Angle Prism Research Articles

Two-dimensional refractive index distribution using polarization phase shifting interferometry and total internal reflection

An effective method to measure the 2-D refractive index distribution of homogeneous liquids: acetic acid and glycerol- water mixture at different concentration and a non- homogeneous mixture of liquids: water, acetic acid, acetone and glycerin but not limited to these liquids is presented. In the present setup a combination of polarization phase shifting interferometry (PPSI) and total internal reflection (TIR) is used. The s-polarized light strikes the boundary of a right angle prism and a tested liquid droplet. When TIR occurs on the interface, the incident light has a phase variation which depends on the refractive index of adhered liquid on prism surface. Two-dimensional index distributions can be easily calculated using the relation among reflection phase shift difference and the liquid index. The results of the tested mixed liquid by proposed technique show the refractive index and its distribution in range 1.433 ± 0.031 to 1.433 ± 0.124.

How mangabey molar form differs under routine vs. fallback hard-object feeding regimes

Background Components of diet known as fallback foods are argued to be critical in shaping primate dental anatomy. Such foods of low(er) nutritional quality are often non-preferred, mechanically challenging resources that species resort to during ecological crunch periods. An oft-cited example of the importance of dietary fallbacks in shaping primate anatomy is the grey-cheeked mangabey Lophocebus albigena. This species relies upon hard seeds only when softer, preferred resources are not available, a fact which has been linked to its thick dental enamel. Another mangabey species with thick enamel, the sooty mangabey Cercocebus atys, processes a mechanically challenging food year-round. That the two mangabey species are both thickly-enameled suggests that both fallback and routine consumption of hard foods are associated with the same anatomical feature, complicating interpretations of thick enamel in the fossil record. We anticipated that aspects of enamel other than its thickness might differ between Cercocebus atys and Lophocebus albigena. We hypothesized that to function adequately under a dietary regime of routine hard-object feeding, the molars of Cercocebus atys would be more fracture and wear resistant than those of Lophocebus albigena. Methods Here we investigated critical fracture loads, nanomechanical properties of enamel, and enamel decussation in Cercocebus atys and Lophocebus albigena. Molars of Cercopithecus, a genus not associated with hard-object feeding, were included for comparison. Critical loads were estimated using measurements from 2D µCT slices of upper and lower molars. Nanomechanical properties (by nanoindentation) and decussation of enamel prisms (by SEM-imaging) in trigon basins of one upper second molar per taxon were compared. Results Protocone and protoconid critical fracture loads were significantly greater in Cercocebus atys than Lophocebus albigena and greater in both than in Cercopithecus. Elastic modulus, hardness, and elasticity index in most regions of the crown were greater in Cercocebus atys than in the other two taxa, with the greatest difference in the outer enamel. All taxa had decussated enamel, but that of Cercocebus atys uniquely exhibited a bundle of transversely oriented prisms cervical to the radial enamel. Quantitative comparison of in-plane and out-of-plane prism angles suggests that decussation in trigon basin enamel is more complex in Cercocebus atys than it is in either Lophocebus albigena or Cercopithecus cephus. These findings suggest that Cercocebus atys molars are more fracture and wear resistant than those of Lophocebus albigena and Cercopithecus. Recognition of these differences between Cercocebus atys and Lophocebus albigena molars sharpens our understanding of associations between hard-object feeding and dental anatomy under conditions of routine vs. fallback hard-object feeding and provides a basis for dietary inference in fossil primates, including hominins.

The modified minimum deviation method for measuring the refractive index

We present a modified method for measuring the refractive index (RI) based on the minimum deviation technique, which allows us to determine the RI of transparent triangular prisms with unknown apex angles. In the proposed method, the angles of light deviation are measured on three faces of the prism, and RI of the material and prism angles are determined from the solution of a system of equations. A high precision dynamic goniometer was used to implement the proposed method. A set of reference prisms made of optical glass were experimentally studied and the measurement errors were estimated. It is shown that the modified method can be used for high-precision measurements of the RI in cases when the prism angles are unknown, or their measurement is associated with technical difficulties. The method of measuring RI proposed in the article was implemented using the State Primary Standard of the Refractive Index Unit GET 138–2021 of the All-Russian Research Institute for Optical and Physical Measurements. This standard is intended for storing, reproducing, and transmitting the unit size of the RI of solid and liquid substances.

