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Abstract The analytical expression of the spherical wave Rytov variance β 0 2 in oceanic turbulence is derived by using the Elamassie's power spectrum model (EPSM), and its correction is confirmed. The performance indicators of underwater laser radar systems, including the double-pass scintillation index σ I 2 , the aperture averaging factor A , the mean signal-to-noise ratio SNR and the mean bit-error-rate BER of monostatic system (MS) and bistatic system (BS) in oceanic turbulence are investigated. On the other hand, the difference of β 0 2 , σ I 2 and SNR between EPSM and Nikishov's power spectrum model (NPSM) is also studied. It is found that, in weak and moderate turbulence, σ I 2 is underestimated by NPSM when oceanic turbulence is dominated by the temperature fluctuations, while σ I 2 is overestimated by NPSM when oceanic turbulence is dominated by the salinity fluctuations. However, it is inverse situation in strong turbulence. Furthermore, the behavior of SNR between EPSM and NPSM is different from that of σ I 2. The relative difference of σ I 2 and SNR between EPSM and NPSM is larger for MS than that for BS. The relative difference of σ I 2 and SNR between EPSM and NPSM is larger in weak and moderate turbulence than that in strong turbulence. [ABSTRACT FROM AUTHOR]

The specific morphologies of laser induced damages on dielectric coating can cause wavefront modulations and influence the downstream propagation properties of transmitted beam, which is so called wavefront morphologies. In this paper, the modeling and characterization of these wavefront morphologies are carried out. In theory, the modulation effects of different morphologies are discussed and their influence on downstream beam propagation properties are simulated based on diffraction integral. In experiment, a pump-and-probe system is developed to characterize different wavefront morphologies, and in correspondence, their geometric morphologies are characterized by microscopic instruments. The simulation and experiment match well with each other, and the geometric characterization explains the origins of wavefront properties of different morphologies. [ABSTRACT FROM AUTHOR]

Based on the generalized Lorenz–Mie theory (GLMT), a theoretical approach is introduced to study the radiation force exerted on a uniaxial anisotropic sphere illuminated by dual zero-order Bessel beams (ZOBBs). The beams propagate with arbitrary direction, and are expanded in terms of the spherical vector wave functions (SVWFs) in the particle coordinate system using the coordinate rotation theorem. The total expansion coefficients of the incident fields are derived by superposition of the vector fields. Applying the Maxwell's stress tensor, the analytical expressions of the radiation forces on a homogeneous absorbing uniaxial anisotropic sphere are derived. Comparing the radiation forces of dual ZOBBs with those results of dual ZOBBs simplified into single ZOBBs and dual plane waves, the accuracy and correctness of the theory are verified. In order to study the equilibrium state, the effects of beam parameters, particle size parameters, and anisotropy parameters on the radiation forces are discussed in detail. Comparing with the isotropic particle, the equilibrium status is sensitive to the anisotropic parameters. Moreover, the properties of optical force on a uniaxial anisotropic sphere in single ZOBB trap and zero-order Bessel standing wave trap are compared. The theory and results of this paper are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by multi-beams. • Based on GLMT, the radiation force exerted on a uniaxial anisotropic sphere by dual arbitrary incident ZOBBs is studied. • The expansion coefficients of the ZOBB with arbitrary propagation direction in terms of the SVWFs are derived. • Comparing with the isotropic particle, the equilibrium status is sensitive to the anisotropy in ZOBB standing wave trap. • The CP ZOBBs or GB trap is easier capture or confine the anisotropic particle comparing with a single ZOBB or GB trap. [ABSTRACT FROM AUTHOR]

Scintillation index of spherical wave in strongly turbulent oceanic medium is evaluated. In the evaluation, modified Rytov solution and our recent formulation that expresses the oceanic turbulence parameters by the atmospheric turbulence structure constant, are employed. Variations of the scintillation index in strong oceanic turbulence are examined versus the oceanic turbulence parameters such as the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, viscosity, wavelength, the link length, and the ratio of temperature to salinity contributions to the refractive index spectrum. [ABSTRACT FROM AUTHOR]

