This thesis suggests that prior to Ptolemaic and Roman times, ancient Egypt had two distinct and parallel linear systems: the royal system limited to official architectural projects and land measurements, and a great (aA) system used for everyday measurements. A key 1/3 ratio explains ancient Egyptian linear measurements and their agricultural origin. Emmer is 1/3 lighter than barley, consequently, for an equal weight, a container filled with emmer will be 1/3 greater than a container filled with barley. The lengths derived from both containers share the same 1/3 ratio. The second chapter, Previous Studies, lists the work of scholars involved directly or indirectly with ancient Egyptian metrology. The third chapter, The Royal Cubit as a Converter and the Scribe’s Palette as a Measuring Device, capitalizes on the colour scheme (black and white on the reproduction of Appendix A) appearing on the Amenemope cubit artifact to show the presence of two cubits and two systems: the black (royal system) and the white (great [aA] system) materialized by the scribe's palette of 30, 40, and 50 cm. The royal cubit artifacts provide a conversion bridge between the royal and the great systems. The information derived from the visual clues on the Amememope cubit artifact are tested against a database of artifacts scattered in museums around the world. The fourth chapter, The Origin and Evolution of Ancient Egyptian Cubits, historically relates the ancient Egyptian linear systems to the closed metrological systems they belong to. A closed metrological system is a system in which units of length, volume, and weight are related to each other. The conclusion is that the ancient Egyptian metrological system is backward compatible as it is possible - using a hin as a closing volumetric unit and emmer, barley, wheat (triticum durum) and water as commodities - to re-construct the linear metrological systems of all ancient Egyptian periods.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 182-189).

This thesis addresses a comprehensive approach to understanding the time-varying thermal errors in machine tools. Errors in machine tools are generally classified as being time or spatial dependent. Thermal errors are strongly dependent on the continuously changing operating conditions of a machine and its surrounding environment. Uniform temperature rises or stable temperature gradients, which produce time-invariant thermal errors, are considered to be rare in ordinary shop floor environments. Difficulties in analysing time-varying thermal errors are that, first of all, the temperature distribution within the components of a machine should be evaluated, and secondly, the distribution is continuously changing with time. These difficulties can be overcome by introducing a point-wise description method with three thermal parameters. From the theoretical analysis of simple machine elements such as bars, beams and cylinders, and extensive finite-element simulation data for a straightedge subject to room temperature variations, three thermal parameters, i. e. time-delay, time-constant and gain, were identified to obtain a precise description of the thermal deformation of a point of a machine body. Time-delay is dependent largely on thermal diffusivity, and the heat transfer mechanism. The time-constant is governed by heat capacity, heat transfer mechanism and body size. Gain, on the other hand, is determined by the thermal expansion coefficient, heat transfer mechanism and mechanical constraint. The three thermal parameters, in turn, imply that thermal deformation of a point in a body can be described by a simple first- order differential equation. Regarding their dependence on the heat transfer mechanism, a more refined description requires a time-varying linear first-order differential equation. Such an equation can be applied to each point of interest of a machine body. The final form of modelling, using the parameters, is a state-space equation gathering the governing equations for the points of interest. By adopting the point-wise discrete modelling method, we can overcome the difficulty of the spatial distribution of the temperature. Indeed, the calibration of a machine tool is usually performed at discrete points. The completion of this approach was made by presenting the methods by which the three thermal parameters can be evaluated. The first method employs analytical tools based on simplifying assumptions about the shape and boundary conditions of machine components. The second method was to apply numerical techniques to complex machine components. Because there are many drawbacks in theoretical approaches, experimental techniques are essential to complement them. The three thermal parameters can be easily identified using popular parameter identification techniques which can be applied to time-varying cases by their recursive forms. The techniques described were applied to modelling the thermal errors in a single-point diamond turning research machine. It was found that the dominant error component was spindle axial growth. The predictive model for the time-constant was shown to be in agreement with both the machine and with the scaled physical model rig.

