Published Papers

Axicon gratings are computer generated holograms of equally spaced concentric circles printed on a plane substrate. When illuminated by a point source of light they create axes in space defined by a line between the point source and the center of the grating pattern. The axis can be viewed in either transmission or reflection with an autostigmatic microscope. The axis created by the grating can be located to less than 1 um in translation and depending on distance from the grating to less than 1 microradian in angle. Several examples of such a use in alignment are explained.

The positioning accuracy of multi-axis machine tools and coordinate measuring machines are often checked using ball bars or ball plates where the spatial locations of the balls are externally calibrated to provide a traceable artifact [1,2]. In use, the individual ball surfaces are probed in at least 4 places with a tactile sensor and the points of contact fit to the equation of a sphere to determine the center of the ball. The method is tedious, indirect and semi-static. Furthermore, it is difficult or impossible to create artifacts that truly span the three-dimensional work volume of machines because some features become occluded by others and cannot be accessed.

Measuring the quality of alignment of an assembled compound lens is often necessary. This raises the question of what
axis to use as a reference axis for this measurement. We suggest that the reference axis should be the optical axis of the
assembled system and that this axis is unique for each assembly.

INTRO: INTRODUCTION
Almost all optical elements and systems are sym- metric about their optical axes which means there are only 5 degrees of freedom that will affect op- tical alignment. Likewise, stigmatic images of a point source of light imaged by a finite conjugate optical system have 5 types of symmetry. There is a part of the image that is symmetric about the centroid of the image, and there are 4 symmetries in the plane of the image, namely, even-even, odd-odd, even-odd and odd-even. We show there is a one-to-one correspondence between the im- age symmetries and the degrees of freedom op- tical elements can be moved to align them.