Modified prism methods for measuring the refractive index of solid and liquid substances

Methods for measuring the refractive index of optically transparent dielectric materials are considered. Modified methods based on the methods of minimum deviation and constant deviation are proposed and allow determining the refractive index of triangular prisms with unknown apex angles. In the proposed methods, the angles of light deviation on three faces of the prism are measured, and the refractive index of the material and the prism angles are determined from the solution of a system of equations. To implement the proposed methods, a goniometric system is used. That system was designed to measure angles between the flat surfaces of objects in manual and automated modes. Reference prism samples made of N-SF 1 optical glass, and a hollow prism filled with distilled water are studied. The proposed methods are compared and the measurement error is estimated. It is shown that the modified methods can be used for high-precision measurements of the refractive index in cases where the angles of the prism are unknown, or their measurement is associated with technical difficulties.

Phase-shifting by polarizer rotations in a right-angle prism interferometer

In this manuscript it is presented what we believe to be a novel and simple phase-shifting technique based on polarizer rotations, using a right angle prism as the interferometric device. It is possible to generate interference when the right angle edge of the prism is placed parallel to a linearly polarized collimated beam. In this configuration optical phase changes are presented due to the internal reflections in the prism; therefore, a linearly polarized beam turns into elliptical polarization. If the output elliptically polarized interference beam passed through a lineal polarizer, phase-shifting is generated if it rotates by an angle theta. This proposal will be sustained with simulated and experimental shifted interference patterns and with the calculation of wrapped and unwrapped phases.

Experimental study of wind energy harvesting from flow-induced vibration of prisms using magnetostrictive material

A vibration energy harvester was developed using a magnetostrictive material as a power generator and a prism as a wind receiver to harvest energy from low-speed wind by exploiting flow-induced vibration. The present cantilevered vibration power generator has originality for the structure which consists of a U-shaped unimorph beam of Galfenol (iron-gallium alloy). Wind tunnel experiments were conducted for prisms having circular, rectangular, filleted triangular, and V-shaped cross-sections. We focused on transverse vortex-induced vibration for a circular cylinder and low-speed galloping vibration for a rectangular prism with a depth-to-height ratio of 0.2, a filleted triangular prism, and a V-shaped prism. The effect of the width of prisms having a span length of L = 200 mm on the transverse vibration characteristics and the power extracted from the vibration generator was investigated. The maximum power generated by cylindrical, rectangular, filleted triangular, and V-shaped prisms with heights of 50, 50, 60, and 50 mm was 1.28, 3.5, 7.83, and 5.02 mW, respectively. These maximum power levels are enough to run a wireless sensor. Moreover, the angle of the V-shaped prism having a width of 50 mm was varied (i.e., β=60°, 90°, 120°, and 150°) and tested in wind tunnel experiments. The V-shaped prism with β=120° was best from several viewpoints, including low excitation wind speed, safe operation at high wind speed, efficient operation in environmental conditions, and sustainability.

High-Bunch-Charge and High-Energy-Gain Inverse-Cherenkov Particle Accelerator With Prebunched Beam

Dielectric laser accelerator (DLA) is a promising candidate for next-generation on-chip particle accelerator. However, practical applications of DLA to date have been restricted due to low accelerated bunch charge and low energy gain, especially for subrelativistic particles. To break through these limitations, here we propose a multistage DLA scheme with inverse Cherenkov effect. The first stage, formed by a pair of symmetric dielectric prisms, is to prebunch a long (tens to hundreds of laser-wavelengths) electron beam with relatively high bunch charge (several to tens of femto-coulombs) via velocity bunching. The subsequent stages, consisting of pairs of dielectric prism stacks, are to fulfill cascade acceleration of the prebunched beam. The synchronization of subrelativistic particles with laser field is realized via adjusting the prism angles in each stack. With theoretical analyses and simulations, we obtain an energy gain of more than 400 keV for an electron beam with initial energy of 100 keV. Compared with that of a non-prebunched beam, the accelerated bunch charge of a prebunched beam is more than four times higher. This proposed scheme affords an effective way of developing an on-chip particle accelerator with high energy gain and high bunch charge.

Accuracy analysis of the refractive index measurements by modifed prism methods

Goniometric methods of measuring the refractive index of optically transparent materials based on the refraction of light by a triangular prism are considered. Modified method of the minimum deviation and 3 modified constant deviation methods are considered, which allows determining the refractive index of triangular prisms with unknown apex angles. According to modified methods, the angles of light deviation by a prism are measured with goniometer, and the refractive index of the material and the prism angles are determined from solving the systems of equations. Thus, there is no need for preliminary measurement of the prism angles, which requires the use of special autocollimation goniometers. In addition, the modified methods do not use radiation reflected from the faces of the prism, which makes it possible to extend the spectral range of measurement of the refractive index to the infrared and ultraviolet regions. A comparative accuracy analysis of the considered methods for a prism with a refractive index of 1.5 and an angle of 60° as example is carried out. It is shown that the modified methods can be used for high-precision measurements of the refractive index in cases if the apex angles of the prism are unknown or their measurement is associated with technical difficulties. The considered methods can be used to measure the refractive index of triangular prisms made of optically transparent materials, as well as liquids poured into hollow prisms with plane-parallel transparent windows. The practical implementation of such a methods can be useful in the optical, chemical and food industries to control the composition and properties of optically transparent substances.

