Showing papers on "Fresnel zone published in 1973"
TL;DR: The general theory of coded-aperture imaging is presented, first for an arbitrary code and then for an on-axis zone plate, an off-axis Zone Plate, and a one-dimensional zone plate (or linear chirp).
Abstract: The use of a Fresnel zone plate as a coded aperture for imaging incoherent radiation such as gamma rays has been previously reported. The coded image is in many respects similar to a hologram and can be decoded or reconstructed with a coherent optical system. In this paper, the general theory of coded-aperture imaging is presented, first for an arbitrary code and then for an on-axis zone plate, an off-axis zone plate, and a one-dimensional zone plate (or linear chirp). With the on-axis plate, a matched imaging condition is suggested as a guide to optimizing image contrast. With the off-axis zone plate and the linear chirp, it is necessary to use a half-tone screen to spatially heterodyne the object spectrum into the passband of the aperture. In all three cases, expressions for the resolution, depth of field, field of view, and relative efficiency are derived. A simplified noise analysis is presented, and some practical system constraints are discussed.
139 citations
TL;DR: In this paper, the authors solved the mode structure of unstable resonators of rectangular aperture using an asymptotic expansion of the integral for large Fresnel number, which is carried out to terms of order 1/F, where F is the Fresnel numbers, and includes effects of diffraction at the edges of the feedback mirror.
Abstract: The integral equation that describes the mode structure of unstable resonators of rectangular aperture is solved by a new method that makes use of an asymptotic expansion of the integral for large Fresnel number. This expansion is carried out to terms of order 1/F, where F is the Fresnel number, and includes effects of diffraction at the edges of the feedback mirror, as well as a term corresponding to the geometric-optics approximation. Results obtained by this method are in good agreement with those obtained by gaussian integration, even at an effective Fresnel number of unity. The method has the advantage that it involves finding the roots of a polynomial, rather than the eigenvalues of a matrix, and therefore requires less computer time and storage. The results of the present work are at variance with a class of theories based on geometric optics, as regards the higher-loss modes even for very large Fresnel number, although the lowest-loss symmetric mode is correctly given by geometric optics in this limit.
87 citations
TL;DR: A theoretical investigation has been undertaken to study the transverse modes of two-dimensional positive branch, confocal unstable resonators using a numerical-iterative type calculation that uses the Fresnel integral for propagating the cavity radiation back and forth between resonator mirrors.
Abstract: A theoretical investigation has been undertaken to study the transverse modes of two-dimensional positive branch, confocal unstable resonators. Mode amplitude and phase information is obtained from a numerical-iterative type calculation that uses the Fresnel integral for propagating the cavity radiation back and forth between resonator mirrors. Near- and far-field distributions for empty cavity resonators are presented for various resonator Fresnel numbers and magnifications, along with results of resonator mode stability and diffraction losses when cavity perturbations such as mirror misalignment and/or a uniformly saturable gain medium are included. In addition, the diffractive calculations are compared with results obtained from geometric models.
71 citations
TL;DR: In this paper, a new error analysis of approximations made in selective summation of diagram contributions to the iterated moment equations (in integral form) was found for irradiance statistics of a plane wave propagating through uniformly turbulent air.
Abstract: Analytical results are found for irradiance statistics of a plane wave propagating through uniformly turbulent air. They result from a new error analysis of approximations made in selective summation of diagram contributions to the iterated moment equations (in integral form). The results are determined by three regimes of the parameter k7/6L11/6Cn2 determined by its location with respect to powers of the micro- and macroscale Fresnel numbers (κm2L/k)−1/6∾0.3 and (kL02/L)∾104 (the numerical values are for 0.6-μm radiation and a horizontal pathlength L ∾ 1 km). The modified-Rytov result is found in the lowest regime. Irradiance I is log-normal in the intermediate (saturation) regime and the log-amplitude variance decays asymptotically as 0.41 (κm7/3L3Cn2)−1/6. When k7/6L11/6Cn2 far exceeds the macroscale Fresnel number kL02/L, the irradiance tends to an exponential distribution (in agreement with previous results).
40 citations
TL;DR: The simple method of reconstructing and scaling the object intensity distribution, the high efficiency, as well as the resistance against high laser intensities show the MZP to be a convenient tool for laser micromachining of patterns with optional shape.
Abstract: The structure of Fresnel zone plates is considered as a binary carrier of complex modulation functions. Due to the Fourier-transforming properties of this particular carrier, any original object can be reconstructed with a simple monochromatic point source using no additional optics. An analysis of modulated zone plates (MZP) verifying their Fourier-transforming and imaging properties is given. Experiments were performed with several types of computer-drawn MZP’s. Results illustrating the flexibility of this method are in good agreement with theory. The simple method of reconstructing and scaling the object intensity distribution, the high efficiency, as well as the resistance against high laser intensities show the MZP to be a convenient tool for laser micromachining of patterns with optional shape.
