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.     

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.     

Phase retrieval from diffraction intensities by use of a scanning slit aperture

A noniterative method of retrieving the phase of a wave field from intensities measured during scanning of a slit aperture is proposed. In the measurements, one records the diffraction intensities of wave fields transmitted through a slit that is scanned along two directions in the Fresnel-zone plane of an object's field. From these intensities, the phase in the Fresnel-zone plane can be retrieved by a method in which a novel phase calculation technique that uses Fourier transforms is included. Because the method does not require lens systems, it provides a potentially useful means for coherent imaging by use of x rays, electrons, or nuclear particles.     

Experimental study of the effect of surface defects on the finesse and contrast of a Fabry-Perot interferometer

While investigating the instrumental function of a Fabry-Perot interferometer [Appl. Opt. 34, 58 (1995), we noticed some variation in finesse and contrast in the measured spectra when a 1.5-mm-diameter aperture was used at various spots within the standard 8-mm aperture. By comparing experimentally determined finesse versus contrast plots for many such spectra with calculated plots, we found spots on the plates that gave non-Airy-function line shapes over the entire order of interference, unlike the Airy line shape we determined previously by using the entire 8-mm aperture. We have reviewed several models that describe the effects of various types of surface defects, such as Gaussian-height distribution of roughness, curvature and tilt of plates, sinusoidal roughness, and asymmetrical roughness on the finesse and contrast. Our experimental results can be accounted for if we assume that the reflectivity is nonuniform over the Fabry-Perot plates and that there is some reasonable contribution that is due to Gaussian roughness, curvature, or tilt.     

Design, calibration, and testing of a laser flare meter

A laser flare meter, insensitive to corneal, lens, and eye background scattering and calibrated by measurements and theoretical modeling, is reported. Calibration measurements and theoretical calculations of light scattering from albumin solutions were found to agree within the limits of error. The results from in vivo measurements of normal eyes of different ages agreed well with normal protein content of aqueous humor. A special aperture design was used to reduce the unwanted background scattering resulting in signal-to-background ratios between 1:1 and 1:3 for normal eyes. Moderately cataractous eyes, with increased scattering from the lens, could be measured with sufficient accuracy. The reproducibility was measured to be ~ 12%. We studied how the flare is affected by sex, right/left eye, eye color, time of day, pupillary dilation, and an intraocular pressure measurement. No differences of practical importance were found.     

Optimum lens aperture in phase-shifting speckle interferometric setups for maximum accuracy of phase measurement

Negative exponentially distributed intensities of speckle fields seem unfavorable in terms of precision metrology, if interferometric setups are involved with a saturable photodetector and an analog-to-digital converter that imposes a finite resolution. By spatial integration, extended detector apertures modify the intensity distribution toward a less awkward function. However, because the detector aperture also integrates over points of rapidly changing speckle phases, this is done at the expense of a lower modulation of measured intensity during phase shift. An optimum set of parameters is calculated here, consisting of values for the lens aperture, the mean speckle intensity, and the beam ratio. The remaining phase-measurement error assumes its minimum of 10.6 mrad when the space-bandwidth product of the lens-detector system (thus concerning the lens aperture) is 0.31, the mean speckle intensity is 1/11 of the saturation intensity, and the reference intensity is four times higher than the mean speckle intensity. The 90 degrees phase-shift algorithms with either three, four, or five frames turned out to be quite powerful, even with interference signals of rather poor modulation. Not needing a very small lens aperture is interesting, because stopping down the lens is a trade-off with the limited power of the laser.     

Path-length-resolved dynamic light scattering: modeling the transition from single to diffusive scattering

Dynamic light-scattering spectroscopy is used to study Brownian motion within highly scattering samples. The fluctuations of the light field that is backscattered by a suspension of polystyrene microspheres are measured as power spectra by use of low-coherence interferometry to obtain path-length resolution. The data are modeled as the sum of contributions to the detected light weighted by a Poisson probability for the number of events that each component has experienced. By analyzing the broadening of the power spectra as a function of the path length for various sizes of particles, we determine the contribution of multiple scattering to the detected signal as a function of scattering anisotropy.     

Integrated light scattering as a function of wavelength in donor lenses.

