Angle Prism Research Articles

Multi-Source Data Fusion Method for the Truss Structure Stability Measurement of Space Telescope

It is necessary for large aperture space telescopes to achieve high measurement accuracy for mechanical reference mounting surfaces, complex deformation conditions, and difficulty in describing spatial geometric properties. In this manuscript, we propose a measurement method for evaluating the deformation of the trusses structure by fusing multiple sources of data. The multi-source data are obtained from the theodolite, laser tracker, and photogrammetry systems. The datum alignment of the laser tracker and photogrammetry coordinate systems is achieved by establishing the transition coordinate system method of the datum platform, and the alignment accuracy (3σ) is about 8.8″, 5.1″ and 4.2″. Using the laser tracker to establish the relationship between the cubic mirror coordinate system and the geometric coordinate system of the mounting part, the fast and high-precision measurement of the mounting angle of the cubic prism is realized, and the measurement accuracy reaches 2″. The data from multiple sources are fused through datum transfer and alignment to establish a cosine matrix transfer chain between the mechanical characteristic coordinate system of each component and the transition coordinate system of the datum platform, and the Eulerian rotation angle is obtained to describe the angular relationship between the components after solving. Based on the Monte Carlo mathematical error modeling analysis, the datum transfer and alignment simulations were carried out, and related experiments were conducted. The experiments show that the transfer error (3σ) of the XYZ rotation angle is less than 20.6″ after the datum transfer, the maximum error is within 3″ compared to the simulation results, and the deviation of the comparison photographic measurement data is less than 7.6″. The datum transfer method combined with photogrammetry can describe the deformation trend of large-size trusses under different load conditions more objectively and reasonably.

Propagation of errors in a color matching experiment

AbstractWe revisit the problem of propagation of errors in the color matching experiment reported by MacAdam [J. Opt. Soc. Am. 32, 247 (1942)]. The observer made color matchings by tuning the angle of a Rochon prism. The average value and the standard deviations of the angle settings were considered to derive the average tristimulus values and the uncertainty intervals. Here, we use a rigorous statistical method to derive the probability density functions of the tristimulus values assuming a Gaussian distribution for the Rochon prism angle. We analyze how much the actual probability density functions deviate from the Gaussian. We outline two methods to derive the interval of color mismatch and compare their predictions with those derived using the standard procedure.

Измерение показателя преломления с помощью гониометрической системы

The article proposes a method for measuring the refractive index using a goniometric system that does not require measuring the prism angle, which simplifies the measurement process compared to the widely used methods of minimum deviation and autocollimation. This method can be used to measure the refractive index of samples in the form of triangular prisms in the visible, ultraviolet and infrared ranges. To implement the method, a goniometric system was used. To obtain the reflection of the refracted beam, a fixed mirror was used, and the refractive index of the prism material was calculated from the solution of a system of equations. The results of an experimental study of a triangular prism made of optical glass N-BK7 using the proposed method and their comparison with the data obtained on the State Primary Standard of the Refractive Index Unit GET 138-2021 are presented.

Measurement of the refractive index using a goniometric system

The article proposes a method for measuring the refractive index using a goniometric system that does not require measuring the prism angle, which simplifies the measurement process compared to the widely used methods of minimum deviation and autocollimation. This method can be used to measure the refractive index of samples in the form of triangular prisms in the visible, ultraviolet and infrared ranges. To implement the method, a goniometric system was used. To obtain the reflection of the refracted beam, a fixed mirror was used, and the refractive index of the prism material was calculated from the solution of a system of equations. The results of an experimental study of a triangular prism made of optical glass N-BK7 using the proposed method and their comparison with the data obtained on the State Primary Standard of the Refractive Index Unit GET 138-2021 are presented. Keywords: goniometer, refractive index, prism method.

