On the Study of Partial Coherence via Diffraction Experiments

The radiation pattern of a circular aperture illuminated both uniformly and non-uniformly by partially coherent light is calculated in the diffraction limit. Furthermore, the angular resolution of a circular lens is examined for four reasonable correlation functions. Also the effects of the parameters—partial coherence, misalignment, and non-uniform illumination—on the diffraction pattern of a double slit are considered for a particular mathematical model of the radiation field. The results of this analysis are used to discuss the the use of diffraction experiments in the study of the coherence properties of light.     

Three-dimensional diffraction of a thin metallic cylinder illuminated in conical incidence: application to diameter estimation

We present a model to determine the far-field diffraction pattern of a metallic cylinder of infinite length when it is illuminated in oblique incidence. This model is based on the Helmholtz-Kirchhoff integral using the Beckmann conditions for reflection. It considers the three-dimensional nature of the diffracting object as well as the material of which the cylinder is made. This model shows that the diffraction orders are placed in a cone of light. The amplitude at the far field can be divided into three terms: the first term accounts for Babinet's principle, that is, the contribution of the cylinder projection; the second term accounts for the three dimensionality of the cylinder; and the third term accounts for the material of which the cylinder is made. This model is applied to the diameter estimation of the cylinder. Since the amplitude of the Babinet contribution is much larger than the light reflected by the surface, the cylinder diameter can be obtained in a simple way. With this approximation, the locations of the diffraction minima do not vary when the cylinder is inclined. On the other hand, when the reflected light is considered the location of the minima and, hence, the estimation of the diameter, varies. Also, a modification of the diffraction minima is produced by the material of which the cylinder is made. Experimental results are also obtained that corroborate the theoretical approach.     

Effect of quadratic radial variation of phase on single slit diffraction of Laguerre–Gauss vortex beams

Effect of quadratic radial phase variation in the plane of the aperture on Fraunhofer diffraction of Laguerre–Gauss vortex beams by a slit is studied experimentally. For slit positions near the incident beam waist, its effect is to shear the diffraction pattern relative to that at the waist. The magnitude and sense of shear depend on the topological charge and slit location relative to the incident beam waist. For slit positions far from the waist, the diffraction pattern evolves to be significantly different and is dominated by two strong peaks. A closed form analytical expression for the diffraction pattern is presented, which reproduces experimental results quite well for all slit positions.     

Approximate model for surface-plasmon generation at slit apertures

We present a semianalytical model that quantitatively predicts the scattering of light by a single subwavelength slit in a thick metal screen. In contrast to previous theoretical works related to the transmission properties of the slit, the analysis emphasizes the generation of surface plasmons at the slit apertures. The model relies on a two-stage scattering mechanism, a purely geometric diffraction problem in the immediate vicinity of the slit aperture followed by the launching of a bounded surface-plasmon wave on the flat interfaces surrounding the aperture. By comparison with a full electromagnetic treatment, the model is shown to provide accurate formulas for the plasmonic generation strength coefficients, even for metals with a low conductivity. Limitations are outlined for large slit widths (>lambda) or oblique incidence (>30 degrees ) when the slit is illuminated by a plane wave.     

Near-field scattered by a single nanoslit in a metal film

Using a scanning near-field optical microscope, we visualize, in three dimensions, the electromagnetic field distribution near an isolated slit aperture in a thin gold film. At the metal-air interface and for a TM incident polarization, we confirm some recently observed results and show that the slit generates two kinds of surface waves: a slowly decaying surface plasmon polariton and a quasi-cylindrical wave that decreases more rapidly when moving away from the slit. These waves are not generated for a TE incident polarization. In a noncontact mode, we also observe how the transmitted light diverges in free space. At a small distance from the slit (< 2 microm), we find that the emerging light spreads in all directions for TM, forming an electromagnetic cloud, whereas it is concentrated above the slit for TE, forming a more directive light jet. The experimental images are in good agreement with the numerical simulations.     

