Plane-parallel Plate Research Articles

Formulation of perfect-crystal diffraction from Takagi-Taupin equations: numerical implementation in the crystalpy library.

The Takagi-Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

Refractive index measurement for plane parallel plate using fiber point diffraction lateral interference and numerical modeling

A plane-parallel-plate (PPP) refractive index (RI) measurement method based on fiber point diffraction lateral interferometry and numerical modeling is proposed. Two fiber point light sources (PLSs) generate lateral interference through PPP, and the interferograms are collected by a linear array camera (LAC). Employing ray tracing of an ideal PLS and numerical simulation, the theoretical model of RI measurement is established by polynomial fitting with the RI of PPP as the output, the PPP thickness and the phase change at specific positions of the LAC detector as the inputs. To enhance measurement accuracy, the theoretical model is further corrected using PPP samples with known RI, measured thicknesses and phase changes. The experimental results indicate that the RI measurement accuracy can reach 10−4. Remarkably, this method features a simple structure and eliminates the intermediate optical components, except for the fiber PLSs, PPP samples, and LAC. We demonstrate how to simulate an ideal PLS with fiber PLSs and correct the numerical simulation model to improve the accuracy of RI measurement. Furthermore, this approach can be extended to other optical measurements.

Force Metrology with Plane Parallel Plates: Final Design Review and Outlook

During the past few decades, abundant evidence for physics beyond the two standard models of particle physics and cosmology was found. Yet, we are tapping in the dark regarding our understanding of the dark sector. For more than a century, open problems related to the nature of the vacuum remained unresolved. As well as the traditional high-energy frontier and cosmology, technological advancement provides complementary access to new physics via high-precision experiments. Among the latter, the Casimir And Non-Newtonian force EXperiment (Cannex) has successfully completed its proof-of-principle phase and is going to commence operation soon. Benefiting from its plane parallel plate geometry, both interfacial and gravity-like forces are maximized, leading to increased sensitivity. A wide range of dark sector forces, Casimir forces in and out of thermal equilibrium, and gravity can be tested. This paper describes the final experimental design, its sensitivity, and expected results.

Characterization of High-polarization Stars and Blazars with DIPOL-1 at Sierra Nevada Observatory

We report here the performance and first results of the new multiband optical polarimeter DIPOL-1, installed at the Sierra Nevada Observatory 90 cm T90 telescope (SNO, Granada, Spain). DIPOL-1 is equipped with a plane parallel calcite plate and λ/2 retarder for modulating the intensity of two perpendicularly polarized beams, and a high readout speed CMOS camera that allows for fast, time-dense coverage. We characterize the performance of this instrument through a series of tests on zero- and high-polarization standard stars. The instrumental polarization in the Nasmyth focus was well determined, with a very stable contribution of 4.0806% ± 0.0014% in the optical R band. For bright high-polarization standards (m R < 8) we reach precisions <0.02% in polarization degree and 0.°1 in polarization angle for exposures of 2–4 min. The polarization properties of these stars have been constrained, providing more recent results also about possible variability for future studies of some of the most used calibrators. Moreover, we have tested the capability of observing much fainter objects, in particular through blazar observations, where we reach a precision of <0.5%−0.6% and <0.°5 for faint targets (m R ∼ 16.5) with exposures of ∼1 hr. For brighter targets (m R ∼ 14.5−15), we can aim for time-dense observations with errors <0.2%−0.4% and <1°−1.°5 in 5–20 min. We have successfully performed a first campaign with DIPOL-1, detecting significant polarized emission of several blazars, with special attention to the highest ever polarization degree measured from blazar 3C 345 at ∼32%.