We experimentally demonstrate that spherical-and-oblique-phase-attached circular Airy beams (SOPA-CAB) can be used to realize the two dimensional large-scale optical manipulation of microparticles. The spherical and oblique phases are attached to CAB based on fourier-space generation method with the assistance of a spatial light modulator (SLM). By changing the hologram coded on the SLM through programming, the autofocusing focus of the SOPA-CAB goes further longitudinally compared with CAB and shifts freely on the focal plane, such that it can drive microparticles to move around on the plane within a maximum diameter of 108 microns. [ABSTRACT FROM AUTHOR]

A method of generating spherical focal spot is demonstrated through reversely propagating and tightly focusing the electric field at the pupil plane radiated from an infinite biconical antenna centered at the foci of two confocal high numerical aperture aplanatic objective lenses. The required incident field distribution at the pupil plane is found by solving the inverse problem of radiation from an infinite biconical antenna using the Richards–Wolf vectorial diffraction theory. Numerical simulations show that a focal spot of excellent spherical symmetry along with extremely low sidelobe (~4.72% of the peak) and diffraction limited spot size of 0.432 λ can be obtained in a 4Pi focusing system. It is also shown that the generated focal spot can be shifted along the optical axis while still maintaining its spherical shape and diffraction limited size through introducing a phase difference between the pupil illumination fields of the two objective lenses used in the 4Pi focusing system. [ABSTRACT FROM AUTHOR]

The evaluation of beam shape coefficients (BSCs) which encodes the description of the illuminating beam is an essential issue in light scattering theories of spherical particles, such as the generalized Lorenz–Mie theory (GLMT). Different methods have been developed in this context, including the traditional (quadratures, finites series, localized approximations), to be complemented by use of the angular spectrum decomposition (ASD). The present paper is devoted to a comprehensive study of the relationship between the traditional quadrature method and the ASD method to the evaluation of BSCs. We shall establish that evaluation of BSCs using the quadrature method can be modified into expressions in the spectral space, leading to the same results as those obtained using the ASD. These BSCs are afterwards approximated under the paraxial conditions, leading to the same results as these obtained by using the localized approximations. The TEM 0 l ∗ doughnut beam is taken as an example of the shaped beam and the theoretical analysis is confirmed by numerical calculations. • Angular spectrum representation of the beam field is introduced into the quadrature method of the GLMT. • The connection between the ASD method and the quadrature method is studied. • The agreement between the approximation of the ASD method and the localized approximation is achieved for beams having simple symmetry. • Spherical wave expansion of the TEM 0 l ∗ doughnut beam is studied. [ABSTRACT FROM AUTHOR]

Two distinct methods based on which two different quadratic-form expressions for the two-source spherical wave structure function (WSF) can be derived are reviewed. The validity of closed-form expressions for the beam-wave cross-spectral density function (CSDF) due to generalized atmospheric turbulence featuring an arbitrary spectral index ranging from 3 to 4, developed based on the quadratic two-source spherical WSFs, is examined in detail. New formulations for the conditions under which the said closed-form expressions for the beam-wave CSDF are strictly valid are developed and several novel interesting findings are elucidated. In particular, the closed-form beam-wave CSDF derived based on the small-separation asymptotic two-source spherical WSF can be considered a rigorous asymptotic solution under the strong-turbulence condition only when the separation distance between the two observation points is much smaller than the inner scale of turbulence; moreover it is also a rigorous asymptotic solution when a certain relation among the initial beam radius, initial transverse coherence width and inner scale holds, regardless of the turbulence strength and spectral index. On the other hand, the accuracy of the closed-form beam-wave CSDF derived based on the large-separation-approximation two-source spherical WSF depends on the spectral index, and a spectral index closer to 4 results in better accuracy. [ABSTRACT FROM AUTHOR]

Abstract: An improved joint transform correlation technique is proposed for efficient multiple-target detection. The proposed technique employs off-focus inputting and spherical wave illuminating joint power spectrum to overcome false-target detection by eliminating the false correlation peaks while alleviating the effects of noise and other artifacts. Compared with the reported techniques, the proposed method does not need preprocessing for reference image and Fourier plane phase filtering, which makes the recognition process more suitable for all-optical setup to be realized. Thus the speed advantage of the recognition system is more prominent. Moreover, the proposed technique can maximize the utilization efficiency of the space–bandwidth product and the CCD by the new input method. The feasibility and effectiveness of the proposed method are demonstrated by numerical results. [Copyright &y& Elsevier]

