Complex self-coherence function determination using geometric phase techniques

Method of generating a vortex array embedded in a partially coherent beam is proposed and experimentally demonstrated. The vortex array exists in the complex coherence function of a random field arising due to interference of three independent coherence functions with appropriate phase profiles. Existence of the vortex array is confirmed by presenting amplitude and phase distributions of the complex coherence function. The phase structure of the complex coherence function, embedded with a vortex array, is obtained by interfering it with an independent fourth coherence function known as a reference and applying the Fourier fringe analysis technique to the cross-covariance of the intensity of the resultant random field.

We investigate the possibility of interferometric optical field sensor with DMD forming a series of sampling interferometers in the pupil of an optical system. Our preliminary experiment validates the feasibility of our approach for the field reconstruction in the case of coherent field. We believe that this approach can be extended to sensing of speckle patterns and even incoherent fields, by analyzing not only the intensity and phase, but also the amplitude and the visibility of the interference patterns. Such analysis would yield the complete complex amplitude and/or coherence function, making the approach directly applicable to a wide range of inverse source problems in optics.

The generating of vortex beams in the terahertz (THz) band attracts significant attention due to their applications in high-speed communication and high-resolution imaging. In this article, a novel reflective metasurface working in the THz band is designed to generate four vortex beams with different topological charges in different directions. The unit cell is designed based on the geometric phase, and it consists of two metallic (gold) layers and one dielectric layer in between. The top layer of the unit cell includes an elliptic patch and a circular ring, and the bottom layer of the unit cell is a metallic ground. The reflection efficiency of the unit cell is very high due to the presence of metallic ground. To break through the limitations of traditional methods, the metasurface is a good choice to generate beams that carry orbital angular momentum (OAM). Using the concept of geometric phase, the reflection phase of reflective circular polarization (CP) electromagnetic waves can be controlled in an ingenious way. Owing to the property of the geometric phase, inverse phase shift can be achieved for left-handed circular polarization and right-handed circular polarization waves. By utilizing this trait of geometric phase, one can decompose a linear polarization wave into two orthogonal circular polarization waves and control their properties respectively. By rotating the top layer of the unit cell, 360-degree phase shift and the phase distribution satisfying the requirement for generating the multi-beam multi-mode vortex beam can be achieved. In order to control the direction and the topological charge of each beam, based on the geometric phase, the theory of reflectarray and the phase composition principle, the phase distribution of the reflective metasurface is calculated to provide the phase compensation to make the vortex beams point to certain directions. It is worthwhile to point out that the method presented in this paper provides a way to generate complex multi-mode vortex beams in the THz band. The simulations and measurements show that the metasurface can generate four vortex beams with topological charges <i>l</i> = ± 1 and ± 2 in different directions in the THz band. These results also indicate that our design has great potential applications in wireless communication and high-resolution imaging.

Geometric phase metasurfaces, as one of the main branches of meta‐optics, have attracted enormous interest in the last two decades. Recently, through rotating a set of subwavelength dipole sources, geometric phase concept has been extended to near‐field regime for the control of surface plasmons (SPs). Despite this progress, puzzles and shortcomings still exist: it is curious that geometric phases equal to once and twice the rotation angle of dipole source are both reported for SP controls, and the control strategies examined thus far only work for a single wavelength. Hereby, a rigorous derivation of the SP excitation of dipole sources upon circularly polarized illumination is performed, and the rotation dependence and in‐plane coordinate correlation of geometric phase control of SPs is clarified. Moreover, a holographic approach is proposed to implement multiplexed geometric phase control, experimentally demonstrating several metalenses that can couple and steer the incident circular polarizations of four wavelengths and two spin directions to different SP focusing beams. This work will pave an avenue toward the development of integrated and multiplexed SP devices.

We demonstrate an optimized two-step procedure for measuring the full complex coherence function. The measurement relies on a wavefront shearing interferometer that permits characterizing nonstationary fields over an extended angular domain. The accuracy of the coherence measurement was demonstrated by excellent agreement with theoretical predictions.