Numerical Analysis of Chaos in a Phononic Crystal Waveguide with Circular Inclusions of Real Materials

Phononic crystal waveguides (PnCW) have been of great interest due to their properties of manipulating or filtering the acoustic waves with which they interact. Similarly, the presence of the phenomenon of chaos in the classical transport of particles through billiards with analogous geometries has been investigated. With this in consideration, in the present work an acoustic system of a two-dimensional PnCW is modeled, composed of two plane-parallel plates and a periodic arrangement of circular cylindrical inclusions with acoustic surfaces of real materials. In this system, we use the numerical technique of the integral equation, which allows us to obtain the pressure field corresponding to the normal modes in a range of frequencies. In addition, spatial statistical properties of pressure intensity such as the autocorrelation function (ACF) and its standard deviation called correlation length were calculated. The results show that when the correlation length is very small, the system presents disordered patterns of field intensities. Thus under certain conditions, the system under consideration presents a chaotic behavior, similar to the corresponding classical system.

Caustics and wavefronts produced by multiple refraction-reflections through plane-parallel plates

We study the formation of caustics and wavefronts produced by multiple refraction-reflections through a plane-parallel transparent plate, assuming a point source placed at an arbitrary position along the optical axis. The caustic surfaces are obtained by using the envelope’s method. Subsequently, the wavefronts are directly related to the involutes, which are associated with the envelopes for all the rays. Hence by using the Malus–Dupin theorem, we obtain their respective wavefronts produced by multiple refraction-reflections through a plane-parallel transparent plate. On the other hand, we implement Huygens’ principle to obtain the wavefronts leaving the plate after undergoing multiple reflections inside the plate, which we have called zero-distance phase wavefronts. Finally, we establish the correspondence between the wavefronts obtained by Huygens’ principle and the involutes associated with caustic surfaces; they are brought in coincidence assuming parallel curves from each other.

Spatial micro-scanning of plane-parallel glass plate surface by the interference method

Spatial micro-scanning of plane-parallel glass plate surface by the interference method

Determination of the polarization plane specific rotation in gyrotropic crystals of the middle category by the spectrophotometric method

A large number of modern functional single crystals of the middle category belong to gyrotropic media. In these crystals, when light propagates along the optical axis, rotation of the plane of its polarization is observed. In this work a spectrophotometric method was used to obtain the dispersion dependences of the rotation angle of the polarization plane. This method is based on measuring the intensity of light passing through the polarizer–crystal–analyzer system, the crystal is a polished plane-parallel plate of a uniaxial gyrotropic crystal cut perpendicular to the optical axis. Measurements were carried out on a UV-Vis-NIR spectrophotometer Cary-5000 in the wavelength range of 200—1200 nm using polarizers — Glan–Taylor prisms. Polished plane-parallel plates of known SiO2 and α-LiIO3 crystals were used as samples. The obtained dispersion dependences of the spectral transmission coefficients are oscillating. Discrete values of the specific angles of rotation of the plane of polarization of light are calculated from the extremes on these dependencies. These discrete values can be approximated by the formulas Drude, Chandrasekhar and Vyshina, depending on what determines the nature of the rotational ability of the plane of polarization of light in each particular material. For the studied crystals, dependences of the modified Drude formula of the form 1/ρ = f(λ2) are plotted, these dependences should have a linear character in the case of an ideal crystal. The obtained experimental results correlate well with the available literature data. The advantages of this method are efficiency, the possibility of obtaining dispersion dependences of the specific rotation angle of the polarization plane, the need for a single sample, the possibility of assessing the nature of the rotational ability of specific crystals, the possibility of evaluating the structural perfection of the studied crystals.

A novel two-dimensional reflective coherent gradient sensor and its applications in residual deformation measurement of laser repaired metal components

