Fraunhofer Diffraction Research Articles

Tunable telephoto: governable Fourier spectrum anamorphic scaling

We discuss the Gaussian design of a device that controls the scale, in an anamorphic fashion, of Fraunhofer diffraction patterns. The device uses two pairs of varifocal cylindrical lenses. For spherical lenses, the optical powers can be predicted by using a previously known high-level solution. We emphasize the anamorphic capabilities, by considering the case My = 1/ Mx. The proposed device does not introduce vignetting, and it does not alter the axial location of the Fraunhofer diffraction patterns. Since the composing elements work at fixed inter-lens separation, the device does not require mechanical compensation.

Photon wave-mechanical theory of single-photon diffraction from a mesoscopic hole

A quantum electrodynamical theory for single-photon diffraction of light from a mesoscopic hole in a quantum well (QW) screen with (Schrödinger) electron dynamics is established. Photon wave mechanics (PWM) is used to extend and bridge the gap between hitherto used semiclassical and quantum optical theoretical approaches for analyses of diffraction of light. An essentially complete calculation is carried out for a paradigm example: (i) a single-photon point-like electric-dipole (ED) primary source, emitting (ii) a wave packet photon toward (iii) a two-level QW screen possessing (iv) in-plane jellium electrodynamics with (v) a single mesoscopic ED hole. The PWM description is based on the, in this context attractive, Riemann–Silberstein–Oppenheimer–Bialynicki formulation. The effective size of the hole is determined on the basis of a quantum mechanical extinction theorem for the in-plane jellium electron dynamics in the vicinity of the hole. The incident electrodynamic field induced current density in the screen (with hole) allows one to obtain the single-photon probabilities for scattering from the hole and the screen. A one-photon wave train emitted by the primary ED point-like source is assumed to drive the scattering process. The far-field hole-screen diffraction pattern is calculated paying particular attention to the spectral diffraction (correlation) pattern, which illustrates the interplay between the wave-train frequency, the screen/hole local-field resonance frequency, and the Bohr frequency. Our theory shows that the ED hole polarizability is close to that of a one-dimensional single harmonic oscillator with resonance frequency coinciding with the local-field resonance in the two-level QW screen.

Three-state lithography model: an enhanced mathematical approach to predict resist characteristics in grayscale lithography processes

Background: Physical modeling of grayscale lithography processes for the prediction of photoresist heights leads to complex mathematical algorithms. A promiment example is the numerical simulation of the photoresist shape after development through Dill’s equations. These grayscale lithography models exhibit accurate prediction quality but can not directly implemented into mask layout tools to simplify the layout procedure. Limited process windows, changes in the mask design, variations of the used materials or manufacturing tools lead to time-consuming and cost-intensive test procedures to adjust the photoresist model for sufficient results. Aim: The focus of this work is to enhance current grayscale lithography models for a straightforward method with the same precise prediction of remaining photoresist heights to simplify the mask layout process. Moreover, we aim for an uncomplicated optimization of the model to minimize the empirical analysis necessary for its use. Approach: Based on experimental results, we deploy a sectionally defined mathematical expression that includes the theory of Fraunhofer diffraction and illumination-dependent activation of the photo-sensitive component and its solubility in developer. Results: We produced pyramidal, spherical and chess field structures with exposure doses of 3000 and 15 , 000 J / m2 on bare silicon substrates with 100-nm resolution and on silicon substrates with anti-reflective coatings, with accuracy as fine as 20 nm. Conclusion: The proposed three-state lithography model has been verified by experimental evaluation. It is able to operate in a wide process window and can be directly implemented in existing mask layout software. This model ensures a cost-efficient and precisely controlled production of three-dimensional topographies using grayscale lithography processes.

