Far-field Diffraction Intensity Research Articles

Optical parameter design model of hemispherical laser retroreflector arrays for satellite laser ranging

A laser retroreflector array (LRA) with multiple retroreflectors is used to directionally reflect an incident laser beam and aims to enhance the received signal strength into laser ranging ground stations. A comprehensive mathematical equation of the received photons is established by modelling the LRA far field diffraction intensity (FFDI) and the satellite velocity aberration position. Based on this received photon model, a novel method on designing the dihedral angle offset and the aperture of retroreflectors is proposed, which maximizes the received photon under the minimal elevation angle of the ground station. Taking the hemispherical structure parameters of Chinese HY-2 satellite LRA and the specification parameters of the Shanghai Astronomical Observatory, the optimal aperture and the dihedral angle offset of the HY-2 laser retroreflectors are 17 mm and 1.6″, respectively. These two optimal optical parameters make the received photon under the elevation angle of 0° reach ∼0.9 count per laser shot. Until now, ∼851,400 successful observations have been successfully obtained by global ground stations since the first launch of HY-2 satellite series in 2011, which guarantees the high-precise orbit determination of HY-2 satellite series.

Measuring the orbital angular momentum of generalized higher-order twisted partially coherent beams

Recently a new family of partially coherent fields incorporating generalized inseparable cross-coupled phases named generalized higher-order twisted partially coherent beams (GHTPCBs) have been introduced. The twist factor u is a key parameter that not only quantifies the strength of the generalized cross-coupled phase for a given order, but also determines the amount of the concomitant orbital angular momentum (OAM). In this paper, we propose a simple and reliable method to measure the factor u using a two-pinhole mask. Without need of complicated optical system, it only requires to capture the far-field diffraction intensity distribution of the GHTPCB passing through the mask. By analyzing the Fourier spectrum of the intensity distribution, the value of twist factor can be derived nearly in real time. The influence of the separation distance between two pinholes and the pinholes’ diameter and position on the measurement accuracy are thoroughly studied both in theory and experiment. The experimental results agree well with the theoretical results. Our methodology can also be extended to measure the sole factor of similar position dependent phases such as the topological charge of a vortex phase.

Detection of topological charge for composite perfect vortex beams in atmospheric turbulence

Aiming at the problem of detecting the orbital angular momentum (OAM) states of the composite perfect vortex beams (CPVBs) under atmospheric turbulence (AT) channels, we propose and investigate a joint scheme of combing an optical detection method and the Gerchberg-Saxton (GS) algorithm. We firstly used the GS algorithm to pre-compensate the distorted CPVBs, and then the optical intensity distribution, together with the far-field diffraction patterns of the CPVBs after they passing through an elliptical aperture which shields part of the azimuth angle (EA-shielded), can tell us the topological charges (TCs) carried by each sub beam. The results show that the tailing direction of the bright stripes in the CPVBs intensity distribution denotes the sign of the higerh-order TC, counterclockwise is positive, clockwise is negative. The difference between the TCs of the two beams is indicated by the number of stripes, that is, the number of stripes is equal to the absolute values of differences between the two beams. After passing through the EA-shielded, the far-field diffraction intensity patterns is related to the magnitude and sign of the lower-order TC. If the bright stripes are distributed above, the TC is positive, otherwise, the TC is negative, and the number of dark stripes is equal to the lower-order TC-1. The results provide a new method for detecting the TC information of the CPVBs after phase distortion.

Annular phase grating-assisted recording of an ultrahigh-order optical orbital angular momentum.

Ultrahigh-order optical orbital angular momentum (OAM) states of the identification over ±270 orders are implemented by annular phase grating (APG) and Gaussian beams with different wavelengths. Particularly, the far-field diffraction intensity patterns feature the spiral stripes instead of Hermitian-Gaussian (HG)-like fringes. It's worth noting that the spiral stripes present uniform distribution, thus the order of OAM states can be intuitively acquired. More specifically, the OAM states can be confirmed from the total amount and rotating direction of the spiral stripes. Compared with traditional methods, the propose scheme contributes to the perfect-distributed and sharper spiral stripes. Moreover, it also makes an easier observation of the patterns in the CCD camera with limited imaging targets. In our experimental setup, the optical filter is removed and the APG parameters are not strictly required. Therefore, the propose optical transmission system is equipped with the advantages of efficiency, robustness and low cost, which paves a promising way for the communication capacity enhancement.

