Fresnel Diffraction Research Articles

Effects of Hollow–Gaussian beams on Fresnel diffraction by an opaque disk

Effects of Hollow–Gaussian beams on Fresnel diffraction by an opaque disk

Diffraction of Gaussian and Laguerre-Gauss beams from a circular aperture using the moment expansion method.

A method based on the distribution theory is introduced to compute the Fresnel diffraction integral. It is applied to the diffraction of Gaussian and Laguerre-Gauss beams by a circular aperture. Expressions of the diffracting field are recast into a perturbation series describing the near- and far-field regions.

Double Laguerre-Gaussian beams

We show here that the product of two Laguerre-Gaussian (LG) beams, i.e. double LG beams (dLG), can be represented as finite superposition of conventional LG beams with certain coeffi-cients that are expressed via zero-argument Jacobi polynomials. This allows obtaining an explicit expression for the complex amplitude of the dLG beams in the Fresnel diffraction zone. Generally, such beams do not retain their structure, changing shape upon free-space propagation. However, if both LG beams are of the same order, we obtain a special case of a "squared" LG beam, which is Fourier-invariant. Another special case of the dLG beams is obtained when the azimuthal indices of the Laguerre polynomials are equal to n – m and n + m. For such a beam, an explicit expression is obtained for the complex amplitude in the Fourier plane. We show that if the lower indices of the constituent LG beams are the same, such a double LG beam is also Fourier-invariant. Similar to conventional LG beams, the product of LG beams can be used for optical data transmission, since they are characterized by azimuthal orthogonality and carry an orbital angular momentum equal to the topological charge.

Modeling and measurement of human body blockage loss at 28 GHz

ABSTRACT Millimeter-wave (mm-Wave) spectrum is an essential enabler to the fifth generation (5G) wireless technology. Humans are one of the most noticeable blockers that cause temporal variation in indoor radio channels. This paper presents human blockage measurements at 28 GHz, with several humans of different sizes. The effect of the crossing orientations of the human bodies is investigated for three different transmitter heights. A human blockage model based on the Fresnel diffraction scheme is shown to be applicable in estimating the human blockage loss in indoor radio links considering various body sizes, different crossing orientations, and different transmitter heights. The findings reported in this paper could help improve indoor radio channel models at 28 GHz bands for 5G technologies considering the presence of human body blockages.

Fresnel Diffraction Strategy Enables the Fabrication of Flexible Superomniphobic Surfaces.

Doubly re-entrant surfaces inspired by springtails exhibit excellent repellency to low-surface-tension liquid. However, the flexible doubly re-entrant surfaces are difficult to fabricate, especially for the overhang of the structure. Herein, we demonstrate a simple Fresnel aperture diffraction modulation strategy in microscale lithography coupled with a molding process to obtain the flexible doubly re-entrant superomniphobic surfaces with nanoscale overhangs. The negative nanoscale overhang features were formed in a single-layer photoresist due to the fine-modulation of the optical intensity fluctuation of the Fresnel aperture diffraction. The as-prepared flexible non-fluorinated polydimethylsiloxane (PDMS) doubly re-entrant microstructure based on the Fresnel aperture diffraction (D-BF) surface (without any additional treatments) could repel ethanol droplets (21.8 mN m-1) in the Cassie-Baxter state. The robust nanoscale overhangs obtained by the molding process enable the maximum breakthrough pressure for the low-surface-tension ethanol droplets on the D-BF surfaces up to about 230 Pa, allowing ethanol liquids with Weber numbers up to 8.7 to fully bounce off. The fabricated non-fluorinated D-BF superomniphobic surface maintains outstanding liquid repellency after the surface wettability modification and deformation test.

Measurements and Models of 915 MHz LoRa Radio Propagation in an Underground Gold Mine.

Underground mining increasingly relies on wireless communications for its operations. The move to automating many underground mining processes makes an understanding of the propagation characteristics of key wireless technologies underground a topic of considerable importance. LoRa has great potential for communications in underground mines, but data on its propagation are quite scarce. In this paper, we describe our measurements of LoRa radio propagation in an underground gold mine. We took measurements in an extraction tunnel with line of sight and in extraction and access tunnels without line of sight. We observed excellent propagation, both with and without line of sight. Our observations support claims by others that the steel-lined tunnels act as a waveguide. As well as reporting measurements, we also developed models of propagation. For line of sight, we show that pathloss is well modelled by a power law with pathloss index of 1.25 and that variability of signal strength is well modelled by a lognormal distribution. We also successfully modelled propagation without line of sight over short distances using a Fresnel Diffraction and Free Space model.