Two different factors involved in the measurement of photogrammetric plates have been studied. A novel interferometer designed to monitor the position of a microscope stage, to be used to measure photogrammetric plates, has been built. The prototype instrument is able to give the position of the stage with a maximum error of less than 200nm. An algorithm has been developed for a motor driven x-y microscope that is able to search a photographic plate automatically for targets, and record their positions. In a trial survey this system was able to measure the positions of the targets on the plates with an uncertainty of approximately 2gm. This result is comparable with the precision that a human operator could achieve using the same equipment, but without the fatigue effect associated with visual observation. Virtually no human interaction is necessary for the system to function.

New optical designs have necessitated using refractive index data that is accurate to the third and fourth decimal points. Prism coupling refractometry could be attractive for this task because of a combination of factors. It allows for a direct assessment of the refractive index like interferometry or the minimum deviation method while being quick and convenient, like Kramers-Krönig analysis and spectroscopic ellipsometry. However, the accuracy, precision, and repeatability of this technique have not been revisited recently in the literature. This thesis seeks to identify the critical features of this technique that define its uncertainties and then provides some initial improvements to this system. The improvements explored are hardware-based and incorporate a novel approach to fitting this data. The resulting error budget defined by this strategy increases the measured precision, taking the first step towards making the method a standard metrology technique suitable for the shop floor.

In mesoscale manufacturing desired dimensional and surface characteristics are defined, but edge conditions are not specified in design. The final edge conditions that exist in mesoscale objects are created not only by the manufacturing process but, because of their size, also by part handling procedures. In these parts, the concern is not only with burrs, which can be formed by some mesoscale manufacturing processes, but also with the shape and size of the edge. These properties are critically important as the edge can constitute a large percentage of the smallest features of mesoscale objects. Undefined edge geometry can result in measurement, assembly, and operational difficulties. Due to the potential problems caused by edge conditions, it is desirable to have the ability to measure and characterize the edge conditions of parts. This thesis considers mesoscale measurement tools to provide an edge measurement tool recommendation based on edge size and properties. A set of analysis techniques is developed to determine the size and shape of the measured edge, locate any local inconsistencies such as burrs or dents, and track trends in calculated parameters as a function of edge position. Additionally, a standard method for communicating design requirements is suggested in order to differentiate between acceptable and unacceptable edges.

Precisely positioned optical lenses are currently required for many highly repetitive mechanics and applications. Thus the need for micron-scale repetition between opto-mechanical units is evident, especially in industrial manufacturing and medical breakthroughs. In this thesis, a novel optical metrology system is proposed, designed, and built whose purpose is to precisely locate the center of a mechanical fixture and then to assemble a plano-convex optical lens into the located position of the fixture. Center location specifications up to ±3 µm decenter and ±0.001° tilting accuracy are required. Nine precisely positioned lenses and fixtures were built with eight units passing the requirements with a repetitive standard deviation of ±0.15 µm or less. The assembled units show satisfactory results.

Accurate determination of surface texture is essential for the manufacturing of mechanical components within design specifications in engineering and materials science disciplines. It is also required for any subsequent modifications to physical properties and functional aspects of the object. A number of methods are available to characterize any surface through the measurement of roughness parameters that can then be used to describe surface texture. These methods may be divided into those in that direct contact is made with the surface and those where such contact is not required. This report describes two methods approach for the surface profiling of a quartz glass substrate for step height, and tungsten substrate for roughness measure. A stylus profilometer (contact method) and vertical scanning interferometer, (VSI) or (non-contact optical method) were used for step height and roughness parameter measurements. A comparison was made with nominal values assigned to the studied surface, and conclusions drawn about the relative merits of the two methods. Those merits were found to differ, depending on the parameters under consideration. The stylus method gave better agreement of step height values for dimensions greater than a micron. Both methods showed excellent accuracy at smaller dimensions. Both methods also provided accurate average roughness values, although the VSI data significantly overestimated 35% above the peak-to-valley parameter. Likely sources and nature of such differences are discussed based on the results presented, as well as on the previous comparison studies reported in the literature. Because of such method-specific differences, the multi-technique approach used in this work for accurate surface profiling appears to be a more rational option than reliance upon a single method. Both contact and non-contact approaches have problems with specific roughness parameters, but a hybrid approach offers the possibility of combining the strengths of both methods and eliminating their individual weaknesses.