Speckle in polarization structured light

We show that the far-field speckle patterns observed on the transmission of polarization structured light beams through a random diffuser screen have distinct spatial textures, which significantly differ from the texture of the fully developed scalar speckle. In particular, we report on speckle observed using the V-point and C-point polarization singular beams for illumination in this work. The V-point and C-point polarization singularities are generated by a combination of different orbital angular momentum (OAM) states in orthogonal polarizations. When passed through a random diffuser screen, the on-axis far-field diffraction intensity is an incoherent summation of speckle intensities due to the individual OAM states. Unlike the typical grainy structure in the scalar speckle, the speckle patterns observed with V-point and C-point illuminating beams are seen to have a noodle-like and sponge-like textures respectively. The speckle from V-point and C-point illuminations is difficult to distinguish using the usual intensity statistics which does not account for the distinct spatial structure of the speckle patterns. The Gray Level Co-occurrence Matrix (GLCM) methodology was therefore used to extract a number of spatial textural features from the speckle patterns observed using scalar and polarization structured illuminations. The principal component analysis (PCA) technique when applied to the texture parameters shows that it is possible to identify the nature of the illuminating beam by simply observing the texture properties of the resultant speckle pattern. When coherent light beams pass through a random medium resulting in a fully developed speckle pattern, the information regarding the profile of the input beam is generally considered to be lost. Our new observations on distinct textural features in speckle from structured light therefore suggest the possibility of information transmission through random media by means of switching the polarization structure of the incident beam.

Simultaneous identification of the azimuthal and radial mode indices of Laguerre-Gaussian beams using a spiral phase grating

Transfer of information using optical vortex beams as signal carriers can extremely extend the capacity and spectral efficiency in optical communication systems. One of the key problems is to accurately measure the mode indices including radial mode p and topological charge l at the receiver side of an optical vortices transmission system. In this paper, we present a new scheme to determine the mode indices of optical vortices by using spiral phase gratings. Based on the Fresnel diffraction integral theory, the far-field diffraction intensity distributions of vortex beams through the gratings are numerically calculated. Simulation results show that the annular-shaped intensity profiles of incident vortex beams evolve to bright spot array diffraction patterns, which render the information of the mode indices. Specifically, the magnitude of topological charge l and radial index p can be easily determined by counting the number of the corresponding bright stripes. And the orientation of the diffraction optical fields reveals the sign of the topological charge. Experiments are implemented to demonstrate the feasibility and validity of the proposed detecting method by uploading such phase gratings on a reflective phase-only liquid crystal spatial light modulator. The experimental observations are in good agreement with the theoretical predictions.

Analyzing modal power in multi-mode waveguide via machine learning.

A machine learning assisted modal power analyzing scheme designed for optical modes in integrated multi-mode waveguides is proposed and studied in this work. Convolutional neural networks (CNNs) are successfully trained to correlate the far-field diffraction intensity patterns of a superposition of multiple waveguide modes with its modal power distribution. In particular, a specialized CNN is trained to analyze thin optical waveguides, which are single-moded along one axis and multi-moded along the other axis. A full-scale CNN is also trained to cross-validate the results obtained from this specialized CNN model. Prediction accuracy for modal power is benchmarked statistically with square error and absolute error distribution. It is found that the overall accuracy of our trained specialized CNN is very satisfactory for thin optical waveguides while that of our trained full-scale CNN remains nearly unchanged but the training time doubles. This approach is further generalized and applied to a waveguide that is multi-moded along both horizontal and vertical axes and the influence of noise on our trained network is studied. Overall, we find that the performance in this general condition keeps nearly unchanged. This new concept of analyzing modal power may open the door for high fidelity information recovery in far field and holds great promise for potential applications in both integrated and fiber-based spatial-division demultiplexing.

Removal of all mosaic grating errors in a single-interferometer system by a phase-difference reference window.

An interference method to remove all mosaic grating errors using a phase-difference reference window without compensation for coupled mosaic errors or analyzing the far-field diffraction intensity patterns is proposed. The reference window is achieved by adding a small-aperture prism; therefore, the incident light on the mosaic gratings contains two different angles of incidence and optical paths, eliminating the uncertainty of longitudinal mosaic error in the interferometer. The mathematical model of the method is established and optical arrangement is presented. Interference fringes with the reference window and alignment process are simulated and the accuracy of mosaic errors are analyzed. The experimental and simulation results show that our method can eliminate longitudinal mosaic error and all other mosaic grating errors. The accuracy of angle mosaic errors can be less than 1 μrad and position mosaic errors can be to the nanometer level. Compared with the far-field diffraction intensity patterns method, our method reduces the complexity of the optical structure and ensures measurement accuracy.

