The figure is a simplified schematic diagram of a tilt-sensing unequal-path interferometer set up to measure the orientation of the normal vector of one surface of a cube mounted on a structure under test. This interferometer has been named a “theoferometer” to express both its interferometric nature and the intention to use it instead of an autocollimating theodolite.

ImageThe theoferometer optics are mounted on a plate, which is in turn mounted on orthogonal air bearings for near-360° rotation in azimuth and elevation. Rough alignment of the theoferometer to the test cube is done by hand, with fine position adjustment provided by a tangent arm drive using linear inchwormlike motors.

In the operation of the theoferometer, the interference pattern formed by the collimated laser beams reflected from the two cubes is focused onto a charge-coupled device (CCD) detector. The resulting digitized interference fringe pattern is then analyzed by dedicated software to determine the angular misalignment between the two laser beams (and, hence, the misalignment between the cubes) at the sub-arcsecond level. If a null fringe pattern were achieved, it could be concluded that the laser beam points antiparallel to the surface normal of the test cube. Knowledge of the distance from null (via the angular misalignment seen in the interference pattern) coupled with readings from azimuth and elevation encoders calibrated to the laser-pointing direction then gives the orientation of the cube surface normal vector in two (angular) dimensions. This is the same information as would be given by a theodolite aligned to the test cube, albeit with greater accuracy.

This system offers several advantages. The parts used in the prototype unit were off-the-shelf and relatively inexpensive. Whereas the uncertainty of a typical theodolite measurement is 1 to 2 arcseconds, the current theoferometer prototype has a demonstrated uncertainty of about 0.3 arcsecond. Moreover, the theoferometer makes it possible to completely automate the data-taking process, reducing the time required to take measurements. The net result is better metrology at lower cost, relative to metrology by use of an autocollimating theodolite.

This work was done by Ronald W. Toland and Douglas B. Leviton of Goddard Space Flight Center. For further information, access the Technical Support Package (TSP) free on-line at under the Electronics/Computers category. GSC-14753-1