Wavefront reconstruction of vortex beams via a simplified transport of intensity equation and its symmetry based error reduction

Abstract

We present an unexplored non-interferometric approach for wavefront measurement of vortex beams based on the transport of intensity equation (TIE). By exploiting the symmetries of vortexes we are able to simplify the TIE to a reduced expression not reported before in the context of phase imaging. This reduced model can be solved to measure the phase profile of vortexes via one-dimensional operations only without the complexities pertaining the regular TIE. We also use the axial symmetry exhibited by the intensity profile of vortexes to build a noise filtering scheme exclusive to circularly symmetric images and thus address electronic noise in digital imaging systems. We present a series of numerical experiments both to clarify how to apply our proposal step by step and to prove its overall functionality.

Measurement of the spin of the M87 black hole from its observed twisted light

“…The reconstruction of the phase profile from phase-front intensity patterns is a novel non-interferometric technique. It is based on the Transport of Intensity Equation (TIE) method that requires a careful mathematical and numerical analysis of the problem (Lubk et al 2013;Ruelas et al 2018). In our case we limit our analysis to paraxial optics.…”

“…(ii) From the EHT data we extract the intensity I and reconstruct numerically the spatial phase distribution P of the field in the image plane of an asymptotic observer by using well-known phase reconstruction techniques based on the Transport of Intensity Equation (TIE) (Barbero 2006;Schulze et al 2012;Lubk et al 2013;Ruelas et al 2018;Kelly 2018) and build the spiral spectra.…”

“…Since these kind of data are not all available from the EHT observations, in order to obtain the spatial phase distribution, we had to reconstruct the evolution of the wavefront with the well-known non-interferometric technique based on the TIE method and reduced error procedure (Barbero 2006;Schulze et al 2012;Lubk et al 2013;Ruelas et al 2018;Kelly 2018). The TIE equations (see Eq.…”

“…Here we describe how we determined the rotation of the M87* black hole from the brightness temperature distributions (Rybicki & Lightman 2004) provided by EHT, by using the Transport of Intensity Equation (TIE) method (Barbero 2006;Schulze et al 2012;Lubk et al 2013;Ruelas et al 2018;Kelly 2018), adopting a finite-difference method for a series of matrices (250 × 250) of intensity values. As described in the standard literature, the OAM of the EM field can be determined from the spatial phase distribution and the spatial intensity (or amplitude) distribution in the plane of observation of an interferometer (Tamburini et al 2011b).…”

A High-Speed, Wavelength Invariant, Single-Pixel Wavefront Sensor With a Digital Micromirror Device

“…Such wavefront sensing techniques rely on the ability to measure the phase of light which can only be indirectly inferred from intensity measurements. Methods to do so include ray tracing schemes, intensity measurements at several positions along the beam path, pyramid sensors, interferometric approaches, computational approaches, the use of non-linear optics, computer generated holograms (CGHs), meta-materials and polarimetry [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Perhaps the most well-known is the Shack-Hartmann wavefront sensor [22,23].…”