavelength range of 0.3-1.1 µm for a host medium with a refractive index close to that of water. They demonstrate the contribution of the disorder effect to the optical response of the system and allow finding the optimal characteristics of lattice-induced resonances for energy densities on the particle surface. Such data are necessary for solving problems of increasing the efficiency of converting light energy absorbed by the system into other types of energy. The spectra of energy densities obtained under the SASM are in excellent agreement with the data of the numerical finite element method (FEM). To complete the picture, the near-field data are accompanied by far-field data for the incoherent component of the light.
{"title":"Disorder effect in a 2D array of spherical particles on the electromagnetic field on their surface.","authors":"Valery A Loiko, Alexander A Miskevich, Natalia A Loiko","doi":"10.1364/JOSAA.565216","DOIUrl":"https://doi.org/10.1364/JOSAA.565216","url":null,"abstract":"<p><p>The influence of disorder in the spatial arrangement of identical, homogeneous spherical particles of an infinite two-dimensional (2D) array on the energy density spectra of the electric and magnetic fields on their surfaces under normal incidence of a plane electromagnetic wave is studied. The consideration is based on a semi-analytical statistical method (SASM) developed by us. Radial distribution functions based on the hard-disk model are used to simulate particle arrangements in arrays. We wrote a formula for this function describing the perfect azimuthally averaged lattice and analyzed in detail the energy densities for different deviations of particle centers from the nodes of the perfect lattice. The calculation results for a partially ordered array and imperfect and perfect lattices of silver (Ag), crystalline silicon (c-Si), and titanium oxide (<i>T</i><i>i</i><i>O</i><sub>2</sub>) particles with sizes of 50 and 300 nm are presented in the wavelength range of 0.3-1.1 µm for a host medium with a refractive index close to that of water. They demonstrate the contribution of the disorder effect to the optical response of the system and allow finding the optimal characteristics of lattice-induced resonances for energy densities on the particle surface. Such data are necessary for solving problems of increasing the efficiency of converting light energy absorbed by the system into other types of energy. The spectra of energy densities obtained under the SASM are in excellent agreement with the data of the numerical finite element method (FEM). To complete the picture, the near-field data are accompanied by far-field data for the incoherent component of the light.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1890-1899"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Single-molecule orientation localization microscopy I: fundamental limits: erratum.","authors":"Oumeng Zhang, Matthew D Lew","doi":"10.1364/JOSAA.581916","DOIUrl":"https://doi.org/10.1364/JOSAA.581916","url":null,"abstract":"<p><p>This erratum corrects a typographical error in our paper [J. Opt. Soc. Am. A38, 277 (2021)JOAOD60740-323210.1364/JOSAA.411981].</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1880"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Optical system misalignment aberrations caused by various factors such as environmental conditions and mechanical jitter of optical components can lead to a decline in the imaging quality of the system. The non-rotational symmetry structure and the coupling effect of different degrees of freedom of off-axis reflective telescopes make them more sensitive to misalignment aberrations. Moreover, when the Z-axis of the secondary mirror in an off-axis system has eccentricity errors, using a defocused PSF to solve the misalignment will result in a decrease in the accuracy of the lateral misalignment solution. Therefore, this paper proposes a misalignment error detection technology based on the wavelet transform and the Gabor filter and establishes a nonlinear mapping relationship between the wavelet transform-Gabor filter hybrid features of defocused PSF images and the misalignment of the secondary mirror through ShuffleNetV2. Using the hybrid features extracted by the biorthogonal wavelet transform and the Gabor filter as the input of the neural network can reduce the difficulty of decoupling the aberration features of defocused PSF images, thereby improving the accuracy of solving the misalignment of the secondary mirror. The algorithm was verified through an actual off-axis two-mirror afocal system, proving its feasibility and effectiveness.
