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In the basic understanding of measurement, students are expected to be able to subdivide a given whole into a unit and then change the position of that unit along the entire length of the whole. These basic operations of subdivision and change of position are related to the more formal operations of partitioning and iterating. In the context of fractions, partitioning and iterating play a fundamental role in understanding fractions as measures, where students are expected to partition a whole into an iterable unit. In the context of angle measurement, students are expected to measure angles as a fractional amount of a full rotation or a circle, by partitioning the circle into a unit angle and then iterating that unit angle to find the measure of the given angle. Despite this link between measurement, fractions, and angles, research suggests that there is a disconnect between students' concepts of measurement and geometry concepts, including angle and angle measurement. Therefore, one area of study that might help us understand this disconnection would be to investigate the relationship between students' concepts of measurement and their concepts of angle measurement. This current study documents sixth, seventh, and eighth grade students' measurement schemes for fractions and their quantifications of angularity, and then investigates the relationship between them. This research is guided by the following question: What is the relationship between middle school students' measurement schemes for fractions and their quantifications of angularity? Results indicate that the majority of students involved in this study do not possess a measurement concept of fractions nor a measurement concept of angularity. However, these results demonstrate that there is a relationship between students' measurement schemes for fractions and their quantifications of angularity. It is concluded that students who construct more sophisticated fraction schemes tend to construct more sophisticated quantifications of angularity. / Doctor of Philosophy / Although the concepts of measurement, fractions, and angle measurement are related, research suggests that there is a disconnect between students' concepts of measurement and geometry concepts, including angle and angle measurement. Therefore, one area of study that might help us understand this disconnection would be to investigate the relationship between students' concepts of measurement and their concepts of angle measurement. This current study documents sixth, seventh, and eighth grade students' understandings of measurement, as indicated by their fraction schemes, and angle measurement, as indicated by how they quantify angularity or the openness of an angle. This study then investigates the relationship between them. This research is guided by the following question: What is the relationship between middle school students' measurement schemes for fractions and their quantifications of angularity? Results indicate that the majority of students involved in this study do not possess a measurement concept of fractions nor a measurement concept of angularity. However, these results demonstrate that there is a relationship between students' measurement schemes for fractions and their quantifications of angularity. It is concluded that students who construct more sophisticated fraction schemes tend to construct more sophisticated quantifications of angularity.

No description available.

‘Optical Caustics’ represent some of the most visually striking patterns of the light in nature.They occur when light rays from a source, such as the sun, get refracted, or reflected by curved media so as to bend and alter their path. They are ubiquitous and signify the regions of space in which many rays intersect to form bright singularities along a two-or a three-dimensional surface. The associated 2-D patterns (caustic patterns) could be simple or complex in ‘shape and size’ depending upon the optical arrangement used to produce them. Such patterns exhibit either a static or a dynamic behavior which can be controlled sensitively by the medium or the device used to produce them. The present thesis concerns with a few novel contributions in utilization of such optical caustics for the measurement of small angular rotation/tilt of objects. Utilizing a ‘hollow cylinder’ as a novel device for the generation of the optical caustics, the author proposed and demonstrated three new schemes of realizing a position-dependent-behavior of ‘Optical Caustic Patterns’. The said behavior is investigated both analytically as well as experimentally. The results of the investigation are then utilized to propose and demonstrate three methods of magnifying angular displacement of the hollow cylinder. The salient feature of the principle behind each of the said methods is illustrated in the figures below. The patterns in each of the above pictures correspond to two different positions of the hollow cylinder-the pattern in white color corresponds to the initial position while that in red color corresponds to new angular position of the cylinder. Defining S1 = ƒ (LΔΦ), S2= ƒ(TΔΦ) and S3= ƒ(ξ ΔΦ) as new signals from the proposed methods, it has been shown that each of them represent a magnified measure of the change in the angular position of the cylinder ΔΦ. Further, if a plane mirror is used in place of cylinder in the proposed methods, the corresponding signal S for the same change in the angular position ΔΦis represented by ΔD. For a chosen set of the experimental conditions, it is shown that for unit change in ΔΦ, the values of S1, S2 and S3 change 30, 37 and 62 times faster than ΔD. The investigations clearly demonstrate that hollow cylinders can be advantageously used as position-magnifying angle-sensing devices. The results of the investigations also suggest that in application areas such as auto collimation, torsion pendulum and design of motion control stages, this device is expected to bring in new advances.