New type of autocollimator based on the normal tracing method and Risley prisms

In the present study, we proposed a new type of autocollimator for high-accuracy angular measurement within a large angle range. The new system comprises a traditional autocollimator and Risley prisms, and it employs the normal tracing method to measure the angle. By rotating the Risley prisms, the outgoing beam of the autocollimator can be deflected close to the normal direction of the reflecting mirror and then reflected back to the system by the mirror along the near normal direction to realize normal tracing. Based on the angle measured by the the autocollimator and the rotation angles of Risley prisms, we can calculate the tilt angle of the mirror. Since the beam returns to the system close to the original path, the angle error caused by aberration, optical component processing defects, nonuniform refractive index, and so on, can be ignored. Due to the normal tracing measurement method, theoretically, the angle error is not affected by the working distance. ZEMAX non-sequential simulation shows that the angle error caused by aberration in the new system can be significantly reduced.

Ultrashort-pulsed optical parametric oscillator employing Brewster angle prism retroreflectors.

We demonstrate a synchronously-pumped optical parametric oscillator (OPO) cavity in which traditional dielectric mirrors are replaced by all-planar Brewster angle prism retroreflectors, also known as Pellin-Broca prisms. Exploiting total internal reflection, these prisms form a cavity supporting >350-fs chirped signal pulses that were externally compressible to sub-150-fs durations. This simple architecture produces wavelengths tuneable across 1100 - 1350 nm, suitable for basic multi-photon applications.

A technique for measurement of a prism apex angle by optical angle sensors with a reference artefact

A new technique for measurement of the apex angle of a right-angle prism is proposed. A reference artefact is newly employed as the datum for angle measurement, and the apex angle of a target prism is measured by detecting its deviation from that of the reference artefact by using a pair of optical angle sensors. At first, the principle of the apex angle measurement with the reference artefact and the optical angle sensors are addressed. After that, an optical angle sensor capable of evaluating various sizes of right-angle prisms over a large measurement range is designed and developed. A two-dimensional position-sensitive detector is employed as the photodetector for the optical angle sensor so that a high resolution and a wide measurement range can be achieved simultaneously. To avoid the influence of the interference between a directly-reflected beam and an internally-reflected beam when measuring a face of a right-angle prism, the optical setup is designed to have a laser beam that is made incident to a measurement surface with an oblique incidence. After the design and development of the optical angle sensor, the measurement system has been developed and some basic experiments are carried out to evaluate the basic performance of the developed optical angle sensor. The feasibility of the proposed technique of the prism apex angle measurement is also demonstrated through experiments and theoretical measurement uncertainty analysis based on GUM.

Effect of a Superhydrophobic Surface Structure on Droplet Jumping Velocity.

The coalescence-induced droplet jumping on superhydrophobic surfaces is fundamentally significant from an academic or practical viewpoint. However, approaches to enhance droplet jumping velocity are very limited. In this work, the effect of structural parameters of the triangular prism on droplet jumping is studied systematically. The results indicate that droplet jumping velocity can be greatly increased by exploiting structure effects, which is a promising reinforcement method. When the height and apex angle of the triangular prism are fixed, the droplet jumping velocity increases with the length of the triangular prism until a plateau is reached. The ratio of translational kinetic energy to released surface energy during droplet jumping is determined by the apex angle and the height of the triangular prism, which is more effective with a smaller apex angle and a larger height. The results are supposed to provide guidelines for optimization of superhydrophobic surfaces.

Image stitching using an electrowetting-based liquid prism with a fabrication method.

In this paper, we propose a new method for image stitching using an electrowetting-based liquid prism. Several images were obtained by adjusting the voltages applied to four sidewalls of the liquid prism, and a panoramic image was achieved through an image stitching algorithm. The relationship between the tilting angle of the liquid prism and the normal vector of the liquid-liquid interface was presented. Novel fabrication method has been proposed to improve the performance of the liquid prism, including the addition of a new structure to prevent oil isolation, plastic chamber material, plastic laser cutting, and oil selection. The fabricated liquid prism has a size of 5 × 5 × 8 mm, a maximum beam steering angle of ±10.5 °, a response time of 19.1 ms, and a resolution of 14.25 lp/mm. The required number of images according to the overlapping area was presented through the simulation, and the image stitching using two or three images was demonstrated.