27 citations
TL;DR: In this paper, a self-supporting Fresnel zone plate with empty transparent zones was used to focus vacuum-ultraviolet (vuv) radiation with wavelengths as short as 565 A. The zone plate was used as a simple converging lens to form an optical image of an object mesh on a sodium salicylate film, where it was photographically recorded.
Abstract: A self-supporting Fresnel zone plate with empty transparent zones has been used to focus vacuum-ultraviolet (vuv) radiation with wavelengths as short as 565 A. The radiation was produced by two broad-band sources, (i) the molecular continuum of a helium gas-discharge lamp, which extends from 600 to 1100 A with a broad peak at 810 A, and (ii) the synchrotron continuum of an electron storage ring filtered by a Sn filter, which extends from 520 to 750 A with a broad peak at 565 A. The zone plate was used as a simple converging lens to form an optical image of an object mesh on a sodium salicylate film, where it was photographically recorded. Magnifications of 20× and linear resolutions within an order of magnitude of the theoretical resolution limit of the zone plate were obtained. Applications of this device as a vuv microscope are discussed.
25 citations
TL;DR: The formalism is used to derive the conditions under which instantaneous reciprocity exists between a transmitter and receiver in a coherent detection system and it is shown that a maximum useful transmitter diameter exists for computing the average normalized signal-to-noise ratio of this system.
Abstract: The mutual coherence function of a finite laser beam propagating through a random medium is calculated from the extended Huygens principle. Formulas are presented for the transverse coherence from an arbitrarily truncated focused Gaussian beam. Expressions are derived for a modified Kolmogorov spectrum for the refractive index fluctuations and for the case of nonuniform turbulence. The formalism is used to derive the conditions under which instantaneous reciprocity exists between a transmitter and receiver in a coherent detection system. It is also shown that a maximum useful transmitter (as well as receiver) diameter exists for computing the average normalized signal-to-noise ratio of this system. This maximum dimension is the smaller of the turbulence-induced coherence length and a Fresnel zone.
23 citations
TL;DR: The point spread function of such zone plates is measured with a rotating cube scanner and found to agree closely with theory over more than one order of magnitude.
Abstract: Arrays of ~2-mm diam, f/9, diffraction-limited Fresnel zone plates are made and measured. Amplitude zone plates are fabricated by conventional photolithographic techniques, while a specially developed evaporation/etching technique is used for phase zone plates. The point spread function of such zone plates is measured with a rotating cube scanner and found to agree closely with theory over more than one order of magnitude.
16 citations
TL;DR: In this article, it was shown that two properly-scaled Fresnel zone plates in series constitute a useful coded aperture for imaging X-rays, gamma rays or other incoherent radiation.
12 citations
TL;DR: In this article, a formulation for investigating the intensity distribution of Fresnel diffraction by a slit aperture illuminated with partially coherent light is developed for the case that the complex degree of coherence of the illumination contains a quadratic phase term.
11 citations
TL;DR: In this article, it was shown that high quality images can be obtained with Mertz' original encoding method under certain well-defined conditions, under the assumption that the on-axis Fresnel zone plate apertures are fixed.
Abstract: Coded aperture imaging of X ray or y ray emitting objects using on-axis Fresnel zone plate apertures was the original method suggested by Mertz in 1961. Since then other forms of coded aperture imaging have become more popular. We show in this paper that, under certain well-defined conditions, high quality images can be obtained with Mertz' original encoding method.
TL;DR: In this paper, the intensity distribution in the Fresnel diffraction pattern of a slit aperture illuminated with partially coherent light is obtained, as a function of the coherence condition across the aperture, by evaluating the formula developed in a previous paper.
TL;DR: In this article, a quadratic phase term was used to study the intensity distribution in the Fresnel diffraction field of a slit aperture illuminated by a quasi-monochromatic incoherent slit source.
01 Jan 1973
TL;DR: The depolarization, e.g. the polarization change of an E.M. wave is a very frequent phoenomenon ancountered whenever the propagation is influenced by the presence of real media as mentioned in this paper.
Abstract: The depolarization, e.g. the polarization change of an E.M. wave is a very frequent phoenomenon ancountered whenever the propagation is influenced by the presence of real media.
TL;DR: Using a Fresnel zone plate to obtain a reference point source as well as object illumination, a hologram was produced with quasi-thermal light as mentioned in this paper, which is a scaled up simulation of a proposed experiment to produce soft X-ray holograms.
TL;DR: In this article, a formulation for investigating the effect of temporal coherence of the illumination on the intensity distribution in the Fresnel diffraction field of a slit aperture was developed for the case of partially, temporally coherent light.
Abstract: A formulation is developed for investigating the effect of temporal coherence of the illumination on the intensity distribution in the Fresnel diffraction field of a slit aperture. The formula derived is applied to actually obtain the intensity distributions both along the axis normal to the slit aperture and in the Fresnel diffraction patterns for various receiving planes parallel to the aperture plane. It is found that the temporal coherence is less effective on the intensity distribution in the Fresnel diffraction field. The theoretical results for Fresnel diffraction patterns of a slit aperture illuminated by partially, temporally coherent light are experimentally confirmed.
Journal Article•