Research of far-field diffraction intensity pattern in hot atomic Rb sample

In this work we present a study of the far-field diffraction intensity patterns in the Rb atomic medium. It is found that the far-field diffraction intensity patterns are intimately related to the incident frequency, power, the atomic number density and the position of the sample. The results demonstrate that the far-field diffraction intensity patterns can sensitively reflect the nonlinear optical properties of the medium. The information obtained is of meaning in the application fields, such as the nonlinearity of the medium measuring, optical limiting.

Effect of structural recession on the performance of a satellite laser retroreflector

Satellite laser retroreflector (LRR) array is an essential reflect- ing element for satellite laser ranging. Because of the requirements of manufacturing and assembling, the actual LRR reflecting face is placed underneath the top of assembly. We use the ray tracing method to build up the active retroreflecting region model for LRR with a structural reces- sion effect. Combined with the principle of far-field diffraction intensity and velocity aberration, we give the mathematical model for expressing the structural recession effect on the received optical signal intensity (ROSI) by a ground station. As an important factor for determining the performance of LRR, the distribution of ROSI is simulated for an HY-2A LRR array. The simulation shows that the value of ROSI decreases along with the increment of structural recession size. The bigger optical incident angle should bring about further reduction of ROSI. Only considering the structural recession effect on ROSI, we obtain the regularity of difference of range correction. Before and after considering the structural recession effect, the maximum difference of range correction reaches 9.36 mm for the whole incidence condition. It demonstrates that structural recession cannot be ignored for deciding the performance of LRR. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI:

Vortex metrology using Fourier analysis techniques: vortex networks correlation fringes

In this work, we introduce an alternative method of analysis in vortex metrology based on the application of the Fourier optics techniques. The first part of the procedure is conducted as is usual in vortex metrology for uniform in-plane displacement determination. On the basis of two recorded intensity speckled distributions, corresponding to two states of a diffuser coherently illuminated, we numerically generate an analytical signal from each recorded intensity pattern by using a version of the Riesz integral transform. Then, from each analytical signal, a two-dimensional pseudophase map is generated in which the vortices are located and characterized in terms of their topological charges and their core's structural properties. The second part of the procedure allows obtaining Young's interference fringes when Fourier transforming the light passing through a diffracting mask with multiple apertures at the locations of the homologous vortices. In fact, we use the Fourier transform as a mathematical operation to compute the far-field diffraction intensity pattern corresponding to the multiaperture set. Each aperture from the set is associated with a rectangular hole that coincides both in shape and size with a pixel from recorded images. We show that the fringe analysis can be conducted as in speckle photography in an extended range of displacement measurements. Effects related with speckled decorrelation are also considered. Our experimental results agree with those of speckle photography in the range in which both techniques are applicable.

Measuring the topological charge of vortex beams by using an annular ellipse aperture

We theoretically and experimentally investigate the Fraunhofer diffraction pattern of a vortex beam passing through an annular ellipse aperture. It is found that the pattern of the far-field diffraction intensity distribution exhibits some dark spots, which become clearer with increasing the value of the ellipticity factor of the annular ellipse aperture. The diffraction phenomenon is more obvious with increasing the value of the ratio of the inner long axis (or short axis) to the outer side of the annular ellipse aperture. The number of the dark spots in the Fraunhofer diffraction intensity distribution is just equal to the topological charge value of the measured optical vortex, and the centre of each dark spot is just a phase-singularity point. Based on this property, we can measure the topological charge of an optical vortex beam.

Measurement of Fractional Optical Vortex by a Ring-Type Multi-Pinhole Interferometer

We presented a method for measuring the topological charge of a Fractional optical vortex (FOV) by a ring-type multi-pinhole interferometer (RMPI). We retrieved the sampled phase of the FOV passing through a ring-type multi-pinhole plate from the Fourier transform of a single far-field diffraction intensity pattern, and found the phase of FOV around the center approximately be linear with the azimuthal angle, the slope of the phase to the azimuthal angle at the linear part is equal to the topological charge of the FOV. Thus we proposed a method for measuring the l state and determining orbital angular momentum (OAM) of a FOV based on the property.