The purpose of this work is to investigate the light-scattering properties of excised eye lenses with intact lens capsules--more specifically, to compare light scattering with light transmission at different wavelengths in aging and cataractous lenses. A lens is positioned at its focal-length distance from an optical fiber end and collimates the light from one of five laser lines (458-633 nm). By use of an integrating sphere with an extra circular port, the collimated directly transmitted light can be separated from the scattered light. For lenses with low light-scattering levels, integrated scattering showed a dependence on wavelength, but when light scattering increased the wavelength difference tended to level out. Despite the higher percentage of lens light scattering at lower wavelengths, when calculated as an "effective light scattering" (compensated for light transmission), more scattered light actually falls toward the retina at longer wavelengths.     

Measuring the focal length of optical systems by grating shearing interferometry

Using grating shearing interferometry, a new and simple technique to measure the effective focal length of optical systems is described. The diffraction pattern of a phase grating positioned at the focal point of the lens under test is evaluated for this purpose. The relative lateral shift between the undiffracted zero order and the diffracted first orders caused by the grating is measured. By utilizing knowledge of the wavelength of light, the grating period, and the diameter of an aperture stop placed in front of the test lens, we can determine the effective focal length of the test lens. Results of measurements are presented and compared with calculated values. The dependence of the focal length on the wavelength of the light is shown by using two laser sources of different wavelengths. An analysis of the measurement accuracy is given.     

Orbital angular momentum density and spiral spectrum of Lorentz–Gauss vortex beams diffracted by a rectangular aperture

Based on the expansions of the Lorentz distribution and the aperture function, an analytical expression of Lorentz–Gauss vortex beams with a topological charge of ±1 diffracted by a rectangular aperture is derived. One can judge the sign of the topological charge from the normalized intensity and the phase distributions. The effects of the rectangular aperture on the orbital angular momentum density and the spiral spectrum are investigated, respectively. When the length and the width of the rectangular aperture are not equal, the orbital angular momentum density distribution becomes twisted and tilted. When the size of the rectangular aperture increases, the magnitude of the orbital angular momentum density and the weight coefficient of the dominant spectrum both increase, while the weight coefficients of other minor spectra decrease. In addition, the expansion of the spiral spectrum in the case of rectangular aperture is smaller than that in the case of the single slit. The difference between the adjacent spectra in the case of the rectangular aperture is four, which is twice the difference in the case of the single slit. Moreover, the weight coefficient of the dominant spectrum in the case of the rectangular aperture is relatively larger. To measure the topological charge of the diffracted Lorentz–Gauss vortex beam, this research denotes that the rectangular aperture is superior to the single slit.     

Mode analysis for periodically modulated metal slits

We investigate light transport in metal slits filled with a one-dimensional periodic stack of low- and high-index dielectric media. We have analytically extracted an exact independent-mode model where each transverse eigenmode is subject to its own Bragg scattering and dispersion modulation. The analytical model allows for easy analysis of the complex band structures calculated by means of the finite-difference time-domain method, where the physical origin of each band can be identified and assigned to a certain eigenmode of a metal slit. The analytical model is also very efficient and convenient to analyze the optical transmission spectra for these metal slits. The origin of all subtle spectral features can be discerned from the band diagram analysis of the relevant independent eigenmodes. A comparative study shows that the simple analytical independent-mode theory is powerful in handling the intrinsic light transport problems for periodically modulated metal slits and analyzing their complicated spectrum responses.     

Upper and Lower Bounds on Radially Symmetric Optical Transfer Functions

For an optical system under incoherent imaging conditions, the finite aperture and non-negative point-spread function place restrictive bounds on the values of the corresponding optical transfer function. Under the extra condition that the transfer function be radially symmetric, these bounds can be characterized as the eigenvalues of a real symmetric integral operator. In this paper the bounds are calculated first by analytic inequalities that bound the operator norm, then by finding the eigenvalues of a Galerkin approximation to the operator. In contrast to the slit aperture case, the least upper bound and greatest lower bound are found to differ. The pupil functions which achieve these bounds at a given spatial frequency are determined, along with the associated transfer functions.     

Modeling of a slit-scan-type aerial image measurement sensor used for optical lithography

Theoretical modeling of a slit-scan-type aerial image measurement sensor used for optical lithography is presented. Slit transmission properties are fully represented by the slit transfer function in terms of incident and scattering angles of light, which is then incorporated into the scheme of a partially coherent imaging formula to obtain an expression for image profiles measured by slit scanning. As an exemplary case, we analyze the influence of a 100 nm width slit used in an ArF lithography system. To understand the mechanism of image profile changes by slit transmission, we focus on frequency transfer characteristics of sinusoidal patterns.     

