Transmission of an inhomogeneous plane wave through an electrically small aperture in a perfectly conducting plane screen

Most solutions for electromagnetic diffraction by a circular aperture in a perfectly conducting plane screen are for an incident homogeneous (propagating) plane wave. When the aperture is electrically small (dimensions small compared to the wavelength), the well-known transmission coefficient behaves as the fourth power of the diameter/wavelength. We consider the case in which the incident field is an inhomogeneous (evanescent) plane wave. Numerical calculations for the electrically small circular aperture show that the transmission coefficient for an inhomogeneous plane wave can be substantially greater than for a homogeneous plane wave at the same frequency. This observation may be helpful in explaining the increased transmission recently reported for electrically small apertures in plane screens with modifications. The numerical calculations for the electrically small aperture are in agreement with results from approximate analytical expressions that are based on the equivalent electric and magnetic dipole moments for the electrically small complementary disk.     

Modulation of a General Periodic Object with Triangular Transmission Profile by an Annular Aperture Using Incident Incoherent Light

Expressions for the intensity distribution in the diffraction images of a general triangular wave-object have been obtained. The diffracting aperture considered is an aberration-free annular aperture. The circular aperture system appears as a particular case when the obstruction ratio is zero. Use of incoherent light has been assumed throughout. General triangular wave response of such systems to spatial frequencies in the object has been plotted and the object function, which gives a wave response nearly similar to that of the sine wave, has been pointed out.     

层状无砟轨道结构脱层缺陷超声成像

无砟轨道是典型的层状混凝土结构,脱层缺陷是其最常见的损伤形式,影响着高速列车的安全运行。传统的合成孔径聚焦成像方法是基于恒定声速的超声检测方法,忽略层间的声阻抗差异以及声波在层间界面处的折射,导致声束难以在缺陷处聚焦,声波在层状结构中传播的时间误差较大。鉴于此,提出了一种多层结构合成孔径聚焦成像方法,充分考虑多层结构中的层间声速差异,采用射线追踪方法准确获取声波在多层结构中的传播时间。在此基础上,分析了不同入射波模式以及不同激发频率对多层结构合成孔径聚焦成像结果的影响。结果表明：采用多层结构合成孔径聚焦成像方法,使用频率为50 kHz的横波入射成像分辨率更高,对无砟轨道脱层缺陷检测效果更好。该研究为该类缺陷检测提供了理论支撑。     

A Study of Electric Charging Using Low-Magnification Electron Holography

As experimentally found by low-magnification holography, both the size of the condenser aperture and the excitation of the objective lens strongly modify the object wavefunction of an electron wave. For example, the phase by electrically charged polystyrene latex spheres attached to a copper grid increases with decreasing excitation of the objective lens and/or decreasing diameter of the condenser aperture. It was also found that a smaller diameter of the condenser aperture increases the phase shift by a carbon foil or magnetic memory cells. In addition, the phase of the image wave is modified by the lateral position of the aperture, whereas different electron densities of the imaging beam have only minor influence on the detected phase shifts.     

Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence

The calculation of the aperture-averaged angle-of-arrival variance, observed with a telescope with a circular aperture, of a plane or spherical wave propagating through homogeneous and isotropic turbulence is one of the classical problems in the theory of wave propagation through random media. We present and discuss approximate closed-form solutions on the basis of the Rytov approximation. For both plane and spherical waves, the accuracy of the approximations is better than 0.25% for all ratios of aperture diameter and Fresnel length.     

Liquid-crystal Hartmann wave-front scanner

The liquid-crystal wave-front scanner (LCWS) is a highly sensitive wave-front sensor suited to the measurement of aberrations in optical systems and, more generally, of static wave fronts, and it is based on the Hartmann test. In the LCWS an incoming wave front is scanned sequentially by a programmable moving aperture that is implemented by use of a liquid-crystal display. The position of the diffraction spot is recorded behind an observation lens with a CCD detector and provides an estimation of the local slopes in two orthogonal directions at the aperture position. The wave front is then reconstructed from slope data by use of a least-squares method. Experiments are reported for nearly planar wave fronts as well as for strongly aberrated wave fronts, demonstrating both the large dynamic range and the great sensitivity of the LCWS. The LCWS is compared with the Shack-Hartmann wave-front sensor in terms of dynamic range and sensitivity.     