Directed Energy Deposition (DED), known as an important branch of additive manufacturing, are becoming increasingly crucial in different industrial fields. However, this extreme manufacturing process may bring about quality issues for the DED product, and in-situ monitoring for characterizing mechanical parameters of thick DED products still needs to be improved. In this manuscript, for the convenient in-situ bidirectional residual deformation measurement of thick DED metal components, a novel two-dimensional coherent gradient sensor (2D-CGS) is established based on crossed Ronchi gratings. Firstly, the diffraction characteristic of the crossed Ronchi grating used in 2D-CGS is analyzed, and then the principles of 2D-CGS are analyzed in detail for bidirectional out-of-plane displacement gradient measurement. Furthermore, two temporal phase-shifting techniques: plane-parallel plate rotating (PPR) method and prism translation (PT) method, are extended from one dimension to 2D for improving the accuracy of 2D-CGS post-processing, named as 2D-PPR method and 2D-PT method. Verification experiment shows that the 2D-CGS system can synchronously measure the bidirectional curvature fields of the standard spherical reflector with the maximum relative error of 3.80%, which is equivalent to the accuracy of typical CGS. Finally, in the application of zig-zag deposited DED process, the bidirectional residual deformation fields of repaired components are in-situ monitored by portable 2D-CGS system, and the relationship of dwell time between adjacent tracks and the residual deformation is analyzed based on bidirectional centerline curvature on the bottom surface of substrate. A new parameter named as the orthotropic symmetry coefficient is defined based on curvature to analyze the full-field in-plane orthogonal anisotropy. Results show that both the degree of in-plane orthogonal anisotropy and value of residual deformation decreases with the increase of dwell time from 0 to 5 s, while varying a little with the dwell time exceeding 5 s, which also indicates the proposed parameter could well evaluate the degree of full-field orthotropic anisotropy. Meanwhile, the position of maximum curvature also gradually moves from the end toward the beginning in deposition direction. In summary, the proposed 2D-CGS method can measure the full-field bidirectional deformation in high efficiency, which may be promising in future in-situ monitoring applications.

Diferential method for the formation of relative phase shifts between light beams in two-arm interferometer

The possibility of improving technical means that make it possible to introduce phase shifts into light beams in the interferometer paths is considered. An optical-mechanical phase modulator in the form of a plane-parallel glass plate rotated around an axis lying in its plane was adopted as the initial version of these technical means. A differential method is proposed for the formation of relative phase shifts between beams in a two-arm interferometer. A variant of the modulator has been developed in the form of a pair of rigidly interconnected plates, the planes of which are initially rotated at a given angle. In this case, each of the parallel light beams in the interferometer passes through its own plate. It is shown that in this case a practically linear relationship is provided between the generated relative phase shift and the total angle of rotation of the plates. A variant of using a single plate as a modulator under the established conditions for the incidence of two beams propagating in different arms of the interferometer is considered. The operability of the proposed differential method for controlling the phase shift between light beams is confi rmed by the data of a test experiment. The results obtained will be useful in the development of special tools based on the method of digital speckle pattern interferometry for measurements of the displacement fields of deformable bodies

Compression of a Beam of Fast Argon Atoms for Surface Polishing

The results of studying a beam source of fast argon atoms obtained by neutralizing charges of accelerated ions during their flight through an accelerating grid in the form of a set of plane–parallel plates are presented. Ions are accelerated from the plasma emitter by a voltage of negative polarity at the grid, fly into the gaps between its plates, and, when approaching their surfaces, cause the emission of electrons that neutralize the ion charge. The equivalent beam current of fast atoms emitted from the grid is up to 90% of the current in its circuit, and their energy is equal to the ion energy that corresponds to the accelerating voltage between the plasma emitter and the grid. To increase the beam current density of fast atoms on the treated surface, the sections of the grid plates facing the plasma emitter are made in the form of a segment of a circle. The movement of ions and fast atoms that are formed inside the grid to the center of this circle makes it possible to reduce the beam width by an order of magnitude and increase the flow density of fast atoms without reducing the angle of their incidence on the treated surface. The beam compression significantly improves the efficiency of polishing a surface with a beam of fast neutral argon atoms with an angle of incidence on the surface of 80°.

Scalable optical-to-terahertz converter with a prism-coupled plane-parallel lithium niobate plate.