Propagation uniqueness in three-dimensional coherent diffractive imaging

Propagation nonuniqueness in three-dimensional (3D) coherent diffractive imaging (CDI) arises from the fact that an ensemble of solutions, related by propagation, gives an identical far-field diffraction intensity. Tight support constraint and tight allowed phase range behave similarly in constraining the solution of phase retrieval process, thus removing this nonuniqueness in simple cases but not for strong-phase objects. For CDI in Bragg geometry, we introduce a two-step phasing procedure for reconstructing heavily-strained samples that balances the need to define both support and phase constraints.

Detecting the topological charge of vortex beams using an annular triangle aperture

The Fraunhofer diffraction pattern of a vortex beam by an annular triangle aperture is analyzed theoretically and experimentally. It is found that the pattern of the far-field diffraction intensity distribution exhibits a triangular lattice array, which becomes much clearer with the increase of the ratio of the inner to the outer side of the annular triangle aperture. The number of spot points of any external side of the triangular lattice array minus one is just equal to the topological charge value of the measured optical vortex. For the vortex beam with negative topological charge, the triangular diffraction pattern after the annular triangle aperture will be rotated by 180° in relation to the case of the positive topological charge. Based on the above properties, we propose a simple and feasible method to determine the magnitude and sign of the topological charge of an optical vortex beam.

Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array

We propose a new method for phase retrieval and coherent diffraction imaging by a specially designed pinhole sampling array (PSA) based on a liquid crystal spatial light modulation. We demonstrate that the phase and the amplitude of the wave front passing through a pinhole sampling array plate can be directly extracted from the inverse Fourier transform of the far-field diffraction intensity pattern. Scanning the whole surface of the wave front by such a series of the PSA plates, we can assemble the extracted complex amplitude to a two-dimensional discrete distribution of the sampled wave front covering the entire PSA plate plane in the scanning consequence. We called it linear scanning pinhole sampling array (LSPSA). Thus the wave front can be reconstructed which avoids any iterative algorithms. Furthermore, it provides a feasible approach for lensless coherent diffraction imaging in real-time.

Holographic x-ray image reconstruction through the application of differential and integral operators

We introduce a noniterative image-reconstruction technique for coherent diffractive imaging. Through the application of differential and integral operators, an extended reference can be used to recover the complex-valued transmissivity of an object, in closed form, from a measurement of its far-field (Fraunhofer) diffraction intensity. We demonstrate the feasibility of this approach, using a reference of a pair of crossed wires and slits, through numerical simulations and a soft x-ray coherent diffractive imaging experiment.

Characterizing topological charge of optical vortices by using an annular aperture

We explore the spatial frequency property of the far-field diffraction intensity pattern of an optical vortex after passing through an annular aperture in detail. The result reveals that the spatial spectrum consists of alternate bright and dark rings and, in particular, the number of the bright rings is nicely identical to the absolute value of the topological charge. Based on this property, we present and demonstrate a simple technique to characterize the topological charge of an optical vortex through its diffraction intensity pattern after an annular aperture.

Tri-arm multipinhole interferometer for wavefront measurement and diffractive imaging

We propose a tri-arm (or Y-shaped) multipinhole (MP) interferometer for wavefront measurement based on a specially designed tri-arm MP plate. We demonstrate that the complex amplitude of a wavefront sampled by the tri-arm MP plate inserted between the object and the detector plane can be extracted directly from the Fourier transform of a far-field diffraction intensity pattern without the need for any iterative algorithm. A form of coherent diffractive imaging based on a rotatable tri-arm MP plate is also demonstrated, which provides a feasible approach for lensless diffractive imaging in real time.

Diffractive imaging based on a multipinhole plate

We report on a noniterative method for coherent diffractive imaging based on a specially designed multipinhole (MP) plate. We demonstrated that the complex amplitude of the wavefront penetrating through an MP plate inserted between the specimen and the detector plane can be directly extracted from the Fourier transform of a single far-field diffraction intensity pattern without need of any iterative algorithm. A form of scanning diffractive imaging based on a rotatable MP plate is also demonstrated, which provides a feasible approach for lensless diffractive imaging of complex-valued objects.