A new source of X-ray line broadening: inhomogeneous strains induced by uniform homogeneous temperature conditions in polyphase or non-cubic materials

Thermal strains may contribute to X-ray diffraction line broadening in both single-phase non-cubic and in polyphase cubic polycrystalline materials even under uniform temperature conditions. A method is developed for calculating the magnitude of these thermally induced strains directly from the measured diffraction peak profiles. Corrections for particle-size effects can be made readily if particle-size broadening is significant, and the thermal diffuse scattering (TDS) contribution to the diffracted intensity can be taken into account experimentally. By this method, the strains in a Mg-5 wt% Si alloy were found to be increased by as much as 35% by a 190° C temperature change. Even in the case of this relatively low melting point alloy, the TDS effect causes only a maximum of 15% error in these measured strain effects. The interpretation of these isothermally induced strains in terms of crystal anisotropy, grain morphology and orientation and the relative sizes of phases and grains is discussed.     

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.     

Scattering and thermal lensing of 2.12- mum laser radiation in biological tissue

We studied light propagation of holmium:YAG laser radiation (lambda = 2.12 mum) by measuring the two-dimensional laser beam profile before and after propagation through a tissue sample with a modified fast-temperature-measurement technique. The comparison between water and cartilage tissue allowed us to differentiate between beam broadening caused by formation of a thermal lens and broadening due to light scattering. In water, beam propagation is influenced by formation of thermal lensing, whereas in cartilage the broadening was caused by a combination of light scattering and thermal lensing. Additionally, we discovered that the observed effects are subject to dynamic changes during the laser-tissue interaction.     

Modification of the structure of Bessel beams under oblique incidence

The stability of a Bessel beam generated via an annular slit on the focal plane of a convergent lens as a function of the angle of incidence of a plane wave into the slit was measured. Although the paraxial approximation, along with an infinite lens assumption, predicts that the only change in the Bessel beam should be a displacement, experimental results showed that other slight changes were present. It was shown numerically that the way to take into account those changes is to abandon the quadratic phase approximation for the lens. Good agreement was then found between the experimental data and the numerical simulation.     

Performance comparison of aperture codes for multimodal, multiplex spectroscopy

We experimentally evaluate diverse static independent column codes in a coded aperture spectrometer. The performance of each code is evaluated based on the signal-to-noise ratio (SNR), defined as the peak value in the spectrum to the standard deviation of the background noise, as a function of subpixel vertical misalignments. Among the code families tested, an S-matrix-based code produces spectral reconstructions with the highest SNR. The SNR is least sensitive to vertical subpixel misalignments on the detector with a Hadamard-matrix-based code. Finally, the increased sensitivity of a spectrometer using a coded aperture instead of a slit is demonstrated.     

Optical characterization of ophthalmic lenses by means of modulation transfer function determination from a laser speckle pattern

A method is presented for measuring the modulation transfer function of ophthalmic lenses by use of the generation of laser speckle with an integrating sphere. The measurements are performed with a rectangular double-slit aperture positioned at the output port of the integrating sphere. The distance between the lens and the detector determines the spatial frequency being tested; therefore high frequencies are tested close to the lens and low frequencies are tested far away from the lens. We can conclude that the double-slit method can be a versatile technique for comparing the optical quality of ophthalmic lenses from different makers.     

The influence of electron momentum on the shape of backscatter peaks in gamma-ray spectrometers

The shape and intensity of backscatter peaks in pulse-height spectra have a complicated dependence on details of detector design, gamma-ray energy and geometry. In addition they show a remarkably strong systematic dependence on the atomic number of the scattering material and even manifest specifically solid state effects. The external backscatter peak can be regarded as a weighted composite of Compton profiles with an unexploited potential for revealing small changes in the electron momentum spectra of the scattering material. Its sensitivity in this role could be improved by the use of detectors with very thick depletion layers and by a redesign of the coldfinger to diminish the internal backscatter peak. By reduction of the source energy and the use of a small absorber post, the system evolves into a new type of Compton-profile spectrometer of outstanding efficiency and small dimensions.