Semi-analytic simulation of optical wave propagation through turbulence.

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semianalytic approach to evaluating the Fresnel diffraction integral with onephase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen's transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semianalytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semianalytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semianalytic method can compute faster than the angular-spectrum method.

The colibri telescope array for KBO detection through serendipitous stellar occultations: A technical description

We present the technical design, construction and testing of the Colibri telescope array at Elginfield Observatory near London, Ontario, Canada. Three 50-cm telescopes are arranged in a triangular array and are separated by 110–160 m. During operation, they will monitor field stars at the intersections of the ecliptic and galactic plane for serendipitous stellar occultations (SSOs) by trans-Neptunian objects (TNOs). At a frame rate of 40 frames per second (fps), Fresnel diffraction in the occultation light curve can be resolved and, with coincident detections, be used to estimate basic properties of the occulting object. Using off-the-shelf components, the Colibri system streams imagery to disk at a rate of 1.5 GB/s for next-day processing by a custom occultation detection pipeline.The imaging system has been tested and is found to perform well, given the moderate site conditions. Limiting magnitudes at 40 fps are found to be about 12.1 (temporal SNR = 5, visible light Gaia G band) with time-series standard deviations ranging from about 0.035 mag to >0.2 mag. SNR is observed to decrease linearly with magnitude for stars fainter than about G = 9.5 mag. Brighter than this limit, SNR is constant, suggesting that atmospheric scintillation is the dominant noise source. Astrometric solutions show errors typically less than ±0.3 pixels (0.8 arc seconds) without a need for high-order corrections.

Nonlinear primal-dual algorithm for the phase and absorption retrieval from a single phase contrast image.

We propose a nonlinear primal-dual algorithm for the retrieval of phase shift and absorption from a single x ray in-line phase contrast, or Fresnel diffraction, image. The algorithm permits us to regularize phase and absorption separately. We demonstrate that taking into account the nonlinearity in the reconstruction improves reconstruction compared with linear methods. We also demonstrate that choosing different regularizers for absorption and phase can improve the reconstructions. The use of the total variation and its generalization in a primal-dual approach allows us to exploit the sparsity of the investigated sample. On both simulated and real datasets, the proposed nonlinear primal-dual hybrid gradient (NL-PDHG) method yields reconstructions with considerably fewer artifacts and improved the normalized mean squared error compared with its linearized version.

Single-shot quantitative phase imaging with phase modulation of a liquid crystal spatial light modulator (LC-SLM) under white light illumination.

We propose a novel, to the best of our knowledge, single-shot quantitative phase imaging (QPI) technique with the phase modulation of a liquid crystal spatial light modulator (LC-SLM) under white light illumination. By studying the phase modulation characteristics of an LC-SLM under white light illumination, images captured at different wavelengths are equivalent to those captured at different defocus distances when loading a Fresnel lens pattern on the LC-SLM. Consequently, a color camera is able to simultaneously acquire multi-intensity images at different defocus distances. Finally, the phase is retrieved from a single-shot color image using the transport of intensity equation. To demonstrate the flexibility and accuracy of our method, a photoetched phase object and human red blood cells are quantitatively measured. An investigation of living yeast cells is conducted to verify the dynamic measurement capability. The proposed method provides a simple, efficient, and flexible means to accomplish real-time high-resolution quantitative phase imaging without sacrificing the field of view (FOV), which can be further integrated into a conventional microscope to achieve real-time microscopic QPI.

A Fast and High-precision Alignment Method for IFU Based on Optical Interferometry and Fresnel Diffraction

High-precision alignment between the microlens array and the fiber-positioning microplate is of great significance in developing fiber-based integrated field units (IFU). In this paper, we propose a method combining optical interference and a Fresnel diffraction model to realize fast and accurate alignment. The minimum resolution angles of the tip and tilt in the optical interference-assisted alignment experiment are 2.6 × 10−4° and 1.3 × 10−4°, respectively. The errors in the remaining four degrees of freedom, x, y, z, and roll, are simulated by the Fresnel diffraction model. Finally, the output energy of 96.7% of the number of fibers is within a tolerance error of 10% and the relative energy reaches its highest level, which meets the IFU requirement.

