Recovery of complex valued objects from two-point intensity correlation measurement

Abstract

We propose and experimentally demonstrate a technique for the recovery of the wavefront from spatially fluctuating fields using the two point intensity correlation, i.e., fourth order correlation. Assuming spatial ergodicity and Gaussian statistics for the speckle field, we connect the fourth order correlation to the modulus of the corresponding second order correlation. The idea is to retrieve the complex coherence function and consequently the wavefront using the off-axis holography. Application of this technique is demonstrated in the reconstruction of complex field of the object lying behind a weak scatterer. Experimental results of recovery of the complex field of phase objects “vortices” with three values of topological charges are presented.

Complex field measurement in a single pixel hybrid correlation holography

“…The grain size of the random field at the transparency plane is considered to be finer than the spatial structure of the transparency. Spatial resolution is limited by the cap imposed on the spatial finesse of the transparency by the finite correlation length of the illuminating random field [35]. The random fields from the two arms of the interferometer are combined using a beam splitter BS 2 and the intensity is detected by a charged coupled device (CCD).…”

“…On the other hand, over the past few years, correlation holography (CH) has emerged as a promising approach [10,34,35]. The CH reconstructs the object as a distribution of two point spatial coherence.…”

“…In this paper, a new approach to recover the complex object within the HCH framework is proposed. A comparative study (with [35,37]) of basic principles, through theoretical explanations and difference in experimental setups, is included.…”

Correlation assisted in-line holographic imaging through scattering medium

“…However, most of the correlation assisted techniques face the serious imaging challenge of the lost phase information in the image reconstruction due to the amplitude only recovery feature of the intensity correlation approaches. In recent years, a few techniques have been introduced by exploiting the complex-field reconstruction potential of digital holography in combination with the correlation assisted approaches for the complex-valued object imaging through the scattering medium [12][13][14][15][16][17][18][19] . A speckle holography approach utilizing off-axis hologram recovery behind the scattering medium is demonstrated with the capability of single-shot complex-valued object recovery 13 .…”

Perspective: Wavefront shaping techniques for controlling multiple light scattering in biological tissues: Toward in vivo applications

“…55 Alternatively, far-field laser speckle interferometry with two-point intensity correlation measurement was also used to image object though a turbid medium. 56,57 Working toward in vivo applications, however, one should consider the short decorrelation time of live tissues. The decorrelation time of live tissues is inversely proportional to the thickness of the tissue L and is expected to decay even faster for L > l * s due to the loss of directionality.…”