Kevin E. Bowes
Published: 2012
Total Pages: 538
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Spherical optics produced by traditional polishing methods are easy and inexpensive to manufacture. However, these types of optics are currently limited by spherical aberrations induced as a result of the figuring process. In order to alleviate these optical aberrations, and at the same time minimize the number of elements used in an optical system, the required form of the optical element must be of the aspheric or free-form variety. Ultra precision multi-axis diamond machining can be used to manufacture optical quality aspheric and free-form components. Thermal environmental changes while machining a part, especially large parts several meters in size, can lead to significant form deviation. Final inspection is not typically completed while the part is on the machine; rather the part is measured externally with a coordinate measuring machine (CMM), an optical scanner, or an interferometer. Improper operator use of contact measurements can compromise the surface quality, interferometry is best suited to nearly flat or spherical components, and common optical scanning techniques often do not meet desired measurement uncertainties. Further, removing the part for the measurement breaks the connection between the part and machine-tool coordinate systems and re-machining is difficult. Currently, the limiting factor in part manufacturing is the precision metrology used to assess surface form errors. If measurements of the form could be performed in-situ, while the part is being machined, then better parts could be manufactured where inaccuracies in the surface form caused by the machine tool can be corrected. The new measurement system proposed here combines photogrammetry and optical scattering, with beam propagation of a laser from the part. A laser beam is directed toward the surface and reflected from the surface to be measured, passing through and diffusely scattering from two windows. Photogrammetry is used to determine the coordinates of the beam locations at the two windows, which is then used to define the incident and reflected beam orientations. Vector calculus is then applied to determine the surface normal, and finally the profile is extracted via integration. For this metrology technique, it is suggested that uncertainties in the angle of the incident beam with respected to the surface normal, directly correlates to the uncertainties in the localized slope, or sagittal deviation at a particular point. The current limiting factor for the system is its sources of error which can include the proper calculation of the centroid of the scattered laser dot targets generated on the windows, the algorithms used generate the surface profiles, and the overall processing time to perform a full aperture measurement. It was found that the metrology system in its early stages of development can return experimental measurements errors on the level of parts in 10" mm. Two algorithms were compared to examine which was more suitable for the measurement system, the Line-Slope Algorithm (LSA) and the Neighboring Slope Algorithm (NSA). These algorithms were compared in "no-noise" and ""noise" conditions. The LSA seemed to be the best algorithm in a "no-noise" condition. However, real measurement results inherently are noisy. It was found that the NSA would be best suited for the system as it resulted in an order of magnitude lower error from a best-fit value. Also, it was found that an increasing point density resulted in a better surface approximation.