Search results for "Fresnel zone"
showing 10 items of 24 documents
Spectral anomalies in focused waves of different Fresnel numbers
2004
Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.
Axial behavior of diffractive lenses under Gaussian illumination: complex-argument spectral analysis
1999
We present a general procedure to analyze the axial-irradiance distribution generated by an unlimited diffractive lens under coherent, Gaussian illumination. The resulting on-axis diffraction pattern, which is evaluated in terms of the power complex spectrum of the Fresnel-zone transmittance, explicitly depends on the truncation parameter that we define, which evaluates the effective number of zones illuminated by the Gaussian beam. Depending on the value of this parameter, different kinds of axial behavior are observed. In particular, for moderate values a multiple-focal-shift phenomenon appears, and a simple formula for its evaluation is presented. Additionally, for low values of the trun…
Cantor Dust Zone Plates
2013
In this paper we use the Cantor Dust to design zone plates based on a two-dimensional fractal for the first time. The pupil function that defines the coined Cantor Dust Zone Plates (CDZPs) can be written as a combination of rectangle functions. Thus CDZPs can be considered as photon sieves with rectangular holes. The axial irradiances produced by CDZPs of different fractal orders are obtained analitically and experimentally, analyzing the influence of the fractality. The transverse irradiance patterns generated by this kind of zone plates has been also investigated.
Fractal zone plates.
2003
Fractal zone plates (FZPs), i.e., zone plates with a fractal structure, are described. The focusing properties of this new type of zone plate are compared with those of conventional Fresnel zone plates. It is shown that the axial irradiance exhibited by the FZP has self-similarity properties that can be correlated to those of the diffracting aperture.
On-axis diffractional behavior of two-dimensional pupils
2010
We show that, at any Fresnel number, a suitable one-dimensional Fourier transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precisio…
Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system
2000
The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approxi…
Strehl ratio versus defocus for noncentrally obscured pupils.
1994
We discuss from the viewpoint of the Strehl ratio versus defocus, or the normalized axial-irradiance distribution, the influence of decentering the dark mask of an annular pupil. Our treatment, which is valid for pupil apertures with any Fresnel number, permits us to infer that the axial behavior of a noncentrally obscured pupil is equivalent to that of an apodizer with continuous amplitude variations. Hence the Strehl ratio versus defocus of an optical system can be shaped by use of noncentered dark masks that act as continuous gray apodizers. Several numerically evaluated examples are presented.
Polyadic devil's lenses.
2009
Devil’s lenses (DLs) were recently proposed as a new kind of kinoform lens in which the phase structure is characterized by the “devil’s staircase” function. DLs are considered fractal lenses because they are constructed following the geometry of the triadic Cantor set and because they provide self-similar foci along the optical axis. Here, DLs are generalized allowing the inclusion of polyadic Cantor distributions in their design. The lacunarity of the selected polyadic fractal distribution is an additional design parameter. The results are coined polyadic DLs. Construction requirements and interrelations among the different parameters of these new fractal lenses are also presented. It is …
Focal switch: a new effect in low-Fresnel-number systems
2010
It is shown for the first time we believe, that when a spherical wave illuminates a certain type of diffracting screen, in addition to the expected focal-shift effect, depending on the value of the Fresnel number of the focusing system, a focal switch effect can appear, i.e., an increase in the height of the lateral lobe of the axial-intensity distribution over that of the central lobe.
Temporal effects in ultrashort pulsed beams focused by planar diffracting elements
2006
The pulse envelope of an ultrashort pulsed beam is evaluated on the focal points of a Fresnel zone plate. The description of the field dynamics is given in terms of a diffraction-induced pulse train. Within these terms we follow an analytical procedure to characterize the temporal broadening observed at the principal focus, which is significant if the number of Fresnel zones exceeds the number of cycles in the pulse. For Gaussian-type envelopes, the focal field may be accurately expressed in a simple closed form. This expression has a flat-top shape at the principal focus and other odd-order foci, and a two-peak envelope in the case of a low-integer even-order focus. Finally, extremely high…