Comparing multifractal characteristics of soil particle size distributions calculated by Mie and Fraunhofer models from laser diffraction measurements

Particle size distribution (PSD) is a basic soil property, closely related to main soil physical and chemical attributes. Soil PSD determined by laser diffraction (LD) may provide additional information to soil texture determined by traditional methods. In turn, LD may be implemented using either Mie or Fraunhofer calculation methods, based on different assumptions. The multifractal approach has been demonstrated to be useful for characterizing the inner structure of soil PSD. We analysed the PSDs of 18 soil horizons sampled on the most characteristic soil types from Argentina with a wide range of textural classes, from clayey to sandy, mainly developed over loess material. Our aims were to assess the multifractality between PSDs computed using either Mie scattering or Fraunhofer diffraction models, and to compare the scaling properties and multifractal behavior of PSDs from soils with contrasting textures. Fraunhofer model provided PSD curves, which were shifted toward coarser particles compared to those obtained with Mie model. Regardless calculation method, all the PSDs studied displayed a well-defined multifractal structure, as shown by singularity, f(α) versus α, and by Rènyi spectra, Dqvs q. Moreover, all singularity spectra were strong asymmetric, right deviating curves, which is consistent with a greater heterogeneity of the low values of volume frequencies for all the PSDs analysed. Soil PSDs computed by Fraunhofer model showed higher asymmetry than those computed by Mie model for 16 out of 18 horizons studied; this suggests that scaling heterogeneity mainly depends on the support length, which is larger for the PSDs computed by Mie. In addition, other features of the PSDs stemming from soil processes such as weathering intensity of loess materials may also influence multifractality. Stronger correlations were found between multifractal parameters from PSDs calculated by the two models for the most positive q moments of singularity and Renyi spectra, i.e. α10, D10, than for those gathered from the central and negative q moments. The entropy dimension, D1, significantly (P<0.05) increased with increasing clay content, in contrast to previous findings; this may be due either to differences in the inner structure of various PSD data sets compared, or to shortcomings of standard PSD measurement and calculation procedures.

Single-frame coherent diffraction imaging of extended objects using triangular aperture.

We propose a method of single-frame coherent diffraction imaging using a triangular aperture, which can not only reconstruct the projection image of extended objects from a single-frame coherent diffraction pattern, but also improve the image of the wavefield of the probe. In this method, a plane-wave illuminates a triangular aperture. An object is placed immediately after the aperture or in the image plane of the aperture through a lens. A far-field coherent diffraction pattern is collected by a two-dimensional detector. The object image is reconstructed from the single-frame diffraction pattern using a phase retrieval algorithm without support constraints. We simulate feasible experimental setups in the hard X-ray regime and show that this method can be practical use for single-frame coherent diffraction imaging. The present method has the potential exploring dynamic phenomena in materials science and biology with high spatiotemporal resolution using synchrotron radiation/free-electron lasers.

Adjustment on the received optical power of a ground-based optical instrument by a corner cube retroreflector with a curved front-face.

The dihedral angle errors (DAEs) and flatness errors of a nonideal corner cube retroreflector (CCR) determine a ground-based optical instrument's received optical power. The smaller tolerance of the dihedral angle with lower divergence is theoretically beneficial to improving the received optical power but could increase the difficulty in the fabrication and bring about a higher manufacturing cost. We propose a new method that is just dependent on the curvature radius of the front-face (CROF) of the CCR to compensate for the divergence of the output beam from the CCR caused by the DAEs. We build up a mathematical model of the received optical power based on the far-field diffraction pattern (FFDP) of the CCR and the layout of the optical instrument and investigate the effects of the DAEs and the CROF on the FFDP and the received optical power for both the coated and uncoated CCRs. Meanwhile, we present a fitting equation between the compensative CROF and the DAEs based on the principle of maximizing the received optical power. The results demonstrate that the compensative CROF has no dependence on whether the reflecting-faces of the CCR are coated or not and is inversely proportional to the absolute value of DAEs. The received optical power is promptly enhanced by utilizing the compensative CROF. Therefore, it is more feasible to improve the received optical power of the ground-based optical instrument by manipulating the CROF of the CCR rather than the DAEs.