Measurement of the apex angle of a small prism by an oblique-incidence mode-locked femtosecond laser autocollimator

A major modification has been made to the conventional mode-locked femtosecond laser autocollimator so that the apex angle of a small prism, which is a transparent object difficult to be measured by the conventional optical methods, can be measured. In the oblique-incidence optical setup, a collimated mode-locked femtosecond laser is at first made incident to a target prism, and the laser beam reflected from the prism surface is then projected onto a reflective-type grating for angle measurement based on the principle of the femtosecond laser autocollimator. With the robust signal processing technique in the femtosecond laser autocollimator where the spectrum of the first-order diffracted beams emanated from the grating is captured by the fiber detector, high-precision angle measurement can be realized even on a surface having a small area for measurement and/or on a surface having low reflectivity. An oblique-incidence femtosecond laser autocollimator with a fiber-based femtosecond laser source is developed, and its basic characteristics are then evaluated in experiments. An experimental setup composed of the oblique-incidence femtosecond laser autocollimator and a high-precision rotary table is also constructed for prism angle measurement. To avoid the influence of the internally reflected beam in a prism, a method employing the characteristic of Brewster's angle is newly proposed, and its feasibility is verified through experiments. The uncertainty analysis on the measurement of the prism apex angle by the oblique-incidence mode-locked femtosecond laser is also carried out based on GUM.

Analysis of the Rock Failure Cone Size Relative to the Group Effect from a Triangular Anchorage System.

This study employs the numerical analysis and experimental testing to analyze the fracturing mechanics and the size of rock cones formed in the pull-out of a system of three undercut anchors. The research sets out to broaden the knowledge regarding: (a) the potential of the undercut anchor pull-out process in mining of the rock mass, and (b) estimating the load-carrying capacity of anchors embedded in the rock mass (which is distinctly different from the anchorage to concrete). Undercut anchors are most commonly applied as fasteners of steel components in concrete structures. The new application for undercut anchors postulated in this paper is their use in rock mining in exceptional conditions, such as during mining rescue operations, which for safety considerations may exclude mechanical mining techniques, mining machines, or explosives. The remaining solution is manual rock fracture, whose effectiveness is hard to assess. The key issue in the analyzed aspect is the rock fracture mechanics, which requires in-depth consideration that could provide the assistance in predicting the breakout prism dimensions and the load-displacement behavior of specific anchorage systems, embedment depth, and rock strength parameters. The volume of rock breakout prisms is an interesting factor to study as it is critical to energy consumption and, ultimately, the efficiency of the process. Our investigations are supported by the FEM (Finite Element Method) analysis, and the developed models have been validated by the results from experimental testing performed in a sandstone mine. The findings presented here illuminate the discrepancies between the current technology, test results, and standards that favor anchorage to concrete, particularly in the light of a distinct lack of scientific and industry documentation describing the anchorage systems’ interaction with rock materials, which exhibit high heterogeneity of the internal structure or bedding. The Concrete Capacity Design (CCD) method approximates that the maximum projected radius of the breakout cone on the free surface of concrete corresponds to the length of at the most three embedment depths (hef). In rock, the dimensions of the breakout prism are found to exceed the CCD recommendations by 20–33%. The numerical computations have demonstrated that, for the nominal breakout prism angle of approx. 35% (CCD), the critical spacing for which the anchor group effect occurs is ~4.5 (a cross-section through two anchor axes). On average, the observed spacing values were in the range of 3.6–4.0.

A novel transillumination meibography device for in vivo imaging of mouse meibomian glands