Fresnel zone plate point spread function approximation for zeroth order mitigation in millimetric field of view x-ray imaging.

High spatial and temporal resolution x-ray radiography images are required at the National Ignition Facility (NIF) for high-energy density experiments. One technique that is in development to achieve the required resolution uses Fresnel zone plate (FZP) optics to image an object that is backlit by an x-ray source. The multiple FZP diffraction orders do not focus on the same plane, which increases the background and reduces the contrast. Understanding the point spread function of the different diffraction orders will allow the prediction of the expected background using simulations. We find that the two-dimensional point spread function of the FZP can be approximated by the addition of a sharp Gaussian with a disk. This allowed for the estimation of the background in NIF experimental images of Rayleigh-Taylor spikes and their interpretation. An alternative design of FZP is discussed to allow the inclusion of a zeroth order blocker to reduce the background.

Analytical solution for a focused vortex beam radiated by a Gaussian source

Current interest in focused vortex beams is motivated by the ability to trap particles axially and laterally using the resulting radiation force. A simple closed-form solution is obtained in the Fresnel approximation for a sound beam radiated by a Gaussian source with time dependence e−iωt, focal length d, amplitude distribution exp(−r2/a2), and azimuthal phase dependence einθ, where θ is the angle in the plane perpendicular to the beam axis, and the integer n is the topological charge, referred to here as the vorticity. The solution is in good agreement with the pressure field predicted in the paraxial region by numerical evaluation of the Rayleigh integral. Of interest in optics as well as acoustics is the distance from the minimum along the beam axis to the first local maximum, referred to as the vortex ring. The present solution yields rn = ηnd/ka for the vortex ring radius in the focal plane, where k is the wavenumber, and ηn = 1.69 + 0.965(n−1) for vorticities in the range 1 ≤ n < O(20). Within this range the radius rn thus increases linearly with the vorticity. Results are also presented for dependence of the focusing gain on the vorticity. [CAG was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Fresnel diffraction at circular cylinders

Fresnel diffraction is a fundamental wave phenomenon happening near the shadow boundary behind a large opaque object. Previously, it was studied for the case of diffraction at large apertures in a black screen. In this paper, we investigate this phenomenon for perfectly conducting cylinders with large cross-sections. First, this theory is developed for the circular cylinders, then extended to the cylinders of arbitrary shape. It is shown that Fresnel diffraction can be interpreted as interference of the shadow radiation with the incident wave. Analytical equations and numerical data are provided and discussed in detail.

Analysis on the characteristics of vortex beam in field turbulence

In this study, we have investigated the propagation characteristics of single-mode Laguerre–Gaussian (LG) beams under field atmospheric turbulence conditions. We constructed a 1200 meter experimental platform for representing vortex beams in the field. Accordingly, we analyzed the spot changes in an LG beam after transmitted through atmospheric turbulence. Based on the principle of Fresnel diffraction and the random phase screen method, we studied the evolution and spiral spectrum distribution of low-order LG beams transmitted by atmospheric turbulence by numerical simulation. Moreover, we carried out an experimental study regarding the LG beam propagation characteristics mainly based on field experiments. The experimental results indicate that after near-surface turbulent propagation, the LG beam gradually spreads, degree of phase singularity drift becomes larger, and spot size of the Gaussian beam grows faster than that of the LG beam with greater propagation distances. Finally, we concluded that LG beams are not significantly affected by turbulence. It also lays a foundation for the experimental study of vortex beam detection and wavefront correction at the receiving end in multiplexing communication.

New type of vortex laser beams: Squared Laguerre-Gaussian beam

In this paper, we present new type of optical vortex called the squared Laguerre-Gaussian (LG)2 vortex beam. It is theoretically, numerically, and experimentally proved that these beams are Fourier-invariant and retain their structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into a superposition of conventional LG beams, the number of which is equal to the number of rings in the (LG)2 beam. The presented beams are structurally stable in the case of one intensity ring. A more general beam, calculated as a “product” of two LG beams, is also investigated. This beam is Fourier-invariant if the numbers of rings in two LG beams of the “product” coincide to each other. The considered beams supplement the basis of LG modes.

Diffraction enhanced imaging utilizing a laser produced x-ray source.

