Photon correlation holography

Abstract

Unconventional holography called photon correlation holography is proposed and experimentally demonstrated. Using photon correlation, i.e. intensity correlation or fourth order correlation of optical field, a 3-D image of the object recorded in a hologram is reconstructed stochastically with illumination through a random phase screen. Two different schemes for realizing photon correlation holography are examined by numerical simulations, and the experiment was performed for one of the reconstruction schemes suitable for the experimental proof of the principle. The technique of photon correlation holography provides a new insight into how the information is embedded in the spatial as well as temporal correlation of photons in the stochastic pseudo thermal light.

Speckle orientation in paraxial optical systems

“…(4). In the FST case, the speckles lie orientated along lines that pass through the system origin and always have the same projection length onto the optical axis; see [1,10] for detail. As a result, in the directions that pass through the system origin, the further the observation position is away from the optical axis, the larger the speckle grain lengths are.…”

“…We achieve this using a spatial averaging method, where we can approximately measure the correlation function by allowing recorded intensity values, around the two spatial locations of interest, contribute to the averaging process. In order for this assumption to be strictly valid, it requires that the statistical properties of a speckle field are stationary [9,10], i.e., depend only on the distance between the two spatial coordinates and not on their actual spatial locations. In general paraxial systems, this is not true-the correlation function has a spatial dependency for a Fresnel system [11,12]; however, as we shall see later, it does hold for a Fourier transforming system.…”

Three-dimensional static speckle fields Part I Theory and numerical investigation

“…We note that performing such a comparison is not straightforward. The correlation function is mathematically represented by the ensemble average of the intensity values at the two point positions, which can be realized either by time averaging or by space averaging depending on the experimental conditions, i.e., where the generated speckle fields are assumed to be approximately ergodic [22,23]. To illustrate the issues involved assume we have a speckle field generated with a diffuser and a monochromatic light source.…”

“…Once reasonably large datasets have been recorded (>1000 values), the resulting correlation function for these two points can be experimentally estimated by cross-correlating the two data vectors (the mean of each vector being first subtracted from the vector before a normalized cross correlation is performed). This approach is however rather slow, therefore, in this manuscript we replace this form of "time averaging" with a "spatial averaging" [23,24], where for a single diffuser we take intensity values around the two points of interest and use these values to determine the value of the correlation function. While this approximation is not strictly true, our numerical simulations and experimental results (which involve spatial averaging) have been found to be consistent with the prediction of the physical model (involving the use of the ensemble average).…”

Experimental exploration of the correlation coefficient of static speckles in Fresnel configuration

“…Theoretically, ensemble average of speckle intensity requires that a large ensemble of temporally ergodic fields has to be generated. In practice this ensemble average can be realized either by time averaging or by spatial averaging, depending on the speckle fields that are assumed to be ergodic in time or in space [16,17]. To perform time averaging, a large number of intensities for these two specific points have to be measured, where the diffuser used to generate the speckle fields is replaced with a new statistically similar one for each of these measurements.…”