الفهرس 
Chapter One Introduction a nd Literature ReviewOnly 14 pages are availabe for public view
 |  | from | 217 |  |  |
| | | from | 217 | | |
Abstract
Flat and spherical surfaces are essential components of optical systems and imaging devices. Flat surfaces are commonly employed in machining industries and space applications. Moreover, precision spheres are essential as a calibration standard for many high-accuracy instruments in dimensional and mass measurements. Therefore, accurate geometry measurement and eliminating surface irregularities of these surfaces represent a challenge for modern industries. Geometry and surface irregularities can be measured by contact methods (coordinate-measuring machines) or non-contact methods (such as laser interferometers). In this study, a Fizeau laser interferometer (GPI-XP, Zygo) with phase-shifting capability and a displacement-measuring interferometer (ZMI-1000, Zygo) are employed to obtain these measurements.
The absolute flatness obtained for a 101.6 mm-diameter glass flat is 0.0443 µm, with a standard deviation of 0.0018 µm and an expanded uncertainty of ±0.0106 µm. Also, a 30 mm Si-C flat is 0.0067 µm, with a standard deviation of 0.0002 µm and expanded uncertainty of ±0.0042 µm. Also, this work investigates twelve factors that affect the accuracy of flatness measurements, and the associated uncertainty budgets are evaluated.
A spherical surface’s main property is its radius of curvature (ROC). The ROC measurement obtained for a silicon-nitride sphere is 12.499218 mm, with a standard deviation of 0.000064 mm and expanded uncertainty of ±0.00089 mm. Also, the ROC obtained for a ceramic sphere is 14.992913 mm, with a standard deviation of 0.000402 mm and an expanded uncertainty of ±0.000833 mm. In addition, the ROC obtained for a glass sphere is 25.392365 mm, with a standard deviation of 0.000296 mm and expanded uncertainty of ±0.000846 mm.
The default use of the Fizeau laser interferometer (GPI-XP, Zygo Co.) is for testing flat surfaces, lenses, and mirrors of 102 mm diameter, and it is not prepared for testing heavy spheres. This work presents a modification for the interferometric system to expand its capability for testing spheres of diameters up to 145 mm and masses up to 2 kg. The modification is a fabricated stainless-steel holder and an electric rotating platform. The suggested modification proved a considerable success in testing a mass-standard silicon sphere (SiScKg-02-d, PTB Inst.); an average measured value of the surface irregularities is 43.9 nm, with an improved repeatability of 2.8 nm and a minimized measurement uncertainty of ±6.8 nm. Also, the obtained ROC is 46.799274 mm, with a standard deviation of 0.000713 mm and expanded uncertainty of ±0.001067 mm; this value is significant for calculating the sphere’s volume and Avogadro’s constant.
Furthermore, this study investigates seventeen error sources that affect ROC measurement; three of them are newly added by this work: focal shift, optical distortion, and y-axis vibration. The uncertainty budgets for ROC measurements are evaluated individually for each tested sphere.