Recent Advances in Diffraction and Geometry Related Super Resolution Approaches

Zalevsky, Zeev; Fixler, Ohad; Gur, Aviram; Fixler, Dror; Micó, Vicente; Garcı́a, Javier

doi:10.1364/isa.2011.itua1

Cited by 3 publications

(5 citation statements)

References 7 publications

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“…The mask pattern should be different in each acquired frame and it must be known very well for every frame. This assumption about our familiarity with the encoding mask is called a-priori knowledge and many publications in the super-resolution field are based on this assumption [1,4,[8][9][10].…”

Section: Spatial Super-resolutionmentioning

confidence: 99%

“…For a given minimum detail size of interest, the Nyquist-Shannon sampling theorem defines the required sampling spacing. However, the sampling theorem assumes deltafunction sampling, whereas in an optical system the sampling interval may be a significant fraction of the spatial frequency [1] and may in fact reduce the resolvable spatial resolution. In cases where the pixel size constraint is the limiting factor, the smallest detail on the object plane is given by: RΔd/F [1] (where R is the range from the optics to the object, and F is the focal length).…”

Section: Introductionmentioning

confidence: 99%

“…Many of these hardware techniques are based on the use of encoding masks within the optical system [1,6,7]. For example, in [8] a randomly patterned binary mask was placed in the intermediate image plane of the optics, thereby decreasing the effective sampling interval.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spatial super-resolution of colored images by micro mirrors

Dahan

Yaacobi

Pinsky

et al. 2018

J. Opt.

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In this paper, we present two methods of dealing with the geometric resolution limit of color imaging sensors. It is possible to overcome the pixel size limit by adding a digital micro-mirror device component on the intermediate image plane of an optical system, and adapting its pattern in a computerized manner before sampling each frame. The full RGB image can be reconstructed from the Bayer camera by building a dedicated optical design, or by adjusting the demosaicing process to the special format of the enhanced image.

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Section: Spatial Super-resolutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatial super-resolution of colored images by micro mirrors

Dahan

Yaacobi

Pinsky

et al. 2018

J. Opt.

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“…These early attempts indicate already some of the intriguing practical directions in which the phenomenon of superoscillation could be applied to solve various problems in science and technology. The list of such applications includes quantum mechanics [4][5][6][7][8][9], signal processing [10][11][12], optics [13][14][15][16][17][18][19][20][21][22] and radar [23][24][25]. A most useful effort in the field of superoscillations is that of generating analytical superoscillatory functions.…”

Section: Introductionmentioning

confidence: 99%

Optimized shaping and trade-off of superoscillating pulses

Frenkel,

Yehuda,

Schwartz

2024

J. Phys. A: Math. Theor.

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In this article, we consider a special family of pulses, which are a part of a band-limited signal and are “too narrow” considering the band limit of the signal. We dub such pulses “superoscillating pulses” although they can be seen at best as half an oscillation.  While some of our results are of a more generic nature, the article is devoted to the optimization of superoscillating pulses, The first step consists of approximating a given target signal by a band limited signal in a fixed time interval. The signals to be approximated, exhibit in that interval features that seem to involve frequencies higher than the band limit of the approximant. We define the Mean Square Relative Error (MSRE) as a measure of the adherence of the approximant to the original signal in the chosen interval. We find that the minimization of the MSRE conflicts with the necessity to minimize the energy (or power) expense of the superoscillating signal. We obtain the trade-off relation between optimal energy expense and the MSRE for a family of pulses. This makes it clear that within that family, there exists a specific pulse shape that is better approximated by a superoscillating pulse. Finally, we show how to construct a yield optimized superoscillating pulse that, within a given time interval, has a prescribed narrow width without resorting to a target signal at all.

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“…Superoscillatory signals are band limited functions that oscillate over some regions with a frequency larger than that of their maximal Fourier component. A number of examples have been given in the past for such functions with very interesting applications in quantum mechanics [1][2][3][4][5][6][7][8], signal processing [9][10][11][12][13][14][15] and in optics, where superoscillations are intimately related to superresolution [16][17][18] with some recent exciting experimental achievements [19,20]. For a recent review see [21].…”

Section: Introductionmentioning

confidence: 99%

Yield statistics of interpolated superoscillations

Katzav¹,

Perlsman²,

Schwartz³

2016

J. Phys. A: Math. Theor.

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Abstract.Yield Optimized Interpolated Superoscillations (YOIS) have been recently introduced as a means for possibly making the use of the phenomenon of superoscillation practical. In this paper we study how good is a superoscillation that is not optimal. Namely, by how much is the yield decreased when the signal departs from the optimal one. We consider two situations. One is the case where the signal strictly obeys the interpolation requirement and the other is when that requirement is relaxed. In the latter case the yield can be increased at the expense of deterioration of signal quality. An important conclusion is that optimizing superoscillations may be challenging in terms of the precision needed, however, storing and using them is not at all that sensitive. This is of great importance in any physical system where noise and error are inevitable.

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Recent Advances in Diffraction and Geometry Related Super Resolution Approaches

Cited by 3 publications

References 7 publications

Spatial super-resolution of colored images by micro mirrors

Spatial super-resolution of colored images by micro mirrors

Optimized shaping and trade-off of superoscillating pulses

Yield statistics of interpolated superoscillations

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