Turbulence coherence in complex wind field: Focusing on its on-site characteristics based on multi-point clustering

We propose a new analysis method of microtremor circular arrays for detecting phase velocities of Rayleigh waves in microtremors, aiming to conduct the microtremor array observations with fewer restriction of seismometer arrangement than the spatial autocorrelation (SPAC) method. The method is based on the complex coherence function (CCF) of the Rayleigh waves formulated by Shiraishi and Matsuoka (2005) to study the relationship between wave sources and observation points on an array. In this method, the values of the Bessel function J0 (kr) (k: wave number, r: distance between observation points) that generate phase velocities are obtained as a solution of the simultaneous equations of CCFs, while they are calculated from the directional average of CCFs in the SPAC method. Therefore, our method allows observation points not equally spaced on the circumference.From theoretical studies of this method for a circular array, it was found that seismometers on the circumference could be set at almost any place with the condition of symmetrical seismometer arrangement. Moreover, a field experiment have confirmed that the phase velocity obtained from the proposed method agreed with that of the SPAC method.

We review the principle of coherence dynamics proposed recently to explain the origin of coherence vortices, which are the phase singularities in a complex coherence function. Some properties associated with coherence vortex, such as the coherence current describing the circular contrast flow close to a vortex core and conservation laws of coherence, are investigated both theoretically and experimentally.

Propagation of a coherent light through an anisotropic random medium generates randomly polarized field, known as polarization speckle. In this paper, an experimental technique is proposed and demonstrated to recover the transmittance of a polarized object from polarization speckle. Recovery of the polarized object from polarization speckle is made possible by combining the far-field intensity correlation of the object speckle with off-axis holography to determine the complex coherence function of the speckle. The desired object speckle which is uniformly polarized is filtered from the polarization speckle using a polarizer. The results are compared with the case where the complex coherence function is determined in the absence of the polarizer.

The optimal microphone array includes two processing blocks ‐ minimum variance distortionless response (MVDR) beamformer and the single‐channel Wiener filter, which acts as post‐filter. The main drawback of MVDR beamformer is the cancellation of the desired speech signal and its degradation in multi‐path wave propagation environment. To make the adaptive algorithm robust against room reverberation and to prevent desired signal cancellation, an estimation of the unknown desired speaker's transfer function was proposed. The estimation is based on the imperfect signal and the interference covariance matrices estimated from available microphone signals during speaker activity and pause of speech respectively. As MVDR beamformer suppresses coherent interference, post‐filter has to reduce diffuse acoustic noise. The post‐filter proposed in this paper is developed under assumption that complex coherence function is unknown but time invariant. The additional improvement of the post‐processing algorithm on low frequencies is obtained by combining a priori noise power attenuation factor for diffuse noise field with estimated one. The proposed algorithm is tested on simulated room with reverberation, and compared with some known post‐processing algorithms with rather good results.

Coherence holography capable of real-time recording and reconstruction is proposed and experimentally demonstrated with a generic Leith-type coherence hologram. The coherence hologram is optically generated in real-time using a Mach-Zehnder interferometer and reconstructed using a Sagnac radial shearing interferometer. With this method one can create an optical field distribution with a desired spatial coherence function, and visualize the coherence function in real-time as the contrast and phase variations in an interference fringe pattern. The reconstructed image of the complex coherence function has been quantified with the Fourier transform method of fringe-pattern analysis.

We combine a telescopic imaging system with a common-path, lateral-shearing interferometer and use phase-shifting interferometry to measure the complex spatial coherence function (or mutual intensity) of a linearly-polarized optical field. Our telescopic design increases the numerical aperture of the system without distorting the shape of the wave front, and therefore without changing the phase difference between lateral positions in the optical field. Our method of generating lateral-sheared images introduces no additional astigmatism. To demonstrate the use of the interferometer we extract the information contained in the complex spatial coherence function to reconstruct the amplitude and phase of a coherent optical field, and we also show how the spatial coherence function evolves from a coherent field to a partially coherent one as light traverses a random multiple-scattering medium.

The complex coherence function describes information that is necessary to create maps from interferometric synthetic aperture radar (InSAR). This coherence function is complicated by building layover. This paper presents a mathematical model for this complex coherence in the presence of building layover and shows how it can describe intriguing phenomena observed in real interferometric SAR data.

We report a quantitative measurement of the full transverse coherence function of the 14.4 keV x-ray radiation produced by an undulator at the Swiss Light Source. An x-ray grating interferometer consisting of a beam splitter phase grating and an analyzer amplitude grating has been used to measure the degree of coherence as a function of the beam separation out to 30 microm. Importantly, the technique provides a model-free and spatially resolved measurement of the complex coherence function and is not restricted to high resolution detectors and small fields of view. The spatial characterization of the wave front has important applications in discovering localized defects in beam line optics.

We experimentally demonstrate complex-coherence function of incoherent light intercepted by a one-dimensional object in various configurations. By examining only the coherence function, we determine the axial and transverse position and size of the object.