International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada / An original design is presented for a system capable of measuring the relative angle of a flat surface using reflected ultrasonic wave pulses. No physical contact with the surface is necessary. The measurement range is from 0 to 54 degrees. Theoretical resolution is 5 minutes of arc, with actual measured resolution of approximately 20 minutes of arc. The system has performed successfully in limited flight tests, is capable of rates up to 80 angle measurements per second, and has a solid-state memory recording capacity of 24,000 bytes. The measurements are time-tagged as they are recorded and may be transferred to a personal computer at a later time over a standard RS-232 serial communications link. The system is small (approx. 6 by 4 by 1.5 inches) and uses two standard 9-volt batteries as its power source.

The work reported in this thesis has been carried out in the following two areas of Optical metrology: 1. Measurement and correction of prism angles 2. Measurement of refractive indices using a spectrograph. The prism angles are conventionally tested by mechanical bevel protractors, autocol-limators (angle dekkors), simple interference techniques and interferometers. All these methods have their own limitations either in accuracy or in terms of cost. Mechanical methods are usually employed to measure the angles of prisms. Interference techniques and interferometers are also used but they need optically polished components. For both mechanical and simple interference methods of testing, it is essential to fabricate more than a single component in number. The process of building interferometers or purchasing interferometers, angle dekkors and standard angle gauges is not cost effective for many research laboratories, and medium scale industries. To overcome these difficulties simple and inexpensive methods without sacrificing the accuracy in the bargain are suggested for the measurement of prism angles, based on the principles of reflection of light. The refractive indices of prism materials for invisible and weaker spectral lines are usually determined from spectrograms using dispersion formulae and numerical interpolation techniques. In these methods, the accuracy of the results depends on the accuracy of determining the constants of the dispersion formulae. A simple experimental technique, using a spectrograph, is devised for the measurement of refractive indices of solids and liquids both for visible and invisible spectral lines (wavelengths). The thesis has been divided into six chapters. The first chapter starts with the general introduction. The second chapter presents the literature review of the existing methods for angle and refractive index measurements. The third chapter describes the proposed new techniques for prism angle measurements. The fourth chapter presents the experimental results of angle measurements, and the discussion of the accuracy of the results. This chapter also gives the scope for further research. The fifth chapter describes a newly proposed technique for measuring refractive indices and the experimental results. This chapter also gives the scope for further research. The summary of the results, conclusions, and suggestions for further work are presented in chapter six.

