An efficient interpolation algorithm for Fourier and diffractive optics

Roose, Stéphane; Brichau, Bart; Stijns, Erik

doi:10.1016/0030-4018(93)90495-q

Cited by 15 publications

(8 citation statements)

References 3 publications

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“…Due to the usual extreme ratio of the two different scales, approaches such as zero padding can cause difficult memory issues and prevent the calculation of the investigated field components. To prevent this problem, chirp z-transformations can be used to unify the grids without causing memory problems [41,[46][47][48].…”

Section: Full Vectorial Field Reconstructionmentioning

confidence: 99%

Image formation properties and inverse imaging problem in aperture based scanning near field optical microscopy

Schmidt¹,

Klein²,

Paul³

et al. 2016

Opt. Express

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Aperture based scanning near field optical microscopes are important instruments to study light at the nanoscale and to understand the optical functionality of photonic nanostructures. In general, a detected image is affected by both the transverse electric and magnetic field components of light. The discrimination of the individual field components is challenging as these four field components are contained within two signals in the case of a polarization resolved measurement. Here, we develop a methodology to solve the inverse imaging problem and to retrieve the vectorial field components from polarization and phase resolved measurements. Our methodology relies on the discussion of the image formation process in aperture based scanning near field optical microscopes. On this basis, we are also able to explain how the relative contributions of the electric and magnetic field components within detected images depend on the chosen probe. We can therefore also describe the influence of geometrical and material parameters of individual probes within the image formation process. This allows probes to be designed that are primarily sensitive either to the electric or magnetic field components of light.

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Section: Full Vectorial Field Reconstructionmentioning

confidence: 99%

Image formation properties and inverse imaging problem in aperture based scanning near field optical microscopy

Schmidt¹,

Klein²,

Paul³

et al. 2016

Opt. Express

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“…A method derived from the Chirp-Z transform was adapted to perform the required 2D complex interpolation. The key of the method is to express the affine transform as a convolution [2] [3].…”

Section: A Complex Interpolationmentioning

confidence: 99%

First steps towards multimodal georeferencing of 3D VHR optical and X-band SAR imagery

Belmonte

Derauw

Barbier

et al. 2007

2007 IEEE International Geoscience and Remote Sensing Symposium

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With the advent of new, more widely available very high resolution (VHR) SAR and optical sensor satellite constellations, the issue of jointly exploiting the corresponding imaging data in the best possible way naturally arises. Our ultimate goal is the pixel-level fusion of these modalities and their visualization in a 3D context, i.e. draped over terrain data, itself obtained from interferometric SAR processing. In this paper, we investigate the issues associated with adapting tools originally developed for low-resolution C-band SAR imagery to highresolution X-band SAR imagery (both spaceborne). Specifically, we consider the issues associated with SAR interferometry (InSAR) and more particularly those associated with complex interpolation and phase unwrapping. We found that the existing chirp-Z transform complex interpolator previously used at low resolution is perfectly suitable for handling VHR SAR data. We also found that, while the selected phase unwrapping procedure works well when the resolution is reduced by averaging, it is deficient at full resolution, in part due micro-reliefs and specific phase responses.

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“…The techniques used in the chirp-z transform 39,40 are also useful for efficient calculation of the ChT of a given function f(x). Substituting the following expression into Eq.…”

Section: B Fast Numerical Algorithm For the Chirp Transformmentioning

confidence: 99%

“…By using this algorithm, one can freely set the sampling steps in both x and u space, which is very useful under some circumstances such as examining near-field diffraction patterns and interpolation of sparse data in u space. 15,39 One can also choose different numbers of samples in x and u space by means of the implementation techniques in Subsection 3.C.…”

Section: B Fast Numerical Algorithm For the Chirp Transformmentioning

confidence: 99%

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Fast algorithm for chirp transforms with zooming-in ability and its applications

et al. 2000

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A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both x and u space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order 10 Ϫ12 for most cases. As an example of its application to scalar diffraction, this algorithm can be used to calculate near-field patterns directly behind the aperture, 0

show abstract

An efficient interpolation algorithm for Fourier and diffractive optics

Cited by 15 publications

References 3 publications

Image formation properties and inverse imaging problem in aperture based scanning near field optical microscopy

Image formation properties and inverse imaging problem in aperture based scanning near field optical microscopy

First steps towards multimodal georeferencing of 3D VHR optical and X-band SAR imagery

Fast algorithm for chirp transforms with zooming-in ability and its applications

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