{"title":"Off-axis system misalignment detection technique based on hybrid features of the wavelet transform and the Gabor filter.","authors":"Weihua Tang, Wei Tang, Zhengwei Tang, Dong He, Yongmei Huang, Qiang Wang","doi":"10.1364/JOSAA.576467","DOIUrl":"https://doi.org/10.1364/JOSAA.576467","url":null,"abstract":"<p><p>Optical system misalignment aberrations caused by various factors such as environmental conditions and mechanical jitter of optical components can lead to a decline in the imaging quality of the system. The non-rotational symmetry structure and the coupling effect of different degrees of freedom of off-axis reflective telescopes make them more sensitive to misalignment aberrations. Moreover, when the <i>Z</i>-axis of the secondary mirror in an off-axis system has eccentricity errors, using a defocused PSF to solve the misalignment will result in a decrease in the accuracy of the lateral misalignment solution. Therefore, this paper proposes a misalignment error detection technology based on the wavelet transform and the Gabor filter and establishes a nonlinear mapping relationship between the wavelet transform-Gabor filter hybrid features of defocused PSF images and the misalignment of the secondary mirror through ShuffleNetV2. Using the hybrid features extracted by the biorthogonal wavelet transform and the Gabor filter as the input of the neural network can reduce the difficulty of decoupling the aberration features of defocused PSF images, thereby improving the accuracy of solving the misalignment of the secondary mirror. The algorithm was verified through an actual off-axis two-mirror afocal system, proving its feasibility and effectiveness.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1998-2008"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deconvolution methods, originally developed for image deblurring, are foundational to coded aperture imaging (CAI) technologies. Among these, the Lucy-Richardson algorithm (LRA), first introduced over half a century ago, has seen renewed interest in CAI applications in recent years. Uniquely, LRA incorporates both convolution and cross-correlation operations, with the latter effectively functioning as an internal deconvolution step, offering a versatile platform for innovation. This tutorial presents the fundamentals of CAI alongside a detailed formulation of LRA. Strategies for enhancing LRA performance through modifications to the cross-correlation step are explored in depth. Both established variants, such as LRA with power-law transformation and limited support constraint, the Lucy-Richardson-Rosen algorithm, and novel extensions, including the interlooped LRA, are introduced. Future directions for designing LRA variants tailored to specific imaging scenarios are also discussed. Step-by-step MATLAB code examples are provided to guide researchers in developing custom LRA-based deconvolution approaches for advanced imaging applications.
{"title":"Developing variants of the Lucy-Richardson algorithm for coded aperture imaging: tutorial.","authors":"Vijayakumar Anand","doi":"10.1364/JOSAA.573587","DOIUrl":"https://doi.org/10.1364/JOSAA.573587","url":null,"abstract":"<p><p>Deconvolution methods, originally developed for image deblurring, are foundational to coded aperture imaging (CAI) technologies. Among these, the Lucy-Richardson algorithm (LRA), first introduced over half a century ago, has seen renewed interest in CAI applications in recent years. Uniquely, LRA incorporates both convolution and cross-correlation operations, with the latter effectively functioning as an internal deconvolution step, offering a versatile platform for innovation. This tutorial presents the fundamentals of CAI alongside a detailed formulation of LRA. Strategies for enhancing LRA performance through modifications to the cross-correlation step are explored in depth. Both established variants, such as LRA with power-law transformation and limited support constraint, the Lucy-Richardson-Rosen algorithm, and novel extensions, including the interlooped LRA, are introduced. Future directions for designing LRA variants tailored to specific imaging scenarios are also discussed. Step-by-step MATLAB code examples are provided to guide researchers in developing custom LRA-based deconvolution approaches for advanced imaging applications.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1964-1976"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Partially coherent vortex beams have attracted growing interest due to their enhanced robustness and unique propagation characteristics in complex media. In this work, we experimentally investigate the behavior of partially coherent fractional vortex beams as they propagate through atmospheric turbulence. The beams are generated using a phase-only spatial light modulator and a rotating ground-glass disk modeled by the Gaussian Schell framework, and their degree of partial coherence is quantitatively characterized using a Young's double-slit interference plate. After transmission through a 1.2 m turbulence simulator, the effective beam radius exhibits a smoothed, quasi-linear growth trend between successive integer topological charges, indicating the suppression of discrete modal transitions by the combined effects of partial coherence and turbulence. The scintillation index decreases overall with increasing topological charge, while local enhancements near half-integer orders reveal the heightened turbulence sensitivity of modal interference. Moreover, partially obstructed PCFVBs show partial statistical self-reconstruction after turbulent propagation, whereas a fully coherent control under identical conditions shows no appreciable recovery, ruling out a purely diffractive fill-in. These results provide the first, to our knowledge, comprehensive experimental insight into the interplay among coherence, turbulence, and fractional vortex structure, offering new perspectives for designing turbulence-resistant structured-light systems.
