Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered. The far-field diffraction patterns, the transmission coefficient tau, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Ntau/lambda, valid in the scalar region, is extended to the TM polarization case in the vectorial region, lambda being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength lambda. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.     

Polarization contrast imaging of biological tissues by polarization-sensitive Fourier-domain optical coherence tomography

Jones matrix imaging of biological samples by a polarization-sensitive Fourier-domain optical coherence tomography has been demonstrated using a two-dimensional CCD camera to obtain two spectra corresponding to the orthogonal polarization components simultaneously. The measurement results of a quarter-wave plate are compared between the two incident polarization sets, H-V linear and R-L circular polarization. Jones matrix imaging of the bovine tendon is demonstrated. Measured Jones matrix images are converted to equivalent Müller matrix images. Local polarization properties are obtained by longitudinal differentiation of Jones matrix components. The layered structure of the bovine tendon and birefringence are revealed.     

Volume holographic imaging in transmission geometry

We address the performance of transmission geometry volume holograms as depth-selective imaging elements. We consider two simple implementations using holograms recorded with spherical and plane beams. We derive the point-spread function (PSF) of these systems using volume diffraction theory and use the PSF to estimate depth resolution. Furthermore, we show that appropriately designed objective optics can significantly improve the depth resolution or the working distance of plane-wave reference holographic imaging systems. These results are confirmed experimentally and demonstrated for objects with millimeter axial features, imaged from the 5- to 50-cm range.     

Reflection and transmission in pre-stressed stratified multilayers

Summary Time-harmonic wave propagation is investigated in multilayers whose slabs are pre-stressed anisotropic, dissipative solids. The material properties vary continuously within each slab and suffer jump discontinuities at the interfaces. The multilayer is sandwiched between homogeneous half-spaces. The constitutive equations due to the motion are taken to be linear, and hence the governing equations are shown to allow for a Stroh-like form. The solution is determined for any slab, and hence for the multilayer, through an integral-equation formulation, in terms of a propagation matrix which incorporates the jumps at the interfaces. Next the reflection and transmission problem for the multilayer, with an oblique incident wave, is solved by determining the reflection and transmission matrices in terms of the propagation matrix, the parameters of the incident wave and the eigenmode polarization vectors in the halfspaces. By way of application, results are derived in detail for horizontally-polarized waves.     

Optical Diffraction in Close Proximity to Plane Apertures. I. Boundary-Value Solutions for Circular Apertures and Slits

In this paper the classical Rayleigh-Sommerfeld and Kirchhoff boundary-value diffraction integrals are solved in closed form for circular apertures and slits illuminated by normally incident plane waves. The mathematical expressions obtained involve no simplifying approximations and are free of singularities, except in the aperture plane itself. Their use for numerical computations was straightforward and provided new insight into the nature of diffraction in the near zone where the Fresnel approximation does not apply. The Rayleigh-Sommerfeld integrals were found to be very similar to each other, so that polarization effects appear to be negligibly small. On the other hand, they differ substantially at sub-wavelength differences from the aperture plane and do not correctly describe the diffracted field as an analytical continuation of the incident geometrical field.     

Enlightening darkness to diffraction limit and beyond: comparison and optimization of different polarizations for dark spot generation

We compare generation of a dark spot using focusing of beams with azimuthal polarizion, radial polarization with a vortex, and a circular polarization with either a first or second order vortex. By optimization of the amplitude-phase pupil, it is ascertained that azimuthal polarization is the most suitable one to obtain the diffraction bounded dark spot per se whose scalar approximation limit has FWHM=0.29λ. Consequently, for dark spot generation, this polarization plays the role of the radial polarization in creation of the diffraction-limited bright spot. Using azimuthal polarization, it is shown that an amplitude-phase filter allows generation of a subdiffractive dark spot in a prescribed finite area.     