Far-field diffraction pattern of cube corner retroreflector at oblique incidence

&lt;sec&gt;Corner cube retroreflector (CCR) as a main optical component of laser ranging retroreflector array plays a key role in satellite laser ranging (SLR) to cooperative targets. To accurately estimate the echo energy of SLR, it is necessary to precompute photons’ distribution in the distance of SLR station by calculating the Far field diffraction pattern (FFDP) of CCR under various conditions. In this paper, the analysis of the effective reflection area and optical reflectivity of CCR for arbitrary incidence angle are carried out, in which a method to calculate the CCR effective reflection area with a wider applicability is used, and the difference between optical reflectivity of metal-coated CCR and uncoated (total internal reflection) CCR is also discussed. On this basis, combined with optical diffraction theory, a simulation program for CCR FFDP calculation is established, thereby producing FFDPs of CCR for a variety of incidence angles under different coating conditions. The results show that the FFDP of metal-coated CCR is almost unrelated to the azimuth angle of incident light or polarization, but is determined only by elevation angle of incident light. The pattern is always like Airy spot or its tensile deformation. Relatively, uncoated CCR’s FFDP has a more complex figure, its reflected energy is divided into several lobes whose size, number and position are all influenced by elevation and azimuth angle of incidence, and also by the polarization. Generally, the incidence direction which has a large total intensity of far optical field is to an extent the same as that of large effective reflection area and optical reflectivity. Furthermore, simulation results with uncoated CCR presents a higher relevance of incidence direction and FFDP.&lt;/sec&gt;&lt;sec&gt;To verify the reliability and correctness of these simulation results, a diffraction optical experimental system at a wavelength of 1550 nm is set up to conduct laboratory confirmation, including laser, camera, beam expander, rotating platform and other essential optics. A silver-coated CCR and an uncoated CCR (both made of fuse silica, each has different dihedral angle offset) are chosen to measure their FFDPs with random polarization directions at several random incidence angles. All the measurement results are in good agreement with the simulations of FFDPs.&lt;/sec&gt;

Investigating the Effect of the Consciousness Fields on the Behavior of Laser Light in Passing through an Aperture and Heisenberg Uncertainty Principle Observation

Investigating the behavior of light in the vicinity of an aperture and observing Heisenberg’s uncertainty is a classic experiment in optics. Studies of Consciousness Fields according to Taheri include the study of different fields of physics in the systems under study. In these studies, by applying a Consciousness Field to the system under study, one observes changes in the behavior of the system as a function of the field. The present study performed with two aims: (a) Investigation of the effect of Consciousness Fields on the pattern of laser light diffraction through an aperture (in Fraunhofer diffraction patterns). (b) Investigation of the effect of Consciousness Fields on the behavior of light and observation of the Heisenberg's uncertainty principle in these conditions. In the present study, applying Consciousness Fields to the laser light independent from the set-up experiment did not affect the light behavior. On the other hand, applying Consciousness Fields to the set-up of light-passing test through an aperture has a significant effect on the light behavior in passing through the aperture. In such a way that the uncertainty and diffraction width in the state of treatment with the Consciousness Field is reduced compared to the control. This behavior is interpreted as reducing the effect of the observer in optics studies, where the aperture has been considered to be equivalent to an observer. In other words, this change in light behavior as a result of applying the Consciousness Field can be considered as a process of direct observation (without intermediaries) of the system under study using the Consciousness Field. The result of this study indicates the high potential of the impact of Consciousness Fields on the known laws of physics, as an innovative tool in the world of science.