Rotationally Reconfigurable Single-Element Prism for Enhancing Scanning Flexibility of Risley Prism Antenna System

In this letter, we propose a rotationally reconfigurable single-element prism that is compatible with the typical Risley prism antenna system. It consists of a pair of rotating decentered phase plates operating at 30 GHz. The equivalent prism angle can be continuously changed between 0° and 14° by simply rotating these two phase plates. An all-dielectric low-cost prototype has been designed, fabricated, and measured, which demonstrates the peak realized gain of 21 dBi can be achieved with a gain variation less than 0.9 dB within the reconfigurable angle range of 0°–14°. Besides, the combination of phase distribution of two rotating phase plates can be used as a new mechanism avoiding using first-order paraxial approximation to realize two-dimensional beam scanning.

Symmetries of Scan Patterns of Laser Scanners with Rotational Risley Prisms

Laser scanners with rotational Risley prisms produce scan patterns that can be classified as a type of rhodonea curve, because of their symmetry. The present study builds upon the novel, graphical method that we have developed to simulate and analyze such patterns using a commercially available mechanical design program, CATIA V5R20 (Dassault Systems, Paris, France). This graphical method has both the advantage of simplicity (regarding analytical methods) and of generating exact scan patterns (in contrast to approximate methods). The aim of this work is to utilize this method to study symmetry properties of scan patterns produced by a pair of rotational Risley prisms. A multi-parameter analysis is performed, considering the characteristic parameters of the approached scanner: refractive indexes and angles of the prisms, as well as their rotational velocities. Furthermore, Marshall’s parameters are considered: ratios of the rotational velocities and of the prism angles. Because the symmetries are identical for scan patterns generated by all the four possible configurations of a pair of prisms (and only their dimensions are different), the shape of these patterns is studied only for one of these configurations. Therefore, without losing generality, the symmetries of the patterns produced by such scanners are determined, as well as some of their characteristic dimensions. Rules-of-thumb were obtained to be able to generate patterns that are appropriate for a specific application. Moreover, we demonstrated that the existing symmetries simplify the process of obtaining the scan patterns by identifying repetitive parts (defined as structures of symmetry) of a pattern.

The orientational order parameter of some ferroelectric liquid crystals by refractivity and image analysis methods

This manuscript describes the determination of the orientational order parameter of the ferroelectric liquid crystals having chemical formulas C36H47NO5, C37H49NO5 and C39H53NO5. The ordinary and extraordinary refractive indices of these compounds in the nematic phase are measured by using a small angle prism and modified spectrometer. By well-known Vuk’s method the orientational order parameter is estimated. The optical textures of these compounds are apprehended using an optical polarizing microscope. The microscopic textures are analysed using MATLAB software.and the orientational order parameter is estimated. The limitations and merits of the image analysis technique is discussed.

Part geometry-driven crystallographic texture control in a 3D-printed austenitic steel – a strategy for near-monocrystalline microstructure generation

We propose and employ a novel X-shaped geometry to strengthen the 〈001〉 || z crystallographic texture – distinctive of the electron beam powder-bed fusion technique, for a 3D-printed austenitic stainless steel of type 316 L. The prism angles of the X-shaped parts are varied among 60, 90, and 120 degrees (X-60, X-90, and X-120) to investigate the effect it has on the parts’ properties. Strikingly, the strength of the 〈001〉 || z crystallographic texture and columnar grain width with increasing prism angle is seen to follow a ‘bell-curve’ profile which peaks with the X-90 shape. A distinct mechanical response of X-shaped samples is obtained with X-60 samples showing significantly stronger strain-hardening behavior along with cracking concentrated along the grain boundaries between 〈110〉 || z and 〈001〉 || z grains. Molecular dynamics simulations are utilized to rationalize this phenomenon.