Estimation of point-spread functions and modulation-transfer functions of optical devices by statistical properties of randomly distributed surfaces

The point-spread function a(PSF) and the modulation-transfer function (MTF) are important tools to characterize the information transfer through optical devices. They give useful information about the resolution. Several methods have already been achieved to calculate the PSF and the MTF from theoretical aspects of wave propagation or from experimental results. I present a novel way of estimating these two functions. It deals with statistical considerations for a randomly distributed surface involving a statistical determination of the PSF and the MTF. Indeed, in this case the theoretical shape of the autocorrelation function of such surface profiles is known. It is a decaying exponential function α[exp(-β|x|)]. Comparingthe theoretical autocorrelation-function profile with the experimental one and deconvolving in Fourier space leads to an estimation of the MTF of the imaging device. Applying the inverse Fourier transform to the MTF involves the computation of the PSF, assuming that the latter has no imaginary part and is symmetrical. The two-dimensional images are regarded as an iteration of one-dimensional ones according to the orthogonal direction. The MTF's and PSF's are therefore one-dimensional. Different results are presented. The first result proceeds from investigation with scanning near-field microscopy and illustrates the method step by step. The tunneling effect is detected assuming that the information transfer is linear. The last result concerns an optical profilometer, and the influence of the microscope objective is studied.     

Ultrasonic imaging using a computed point spread function

An explicit point spread function (PSF) evaluator in the frequency domain is described for an ultrasonic transducer operating in the pulse-echo mode. The PSF evaluator employs the patch element model for transducer field determination and scattered field assessment from a small but finite "point" reflector. The PSF for a planar transducer in a medium has been evaluated in the near and the far field. The computed PSFs were used to deconvolve and restore surface images, obtained experimentally, of a single hole and a five-hole cluster in an Al calibration block. A calibration plot is arrived at for estimating, without the need for deconvolution, the actual diameters of circular reflectors from apparent diameters obtained experimentally for a single-medium imaging configuration. The PSF, when the transducer and the point reflector are in two media separated by a planar interface, was evaluated in the near and far field. The computed PSFs were used to deconvolve and restore subsurface images, obtained experimentally, of flat bottom holes (FBHs) in an Al calibration block. We show that the PSF, in the presence of a planar interface, can be obtained from a single-medium PSF model using an effective single-medium path length concept. The PSFs and modulation transfer functions (MTFs) are evaluated for spherical focused and annular transducers and compared with those for the planar transducer. We identify imaging distances to get better-resolved images when using planar, spherical focused, and annular transducers.     

Matrix method for two-dimensional waveguide mode solution

In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a ‘folded’ plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.     

Scattering from cylinders using the two-dimensional vector plane wave spectrum

The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.     

Analysis on the polarization property of the eigenmodes in a nonplanar ring resonator

Based on the theory of the Abeles matrix, the reflections from the multilayer dielectric mirrors in a nonplanar ring resonator are discussed in detail considering the imperfect layer thickness and the incident angle errors. The polarization of Gaussian beams in nonplanar ring resonators are analyzed by using a statistical method and the way to analyze the stability of a nonplanar ring resonator in the perspective of polarization is also presented. The results show that a nonlanar ring resonator with a finite mode size may not have the reasonable polarization performances sometimes; the eigenmodes might be right- and left-handed elliptically polarized instead of circularly polarized, and they also have different ellipticity and round trip losses, which are critical for a nonplanar ring resonator. These interesting findings are important to the cavity designs of ring resonators with a nonplanar structure.     

3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging

3D deconvolution is an established technique in microscopy that may be useful for low-cost high-resolution imaging of the retina. We report on a myopic 3D deconvolution method developed in a Bayesian framework. This method uses a 3D imaging model, a noise model that accounts for both photon and detector noises, a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas, a positivity constraint, and a smart parameterization of the point-spread function (PSF) by the pupil phase. It estimates the object and the PSF jointly. The PSF parameterization through the pupil phase constrains the inversion by dramatically reducing the number of unknowns. The joint deconvolution is further constrained by an additional longitudinal support constraint derived from a 3D interpretation of the phase-diversity technique. This method is validated by simulated retinal images.     