逆向哈特曼面形测量法中最佳针孔直径确定

在逆向哈特曼法中,针孔光阑具有选择光线和决定测量分辨率的作用,其直径大小直接影响CCD接收器上光斑的大小以及光线在瞳面上精确位置的确定。用衍射光学理论,推导出了精确计算针孔直径的傅里叶变换表达式,并进一步给出了针孔直径的快速解析计算式。实验证明,在实际非球面面形测量中,快速估算式能够满足计算最佳针孔直径的精度要求并提高计算效率。     

Interference of Acoustically Phase-modulated Light Transmitted by a Semi-transparent Film with a Slit Opening

Spatial interference of acoustically phase-modulated light is explained experimentally and theoretically. If the acoustically phase-modulated light is transmitted by a semi-transparent sheet film with a slit opening, the light diffracted by the slit opening is superposed on the undiffracted background light in the Fresnel diffraction region to yield an acoustically modified interference pattern. This pattern is successfully explained as a result of the partially coherent illumination which is due to acoustic wave modulation. An application of this method is described for measurements of the Raman-Nath parameter and the acoustic wavelength from the variational aspect of the interference fringe pattern.     

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.     

Pattern composed of two-dimensional diffusion dots for showing dynamic images

A new type of diffusion pattern is proposed. The proposed patterns are composed of 2D diffusion dots. The diffusion dots are created on a photoresist plate by recording the image of a local area of a piece of ground glass dot by dot. An imaging lens covered by a mask with a slit aperture is used to form the image. By changing the orientation of the slit aperture on the mask plane, the diffusion dots can have different microintensity distributions for the same incident light beam. Therefore the diffusion dots created by the same slit aperture orientation show the same brightness, and the diffusion dots created by different slit orientations show different brightness for the same illuminating and viewing conditions. Thus a proposed diffusion pattern can show dynamic images by changing its illuminating or viewing directions. By applying the double-exposure technique to the diffusion dots of a pattern, the pattern not only can show dynamic effects but also can possess several hidden features for identifying the pattern. Therefore the proposed patterns are dynamic and anticounterfeiting.     

Quantum theory of light diffraction

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.     

Diffraction of cylinders with longitudinal surface structures

We present a model to determine the light scattered by a metallic cylinder with longitudinal structures when the cylinder is illuminated by a Gaussian light beam in oblique incidence. The model is based on an approximate solution to the Helmholtz-Kirchhoff integral by means of the stationary-phase method. We have studied the variations of the diffraction pattern in terms of the size of the defect and other geometrical parameters. The width of the beam and the misalignment between the beam and the cylinder have also been considered, as well as the optical properties of the surface.     

Diffraction by a circular aperture: an application of the vectorial theory of Huygens's principle in the near field

A vectorial theory that brings new insight into the nature of diffraction is used to obtain mathematical expressions that evaluate diffraction patterns in the near field. The equations allow us to discriminate between the contributions of the vectorial and the scalar approaches. In the near field we studied the pattern of light diffracted through a circular aperture, and it was proved that the vectorial approach is significant in a region very near the circular aperture. In spite of the obvious differences between the circular aperture and other obstacles, the present theory may also be used with other geometries.     

Estimation method for the light extraction efficiency of light-emitting elements with a rigorous grating diffraction theory

The light extraction efficiency of a light-emitting element with microstructured surface is analyzed with a rigorous grating diffraction theory. The grating theory reveals an improvement of extraction efficiency due to diffraction of light by the surface microstructure. The simulation results show that the improvement of extraction efficiency is due mainly to the reflected diffraction rather than to the transmitted diffraction. A part of total-internal-reflection light is diffracted into directions at less than the critical angle. Extraction efficiency is improved by multiple reflection and diffraction of light in a high-refractive-index layer. We propose a simple design method for an efficient surface microstructure from the viewpoint of reflected diffraction.     

Improvement of resolution for phase retrieval by use of a scanning slit

An improved method for resolution of object reconstruction using phase retrieval by use of a scanning slit aperture is proposed. The reconstruction is based on measurements of the Fraunhofer diffraction intensities of wave fields transmitted through a scanning slit in the Fresnel-zone plane of an object. In the improved method, the measurement coordinates of the intensities depend not only on the slit's position used in a previous method but also on the slit's position scaled by the ratio between two distances among the object, Fresnel-zone, and detector planes. The spatial-frequency band for the object reconstruction, which is limited in a previous method by the extent of the Fourier transform of the slit function, can be extended to the bandwidth dependent on the scanning area with the slit. In addition, even in the measurement of the Fresnel diffraction intensities of wave fields transmitted through the slit, the improved resolution can be retained by compensation for a transverse shift of the intensities.     