{"title":"Experimental investigation on the propagation of partially coherent fractional vortex beams in atmospheric turbulence.","authors":"Xiang Xu, Chuankai Luo, Xianmei Qian, Xiaoming Zhou, Wenyue Zhu","doi":"10.1364/JOSAA.574392","DOIUrl":"https://doi.org/10.1364/JOSAA.574392","url":null,"abstract":"<p><p>Partially coherent vortex beams have attracted growing interest due to their enhanced robustness and unique propagation characteristics in complex media. In this work, we experimentally investigate the behavior of partially coherent fractional vortex beams as they propagate through atmospheric turbulence. The beams are generated using a phase-only spatial light modulator and a rotating ground-glass disk modeled by the Gaussian Schell framework, and their degree of partial coherence is quantitatively characterized using a Young's double-slit interference plate. After transmission through a 1.2 m turbulence simulator, the effective beam radius exhibits a smoothed, quasi-linear growth trend between successive integer topological charges, indicating the suppression of discrete modal transitions by the combined effects of partial coherence and turbulence. The scintillation index decreases overall with increasing topological charge, while local enhancements near half-integer orders reveal the heightened turbulence sensitivity of modal interference. Moreover, partially obstructed PCFVBs show partial statistical self-reconstruction after turbulent propagation, whereas a fully coherent control under identical conditions shows no appreciable recovery, ruling out a purely diffractive fill-in. These results provide the first, to our knowledge, comprehensive experimental insight into the interplay among coherence, turbulence, and fractional vortex structure, offering new perspectives for designing turbulence-resistant structured-light systems.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1929-1935"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zixuan Cai, Elvis Pillinen, Meilan Luo, Matias Koivurova
We underline some of the general properties of polarization gratings, discuss their effect on partially coherent and partially polarized light, and discuss how they can be used to produce exotic polarization states. Specifically, we highlight a particular instability in the modulation of linearly polarized input fields, leading to the formation of spatially variant polarization states. In addition, we introduce what we believe to be a new model field called full Poincaré pulse. Our results provide flexibility for generating complex polarization structures from simple input, with potential applications in structured light and polarization-dependent systems.
{"title":"Nontrivial beam modulation with polarization gratings.","authors":"Zixuan Cai, Elvis Pillinen, Meilan Luo, Matias Koivurova","doi":"10.1364/JOSAA.581296","DOIUrl":"https://doi.org/10.1364/JOSAA.581296","url":null,"abstract":"<p><p>We underline some of the general properties of polarization gratings, discuss their effect on partially coherent and partially polarized light, and discuss how they can be used to produce exotic polarization states. Specifically, we highlight a particular instability in the modulation of linearly polarized input fields, leading to the formation of spatially variant polarization states. In addition, we introduce what we believe to be a new model field called full Poincaré pulse. Our results provide flexibility for generating complex polarization structures from simple input, with potential applications in structured light and polarization-dependent systems.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"2009-2014"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christopher R Schwarze, Anthony D Manni, David S Simon, Alexander V Sergienko
We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the operations are enacted by moving from one state to another. This harnesses the particular phase parameterization of an interferometer, allowing entirely linear optics to produce nonlinear operations such as division and powers. This is due to the nonlinear structure of the underlying phase parameterizations. The realized operations are approximate but can be made more accurate by decreasing the size of the input perturbations. For each operation, the inputs and outputs are changes in phase relative to a fixed bias point. The output phase is ultimately read out as a change in optical power.
