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In this work, we investigate and compare propagation of Laguerre–Gaussian (LG) and the recently introduced radial carpet (RC) beams through an indoor convective air turbulence under weak to strong turbulence conditions. By determining the radial displacement of the intensity maxima over the donut ring of the LG beam, and tracing the radial coordinates of the main intensity spots of the RC beam, when the beams are propagating through the turbulence, we estimate the variance of the local displacements for both of the beams in the radial direction. It is shown that, under the same turbulence conditions, the RC beam experiences less disturbance and is more resilient to turbulence, especially when it has a complicated structure. The measured values of the image displacement variance for the RC beam are almost one order of magnitude smaller than the same parameter for the LG beam. In addition, for the LG beam, the symmetry of the beam is broken and in many places the intensity ring is even cut off. Although there are slight changes in the RC beams transverse intensity distribution, the number of the main intensity spots rarely changes. This feature makes the RC beam a good candidate for the transmission of information. We also show that a set of RC beams having different values of the main intensity spots (generated with different radial gratings having different spoke numbers) can be used as an orthogonal bases for free-space optical communication.

In this paper, we introduce a self-referencing microsphere-assisted transmission digital holographic microscopy (DHM) system in real-image operating mode. Self-referencing DHM arrangements provide a compact geometry that are temporally stable against environmental vibrations and suitable for the measurement of dynamic specimens such as cells. These advantages may be more pronounced for microsphere-assisted DHM systems. In the real-image mode, unlike the virtual-image mode, the working distance is increased. This, in turn, provides flexibility for insertion of additional elements for enhancement of the image quality, or for other required tasks. The lateral resolution enhancement is similar to the virtual image arrangement and the axial resolution is decoupled from the lateral one. The methodology is discussed theoretically and validated experimentally by conducting DHM experiments on standard micro-objects and aggregation of micro-particles. Our results show that, by the assistance of a rather big size 550 μm silica microsphere, a 10× microscope objective can resolve the 3D structure of a compact disk. The arrangement may be useful toward having a compact and inexpensive bench-top high-resolution three-dimensional imaging apparatus.

In this paper, first a detailed investigation of the various behaviors of the near- and far-field diffractions from multiplicatively separable (MS) structures in the x and y directions is presented. It is shown that in near-field propagation, the diffraction pattern of a 2D MS structure is same as the product of the corresponding near-field diffractions of the 1D individual components of the structure. For the far-field diffraction, although the resulting diffraction pattern is not equal to the product of the individual 1D structures' diffraction patterns, we show that it is still a 2D MS pattern. Second, a detailed theoretical investigation of the contrast enhancement effect for the multiplication of two 1D orthogonal intensity patterns (not necessarily periodic) is presented. By merging the above-mentioned facts, we deduced that in near-field diffraction, the contrast of the diffraction pattern of a 2D MS structure is always larger than the contrast of each of the diffraction patterns of the corresponding individual 1D structures. In the second part of this paper, we implement the intensity contrast as a quantity to describe self-images of the 2D MS periodic structures. For the first time, two very important results are obtained based on the contrast enhancement effect. We show that the depth of focus of the self-images increases for the 2D periodic structures in comparing to their corresponding 1D structures. We also predict the existence of additional self-images in addition to the Talbot images located at the least common multiple of each of the individual 1D Talbot distances for the 2D MS periodic structures. In addition, in this work we present a very straightforward manner for the prediction of the 1D or 2D forms of the diffraction pattern and the direction of the 1D pattern strips at given propagation distances from the 2D structure by introducing another intensity-contrast-based parameter. Furthermore, we show that the diffraction pattern of a 2D MS periodic structure depends strongly on the square of the ratio of the 1D structure periods in the x and y directions. These theoretical achievements are verified by some experimental works.