Laser reflectogram method for the study of crystal surfaces and epitaxial deposits

When a collimated beam of light is reflected from an etched crystal surface or an epitaxial deposit, the pattern formed by this reflection provides information on the microscopic morphology of the reflecting surface. Using a He/Ne laser as a source of high-intensity collimated light, both SiC etched in CIF₃ and cubic CdS grown epitaxially on GaP have been examined. Certain regions of the SiC were found to give rise to diffraction effects in the resulting reflectrogram. The epitaxial layer of CdS was found to show a threefold symmetry indicative of a {111} deposit and a negligible diffraction effect.     

A multichannel energy filter comprising a cylinder with closed ends and axial filament electrode: Part II

This paper continues theoretical investigation of a new electrostatic multichannel deflector performing energy filtration of charged particles is proposed. The device comprises a cylinder with closed ends and an axial filament electrode. An analytical expression is obtained for a potential distribution formed in the device when a retarding potential (equal to that on the filament) is applied to the rear end wall, while the cylinder and the front wall are grounded. The energy filter operating in this regime provides a sharper focusing of the particle beam as compared to the previously considered case of operation with a grounded rear wall. This circumstance allows the beam intensity to be increased 2–2.5 times at the same exit slit width or the energy filtration to be improved 1.5 times at the same beam intensity.     

Optical imaging with a directional detector

We demonstrate a new optical imaging technique based on a directional detector that measures the intensity of light waves that propagate only in a narrow angular window around a specific direction. Light waves that propagate in other directions do not significantly affect the detector output. The directional detector is obtained by illuminating the interrogated object with a high-coherence light source and measuring the interference between the light wave reflected from the object and a reference wave. By measuring the intensity of the interference pattern with an optical detector that has a finite width and moving the object by use of a rotation stage, one can obtain the angular directionality of the filter. The use of coherent detection in the directional detector makes it possible to increase the sensitivity of the system. The directional detector was analyzed theoretically and demonstrated experimentally for a Gaussian beam scattered from a conducting cylinder. The interference enabled us to theoretically increase the angular resolution by a factor of approximately 10 and experimentally by a factor of 8.5. A configuration for using a directional detector array to reconstruct a two-dimensional object is suggested. Since the directional detector makes it possible to reduce the effect of diffraction and scattering, reconstruction techniques based on nondiffracting sources, as implemented in x-ray tomography, may be used.     

Fraunhofer Diffraction in Partially Space Coherent Light by Slit Aperture with Amplitude Filters

Fraunhofer diffraction patterns produced by a narrow rectangular aperture having a non-uniform illumination with partially coherent light are presented. Graphs of intensity distributions in the diffraction patterns for three cases of amplitude filters and four forms of the mutual coherence at the slit are given. An increase in the half-width at half-height (H.W.H.H.) and a decrease in the intensity at the centre are observed. Tolerances for the value of the correlation interval in the aperture based on the Strehl intensity criterion have been calculated for various amplitude filters.     

Temperature error in radiation thermometry caused by emissivity and reflectance measurement error

A general expression for the temperature error caused by emissivity uncertainty is developed, and it is concluded that lower-wavelength systems provide significantly less temperature error. A technique to measure the normal emissivity is proposed that uses a normally incident light beam and an aperture to collect a portion of the energy reflected from the surface and to measure essentially both the specular component and the biangular reflectance at the edge of the aperture. The theoretical results show that the aperture size need not be substantial to provide reasonably low temperature errors for a broad class of materials and surface reflectance conditions.     

Spectral shifts and spectral switches of a pulsed Gaussian beam from a rectangular aperture in the far field

The far-field anomalous spectral behaviours of a space–time-dependent Gaussian pulsed beam passing through a rectangular aperture are studied. By expanding a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral intensity of a space–time-dependent Gaussian pulsed beam passing through a rectangular aperture is derived. Meanwhile, the corresponding closed-forms for the slit and the unapertured cases are also given as special cases of the general results. The red and blue shifts and the spectral intensity distribution are studied and illustrated with numerical calculations. Specifically, it is shown that the spectral switch takes place when the truncation parameter is equal to particular values or the observation position is at the critical diffraction angle. The possibility of tunable spectral switching in the far field with an apertured pulsed beam by varying the size of the rectangular aperture is highlighted.