Determination of complex refractive index using maximum deviation angle through prism

Light-absorbing materials are widely used, and their optical properties are an important factor. Snell's law does not hold in materials that partially absorb light. Hence, the optical path in refraction is calculated from Maxwell's law. We used the optical path to obtain the deviation angle when a light passes through a prism made of light-absorbing material. The deviation angle has a local maximum. The deviation angle near the maximum is sensitive to the real and imaginary parts of the refractive index. The local maximum deviation angle and its incident angle are used to determine the complex index of refraction. This measurement has the same advantages as measuring the minimum deviation angle of a transparent prism. The detection is easy. Then, it is necessary to determine the complex refractive index from the measured maximum deviation angle and its incident angle. These two angles are plotted parametrically by varying the real part of the refractive index under a fixed imaginary part. The similar curves are drawn under the fixed real parts. Each curve has a fixed value for the real or imaginary part of the refractive index. Drawings of these many curves are made prior to measurement. Then we select the four curves that are closest to the measured local maximum deviation angle and its incident angle. Four fixed values attached to each of the four curves determine the complex index of refraction. The method in this paper can easily determine the complex refractive index and can be used for material identification.

How a ball free to orbit in a circular track mitigates the galloping of a square prism

Transverse galloping is a type of flow-induced vibration (FIV) that leads to critical design considerations for engineering structures. A purely nonlinear energy sink (NES) composed of a ball free to rotate in a circular track experimentally mitigated the galloping of a square in a previous study. The current study introduces a model for simulating the dynamics of the square prism coupled with a ball-in-track (BIT) NES and predicting the system behaviour at high flow speeds beyond the limits of the previously presented experiments. Numerical simulations employ the fitting of experimental data as inputs to define parameters. Wind tunnel static experiments provide the galloping force coefficient \(C_y\) relative to the prism angle of attack. Additionally, free rotation tests allow evaluating the ball damping coefficient \(c_\theta \) as a function of its mass and the NES track radius. The result of the rotation tests provides a critical angular speed beyond which the ball damping increases nonlinearly. We point out the damping variation as an advantage of the BIT-NES; less damping at low angular velocities helps the ball start its rotation, while relatively large damping at higher speeds dissipates more energy from the vibrating system. Numerical results exhibit four response modes for the NES: oscillatory at low flow speeds, intermittent within a small range of higher flow speeds, rotational at higher flow speeds, and ineffective regime at flow speeds out of the NES effective range. Modelling the primary mass as a parametric excitation source for the NES provides an analytical estimation of the boundary between the oscillatory and intermittent regimes. Furthermore, we advance an analytical analysis of the power flow across the integrated prism-NES system to explain the NES behaviour and predict the limit of its effective range.

A design method for direct vision coaxial linear dispersion spectrometers.

A spectrometer design method based on the prism-prism-grating (PPG) dispersion module is proposed in this paper to correct the serious nonlinear dispersion that prism and grating spectrometers and other dispersive spectrometers suffer from. First, we determine the criteria for selecting the optical materials of the PPG module by analyzing the dispersion characteristics of prisms and gratings. Second, a loop traversal algorithm is used to optimize the system structure parameters after selecting optical materials. Next, the direct vision coaxial condition of the PPG module is derived according to basic optical principles and the geometrical relationship between optical elements. Then, the dispersion equation of the PPG module is used to establish the spectral linearity index of the system. Finally, combined with the design index, the structural parameters of the PPG module to meet the linear dispersion requirements are determined. A direct vision coaxial linear dispersion spectrometer is designed and realized under the condition that the working band is 400-990 nm, the deviation angle and offset of the emitted ray with a central wavelength of 695 nm with respect to the optical axis are 0, and the dispersion angle is not less than 15°. The results simulated by ZEMAX show that the actual simulation results are consistent with the theoretical calculation results, the spectral resolution of the spectrometer is less than 1.5 nm, and the spectral smile and keystone are less than 3.89% pixels. In the discussion section, the influences of the dispersion ability of optical materials and the incident angles of prisms and gratings on the spectral dispersion linearity of the PPG module are analyzed and studied. The universality of the spectrometer design method developed in this paper is discussed, and its universality is simulated and verified in the 1000-1600 nm and 1600-2200 nm bands. In addition, some advantages compared with other dispersion structures are analyzed.

Method to traceably determine the refractive index by measuring the angle of minimum deviation

The refractive index (RI) of a solid depends on the illumination wavelength, temperature and material properties, such as the chemical composition, crystal structure, and isotropy. RI measurements, however, also depend on environmental conditions, such as the temperature, pressure, CO2 concentration and humidity of the surrounding air. As these environmental conditions are not always reported, reported values of the RI are often irreproducible. Here we describe a new optical set-up based on the angle of minimum deviation to traceably measure the RI at controlled temperature, pressure, humidity, and CO2 concentration of the surrounding air. Advantages of the reported method are that (I) we perform RI measurements without the need for an independent measurement of the prism angles, and (II) correlations in the uncertainty propagation reduce the sensitivity coefficients greatly. The absolute RI of fused silica at 20.00 °C is 1.470 091 at 404.66 nm, 1.467 169 at 435.83 nm, 1.460 459 at 546.07 nm, and 1.459 237 at 579.07 nm. The expanded uncertainty (k = 2) of the set-up and procedure is 1.4 × 10−6 for 404.66 nm, 435.83 nm, and 546.07 nm and 1.7 × 10−6 for 579.07 nm. The main factors affecting the expanded uncertainty are the calibration uncertainty of the rotary stage, and the repeatability of the measurement.