PurposeWhile mouse models of dry eye disease (DED) have been developed, studies evaluating the role of the meibomian glands limited by the inability to temporally document changes. In this report we describe the development of a novel mouse transillumination meibography device and assess the ability of this device to detect age-related changes in the meibomian glands of young and old mice. MethodsThe mouse meibography device was comprised of a 3 mm wide right angle prism attached to broad spectrum light source by an optical fiber. Eyelids were then pulled over the prism using double tooth forceps and imaged using a stereomicroscope and low light level camera. Meibomian glands from four young and four old male, BALB/c mice were then imaged and analyzed using ImageJ. ResultsIn young mice, meibography documented the presence of 7–8 meibomian glands appearing as black and distinct eyelid structures with the length shorter in the lower eyelid compared to the upper eyelids. Eyelids of old mice showed apparent dropout of meibomian glands along with smaller and more irregularly shaped acini. The mean acini area of one meibomian gland was 0.088 ± 0.025 mm2 in young mice and 0.080 ± 0.020 mm2 in old mice (p = 0.564), but the Meibomian gland density was significantly lower in older mice (41.7 ± 6.4%, 27.3 ± 4.2%) (p = 0.021). ConclusionWe have developed an in vivo meibography device that may prove useful in sequentially documenting changes during development of meibomian gland dysfunction and following treatment.

Dispersion-compensated polarization Sagnac interferometer with high imaging quality

Multistage diffraction of a dispersion-compensated polarization Sagnac interferometer (DCPSI) reduces the fringe visibility of interference fringes generated in a focal plane array, thereby leading to the poor quality of the reconstructed polarization images. In this paper, a double total reflection prism between the DCPSI and imaging lens is added to limit the effect of multistage diffraction and improve the imaging quality. First, the influence of multistage diffraction on the interference fringes and the ratio of fringe amplitude to the background was analyzed. Second, the range of angles of the two right angle prisms was calculated. Simulation and experiment were carried out to prove the superiority of the proposed method. Result shows that the ratio of fringe amplitude to the background increases from 1/5 to 1/3 and from 1/10 to 1/6 in simulation and experiment when a double total reflection prism structure is added respectively. This method can reduce the influence of multistage diffraction on interference fringes and improve the image quality of DCPSI effectively.

Rotational Doppler shift upon reflection from a right angle prism

This Letter reports the observation of a rotational Doppler shift on reflected beams carrying Orbital Angular Momentum (OAM). More precisely, we study the beat frequency of two optical beams carrying OAM with opposite signs, reflected on a right angle prism. We show that the interference of the two beams leads to a daisy-like pattern that rotates at twice the rotating frequency of the prism. The rotational Doppler frequency shift is equal to the OAM topological charge change times the rotational frequency. Possible applications in the positioning and detection of rotation of objects are then discussed.

Интерферометр для контроля углов клиньев

The paper considers an optoelectronic laser interferometer system to control wedge angles. This system records an interference pattern on an image sensor. The interferometer makes it possible to estimate the small angle of the wedge under investigation by the variation it introduces into the shape of the optical radiation wavefront, which the interferometer then converts into changing the size of the interference pattern. In the interferometer considered, the wedge under investigation refracts the incident ray cone. The error inherent in surface finishing causes the deformation of the working wavefront to be 2 to 4 times smaller as compared to the deformation in previously known control setups involving reflection from the wedge surfaces. The interferometer developed ensures highly accurate control of wedge angles at the surface polishing stage, including potential detection of wedge direction. If required, the interferometer may be used for comprehensive quality control of wedge manufacturing, assessing not only the surface nonplanarity, but also glass inhomogeneity; it may also be used to control prism angles

The effect of the thickness of the glass plate of a hollow prism on the accuracy of measuring the refractive index of edible oil

Effect of the thickness of the ordinary commercial glass plate utilized for making hollow prism on accuracy of measuring the refractive index of edible oil was investigated. The edible oil sample was filled into the prism cavity and then a laser beam (helium neon, He–Ne) is passed through the prism cavity. The prism angle and the deviation angle of the refracted laser beam is used for calculation the refractive index. The thickness of the glass plate used to make hollow prisms was varied from 2 mm to 5 mm. The effect of the glass plate thickness to measurement accuracy was examined using the fluid prisms with different prism angles of 30°, 45° and 60°, respectively. It was discovered that refractive index of edible oils can accurately be determined by employing the hollow prisms constructed from the ordinary commercial glass plate. It was also found that the thickness of the glass plates utilized for constructing the hollow prism significantly influences the measured refractive index, namely the refractive index increases with increasing thickness of the glass plate. This implies that the glass plate thickness constitutes the measurement accuracy. The commercial glass plate thickness giving to the highest measurement accuracy is 2 mm.

