We propose and experimentally demonstrate a noninterferometric method to quantitatively determine the topological charge and complete phase structure of a vortex beam scrambled by a random scattering medium. In the proposed technique, the vortex beam with an arbitrary topological charge coaxially enters into the scattering medium with another nonvortex beam with an orthogonal polarization state. This couples the spatial and polarization modes of the coherent light prior to entering the scattering medium. Correlation of the orthogonal polarization states of a random field encodes the signature of the twisted mode of the vortex beam. Recovery of the complex polarization correlation functions and hence twisted modes of the beam are retrieved from the Stokes parameters of a randomly scattered field. Two-point correlations of the Stokes parameters form a 4 × 4 matrix with a total of 16 elements. Out of these 16 elements, only four elements of the matrix are used to retrieve real and imaginary parts of the complex polarization correlation function and are subsequently applied in the reconstruction of twisted wavefronts. A complete theoretical basis is developed to retrieve the twisted wavefront of propagating light through random scattering media and is also supported by numerical simulation and experimental demonstration. As an application of the proposed technique, recovery of the complete phase maps of the different vortex beams from the random light is experimentally demonstrated and the twisted modes of the incident light are quantitatively analyzed using orthogonal projections. The experimental results are in good agreement with the theoretical basis and numerical results.

We propose and experimentally demonstrate an on-axis phase-shifting correlation holography technique with un-polarized light. The randomness of the un-polarized light is exploited to evaluate the higher-order polarization correlation and to consequently apply it in the reconstruction of the hologram from the randomness. A detailed theoretical analysis is developed and verified by numerical simulations and followed by experimental demonstrations. To validate the application of the proposed technique, imaging of different helical phase objects with randomness is presented. A good affinity is found between simulation and experimental results, which validates the accuracy of the proposed technique.

We present and experimentally demonstrate a holography technique with a higher-order Stokes correlation of the random light field. The proposed technique is capable to reconstruct the complex-valued object from the random light field, and overcome twin image issues in the higher-order correlation holography without angular shift, phase shifting, and iterations. A basic principle of the proposed technique is presented and its application is demonstrated by establishing a connection between the higher-order Stokes fluctuations correlations and the far-field complex coherence function of the random field in a lensless configuration. The viability of our technique is demonstrated by considering incoherent reconstruction of the hologram and reconstructing the complex-valued information encoded into the hologram as a distribution of complex coherence function.

In this Letter, we propose and experimentally demonstrate a new, to the best of our knowledge, non-interferometric and highly stable technique to unscramble the incident orbital angular momentum (OAM) state and quantitatively measure the phase structure from the non-imaged random light. A new theoretical basis is developed and also verified by numerical simulation and experimental demonstration. We also quantitatively investigate the OAM modes of the incident light using orthogonal projection.

The Hanbury Brown–Twiss approach, associated with the correlation of intensity fluctuations at two different points in a wave field, unveils fundamental aspects of light. Here, we propose and experimentally demonstrate an imaging and phase recovery technique through a dynamic scattering medium using the Hanbury Brown–Twiss approach. A detailed theoretical basis is presented and verified by experimental demonstrations. To validate the application of the proposed technique, the randomness of the dynamically scattered light is exploited using temporal ergodicity for evaluating the correlation of intensity fluctuations and consequently applying it in the reconstruction of the object hidden behind the dynamic diffuser.