Optical alignment and position measurement accuracy: Fundamental limitations and the effects of a turbulent environment

Paul Gregory Backes, Purdue University

Abstract

Fundamental limitations on optical position measurement accuracy when imaging in manufacturing environments were studied. Applications include determination of part location, machine tool alignment, and machine calibration. An image of an object feature or illuminated spot or an unfocused laser beam may be used in such a measurement. The image centroid defines the object position and measurement accuracy is determined by how well the exact centroid can be located. Measurement accuracy can be affected by both the centroid determination method used and the nature of the imaging process itself. Both of these effects were studied. First, the attainable accuracy of image centroid measurements using matrix optical sensors and quadrant photodiodes was determined experimentally. Image position errors using a matrix optical sensor with pixel spacing of approximately 40 $\mu$m were less than 1.5 $\mu$m and errors less than 0.2 $\mu$m were found when using a quadrant photodiode. Then the effects of a turbulent refractive index environment in the optical path were studied both theoretically and experimentally. A theoretical expression for incoherent image centroid variance when imaging in a turbulent environment over the short propagation paths typical of manufacturing applications was developed. The centroid variance expression is dependent on object size, imaging lens diameter, propagation path length, and turbulence level. Centroid motion predicted by this expression was compared with results obtained in laboratory experiments conducted under conditions of known turbulence. Experimental results agreed well with the trends predicted by the theory, but differed in magnitude by a constant factor of 6.6. Laser beam wander caused by effects internal to a laser and by the thermal boundary layer at the front face of a laser as well as methods for reducing or compensating for such beam wander were studied. Experimental results indicate that beam wander due to these effects can be compensated for by splitting the beam into reference and test beams and measuring the motion of the reference beam. Beam wander due to the thermal boundary layer at the front face of a laser can be reduced by extending a tube or enclosed insulated tunnel from the laser.

Degree

Ph.D.

Advisors

Stevenson, Purdue University.

Subject Area

Mechanical engineering

COinS