We propose and experimentally demonstrate a single-path interferometric approach to quantify the higher-order topological charge and phase structure of a vortex beam embedded into a low-coherence background. The topological charge is determined by an in-line and common path configuration for superposing the fluctuating coherent beams loaded with vortex and non-vortex features. Ensemble average of the intensities of the superimposed fluctuating fields generates petal structure and the number of petals infers the absolute value of the topological charge of the vortex beam. Furthermore, a three-step phase-shifting method along with a single-path interferometer is utilized to recover the phase and spectra of the TCs in the beams embedded into a low-coherence background. The results of our experiment demonstrate successful measurement of vortex beam with TCs up to 150. We believe that such petal patterns with incoherent light will be useful in sensing the rotation and motion of optically rough objects.

A vectorial holography technique is presented to reconstruct the complex-valued object in terms of the coherence-polarization (CP) matrix elements of the random field. These CP matrix elements are then used to extract polarization information of the incident vector beam.

This paper presents a method to shape and synthesize spatial distribution of the beam coherence with the Gerchberg-Saxton (GS) algorithm and a Spatial Light Modulator (SLM). By modifying the polarization and spatial mode of light, we synthesize a light source with desired correlation structure. Furthermore, the Hanbury Brown–Twiss approach with the polarization basis is applied to examine two-point Stokes correlation to experimentally measure the spatial coherence of the synthesized source. Initial experimental results are presented. This comprehensive method for studying and utilizing coherence has potential applications in optical communications, microscopy, and quantum information processing.

Singularity in a two-point complex coherence function, known as coherence vortices, represents zero visibility with a helical phase structure. In this paper, we introduce a novel technique to generate the coherence vortices of different topological charges by incoherent source transmittance with exotic structured binary pinholes. The binary pinhole structures have been realized by lithography, followed by wet etching methods. We control the transmittance from the incoherent source plane using these exotic apertures, which finally results in a coherence vortex spectrum that features multiple and pure orbital angular momentum modes. The generation of the coherence vortices is achieved within the two-point complex spatial coherence function. The spatial coherence function exhibits the helical phase profile in its phase part, and its absolute part shows a doughnut-shaped structure. A theoretical basis is developed and validated with simulation, and experimental results. The coherence vortex spectra with OAM modes superposed with opposite topological charges, known as photonic gears, are also generated with the proposed theory.