Generating radial or azimuthal polarization by axial sampling of circularly polarized vortex beams

A laser beam with circular polarization can be converted into either radial or azimuthal polarization by a microfabricated spiral phase plate and a radial (or azimuthal)-type linear analyzer. The resulting polarization is axially symmetric and is able to produce tightly focused light fields beyond the diffraction limit. We describe in detail the theory behind the technique and the experimental verification of the polarization both in the far field and at the focus of a high numerical aperture lens. Vector properties of the beam under strong focusing conditions were observed by comparing the fluorescence images corresponding to the focal intensity distribution for both radial and azimuthal polarizations. The technique discussed here may easily be implemented to a wide range of optical instruments and devices that require the use of tightly focused light beams.     

一种新型偏振分光棱镜的设计和应用

一种新型的偏振分光棱镜结构,实现了将偏振态相互垂直的光以不同的角度输入后合为一 束的功能,尤其能与双光纤准直器配合使用。通过计算说明二者角度可相互匹配,并分析了在准直器的角度加工出现小的偏差时,通过微量调节输入光束的方向能予以补偿。实验将该棱镜用于偏振光合束器和光学环行器等无源器件中取得了良好效果。     

Simple interferometric technique for generation of a radially polarized light beam

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.     

Restoration of medical ultrasound images using two-dimensionalhomomorphic deconvolution

Describes how two-dimensional (2D) homomorphic deconvolution can be used to improve the lateral and radial resolution of medical ultrasound images recorded by a sector scanner. The recorded radio frequency ultrasound image in polar coordinates is considered as a 2D sequence of angle and depth convolved with a 2D space invariant point-spread function (PSF). Each polar coordinate sequence is transformed into the 2D complex cepstrum domain using the fast Fourier transform for Cartesian coordinates. The low-angle and low-depth portion of this sequence is taken as an estimate of the complex cepstrum representation of the PSF. It is transformed back to the Fourier frequency domain and is used to compute the deconvolved angle and depth sequence by 2D Wiener filtering. Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo. It was better than lateral or radial homomorphic deconvolution alone, and better than 2D Wiener filtering with a PSF recorded in vitro     

A Novel Beamsplitter for Optical Polarization State Interferometry

Abstract

We propose an evanescent-field optical beamsplitter, ideal for experiments in polarization state interferometry. It splits an incident wave into two beams, both being in the same polarization state, related to the incident state by a predetermined SU(2) operation on the Poincaré sphere. The operational characteristics of such beamsplitters are described.     

Vector diffraction and polarization effects in an optical disk system

The track pitch of current optical disks is comparable with the wavelength of the laser source. In this domain of the pitch-to-wavelength ratio, the complex-diffraction amplitudes are different for different incident polarization states, and the validity of the scalar diffraction theory is questionable. Furthermore, the use of multilayer coatings and high-numerical-aperture beams in modern optical disk technology inevitably entails the excitation of surface waves, which can disturb the baseball pattern significantly. To describe the interaction of a focused beam with a grooved multilayer system fully, it is necessary to have a rigorous vector theory. We use a rigorous vector theory to model the diffraction of light at the optical disk. We present the simulation and the experimental results and demonstrate the ability of this approach to predict or model accurately all essential features of beam-disk interaction, including the polarization effects and the excitation of surface waves.     

Angular dependence of polarizing beam-splitter cubes

The field-of-view dependence of polarizing beam-splitter cubes has been studied to characterize their behavior in imaging systems such as optical computers and optical correlators and in other applications that involve noncollimated light. Significant polarization aberration is present in polarizing beamsplitter cubes for two reasons: (1) the s- and p-component orientations, which define the polarizing axes, at the beam-splitting interface vary with the direction of propagation, and (2) the performance of the coating is a function of the angle of incidence. We describe the polarization aberration of a polarizing beam-splitter cube in terms of its diattenuation (polarizing efficiency). We use an imaging polarimeter to measure six figures of merit for three polarizing beam-splitter cubes demonstrating typical polarization aberrations. Finally, we derive the Mueller matrix for a polarizing beam-splitter cube in terms of the s and p transmittance and reflectance and the phase retardances, the parameters generally calculated with thin-film analysis programs.