The influence of the load’s geometrical characteristics on the generation of the electro-thermo-mechanical instability in a single wire Z-pinch

The Z-pinch plasma device is a type of plasma confinement system that uses electrical current to generate a magnetic field which compresses a current-carrying wire. In a previous proof-of-principle study, we demonstrated that in the interaction of a single wire with a pulsed current, the generated Electro-Thermo-Mechanical (ETM) instability in the solid phase acts as a seeding mechanism for the later developed instabilities observed in the plasma phase. In this study, the influence of the geometrical characteristics, such as length and thickness of the load-wire, on the generation of the ETM instability are investigated. Finite element multiphysics-multiphase simulations starting from the solid state are coupled with Magneto-Hydro-Dynamics (MHD) simulations to study the solid to plasma phase transition and the matter’s dynamics. The numerical results of the wire expansion dynamics prior to plasma formation are validated by experimental results from a modified Fraunhofer diffraction diagnostic, while in the plasma phase the simulated plasma dynamics is validated by shadowgraphic and interferometric experimental results. The numerical and experimental results demonstrate a satisfactory agreement for the wire expansion dynamics and the growth rate of the developed instabilities, for varying wire thickness and length.

The Role of Thermal Accumulation on the Fabrication of Diffraction Gratings in Ophthalmic PHEMA by Ultrashort Laser Direct Writing.

The fabrication of diffraction gratings by ultrashort direct laser writing in poly-hydroxyethyl-methacrylate (PHEMA) polymers used as soft contact lenses is reported. Diffraction gratings were inscribed by focusing laser radiation 100 µm underneath the surface of the samples. Low- and high-repetition rate Ti:sapphire lasers with 120 fs pulsewidth working at 1 kHz and 80 MHz respectively were used to assess the role of thermal accumulation on microstructural and optical characteristics. Periodic patterns were produced for different values of repetition rate, pulse energy, laser wavelength, distance between tracks, and scanning speed. Compositional and structural modifications of the processed areas were studied by micro-Raman spectroscopy showing that under certain parameters, thermal accumulation may result in local densification. Far-field diffraction patterns were recorded for the produced gratings to assess the refractive index change induced in the processed areas.

Study on optical hierarchical sorting of particles based on the Fraunhofer diffraction field of spiral phase plate array

Optical hierarchical sorting has attracted significant attention in recent years. The existing approaches use either complex numerical calculation or computer-aided experimental tools for optical hierarchical sorting. We proposed a method to perform hierarchical sorting, which is computationally simple and does not need computer aid. In particular, we employed a focused optical vortices array (FOVA), which is generated and focused by a spiral phase plate array (SPPA) and a microlens array, respectively. We designed different heights for the spiral phase plate in different columns of the SPPA. This enabled different columns of the FOVA to carry different topological charges and consequently possess different capture capabilities. To realize hierarchical sorting, we exploited the properties of FOVA by deploying it in a microfluidic chamber containing particles of various sizes. The four columns of the FOVA formed four corresponding capture regions in the flow area of the particles. From our theoretical analysis and numerical results, we observed that particle sizes in the range of 1 to 582 nm could be sorted. Our approach provides a theoretical framework that can be readily employed in experiments for optical hierarchical sorting.

Single-frame far-field diffractive imaging with randomized illumination.

We introduce a single-frame diffractive imaging method called randomized probe imaging (RPI). In RPI, a sample is illuminated by a structured probe field containing speckles smaller than the sample's typical feature size. Quantitative amplitude and phase images are then reconstructed from the resulting far-field diffraction pattern. The experimental geometry of RPI is straightforward to implement, requires no near-field optics, and is applicable to extended samples. When the resulting data are analyzed with a complimentary algorithm, reliable reconstructions which are robust to missing data are achieved. To realize these benefits, a resolution limit associated with the numerical aperture of the probe-forming optics is imposed. RPI therefore offers an attractive modality for quantitative X-ray phase imaging when temporal resolution and reliability are critical but spatial resolution in the tens of nanometers is sufficient. We discuss the method, introduce a reconstruction algorithm, and present two proof-of-concept experiments: one using visible light, and one using soft X-rays.