Disertacijoje nagrinėjamos geodezinių kampus matuojančių prietaisų patikros bei kalibravimo metodai bei priemonės. Pagrindinis tyrimo objektas yra geodezinių prietaisų tikslumo parametrų matavimo būdų ir priemonių analizė, kalibravimo įrenginio kūrimas, jo tikslumo charakteristikų tyrimas bei įrenginio tobulinimas. Šie objektai yra svarbūs vykdant geodezinių prietaisų kalibravimą, kas savo ruožtu yra labai svarbu užtikrinant reikiamą šių prietaisų matavimų tikslumą geodezijoje, statybose, mašinų gamyboje ir t. t. Pagrindinis disertacijos tikslas – geodezinių kampų matavimo prietaisų kalibravimo galimybių analizė ir sukurto kalibravimo įrenginio tikslumo parametr�� tyrimas. Darbe sprendžiami keli pagrindiniai uždaviniai: plokščiųjų kampų matavimo metodų bei įrenginių, tinkamų geodeziniams prietaisams kalibruoti, analizė; daugiaetalonio kampų kalibravimo stendo kūrimas Vilniaus Gedimino technikos universiteto Geodezijos institute bei jo tikslumo charakteristikų tyrimas; stendo tikslumo didinimo galimybių bei priemonių tyrimas, ir apskritiminių skalių kalibravimo būdų tobulinimas. Disertaciją sudaro šeši skyriai, įvadas, išvados, literatūros sąrašas bei priedai. Įvade nagrinėjamas problemos aktualumas, formuluojamas darbo tikslas bei uždaviniai, aprašomas mokslinis darbo naujumas, pristatomi autoriaus pranešimai ir publikacijos, disertacijos struktūra. Pirmasis skyrius skirtas labiausiai paplitusių plokščiųjų kampų matavimo būdų bei priemonių tinkamų geodeziniams prietaisams... [toliau žr. visą tekstą] / The main idea of current PhD thesis is an accuracy analysis of testing and calibration of geodetic instruments. The object of investigation is an analysis of means and methods for testing and calibration of geodetic instruments for plane angle measurement, development of such calibration equipment, its accuracy investigation and the research of its accuracy increasing possibilities. These objects are important for successful testing or calibration of geodetic instruments for angle measuring which is essential in ensuring the precision of measurements taken in surveying, construction, mechanical engineering, etc. There are several main goals of the presented work. First one is an analysis of the angle measuring methods and devices suitable for the testing and calibration of geodetic instruments, according to the results of the mentioned analysis the second task can be formulated – creation of a multi-reference plane angle testing and calibration equipment at Institute of Geodesy, Vilnius Gediminas Technical University and investigate the parameters of its accuracy. The third task is to investigate the accuracy increasing possibilities of the equipment, and implementation some of them into the practice. The thesis consists of four chapters, introduction, conclusions, list of references and appendixes. Introduction is dedicated for an introduction to the problem and its topicality. There are also formulated purposes and tasks of the work; the used methods and novelty of... [to full text]

Development of composite material is very much progressive sector and leads to evolution of material with new property. This type of material has one, but important deficiency. It is small adhesion armature to matrix. My study is sight on improvement adhesion the surface by deposition self assembled (SA) monolayer from organosilanes. Property of this layer, like thickness, surface tension, homogenity and wettability, was evaluated by the contact angle measurement and spektroscopical elipsometri.

Mellan år 2020 och år 2021 registrerades 381 operationer av böjsenskador i Sverige. Rehabiliteringsprocessen efter en böjsenskada är lång och kräver kontinuerlig uppföljning. Uppföljningen sker genom mätningar av böj- och sträckförmågan i de fingrar som patienten opererat. Mätningarna utförs i nuläget manuellt med goniometer, där vinklarna i fingrarnas leder mäts, en gång per vecka på en handkirurgisk mottagning. Handkirurgiska kliniken på Södersjukhuset i Stockholm efterfrågade ett digitalt mätverktyg som skulle göra det möjligt för patienten att på ett tillförlitligt sätt mäta vinklarna hemma i stället för på kliniken. Målet med projektet var således att skapa ett mätverktyg som mäter vinklarna med ett mätfel på högst 5 grader. Ett mätverktyg utvecklades som utför mätning av vinklar med hjälp av en bild användaren tagit. Mätverktyget är kompatibelt med Androidenheter och kan implementeras i en redan existerande Androidapplikation. Tester visade att mätverktyget har ett mätfel med ett medelvärde på 5 grader eller lägre för proximala interfalangealleden och distala interfalangealleden. Vidare var medelfelet 7,3 grader respektive 6,4 grader för metakarpofalangealleden vid böjt respektive sträckt finger, samt 10 grader för totalt aktivt rörelseomfång (total active motion). / Between 2020 and 2021, 381 operations for flexor tendon injuries were registered in Sweden. The rehabilitation following surgery is long and requires continuous monitoring. Presently the monitoring is done through manual measurements of the patients flexing and extending capability of the fingers affected. The measurement is performed at a hand surgery department with a handheld goniometer, initially once a week. The hand surgery department at Södersjukhuset in Stockholm requested a digital tool that allows the patient to reliably measure the angles of the fingers bending and stretching capability at home instead of at the clinic. The objective of the project was therefore to create a measurement tool that measures these angles with a maximum error of 5 degrees. A measurement tool was developed where the measurement of angles takes place from an image taken by the user. The measurement tool is compatible with Android devices and can be implemented in an existing Android application. Tests showed that the measurement tool has a mean measurement error of 5 degrees or less for the proximal interphalangeal joint and the distal interphalangeal joint. In addition, the mean error was 7.3 degrees and 6.4 degrees for the metacarpophalangeal joint, bent and stretched respectively, and 10 degrees for total active motion.