A nonlinear optical converter of femtosecond laser pulses to terahertz radiation, which combines the tilted-pulse-front pumping and prism coupling techniques, is proposed and experimentally tested. In contrast to the conventional tilted-pulse-front scheme with a prism-shaped LiNbO3 crystal, the converter consists of a plane-parallel LiNbO3 plate sandwiched between two dielectric prisms. One prism is used to couple the pump beam into the LiNbO3 plate, another prism couples the generated terahertz radiation out of the plate. The proposed scheme enables scaling to large-diameter LiNbO3 wafers and large-aperture high-energy pump laser beams resulting in generation of strong terahertz fields. In a proof-of-principle experiment with a 1-mm thick, small size (1 × 2 cm2) LiNbO3 plate pumped by a mJ-class laser, the conversion efficiency comparable to that of the conventional scheme (∼0.1%) was demonstrated.

Интерферометр для контроля выпуклых гиперболических поверхностей малого диаметра

We used Fourier transforms to perform a theoretical analysis of how the process of interference pattern formation in a laboratory-scale Fizeau laser interferometer is affected by the error in the working wave front. The interferometer is designed to monitor convex hyperbolic surfaces characterised by small diameters and low aperture angles. We indicate their application scope. The interferometer consists of a laser illuminator, a microlens, a beam splitter, that is, a thin plane-parallel plate with a semitransparent coating on its front surface, and a screen. A thin translucent plate located perpendicular to the line connecting the geometric foci of the hyperbolic surface acts as a separator and a reference simultaneously. The paper provides the main equations describing the wave aberration of the working branch and the position of optical elements in the interferometer design. We present an example of computing aberration in the working branch of the interferometer. This calculation reveals that aberrations in the thin plane-parallel plate can be discarded at low aperture angles. The interferometer forms a high-precision optical surface map, that is, interference band distortion caused by the interferometer error does not exceed 0.1 of the distortion caused by the error inherent to the surface being monitored. The interferometer provides highly accurate measurement of hyperbolic surfaces while featuring an obviously simple design

Self-organized ensembles of nematic domains in magnetic and electric fields.

The structural and magneto- and electro-optical properties of a self-organized ensemble of nematic domains formed on a polycarbonate film in the presence of a residual solvent are studied. The film covered one of the plane-parallel glass plates of a liquid crystal cell. The magnetic field stabilizing the planar alignment of the liquid crystal was applied parallel to the cell surfaces and the reorienting electric field, perpendicular to them. The voltage dependences of the intensity of light transmitted through the domain ensemble were obtained at different constant values of the magnetic field. The comparison of the experimental dependences with the dependences calculated using the liquid crystal free-energy minimization procedure has shown good agreement between them. The mutual effect of structural elements of the ensemble and the effects of phase modulation of light are analyzed by comparing the structural, magnetic, and electric coherence lengths.

Optical ceramics based on TlCl0.74Br0.26 – AgI system transparent from visible to far IR region

The article is devoted to the study of the TlCl0.74Br0.26 – AgI solid solution system's phase diagram and the synthesis of optical materials based on it. The phase diagram showed the possibility of synthesizing crystals with a content 0–4 mol. % AgI in TlCl0.74Br0.26 and obtaining optical ceramics with content AgI in TlCl0.74Br0.26 from 4 to 34 mol. %. Were synthesized optical ceramics with a composition of 7, 14, 20, 27 mol. % AgI in TlCl0.74Br0.26, from which plane-parallel plates were made. The optical transmission of ceramic plates covers the region from 0.4 to 50.0 μm without absorption windows. The material refractive index varies depending on the composition from 2.348 to 2.419 at the short-wavelength absorption edge and from 2.179 to 2.236 at a wavelength of 10.6 μm. The optical properties of ceramics showed the efficiency of doping TlCl0.74Br0.26 with silver iodide, since this made it possible to expand the transmission range without absorption windows in the far IR region up to 50 μm.

Ultrahigh dose rate pencil beam scanning proton dosimetry using ion chambers and a calorimeter in support of first in-human FLASH clinical trial.