Abstract: Based on the vectorial Rayleigh–Sommerfeld integrals, the general propagation integral expressions for on-axis nonparaxial vectorial spherical wave diffracted at a circular aperture are derived. The results are strict integral formulae for the light field on the axis, valid for either strong or weak focusing, both far and near zones, and for the systems in which the size of the aperture is comparable to or smaller than the wavelength. Thus, it has the advantage for general application. For convergent spherical waves, the numerical calculation results are compared with those obtained by using the integral formulae of scalar paraxial approximation and scalar nonparaxial approximation, confirming the consistence in the situation of scalar approximation. [Copyright &y& Elsevier]

The expressions for the wave and the phase structure functions of a plane wave and a spherical wave propagating in the natural water turbulence characterized by the recently developed spatial power spectrum (Yao et al., 2020) are evaluated in general and in the limits of large and small separations. The spatial coherence radius for both plane and spherical waves is then deduced. The angle-of-arrival variance of these wavefronts at the collecting lens of the receiving system is also evaluated. In-depth numerical illustrations of the dependence of these quantities on the average temperature/salinity, temperature/energy dissipation rates, and the temperature–salinity gradient ratio are included. Our results are of utmost importance for underwater imaging and sensing technologies. • Wave structure function for plane and spherical wave in underwater turbulent medium is found. • Phase structure function for plane and spherical wave is found. • Angle of arrival fluctuations for plane and spherical wave is found. • Underwater is governed by Oceanic Turbulence Optical Power Spectrum (OTOPS) model. [ABSTRACT FROM AUTHOR]

Abstract: Starting from the Fresnel–Kirchhoff diffraction integral formula and taking into consideration the inclination factor and wave-front integration, the general expressions for on-axis convergent and divergent spherical waves diffracted at a circular aperture are derived. Our results are valid for the case |f|> a, where f and a are the focal length and aperture radius, respectively. The numerical results are consistent with the experimental data of divergent spherical waves diffracted at a circular aperture. For convergent spherical waves the results are compared with those by using the Li–Wolf formula, showing the more general applicable advantage of our formulae. [Copyright &y& Elsevier]

Higher resolution has always been the goal of imaging. Resolution enhancement in most holographic imaging methods are achieved by collecting more object spectrum. As a computational imaging technology, the resolution of digital holography is determined by the utilized bandwidth in both optical recording and numerical reconstruction. There is little study on whether the collected spectrum is effectively utilized during reconstruction. In this work, we propose a resolution-enhanced digital in-line holography under spherical wave illumination. The collected object spectrum, which cannot be fully used by conventional methods, is effectively utilized by the developed band-extended angular spectrum method with improved computational efficiency. Numerical analysis and optical experiments have been performed to demonstrate that the proposed method can effectively enhance the imaging resolution of digital in-line holography by extension of the computational bandwidth. [ABSTRACT FROM AUTHOR]

In this work, we show that unequal-arm two-beam interferometers, for example, single-pass Mach–Zehnder interferometer or double-pass Michelson interferometer, illuminated with coherent point source (spherical wave front) or coherent line source (cylindrical wave front), unambiguously determine the sign of the phase shift. Theoretical consideration shows that a pattern with finite diameters of interference fringes is asymmetric with respect to the sign of the optical path difference (OPD) or phase shift (PS). In a short arm of the interferometer, the light passing through the layer of medium, characterized by positive OPD (positive PS), leads to the decrease of the diameter of interference fringe. The layer of the medium with negative OPD increases the diameter of inference fringe. When placing an object in the long arm of the interferometer, the contrary situation is observed. For variants with a coherent linear source, the above results relate to the distances between strait fringes of the same order. Experiment demonstrates that the positive optical path length of a conventional material can be compensated in air by a layer of metamaterial with a negative optical path length located at a distance significantly longer than the wavelength of light. [ABSTRACT FROM AUTHOR]