Image formation by Fresnel diffraction utilizes both absorption and phase-contrast to measure electron density profiles. The low spatial and spectral coherence requirements allow the technique to be performed with a laser-produced x-ray source coupled with a narrow slit. This makes it an excellent candidate for probing interfaces between materials at extreme conditions, which can only be generated at large-scale laser or pulsed power facilities. Here, we present the results from a proof-of-principle experiment demonstrating an effective ∼2 μm laser-generated source at the OMEGA Laser Facility. This was achieved using slits of 1 ×30μm2 and 2 ×40μm2 geometry, which were milled into 30 μm thick Ta plates. Combining these slits with a vanadium He-like 5.2keV source created a 1D imaging system capable of micrometer-scale resolution. The principal obstacles to achieving an effective 1 μm source are the slit tilt and taper-where the use of a tapered slit is necessary to increase the alignment tolerance. We demonstrate an effective source size by imaging a 2 ± 0.2 μm radius tungsten wire.

Deep Machine Learning for Acoustic Inspection of Metallic Medium

Acoustic non-destructive testing is widely used to detect signs of damage. However, an experienced technician is typically responsible for interpreting the result, and often the evaluation varies depending on the technician’s opinion. The evaluation is especially challenging when the acoustic signal is analyzed in the near field as Fresnel range diffraction complicates the data. In this study, we propose a Convolutional Neural Network (CNN) algorithm to detect anomalies bearing in mind its future application to micro-scale specimens such as biomedical materials. Data are generated by emitting a continuous sound wave at a single frequency through a metal specimen with a sub-millimeter anomaly and collecting the transmitted signal at several lateral locations on the opposite side (the observation plane) of the specimen. The distance between the anomaly and the observation plane falls in the quasi Fresnel diffraction regime. The use of transmitted signals is essential to evaluate the phase shift due to the anomaly, which contains information about the substance in the anomaly. We have developed a seven-layered CNN to analyze the acoustic signal in the frequency domain. The CNN takes spectrograms representing the change in the amplitude and phase of the Fourier transform over the lateral position on the observation plane as input and classifies the anomaly into nine classes in association with the lateral location of the anomaly relative to the probing signal and the material of the anomaly. The CNN performed excellently demonstrating the validation accuracy as high as 99.9%. This result clearly demonstrates CNN’s ability to extract features in the input signal that are undetectable to humans.

Enlarging the FOV of lensless holographic retinal projection display with two-step Fresnel diffraction

The field of view (FOV) of holographic retinal projection display (RPD) is always restricted by the diffraction angle of a spatial light modulator (SLM). In this paper, we demonstrate a large FOV holographic RPD by using two-step Fresnel diffraction calculation. By adding the pupil plane as the intermediate plane and decreasing the sampling interval, the FOV can be enlarged to nearly two times of the diffraction angle limit without any physical change. Due to the added spherical wave phase, the influence of aliasing is eliminated because the adjacent orders are projected to different viewpoints. The nonuniform image intensity caused by the sinc function modulation is compensated by image pre-processing. Optical experiments verify that the proposed method can present a uniform holographic near-eye display with a large FOV and adjustable viewpoint position.

Modeling and verification of astigmatic digital off-axis holography for burning droplet measurement in a flame tube

It is difficult to measure fuel droplets in cylindrical combustors under combustion conditions, but of significance, since fuel behavior is related to combustion performance. In this study, digital off-axis holography and corresponding data treating algorithms are applied to quantify irregular spray droplets in combustion field inside a thick silica flame tube. The analytical expression of an off-axis hologram passing through a pipe is derived based on optic matrix theory and Fresnel diffraction transform. The interference fringes and phase distribution show consistency with the experimental results under the same condition. A modified convolution reconstruction method facing off-axis holography is proposed to locate and quantify the particles in a pipe. The theoretical simulation and experimental results indicate that the proposed method can obtain a clear reconstructed droplet. The image field of view does not change with the reconstruction distance. The particle field obtained through this method has distortion due to the refraction of the curved surface, and can be corrected through ABCD transfer matrix. The calibration method and modified results reveal that the overall droplet size error is lower than 1-pixel width, and real x and y locating errors after correction are lower than 1-pixel width. The depth position error is also discussed through experimental validation. The visualization and quantification results of fuel droplets in the real turbulent spray flame in a circular flame tube prove the feasibility of the proposed theoretical analysis and the reconstruction method.