Position measurement-induced collapse states and boundary bound diffraction: an idealised experiment

In an earlier work, it was shown that single-slit diffraction of matter waves can be considered as position measurement of particles and that the Fresnel and Fraunhofer diffraction patterns result from the time evolution of the same collapsed quantum wave function. This quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the ‘position measurement-induced collapse’ (PMIC) states. In the present work, an idealised experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd’s mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called ‘quantum carpets’, first discovered by Berry. The PMIC formalism in this case closely follows the ‘boundary bound diffraction’ analysed in a previous work by Tounli, Alverado and Sanz. In addition to having obtained their results, we have identified that the Fresnel and Fraunhofer patterns are indeed present here. It is anticipated that the verification of fractal and nonfractal features of the wave function at various times and also the predicted revival distances to the screen by this experiment will help to better understand ‘quantum collapse’.

Sublethal Supraphysiological Shear Stress Alters Erythrocyte Dynamics in Subsequent Low-Shear Flows

Blood is a non-Newtonian, shear-thinning fluid owing to the physical properties and behaviors of red blood cells (RBCs). Under increased shear flow, pre-existing clusters of cells disaggregate, orientate with flow, and deform. These essential processes enhance fluidity of blood, although accumulating evidence suggests that sublethal blood trauma—induced by supraphysiological shear exposure—paradoxically increases the deformability of RBCs when examined under low-shear conditions, despite obvious decrement of cellular deformation at moderate-to-higher shear stresses. Some propose that rather than actual enhancement of cell mechanics, these observations are “pseudoimprovements” and possibly reflect altered flow and/or cell orientation, leading to methodological artifacts, although direct evidence is lacking. This study thus sought to explore RBC mechanical responses in shear flow using purpose-built laser diffractometry in tandem with direct optical visualization to address this problem. Freshly collected RBCs were exposed to a mechanical stimulus known to drastically alter cell deformability (i.e., prior shear exposure (PSE) to 100 Pa × 300 s). Samples were subsequently transferred to a custom-built slit-flow chamber that combined laser diffractometry with direct cell visualization. Cell suspensions were sheared in a stepwise manner (between 0.3 and 5.0 Pa), with each step being maintained for 15 s. Deformability and cell orientation indices were recorded for small-scatter Fraunhofer diffraction patterns and also visualized RBCs. PSE RBCs had significantly decreased visualized and laser-derived deformability at any given shear stress ≥1 Pa. Novel, to our knowledge, observations demonstrated that PSE RBCs had increased heterogeneity of direct visualized orientation with flow vector at any shear, which may be due to greater vorticity and thus instability in 5-Pa flow compared with unsheared control. These findings indicate that shear exposure and stress-strain history can alter subsequent RBC behavior in physiologically relevant low-shear flows. These findings may yield insight into microvascular disorders in recipients of mechanical circulatory support and individuals with hematological diseases that alter physical properties of blood.

Fraunhofer oscillations of the critical current at a varying Zeeman field in a spin-orbit coupled Josephson junction

The Zeeman interaction results in spontaneous current through a Josephson contact with a spin-orbit coupled normal metal, even in the absence of any voltage, or phase bias. In the case of the Rashba spin-orbit coupling of electrons in a two-dimensional (2D) electron gas this effect takes place for the Zeeman field which is parallel to the 2D system and to superconducting contacts. At the same time, the spontaneous current is absent when this field is perpendicular to the contacts. It is shown that in the latter case it may manifest itself in oscillations of the critical Josephson current at varying Zeeman energy. These oscillations have a form of the Fraunhofer diffraction pattern. The Josephson current under the phase bias was calculated based on the semiclassical Green's functions for a disordered 2D electron gas with the strong spin-orbit coupling, as well as for surface electrons of a three-dimensional topological insulator. In the latter case the diffraction pattern was found to be most pronounced, while in the Rashba gas the oscillations of the critical current are weaker.

Layered holographic three-dimensional projection using region-partitioned processing

We present two simple yet effective methods to realize holographic three-dimensional (3D) display by partitioned Fresnel diffraction (PFreD) and partitioned Fraunhofer diffraction (PFraD). After a 3D object is divided into a set of layers in axial direction, these layers are calculated into corresponding sub-holograms. These two methods are used to develop a tiling approach to hologram construction and reconstruction. Both simulations and experiments are carried out to verify the feasibility of the proposed methods. The similarities and differences between PFreD and PFraD are analyzed in details for better understanding. These two methods may provide promising solutions in future holographic 3D realization with their own characteristics and scope of application.

