Dayan Li

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

When monochromatic light is scattered from an optically rough surface a complicated three-dimensional (3D) field is generated. These fields are often described by reference to the 3D volume (extent) of their speckles, leading to the definition of lateral (x,y) and longitudinal speckle sizes (z). For reasons of mathematical simplicity the longitudinal speckle size is often derived by examining the decorrelation of the speckle field for a single point lying on axis, i.e., x=y=0, and this size is generally assumed to be representative for other speckles that lie further off-axis. Some recent theoretical results, however, indicate that in fact longitudinal speckle size gets smaller as the observation position moves to off-axis spatial locations. In this paper (Part I), we review the physical argument leading to this conclusion and support this analysis with a series of robust numerical simulations. We discuss, in some detail, computational issues that arise when simulating the propagation of speckle fields numerically, showing that the spectral method is not a suitable propagation algorithm when the autocorrelation of the scattering surface is assumed to be delta correlated. In Part II [J. Opt. Soc. Am. A28, 1904 (2011)] of this paper, experimental results are provided that exhibit the predicted variation of longitudinal speckle size as a function of position in x and y. The results are not only of theoretical interest but have practical implications, and in Part II a method for locating the optical system axis is proposed and experimentally demonstrated.

Dual wavelength digital holographic Laplacian reconstruction

Access to the spatial derivatives of an optical wave field can be used to enhance edge detection, focusing, and holographic imaging. It was recently shown that, by using digital holographic techniques, the Laplacian of an object field can be extracted. Here it is demonstrated that equivalent results can be found using two holograms captured at either two distances or with two appropriately related wavelengths. Experimental and numerical results confirming the theoretical analyses are presented. The proposed two-wavelength-based system requires no mechanical repositioning of the object and is shown to provide superior performance.

Speckle orientation in paraxial optical systems

The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.

Speckle suppression by doubly scattering systems

Speckle suppression in a two-diffuser system is examined. An analytical expression for the speckle space-time correlation function is derived, so that the speckle suppression mechanism can be investigated statistically. The grain size of the speckle field illuminating the second diffuser has a major impact on the speckle contrast after temporal averaging. It is shown that, when both the diffusers are rotating, the one with the lower rotating speed determines the period of the speckle correlation function. The coherent length of the averaged speckle intensity is shown to equal the mean speckle size of the individual speckle pattern before averaging. Numerical and experimental results are presented to verify our analysis in the context of speckle reduction.

K speckle: space–time correlation function of doubly scattered light in an imaging system

The scattering of coherent monochromatic light at an optically rough surface, such as a diffuser, produces a speckle field, which is usually described by reference to its statistical properties. For example, the real and imaginary parts of a fully developed speckle field can be modeled as a random circular Gaussian process. When such a speckle field is used to illuminate a second diffuser, the statistics of the resulting doubly scattered field are in general no longer Gaussian, but rather follow a K distribution. In this paper we determine the space-time correlation function of such a doubly scattered speckle field that has been imaged by a single lens system. A space-time correlation function is derived that contains four separate terms; similar to the Gaussian case it contains an average DC term and a fluctuating AC term. However, in addition there are two terms that are related to contributions from each of the diffusers independently. We examine how our space-time correlation function varies as the diffusers are rotated at different speeds and as the point spread function of the imaging system is changed. A series of numerical simulations are used to confirm different aspects of the theoretical analysis. We then finish with a discussion of our results and some potential applications, including controlling spatial coherence and speckle reduction.

Feasibility investigation of using tunable infrared communications laser for multiwavelength digital holographic Laplacian reconstruction

Access to both the phase and intensity of an image can be provided using digital holographic (DH) imaging techniques. Recently, the difference of two holograms captured with two appropriately related wavelengths was demonstrated to produce the Laplacian of an object field. Applying telecommunication lasers the feasibility of infrared (IR) DH and DH Laplacian reconstruction and the associated theoretical analyses are presented. This is achieved by combining a tunable mid-IR laser source and mid-IR sensitive InGaAs-based digital camera.

Measuring refractive index of glass by using two captures under speckle field illumination

Measurement of the refractive index of regular shaped glass by speckle correlation is reported. One intensity image in the diffraction field of a speckle-illuminated sample is captured by a CCD before the presence of glass sample and another intensity image is captured after the presence of glass sample. As the position of peak correlation coefficient is quantitatively related to the change in optical path length arising due to the presence of glass, the refractive index of the glass can be evaluated by the correlation of the intensity images before and after the glass insertion. The theoretical correlation function is first derived that describes the relationship between optical path length change and speckle decorrelation. In experiment, various regular shaped glasses are measured to demonstrate the accuracy and robustness of the proposed technique.

Some Characteristics of Doubly Scattered Speckle Fields

In this manuscript we investigate the space-time intensity correlation function of doubly scattered speckle, that is, the observed speckle generated by the passage of a laser light through two sequential random phase screens. It has been shown that the amplitude and intensity of the doubly scattered speckle in this case obeys a K distribution [1]. Unlike circular Gaussian speckle field, Reed’s theorem [2, 3] is not applicable for the K distributed speckle. Thus a direct derivation of the fourth-order moment is required in order to obtain a space-time intensity correla-tion function. Unfortunately, the derivation of fourth-order moment is cumbersome [4], meaning that the analytic space-time intensity correlation function for doubly scattered speckle is rarely seen. Our main goal here is to demonstrate an approach that can solve this problem.

Speckle: two new metrology techniques

Speckle fields are formed when quasi-monochromatic light is scattered by an optically rough surface. These fields are usually described by reference to their first and second order statistical properties. In this paper we review and extend some of these fundamental properties and propose a novel technique for estimating the refractive index of a smooth sample. Theoretical and experimental results are presented. Separately, we also report on a preliminary experiment to determine some characteristics of speckle fields formed in free space by a rotating compound diffuser. Some initial measurements are made where we examine how the speckle intensity pattern in the output plane changes as a function of the relative rotation angle.