Fast vectorial calculation of the volumetric focused field distribution by using a three-dimensional Fourier transform

Lin, Jiao; Rodríguez-Herrera, Oscar G.; Kenny, Fiona; Lara, David; Dainty, J. C.

doi:10.1364/oe.20.001060

Cited by 42 publications

(21 citation statements)

References 14 publications

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“…In this section we describe the analytical (far-field) electrical field derivation at the back focal plane which is required in Eq. in a sample with refractive index m n , placed above an oil immersion objective with refractive index imm n .The emission from the source can be described by the far-field Green tensor 0 ( , ) ff G r r [31,32,49], which links between the 3 polarizations of the emitter to the electrical field generated at the far field position ( , , ) r x y z :…”

Section: Appendix Amentioning

confidence: 99%

VIPR: Vectorial Implementation of Phase Retrieval for fast and accurate microscopic pixel-wise pupil estimation

Ferdman

Nehme

Weiss

et al. 2020

Preprint

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In microscopy, proper modeling of the image formation has a substantial effect on the precision and accuracy in localization experiments and facilitates the correction of aberrations in adaptive optics experiments. The observed images are subject to polarization effects, refractive index variations and system specific constraints. Previously reported techniques have addressed these challenges by using complicated calibration samples, computationally heavy numerical algorithms, and various mathematical simplifications. In this work, we present a phase retrieval approach based on an analytical derivation of the vectorial diffraction model. Our method produces an accurate estimate of the system phase information (without any prior knowledge) in under a minute.

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Section: Appendix Amentioning

confidence: 99%

VIPR: Vectorial Implementation of Phase Retrieval for fast and accurate microscopic pixel-wise pupil estimation

Ferdman

Nehme

Weiss

et al. 2020

Preprint

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“…This provides useful insights into the nature of evanescent fields by separately evaluating the propagating regime in which jk T j < k 0 and the evanescent regime in which jk T j < k 0 [18,52,53]. The 3D diffraction calculation can then be formulated as a 3D Fourier transformation of the k-space representation of the propagating field [54,55], which can be further generalized to the isotropic vectorial regime [56].…”

Section: Isotropic Mediamentioning

confidence: 99%

Vector Fourier optics of anisotropic materials

McLeod

Wagner

2014

Adv. Opt. Photon.

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The Fourier optics technique is founded on the transfer function derived from the scalar wave equation and thus has traditionally been applied to monochromatic scalar fields propagating paraxially in isotropic lossless materials. We review scalar and vector diffraction theory to show that the scalar Fourier optics technique can be seamlessly extended to the case of time-dependent nonparaxial and evanescent vector fields propagating in anisotropic and/or absorbing materials. The missing piece is shown to be the Fourier-domain vector boundary conditions that have recently been derived from the real-domain vector Rayleigh-Sommerfeld diffraction integral. These boundary conditions, complemented by the anisotropic transfer functions provided by the roots of the Booker quartic, combine the rigor of Green's function integrals with the intuitive simplicity and general applicability of Fourier optics. We illustrate the power of this technique via analytically simple solutions to traditionally complex problems such as Fresnel transmission between arbitrary media, uniaxial conoscopy, and biaxial conical refraction. The accuracy of vector near-field diffraction is validated via comparison with the finite-difference time-domain method.

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“…We calculated the resulting focal field using McCutchen's method [24,25], which is a Fourier-transform based method to implement vectorial diffraction theory. This method greatly simplifies and speeds up the calculation of tightly focused fields resulting from spatially variant polarization distributions [26,27]. The irradiance of the focal field resulting from this polarization state distribution is shown in Fig.…”

Section: Example Of Splitting the Focal Field Into Two Perpendicularlmentioning

confidence: 99%

Complete polarization and phase control for focus-shaping in high-NA microscopy

et al. 2012

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We show that, in order to attain complete polarization control across a beam, two spatially resolved variable retardations need to be introduced to the light beam. The orientation of the fast axes of the retarders must be linearly independent on the Poincaré sphere if a fixed starting polarization state is used, and one of the retardations requires a range of 2π. We also present an experimental system capable of implementing this concept using two passes on spatial light modulators (SLMs). A third SLM pass can be added to control the absolute phase of the beam. Control of the spatial polarization and phase distribution of a beam has applications in high-NA microscopy, where these properties can be used to shape the focal field in three dimensions. We present some examples of such fields, both theoretically calculated using McCutchen's method and experimentally observed.

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Fast vectorial calculation of the volumetric focused field distribution by using a three-dimensional Fourier transform

Cited by 42 publications

References 14 publications

VIPR: Vectorial Implementation of Phase Retrieval for fast and accurate microscopic pixel-wise pupil estimation

VIPR: Vectorial Implementation of Phase Retrieval for fast and accurate microscopic pixel-wise pupil estimation

Vector Fourier optics of anisotropic materials

Complete polarization and phase control for focus-shaping in high-NA microscopy

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