Mathematical concepts of optical superresolution

Lindberg, Jari

doi:10.1088/2040-8978/14/8/083001

Cited by 131 publications

(97 citation statements)

References 305 publications

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“…Our discussion here is, of course, only an example to illustrate how this communications mode approach relates to resolution limits. Such limits are well understood and have been comprehensively reviewed [86,87]. [88 -90] are examples of using such a modal approach experimentally for superresolution, based on the analytic prolate spheroidal functions and/or equivalent "sampling theory" approaches (see section 7.3 and [33]).…”

Section: Notes On Passing the Diffraction Limitmentioning

confidence: 99%

Waves, modes, communications, and optics: a tutorial

Miller¹

2019

Adv. Opt. Photon.

144

105

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Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for counting the best orthogonal channels for communicating between surfaces or volumes, or for optimally describing the inputs and outputs of a complicated optical system or wave scatterer, requires a different approach. The singular-value decomposition approach we describe here gives the necessary optimal source and receiver "communication modes" pairs and device or scatterer input and output "mode-converter basis function" pairs. These define the best communication or input/output channels, allowing precise counting and straightforward calculations. Here we introduce all the mathematics and physics of this approach, which works for acoustic, radio-frequency and optical waves, including full vector electromagnetic behavior, and is valid from nanophotonic scales to large systems. We show several general behaviors of communications modes, including various heuristic results. We also establish a new "M-gauge" for electromagnetism that clarifies the number of vector wave channels and allows a simple and general quantization. This approach also gives a new modal "M-coefficient" version of Einstein's A&B coefficient argument and revised versions of Kirchhoff's radiation laws. The article is written in a tutorial style to introduce the approach and its consequences. Hermitian adjoints and Dirac bra-ket notation

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Section: Notes On Passing the Diffraction Limitmentioning

confidence: 99%

Waves, modes, communications, and optics: a tutorial

Miller¹

2019

Adv. Opt. Photon.

144

105

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show abstract

“…The larger the eigenvalues, the more efficient is information about the object transferred through the eigenfunctions (which are the prolate spheroidal wave functions) to the image. An abrupt information loss is found for the small eigenvalues associated with higher terms of the expansion [91,93]. Thus, the higher spatial frequencies being necessary to describe the object completely in terms of the Fourier transform of the PSF (which is the optical transfer function, OTF) are lost or cut-off, since the objective lens cannot gather frequencies beyond the support of its OTF.…”

Section: Analysis Of Cholesterol Organization and Dynamics Using Fluomentioning

confidence: 99%

Imaging approaches for analysis of cholesterol distribution and dynamics in the plasma membrane

Wüstner

Modzel

Lund

et al. 2016

Chemistry and Physics of Lipids

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“…Inverse problems occur in many other branches of science and technology as well. Ill-posedness in this context means that the successful reconstruction of grating parameters from the far field may not be possible, or may not be unique [4,5]. This implies that even a very precise and accurate experimental far field signal does not always provide enough information content for reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry

et al. 2014

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Abstract:Optical scatterometry is the state of art optical inspection technique for quality control in lithographic process. As such, any boost in its performance carries very relevant potential in semiconductor industry. Recently we have shown that coherent Fourier scatterometry (CFS) can lead to a notably improved sensitivity in the reconstruction of the geometry of printed gratings. In this work, we report on implementation of a CFS instrument, which confirms the predicted performances. The system, although currently operating at a relatively low numerical aperture (NA = 0.4) and long wavelength (633 nm) allows already the reconstruction of the grating parameters with nanometer accuracy, which is comparable to that of AFM and SEM measurements on the same sample, used as reference measurements. Additionally, 1 nm accuracy in lateral positioning has been demonstrated, corresponding to 0.08% of the pitch of the grating used in the actual experiment.

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Mathematical concepts of optical superresolution

Cited by 131 publications

References 305 publications

Waves, modes, communications, and optics: a tutorial

Waves, modes, communications, and optics: a tutorial

Imaging approaches for analysis of cholesterol distribution and dynamics in the plasma membrane

Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry

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