Since 1975 McCarthy and Low have conducted a program of Michelson spatial interferometry at infrared wavelengths, measuring a large number of evolved stars and protostellar objects. This dissertation discusses the development of an infrared speckle interferometer which was used to extend those observations. This instrument uses a modified version of the technique pioneered by Sibille, Chelli, and Lena. The secondary mirror is used to scan the image across a narrow slit. Each scan is fourier transformed, and the modulii squared of many such transforms are coadded. Both the object of interest and a point source are observed. The square root of the ratio of their power spectra is the visibility as defined by Michelson. This system was assembled for the most part with existing equipment and the design should be readily adaptable to other observatories. Initial tests were made with the 154 cm telescope of the University of Arizona since it had a preexisting mechanism for scanning the secondary. However most of the observations were carried out with the University's 229 cm telescope. A new linear servo was added to the existing hard-stop chopper for this telescope's f/45 secondary. Three detector systems were used to provide wavelength coverage from 2 to 12 microns. An N₂ cooled InSb and a He cooled bolometer were available from the Michelson program. In addition a high sensitivity He cooled InSb detector from the Steward Observatory FTS was used. Slits with an angular size of λ/2D, where D is the telescope diameter were placed at the focal plane in the dewar. The narrow slit results in diffraction losses when used with conventional dewar optics. The loss could be eliminated with optics optimized for this application. However even with the loss, a large number of objects could be observed. Test results at 2 microns were obtained for a double star, the asteroids Vesta and Ceres, and the Galilean satellites Ganymede and Callisto, The protostellar objects W3 IRS 5, S140, and Mon R2 IRS 3 were resolved. The separation, orientation, and relative brightness of the two components IRS 5 were measured at 5 microns. The separation is 1.26" ±0.06 and the position angle is 37° ±5. The brightness ratio is approximately 0.59. S140 and Mon R2 IRS 3 were observed at 2 microns. S140 shows some indication of an extended region of greater than 1" contributing half the flux. IRS 3 has a size of approximately 1" but the data is too noisy for an exact fit. Upper size limits were determined for BN, GL 490, GL 2591, and NGC 2264 IRS. A large number of evolved stars were observed. The size of the shell around Alpha Ori was found to be ∼4" at 11 microns. Observations were obtained for IRC + 10216 at 2, 5, 8, and 11 microns which further define the asymmetrical shape of this object. Observations were also obtained for VY CMa. Upper size limits were established for Omicron Ceti, IRC + 10011, RX Boo, R Hyd, W Hyd, and CIT 6.

This work examines a novel method of dynamic single frame interferometry. In this dynamic approach to phase shifting measurements, steps are taken to combat performance degradation due to environmental factors such as air turbulence and vibration. We explore the system functionality and performance, and examine some of the limiting factors using this technique such as effects due to imperfect system components, irradiance variations and sensitivity of the instrument accuracy based on calculation methodology. We present the errors associated with these various aspects of the system and show the majority cause phase calculation errors less than 0.005λ P-V to the calculated wavefront. This new approach involves the placement of a micropolarizer phase-shifting array directly onto a CCD camera which allows the construction of a dynamic single frame interferometric system. Hardware and manufacturing preparations such as inspection, positioning and alignment are discussed. Experimental results of system performance are combined with mathematical simulations to provide a performance baseline. We present experimental results showing the effects of averaging on measurement data, which results in a reduction of fringe print-through errors associated with a combination of many of the system error sources.