Intervals of color mismatch in chromaticity coordinates and in cone‐fundamental‐based (LMS) space

AbstractWe discuss the uncertainties in chromaticity coordinates in the color matching experiment reported by MacAdam (Journal of the Optical Society of America, 1942). We also derive the uncertainties in cone‐pigments based excitation space. The observer made color matchings by tuning the angle of a Rochon prism. The intervals of color mismatch were obtained using the average value and the SD of the angle settings. We use in this work a rigorous statistical method to derive the probability density functions (PDFs) of chromaticity coordinates assuming a Gaussian distribution for the Rochon prism angle. We also derive the PDFs of the L‐, M‐, and S‐ tristimulus values. We analyze how much the actual PDFs deviate from the Gaussian. Finally, we determine the bounds of the intervals of color mismatch assuming that the areas of the tails of each PDF are equal. The so derived intervals are compared to those reported in the original investigation due to MacAdam. We show that color‐differences for a certain confidence level cannot be obtained as a simple common scaling factor of the color differences computed for a lower confidence level. The results obtained in LMS space at corneal level exhibit asymmetries between increment and decrement thresholds.

Subwavelength twin ultrasound focused (STUF) beam generated by shear-to-longitudinal mode conversion in a triangular prism

Focusing ultrasound fields in regions below the incident wavelength using elementary objects (such as spherical and cylindrical) as acoustic lenses have been successfully demonstrated over the last five years. This unique way to tightly concentrate the energy of acoustic fields is interesting for the development of new high resolution ultrasound systems. Usually, an incident longitudinal beam interacts with these lenses to produce a subwavelength beams at its shadow region. However, no shear-wave beam has been reported to produce subwavelength beams using objects as acoustic lenses. In this work, we numerically and experimentally report the generation of a subwavelength twin ultrasound focusing (STUF) beam using a 1 MHz shear transducer coupled to a Rexolite triangular prism. Numerical simulations were performed in order to study the generated field as a function of the apical angle of the prism and to find the mechanical configuration for the experimental validation. The results show that by changing the apical angle of the triangular prism, the main features of the STUF beams can be changed. To validate the numerical model, a prism with apical angle of 90o was built and the acoustic field distribution was measured by a needle hydrophone. A STUF beam with width of 0.8λ and depth of focus (DOF) 3λ was generated. A good agreement between numerical and experimental results was reported. The proposed system open new possibilities to design and built a simple and low cost acoustic system for microparticle trapping applications.

Flexible and wide-range tuning of liquid crystal polarization grating period based on single and interference-free exposure.

We propose a period control method of liquid crystal polarization grating (LCPG) based on an nterference-free and single exposure process. By adjusting three parameters of exposure setup, including incident angle of exposure beam, wedge angle of birefringent prism and tilt angle of the sample, polarization distribution of the exposure beam is changed. The spatially variant polarization of the exposure beam is transferred to liquid crystal (LC) molecules by an azo-dye photo-sensitive layer. Consequently, the LCPG with the target period is obtained. The proposed method has high flexibility and a wide range of period adjustment covering several microns to more than thousands of microns according to calculated results. Experimental results fit well with calculations. The LCPGs with different values of period from 4.5µm to more than 200µm have been realized experimentally. The proposed interference-free method would accelerate the application of LCPGs with a robust and simple fabrication process.

36‐2: Optimizing Brightness with Micro Lens Array Gain Enhancing Films for Edge‐Lit Back Light Units

The on‐axis brightness of a conventional edge‐lit back light unit (BLU) was optimized by replacing the conventional down diffuser with a Micro Lens Array (MLA) gain enhancing diffuser (GEF). It was found that the brightness could be increased ~29% by using a GEF with a 90 degree apex angle prism facing the light guide plate (LGP) and pyramidal structures on the backside of the GEF. The angular orientation of the prism relative to the cross brightness enhancing films (xBEF) and the orientation ofthe xBEF relative to the light propagation direction is critical. Different edge‐lit BLUs will require different MLA‐based GEF to maximize brightness.