The present thesis concerns with a few investigations on sensing/measurement of small angle rotation/tilt using Pattern Imaging Method. The methodology involves looking at the tailored-objects located adjacent to the observer (CCD camera) through a mirror and extracts the angular position of the mirror from their images by processing the latter through object specific algorithm. Its principal advantage stems from the fact that small-angle measurement can be done using ambient light which is neither collimated nor filtered for single wavelength. This makes the associated optical configuration not only simple but also robust for the said application, in comparison to currently competing technologies based on Autocollimation and Interferometry. The present thesis elaborates specifically four new Pattern-Designs proposed for tailoring the spatial-brightness of the objects. Introducing for the first time, processing algorithms based on ‘Modified Fringe-Processing Strategy’ and ‘Phase-Only-Correlation’, the investigations demonstrate enhanced performance for small angle measurement with all the proposed pattern designs. The first three designs for the pattern are evaluated for 1-D measurement through fringe processing approach while the fourth pattern design is evaluated for 2-D measurement through Phase-only-Correlation. The results of the investigations are utilized to propose, design and develop a novel optical inclinometer which can work with any of the proposed pattern designs as the object. The first three pattern-designs rely upon sinusoidal modulation of the object surface and utilize three custom developed algorithms -Algorithm-A, Algorithm-B and Algorithm-C -to extract two quantities namely wrapped phase Δαw and unwrapped phase Δαuw , from the captured images. Each of these quantities will have an associated measurement range and accuracy corresponding to any of the three pattern designs. All measurements are carried out keeping the object/camera to mirror distance constant at 250 mm. From wrapped phase measurement, all the three designs, each with pitch of 2mm for sinusoidal modulation and held at a distance of 250 mm from the mirror, have been found to facilitate reliable angle measurement over a range of 850 arc seconds with accuracy better than 1 arc second after curve fitting the experimentally obtained data. From unwrapped phase measurement, the color coded as well as BCD coded composite patterns, when tested using five bands of sinusoidal modulation (with a pitch of 2mm) and held at a distance of 250 mm from the mirror, facilitated reliable angle measurement over a larger range of nearly 10 . The 2-D angle measurement using fourth pattern-design and the Algorithm-D, facilitated measurement over a range of 10 with an accuracy of 9 arc seconds when the distance between the mirror and the pattern is held at 250 mm. A comparison of the results from the present investigation with the best performance from other investigators reveals the following. The proposed modifications in the processing algorithms as well as the pattern designs help to achieve a measurement range of 750 arc seconds with accuracy better than 1 arc second from this method, with an object pattern whose lateral size is smaller by a factor of nearly 15. Such a size reduction in the object as well as the associated mirror would help to construct angle measuring instruments that work on this method more compactly. The results of the investigation have been utilized to propose and demonstrate a novel prototype optical inclinometer which has been experimentally found to work in a range of 0.40 with accuracy nearly 6 arc seconds.