PurposeTo provide ultrahigh dose rate (UHDR) pencil beam scanning (PBS) proton dosimetry comparison of clinically used plane‐parallel ion chambers, PTW (Physikalisch‐Technische Werkstaetten) Advanced Markus and IBA (Ion Beam Application) PPC05, with a proton graphite calorimeter in a support of first in‐human proton FLASH clinical trial.MethodsAbsolute dose measurement intercomparison of the plane‐parallel plate ion chambers and the proton graphite calorimeter was performed at 5‐cm water‐equivalent depth using rectangular 250‐MeV single‐layer treatment plans designed for the first in‐human FLASH clinical trial. The dose rate for each field was designed to remain above 60 Gy/s. The ion recombination effects of the plane‐parallel plate ion chambers at various bias voltages were also investigated in the range of dose rates between 5 and 60 Gy/s. Two independent model‐based extrapolation methods were used to calculate the ion recombination correction factors ks to compare with the two‐voltage technique from most widely used clinical protocols.ResultsThe mean measured dose to water with the proton graphite calorimeter across all the predefined fields is 7.702 ± 0.037 Gy. The average ratio over the predefined fields of the PTW Advanced Markus chamber dose to the calorimeter reference dose is 1.002 ± 0.007, whereas the IBA PPC05 chamber shows ∼3% higher reading of 1.033 ± 0.007. The relative differences in the ks values determined from between the linear and quadratic extrapolation methods and the two‐voltage technique for the PTW Advanced Markus chamber are not statistically significant, and the trends of dose rate dependence are similar. The IBA PPC05 shows a flat response in terms of ion recombination effects based on the ks values calculated using the two‐voltage technique. Differences in ks values for the PPC05 between the two‐voltage technique and other model‐based extrapolation methods are not statistically significant at FLASH dose rates. Some of the ks values for the PPC05 that were extrapolated from the three‐voltage linear method and the semiempirical model were reported less than unity possibly due to the charge multiplication effect, which was negligible compared to the volume recombination effect in FLASH dose rates.ConclusionsThe absolute dose measurements of both PTW Advanced Markus and IBA PPC05 chambers are in a good agreement with the National Physical Laboratory graphite calorimeter reference dose considering overall uncertainties. Both ion chambers also demonstrate good reproducibility as well as stability as reference dosimeters in UHDR PBS proton radiotherapy. The dose rate dependency of the ion recombination effects of both ion chambers in cyclotron generated PBS proton beams is acceptable and therefore, both chambers are suitable to use in clinical practice for the range of dose rates between 5 and 60 Gy/s.

Effect of electrode separation and electrode backscatter thickness of a parallel plate ionization chamber on the measurement of dose to tissue in beta radiation fields

Plane parallel plate ionization chamber (PPC) is used in dosimetry especially for beta particles and low energy electron beam. The response of the PPC is affected by the electrode separation, thickness and material of backscatterer. The effect of electrode separation arises due to the well-known inscattering effect of electron which causes fluence perturbation inside the chamber cavity. The perturbation is caused due to reduced electron scattering in the chamber cavity compared to an ideal phantom material and it depends on the thickness of the cavity. Furthermore, the response of PPC also gets affected by the material behind the air cavity. Variation in the response depends on the thickness and the atomic number of the material behind collecting electrode of the PPC. The theoretical studies on the effect of collecting electrode backscatter thickness and electrode separation on the response of a PPC used as a transfer standard in ISO 6980 reference beta radiation field from 85Kr, 90Sr–90Y and 106Ru–106Rh radionuclides are presented. Multi-particle transport code FLUKA is used for the studies. The Polymethyl Methacrylate (PMMA) plate having 3.5 mm thickness is found to provide full backscatter for the above beta radionuclides. It is also observed that even for a well-guarded PPC, as the chamber electrode separation increases, the measured depth dose curve deviates from the ideal depth dose curve and the effective point of measurement (EPOM) of the PPC shifts towards downward direction from chamber reference point. It is also observed that the deviation between ideal and measured depth dose curve (related to EPOM shift) depends on the cavity thickness of the PPC. In the present work, optimization of design parameters of a PPC is carried out to establish it as a transfer standard in compliance with ISO 6980 for the standardization of reference beta radiation fields from 85Kr, 90Sr–90Y and 106Ru–106Rh radionuclide.