The use of moire pattern of superimposition of linear forked gratings (LFGs) and Fresnel zone plates (ZPs) has already been reported for study of different physical effects. In spite of a considerable number of applications, there is no comprehensive formulation for this kind of moire pattern. In this work, we introduce a new family of ZPs containing topological defects that we named defected ZP (DZP) and we present a very simple, uniform, and comprehensive formulation for the moire pattern of superimposition of two LFGs, two DZPs, and superimposition of an LFG on a DZP, using the reciprocal vector approach. For the case of the two LFGs superimposition, we show that the resulting moire pattern has a starlike shape or is a large-scale LFG pattern. In the case in which two DZPs are superimposed, we show that the resulting moire pattern has three general forms: large-scale DZP pattern, starlike pattern, and large-scale LFG pattern. In the superimposition of an LFG on a DZP, in special conditions a new spiral ZP having a topological defect is produced in which its defect number related to the superimposed gratings structures. The presented formulation has potential applications in singular optics measurements.

Using a novel set up, experimental study of the statistical properties of a light beam propagating horizontally through indoor convective air turbulence in the presence of a 2D temperature gradient (TG) is presented. A laser beam enters a telescope from its back focal point by virtue of an optical fiber and is expanded and recollimated by it and then passes through the turbulent area. Then the beam enters another telescope’s aperture. A mask consisting of four similar widely separated small subapertures was installed in front of the second telescope’s aperture. The subapertures were equidistant from the optical axis of the telescope and located at the corners of a square. A flat plane heater is used to produce a vertical TG in the medium. Due to the limited width of the heater, a horizontal component for the TG appeared. Near the focal plane of the second telescope, four distinct images of the source are formed and recorded by a CCD camera. Due to the turbulence all the images (spots) in the successive frames fluctuate. Using the four spot displacements we have calculated the fluctuations of the angle of arrival (AA) over the subapertures. The statistical properties of the optical turbulence are investigated using variance analysis of the AA component fluctuations at horizontal and vertical directions over the subapertures for different temperatures of the heater at different heights of the beam path from the heater. Experimental results show that when the heater is turned off, the variances of horizontal and vertical components of the AA fluctuations are approximately equal to zero over all the subapertures. When it is turned on, the variance of the horizontal component of the AA fluctuations over all of the subapertures are larger than those from the vertical one. In addition, in this case, we find a significant dependence of the variance of the AA components on the height from the heater.

Recently, an adjustable, high-sensitivity, wide dynamic range, two-channel wavefront sensor based on moire deflectometry was proposed by Rasouli et al (2010 Opt. Express 18 23906). In this work we have used this sensor on a telescope for measuring turbulence-induced wavefront distortions. A slightly divergent laser beam passes through turbulent ground level atmosphere and enters the telescope’s aperture. The laser beam is collimated behind the telescope’s focal point by means of a collimator and the beam enters the wavefront sensor. First, from deviations in the moire fringes we calculate the two orthogonal components of the angle of arrival at each location across the wavefront. The deviations have been deduced in successive frames which allows evolution of the wavefront shape and Fried’s seeing parameter r0 to be determined. Mainly, statistical analysis of the reconstructed wavefront distortions are presented. The achieved accuracy in the measurements and comparison between the measurements and the theoretical models are presented. Owing to the use of the sensor on a telescope, and using sub-pixel accuracy for the measurement of the moire fringe displacements, the sensitivity of the measurements is improved by more than one order of magnitude. In this work we have achieved a minimum measurable angle of arrival fluctuations equal to 3.7 × 10−7 rad or 0.07 arc s. Besides, because of the large area of the telescope’s aperture, a high spatial resolution is achieved in detecting the spatial perturbations of the atmospheric turbulence.

In this paper, we have presented a simple, stable, highly sensitive and timesaving method based on a double-grating interferometer in conjunction with a pump–probe technique for measuring the nonlinear refractive index. A pump laser beam is aligned collinearly with an expanded plane parallel probe beam by a dichroic mirror. These beams pass through the sample, while right behind the sample using a suitable bandpass filter the pump beam is intercepted. The distorted probe beam then passes through a double-grating interferometer. One of the lateral shearing interference patterns is recorded by use of a CCD camera and, after digitization, has been stored in a computer. The interference pattern is analyzed by means of a Fourier transform algorithm. The refractive index changes have been obtained from phase distribution of the recorded fringe patterns. The implementation of the technique is straightforward and the arrangement is very simple and stable yet its sensitivity is comparable with other interferometry methods. It is also not a time consuming method. The method is applied for measuring the thermal nonlinear refractive index n2 of colloidal gold nanoparticles in water solution.