{"title":"Scalar computational primitives with perturbative phase interferometry.","authors":"Christopher R Schwarze, Anthony D Manni, David S Simon, Alexander V Sergienko","doi":"10.1364/JOSAA.574393","DOIUrl":"https://doi.org/10.1364/JOSAA.574393","url":null,"abstract":"<p><p>We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the operations are enacted by moving from one state to another. This harnesses the particular phase parameterization of an interferometer, allowing entirely linear optics to produce nonlinear operations such as division and powers. This is due to the nonlinear structure of the underlying phase parameterizations. The realized operations are approximate but can be made more accurate by decreasing the size of the input perturbations. For each operation, the inputs and outputs are changes in phase relative to a fixed bias point. The output phase is ultimately read out as a change in optical power.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1907-1921"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce two families of vergence functions to express ocular wavefront aberrations in diopters, bridging aberrometry, and clinical refraction. First, we build a fully orthogonal vergence basis (V~), analogous to Zernike polynomials, which preserves mode orthogonality and supports unbiased coefficient statistics. In our VL-VH basis (V), a clear separation between low-degree and high-degree prevents the intrusion of low-degree terms into high-degree modes, which could otherwise hinder direct clinical interpretation. The vergence function expansions in both bases are derived from wavefront slopes through radial differentiation. We demonstrate their clinical utility through three cases: a normal eye, a keratoconic eye, and a post-myopic LASIK eye. The VL-VH basis provides stable refraction estimates across pupil sizes by fitting low-degree terms over central regions, closely matching subjective refraction. In contrast, the orthogonal V~ basis shows pupil-dependent refraction due to peripheral wavefront influence. In eyes with significant spherical aberration, the bases yield markedly different refractive predictions, with VL-VH better aligning with clinical measurements. Pyramid plots, dioptric maps, and coefficient histograms facilitate aberration visualization and diagnosis. These vergence-based tools enhance the integration of advanced aberrometry into clinical practice.
{"title":"Vergence-based ocular wavefront expansions in diopters: orthogonal functions, clinical metrics, and visualization tools.","authors":"Damien Gatinel, Jacques Malet","doi":"10.1364/JOSAA.576308","DOIUrl":"https://doi.org/10.1364/JOSAA.576308","url":null,"abstract":"<p><p>We introduce two families of vergence functions to express ocular wavefront aberrations in diopters, bridging aberrometry, and clinical refraction. First, we build a fully orthogonal vergence basis (<i>V</i>~), analogous to Zernike polynomials, which preserves mode orthogonality and supports unbiased coefficient statistics. In our VL-VH basis (<i>V</i>), a clear separation between low-degree and high-degree prevents the intrusion of low-degree terms into high-degree modes, which could otherwise hinder direct clinical interpretation. The vergence function expansions in both bases are derived from wavefront slopes through radial differentiation. We demonstrate their clinical utility through three cases: a normal eye, a keratoconic eye, and a post-myopic LASIK eye. The VL-VH basis provides stable refraction estimates across pupil sizes by fitting low-degree terms over central regions, closely matching subjective refraction. In contrast, the orthogonal <i>V</i>~ basis shows pupil-dependent refraction due to peripheral wavefront influence. In eyes with significant spherical aberration, the bases yield markedly different refractive predictions, with VL-VH better aligning with clinical measurements. Pyramid plots, dioptric maps, and coefficient histograms facilitate aberration visualization and diagnosis. These vergence-based tools enhance the integration of advanced aberrometry into clinical practice.</p>","PeriodicalId":17382,"journal":{"name":"Journal of The Optical Society of America A-optics Image Science and Vision","volume":"42 12","pages":"1846-1863"},"PeriodicalIF":1.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145781579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}