FFT-based convolution algorithm for fast and precise numerical evaluating diffracted field by photon sieve

Sabatyan, Arash; Elahi, Leila

doi:10.1016/j.ijleo.2013.03.042

Cited by 36 publications

(9 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerical computations rely on the FFT-based (fast Fourier transform) method [19] . To this end, one may rewrite Fresnel-Kirchhoff integral using the F F T convolution theorem as the following [30]…”

Section: Theoretical Discussion and Computational Resultsmentioning

confidence: 99%

Simple and efficient realization of transverse linear dark beams by azimuthal phase-shifted square zone plate

Asghari

Sabatyan²

2022

Optik

Self Cite

View full text Add to dashboard Cite

Section: Theoretical Discussion and Computational Resultsmentioning

confidence: 99%

Simple and efficient realization of transverse linear dark beams by azimuthal phase-shifted square zone plate

Asghari

Sabatyan²

2022

Optik

Self Cite

View full text Add to dashboard Cite

“…Finally, using the Fresnel approximation, the axial irradiance can be calculated by the paraxial diffraction as 42 where u = a 2 /( 2λz ) is the reduced axial coordinate, a is the radius of the BDL. λ and z are the designed operating wavelength and axial distance, respectively.…”

Section: Designmentioning

confidence: 99%

“…( 1) and ( 2) into the transmittance function q inner (ζ) and q outer (ξ), respectively. It should be noted that the BDL is a combination of these two types of rings, so the transmittance function q(ς) of the BDL can be expressed as Finally, using the Fresnel approximation, the axial irradiance can be calculated by the paraxial diffraction as 42 where u = a 2 /(2λz) is the reduced axial coordinate, a is the radius of the BDL. λ and z are the designed operating wavelength and axial distance, respectively.…”

Section: Designmentioning

confidence: 99%

Bifocal flat lens with different imaging characteristics for a dual-sensor imaging system

Zhou

Kuang

et al. 2022

Sci Rep

View full text Add to dashboard Cite

Wide field of view (FOV) images and magnified images can be taken simultaneously by dual-sensor imaging systems. Here, we propose an approach for creating a bifocal flat lens with different imaging characteristics of its two foci, which makes dual-sensor imaging systems more integrated and miniaturized. That is, two special parts of two different conventional ZP are extracted and then combine the two elements in a specific way. So that there are two foci with different characteristics along the optical axis, one is long focus with higher resolution, the other is short focus with long depth of focus (DOF). Under the proposed approach, a thin and light bifocal diffractive lens (BDL) with thickness of 0.6 μm is developed. The long and short focal lengths of the BDL are ~ 81 mm and ~ 27 mm, respectively, with a diameter of 6 mm. We experimentally demonstrate that the long focus of the BDL is capable of taking high-resolution magnified images, and its resolution is up to 21.90″. The short focus is able to take wide FOV with long DOF images, and two objects spread 2880 mm apart can be imaged clearly. The experiment results demonstrate that all of these metrics are better than those of a conventional refractive lens.

show abstract

“…The focusing properties of photon sieves have been earlier analyzed through Fresnel-Kirchhoff diffraction integrals [1], Fresnel integrals [44,45] and Rayleigh-Sommerfeld diffraction [46]. While the calculations in [1] were limited to point sources only, the approximate treatment of Fresnel diffraction [44], numerical Fresnel propagation [45], and Rayleigh-Sommerfeld diffraction [46] were computed for the half of the imaging system considered here (i.e. only from the photon sieve plane to the image plane), hence requiring the knowledge of the complex-valued field at the photon sieve plane.…”

Section: Introductionmentioning

confidence: 99%

Analytical Fresnel imaging models for photon sieves

Oktem¹,

Kamalabadi²,

Davila³

2018

Opt. Express

View full text Add to dashboard Cite

Photon sieves are a fairly new class of diffractive lenses that open unprecedented possibilities for high resolution imaging and spectroscopy, especially at short wavelengths such as UV and x-rays. In this paper, we model and analyze the image formation process of photon sieves using Fourier optics. We derive closed-form Fresnel imaging models that relate an input object to the image formed by a photon sieve system, both for coherent and incoherent illumination. These analytical models also provide a closed-form expression for the point-spread function of the system for both in-focus and out-of-focus cases. All the formulas are expressed in terms of Fourier transforms and convolutions, which enable easy interpretation as well as fast computation. The derived analytical models provide a unified framework to effectively develop new imaging modalities enabled by diffractive lenses and analyze their imaging capabilities for different design configurations, prior to physical production. To illustrate their utility and versatility, the derived formulas are applied to several important special cases such as photon sieves with circular holes and pixelated diffractive lenses generated by SLM-type devices. The analytical image formation models presented in this paper provide a generalizable and powerful means for effective analysis and simulation of any imaging system with a diffractive lens, including Fresnel zone plates, Fresnel phase plates, and other modified Fresnel lenses and masklike patterns such as coded apertures.

show abstract

FFT-based convolution algorithm for fast and precise numerical evaluating diffracted field by photon sieve

Cited by 36 publications

References 4 publications

Simple and efficient realization of transverse linear dark beams by azimuthal phase-shifted square zone plate

Simple and efficient realization of transverse linear dark beams by azimuthal phase-shifted square zone plate

Bifocal flat lens with different imaging characteristics for a dual-sensor imaging system

Analytical Fresnel imaging models for photon sieves

Contact Info

Product

Resources

About