Simulation of confined and enhanced optical near fields for a long narrow aperture in a pyramidal structure on a thick metallic screen

A new type of long narrow aperture in a pyramidal structure on a thick metallic screen is proposed, and optical wave scattering by this structure is simulated. This aperture structure provides high emission intensity and small spot size simultaneously through excitation of the surface plasmon polaritons on the sidewalls of the pyramidal structure. Scattering of optical waves by this structure in the thick metallic screen is solved numerically with a volume integral equation by generalized conjugate residual iteration and fast Fourier transformation. The basic characteristics of the near-field intensities of the aperture are investigated in detail.     

基于合成孔径雷达图像内波参数反演方法

总结了目前已有的通过合成孔径雷达图像反演内波参数的方法,并按照内波深度、波速、特征宽度以及振幅的分类对不同的方法进行了描述.将各种参数反演方法应用于合成孔径雷达图像,对内波反演结果与同一区域的实测数据进行了比较.首次对同一内波参数的不同反演方法进行对比,并对各参数反演方法的适用条件进行了讨论.     

Propagation and backpropagation for ultrasonic wavefront design

Wave backpropagation is a concept that can be used to calculate the excitation signals for an array with programmable transmit waveforms to produce a specified field that has no significant evanescent wave components. This concept can also be used to find the field at a distance away from an aperture based on measurements made in the aperture. For a uniform medium, three methods exist for the calculation of wave propagation and backpropagation: the diffraction integral method, the angular spectrum method, and the shift-and-add method. The boundary conditions that are usually implicitly assumed by these methods are analyzed, and the relationship between these methods are explored. The application of the angular spectrum method to other kinds of boundary conditions is discussed, as is the relationship between wave backpropagation, phase conjugation, and the time-reversal mirror. Wave backpropagation is used, as an example, to calculate the excitation signals for a ring transducer to produce a specified pulsatile plane wave with a limited spatial extent.     

Fabrication of extreme-ultraviolet point-diffraction interferometer aperture arrays

Interferometric testing at the design wavelength is required for accurately characterizing the wave front of an imaging system operating in the extreme ultraviolet. The fabrication of point-diffraction interferometer apertures for extreme ultraviolet wave-front aberration analysis is described. The apertures are formed in a 200-nm-thick low-pressure chemical-vapor-deposited Si(3)N(4) film and vary in size from approximately 0.10 to 0.50 μm to generate a reference wave front of varying numerical aperture. A graded absorber overcoat is used to control the intensity of the aberrated wave front.Optimal fringe contrast can be obtained when the aperture that provides the maximum uniformity and contrast in the interference plane is selected.     

Focal shifts in focused nonuniformly polarized beams.

We present a simple formula to evaluate the relative focal shift in a circular-aperture lens system illuminated by a nonuniformly polarized (NUP) light wave. Specifically, it is shown that the relative focal shift is determined by the effective Fresnel number. The effective Fresnel number is equal to the product of the Fresnel number of the lens aperture and the parameter sigma, which describes the uniformity of the polarization distribution of the NUP beam across the lens aperture. Some examples are given to illustrate the use of this approach. The influence of the polarization distribution of the incident NUP light wave on the polarization distribution in the axial points of the focused field is also presented.     

The diffraction pattern of large aperture bowl transducers

A new examination has been made of the diffraction pattern in the vicinity of the focus, for large aperture concave bowl ultrasonic transducers. The study gives results which show a departure from those derived from optical theory, hitherto accepted. This departure increases progressively with increase in bowl aperture and leads to the expectation that large aperture ultrasonic microscopes will provide a resolution somewhat greater than indicated by classical theory.The study has also shown that the major part of the wave energy radiated by the transducer is confined near the focus within a cylindrical region, in which it is propagated as a plane wave. By a suitable choice of bowl dimensions and ultrasonic frequency the radius of this region may be made a fraction of a milimetre, while its length is several milimetres.From the realisation of the plane wave nature of propagation near the focus a technique has been developed for the determination of the ultrasonic velocity in samples of solids of very small volume of the order of 50 mm³.     

Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed

A matrix method is developed that allows a new set of Zernike coefficients that describe a surface or wave front appropriate for a new aperture size to be found from an original set of Zernike coefficients that describe the same surface or wave front but use a different aperture size. The new set of coefficients, arranged as elements of a vector, is formed by multiplying the original set of coefficients, also arranged as elements of a vector, by a conversion matrix formed from powers of the ratio of the new to the original aperture and elements of a matrix that forms the weighting coefficients of the radial Zernike polynomial functions. In developing the method, a new matrix method for expressing Zernike polynomial functions is introduced and used. An algorithm is given for creating the conversion matrix along with computer code to implement the algorithm.     

Effect of numerical aperture on interference fringe spacing

The effect of numerical aperture on the fringe spacing in interferometry is analyzed by the use of wave optics. The results are compared with published experimental results, and the influence of apodization of the wave front is discussed. The effects of central obscuration and surface tilt are also considered.     

Wave Theory for a Simple Lens

A new wave theory describing image formation by a simple lens is formulated in the angular spectrum representation. It is closely related to Luneburg's theory of instrumental optics but is free of certain geometrical approximations made in his theory. The validity of Luneburg's essentially geometrical treatment of the lens aperture is discussed and the approximations involved are found to be justified for isoplanatic optical systems with small numerical aperture. Some concepts usually found in lens theories based on geometrical optics are seen to have analogues in the present wave theory. In particular, a connection is made between homogeneous plane waves in an angular spectrum expansion of the field and the light rays belonging to a family of rays that pass through the lens. The fundamental relations assumed in Fourier optics are shown to follow from this theory when they are applied to the special case of isoplanatic optical systems with small numerical aperture. The image field of a scalar dipole formed by a diffraction-limited lens is calculated using these results.     

Analysis of a simple method for the reduction of phonon peak broadening in surface Brillouin light scattering

We present an investigation of the effect of the collecting lens aperture on the line shape of phonon peaks observed in surface Brillouin light scattering (SBLS) from surfaces of opaque materials and transparent thin films. In general, the broadening that is due to the aperture is asymmetric and can be as large as 60% of the peak frequency shift in the case of a f/1.4 aperture with an angle of incidence theta(i) = 30 degrees . We calculated SBLS spectra accounting for the spread in scattering wave vectors across the collecting lens aperture, the polarization and angular dependence of the scattering, and the spectrometer instrumental function. By performing a detailed comparison between measured and calculated SBLS spectra for Si(001), we identified a set of simple rules for the placement of a rectangular slit in the collecting lens aperture to reduce the effects of aperture broadening. By use of a slit, the peak linewidths can be reduced substantially, without reducing the peak heights significantly, while eliminating false shifts in the measured frequency values.     

Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.     

Fresnel diffraction as an aperture edge integral

Abstract

The standard Fresnel diffraction wave field from an aperture in a plane screen involves an integral over the aperture area. Here it is reduced to an aperture edge integral instead. The reduction really amounts to performing one integral but can be considered as the reduction of the ‘Maggi-Rubinovics’ edge formula from Kirchhoff optics to paraxial (i.e. Fresnel) optics.     

Axial irradiance distribution throughout the whole space behind an annular aperture: comments

We comment on the recent paper by Harvey and Krywonos [Appl. Opt. 41, 3790-3795 (2002)], in which approximate irradiance calculations along the axis of a circular aperture illuminated by a plane wave are performed. As the starting point of their calculations, an approximated version (valid for z > lambda) of the Rayleigh-Sommerfeld diffraction integral is used. They based their numerical conclusions on a misleading "near field criterion," which guides the readers to the wrong idea that their calculations are valid even for the very near field behind the aperture. Their ideas are not original; the exact calculations of diffracted fields behind a circular aperture have been known for 40 years.