Phase Retardation Analysis in a Rotated Plane-Parallel Plate for Phase-Shifting Digital Holography.

In this paper, we detail a phase-shift implementation in a rotated plane-parallel plate (PPP). Considering the phase-shifting digital holography application, we provide a more precise phase-shift estimation based on PPP thickness, rotation, and mutual inclination of reference and object wavefronts. We show that phase retardation uncertainty implemented by the rotated PPP in a simple configuration is less than the uncertainty of a traditionally used piezoelectric translator. Physical experiments on a phase test target verify the high quality of phase reconstruction.

Production of nanoporous silicate matrices—problems of optical homogeneity

Subject of study. This paper discusses the main stages of the fabrication of porous silicate matrices composed of two-phase borosilicate glass and how they affect the optical quality of the fabricated samples, as well as how to quantitatively characterize the optical inhomogeneity of the porous matrices, caused by nonuniformity of the pore distribution over the volume of the sample. How the geometry of the chemical processing of the samples is associated with their optical quality is also studied. Method. Digital holographic interferometry implemented on a laboratory-fabrication test stand is used to monitor the optical homogeneity. A technique is worked out to obtain interferograms that characterize the state of the sample in the form of a plane-parallel plate at the preform stage and after acid and alkali processing, as well as a technique for analyzing the experimental data. The quantitative results obtained at the early fabrication stages of the matrices were compared on the same section of the sample (to within 0.1 mm). The spectral transmission of the samples was measured in the 350–100-nm region. The free volume of the sample occupied by pores was determined by weighing, using the mass of the sample in the air-dried state and with the pores filled with water. Main results. A technique was developed for monitoring the optical quality of nanoporous silicate matrices, using a laboratory test stand for digital holographic interferometry. The optical homogeneity of a porous sample was monitored by diagnosing the relative variations of the sample’s optical thickness (the product of the refractive index times the sample’s geometrical thickness). These variations in the blank occur because the sides of the sample are not parallel. They are caused in a porous matrix both by the nonparallelness of the sides of the blank and by the inhomogeneity of the spatial variations of the refractive index due to inhomogeneous distribution of the pores in the volume of the sample. Based on this, quantities are introduced that characterize the optical quality of the blank and of the porous matrix. The optical quality of a plane-parallel blank was determined in this paper from a sample with nonparallel sides, while the optical quality of the nanoporous structure was determined from the refractive-index variation on a given section. It is shown that the orientation of a sample relative to the direction of the gravitational field during chemical processing significantly affects its optical quality. It is experimentally established that, when plane-parallel samples are oriented perpendicular to the gravitational field during chemical processing, it is possible to guarantee the optical quality of the porous matrices in the region where they are transparent, compared with the optical quality of the blank. Practical significance. A technique is presented that makes it possible to quantitatively characterize the optical inhomogeneity on a given section of a porous sample in the region where it is transparent and to separate the amount by which the quality of the blank and the optical inhomogeneity of the porous structure contribute to the optical quality of the fabricated nanoporous matrices. Our experiments showed that nanoporous silicate matrices that are transparent in the visible and near-IR regions and that are horizontally oriented during chemical processing possess optical homogeneity comparable with the optical quality of the blank. The technique for monitoring the quality of the samples can be used when developing and optimizing regimes for obtaining nanoporous matrices from two-phase glasses, intended for creating optical elements based on them that meet specifications in optical homogeneity.

Propagation of Bessel-correlated specular and antispecular beams.

We address the specular properties of Bessel-correlated fields, generated by illuminating a tilted rotating plane-parallel glass plate with a coherent Gaussian beam and passing the output beam though a mirror-based wavefront folding interferometer. This device allows us to produce beams whose specular properties are preserved in propagation. In the far zone, the specular nature of these partially coherent fields is shown to produce intensity-profile oscillations in the sub-diffraction-limit scale. The analytical results at various propagation distances are verified experimentally by using another wavefront-folding interferometer for coherence measurements.