The Transcollimator, a Two-Axis Optical Translation Sensor

The PDF papers on this page may be downloaded directly from this website with the Adobe Acrobat Reader.

Advantages of Optical Position Measurement

The three-axis Drag-Free satellite, DISCOS flown in 1972, used Capacitive Sensors to detect the position of the proof mass in its cavity. For high-precision Drag-Free satellites, however, it is desirable to detect the position optically. Detecting optically avoids deliberate electric fields in the cavity and allows wide gaps and very high precision.

The Principle of Operation

The Transcollimator is a precision two-axis optical sensor which is identical to an Autocollimator with only one minor change: the focal length of the collimating lens is altered to focus the exit beam at the center of the spherical Drag-Free proof mass. When this is done, the Transcollimator is insensitive to rotation of the proof mass but detects translation of its CM in the two axes perpendicular to the light beam.

One advantage to the Transcollimator approach to sensing the position of the proof mass is that it is a very minor modification of a well-understood existing instrument. This means that many of the problems which one would normally have with a new instrument concept have already been solved.

Accuracy, Noise Equivalent Translation

R. V. Jones constructed one of the most accurate Autocollimators ever built. (R. V. Jones and J. C. Richards, J. of Sci. Instr., 36, 2, 90, (1961) and R. V. Jones, J. of Sci. Instr., 38, 2, 37 (1961)). The Noise Equivalent Translations of the Transcollimators discussed in this page are based on Jones' design.

There is a simple relation between an equivalent Autocollimator's sensitivity to the rotation of an optical flat and a Transcollimator's sensitivity to the translation of a sphere. It is x = a * theta where a is the radius of the sphere, theta is the rotation-angle sensitivity of the Autocollimator, and x is the translation sensitivity of the Transcollimator. The theoretical sensitivity of a Jones-type Autocollimator is discussed in Appendix C (PDF) of the Relativity-Gyro paper. It should be remembered, however, that Jones got this performance experimentally in the laboratory in air at room temperature.

A two-color version of the Transcollimator (to detect the position of a sphere and a surrounding shell separately) is discussed in a paper given at the Eight Marcel Grossmann Meeting in Jerusalem (PDF) (B. Lange, The Two-Color Transcollimator, a Precision Position Detector for a Satellite Two-Sphere Equivalence-Principle Experiment, Proceedings of the 8th Marcel Grossmann Meeting, Edited by T. Piran and R. Ruffini, 1997, p. 1226).