Variation in the timing of enamel formation in modern human deciduous canines

ObjectivesDeciduous canines are now used increasingly in archaeological and forensic studies to establish the time of birth and as a retrospective source of trace elements incorporated into enamel before and after birth. However, data on the variability of deciduous enamel formation times are scarce. Our objectives were to use daily incremental markings to estimate daily secretion rates, the timing of prenatal, postnatal and total enamel formation and any changes in enamel coverage or prism and stria orientation that occur during enamel formation. Materials and MethodsLongitudinal ground sections of 81 deciduous canines were studied with transmitted light microscopy. High-resolution digital images were imported from an Olympus VS-120 virtual slide scanning system into a geographic information system (ArcGIS, ESRI USA) for quantitative and statistical analyses of linear, angular and area measurements of buccal enamel. ResultsDaily rates of enamel secretion close to the EDJ were faster than in permanent enamel (3.23 μm/day, SD = 0.54). Prism and stria angles subtended to the EDJ both increased through crown formation. Enamel coverage was low in the cusp and cervix but maximal ∼150 days after birth. The mean prenatal enamel formation time was 118 days (range 60−150, SD, 29.2, n = 24). The overall mean postnatal enamel formation time was 319 days (range 210–420, SD 50.6, n = 67). ConclusionsDaily enamel secretion rates compared well with previous studies of deciduous enamel, however, enamel extension rates in deciduous cuspal enamel were notably lower. The variability of both prenatal and postnatal deciduous enamel formation times was greater than previously reported.

Optical design of light guide prisms with surface roughness for automotive tail lights

This study presents the optical design of light guide prisms for automotive tail light applications to obtain the optimum luminous intensity and the illuminance uniformity. The design was achieved using optical design software, SPEOS. By considering the axial luminous intensity and legal requirements, the optimum prism angles of light guides were determined by simulations. After determining the prism angles, the effect of different surface roughness on the luminous intensity and the illuminance uniformity was investigated. The light guides designed by considering data from the simulation were manufactured as prototypes and their photometrical measurements were made. These measurements were compared to the simulation results. It was observed that simulation and prototype results are well in agreement with each other. Furthermore, it was found that as the surface roughness increases both the luminous intensity decreases and the illumination becomes more uniform.

Celdas en cuña para refractometría: criterios de selección de materiales y parámetros

Este trabajo presenta criterios de selección de materiales y parámetros de celdas en cuña para refractometría en el rango visible. Estas celdas consisten en dos prismas de ángulo recto enfrentados, que definen una cavidad con forma de cuña entre ellas, en la que se coloca la muestra cuyo índice de refracción se desea medir. Éste se determina a partir de la desviación de un haz luminoso que atraviesa la celda. Este modelo para fines de ingeniería tiene en cuenta la geometría de la celda y los índices de refracción del material de la celda y de la muestra. A partir de allí realizamos el cálculo numérico y trazado de rayos correspondiente al sistema óptico. También proponemos ajustes polinómicos para simplificar el tratamiento numérico, como complemento de las ecuaciones completas. Estos polinomios dan el índice de refracción de la muestra como una función explícita del ángulo de deflexión. Se incluye además el análisis de los errores de la aproximación.

Single-volume dual-channel acousto-optical tunable filter.

In this paper, we present a novel approach to spectral stereoscopic imaging. It is based on simultaneous spectral filtration of two light beams with a tunable acousto-optical filter (AOTF) of original design. It does not require large crystals and complicated optical relay systems, because two beams diffract in the same volume of the crystal medium but at different angles. We show that this geometry can be composed of a common-type AO cell and two triangular prisms of the same material. We derive equations, which specify the prism angles ensuring the necessary orientation of beams trajectories inside the crystal medium as well as parallel propagation of input and output beams. Some angles were additionally optimized for aberrations minimization by means of ray-tracing simulation. Experimental testing demonstrates rather high quality of spectral images, which is necessary for stereoscopic reconstruction procedure. The proposed approach makes possible development of spectral stereo-imaging components based on different types of previously developed AOTFs.