Soot formation in turbulent swirl-stabilized spray flames in a model combustor fueled with n-butanol/Jet A-1 blends

Information on sooting characteristics of n-butanol/middle distillate fuels from well-described spray flames is lacking but desirable as a benchmark which could help in better interpretation of the reciprocating engine data and can be used in numerical simulation validation efforts. The effects of n-butanol addition to turbulent swirl-stabilized JetA-1 spray flames were studied experimentally in a model gas turbine combustor with 94 mm × 94 mm cross-section and 188 mm length. n-Butanol was added in concentrations of 10% and 20% by energy content such that the total thermal power output was maintained at 10 kW in the globally fuel lean flames. Spray droplet size distributions and velocity fields were obtained using a Fraunhofer diffraction based droplet sizer and stereoscopic particle image velocimetry, respectively. Spatially resolved soot volume fraction and mean primary particle sizes were measured with auto-compensating laser-induced incandescence. Measurable differences in droplet size distributions were observed with n-butanol addition. Flow fields were similar in all flames. Time-averaged soot volume fraction peaks were observed in all flames at radial positions of approximately 0 mm and 27 mm and axial heights of approximately 20 mm and 40 mm, respectively. Soot production decreased monotonically throughout the flames with n-butanol addition. Primary soot particle diameters were generally within the range of 25 to 50 nm. Potential mechanisms explaining the changes observed with n-butanol substitution in jet fuel are discussed.

Wave field reconstruction and phase imaging by electron diffractive imaging.

In electron diffractive imaging, the phase image of a sample is reconstructed from its diffraction intensity through iterative calculations. The principle of this method is based on the Fourier transform relation between the real-space wave field transmitted by the sample and its Fraunhofer diffraction wave field. Since Gerchberg's experimental work in 1972, various advancements have been achieved, which have substantially improved the quality of the reconstructed phase images and extended the applicable range of the method. In this review article, the principle of diffractive imaging, various experimental processes using electron beams and application to specific samples are explained in detail.

Domain Structure and Reversal Mechanisms through Diffracted Magneto-optics in Fe80B20 Microsquare Arrays

In this paper, the predictive power of diffracxtive magneto-optics concerning domain structure and reversal mechanisms in ordered arrays of magnetic elements is demonstrated. A simple theoretical model based on Fraunhoffer diffraction theory is used to predict the magnetisation reversal mechanisms in an array of magnetic elements. Different domain structures and simplified models (or educated guesses) of the associated reversal mechanisms produce marked differences in the spatial distributions of the magnetisation. These differences and the associated magnetisation distribution moments are experimentally accessible through conventional and diffractive magneto-optical Kerr effect measurements. The domain and magnetisation reversal predictions are corroborated with Magnetic Force Microscopy (MFM) measurements.

Experimental investigations on atomization characteristics of dual-orifice atomizers part I: Optimization method formation

In this paper, influences of structure parameters on mass flow and atomization characteristics (spray cone angle, SMD, liquid film fusion and separation) of dual-orifice atomizers were investigated using Fraunhofer diffraction optical instrument and high-speed shadowgraph technique. The main influential structure parameters are obtained by structural parameter sensitivity analysis. Liquid film fusion and separation is an important atomization characteristic lacking of in-depth research. Results of liquid film fusion and separation illustrate that three patterns (separation-fusion-secondary separation) of main stage liquid film and pilot stage liquid film appear with the increase of Δ P. Liquid film fusion makes SMD larger, and there is a delay in liquid film separation when reduce Δ P after liquid film fusion. In addition, mass flow and spray cone angle are key factors which affect liquid film fusion pressure, liquid film secondary separation pressure and distance between two liquid films. The smaller the pilot stage mass flow is, the larger the effect of the main stage on pilot stage spray cone angle will be. Results in this paper could be used to the design and optimization of new dual-orifice atomizers.