Mapping can be an effective tool to reduce errors in positioning systems. Sources of error amenable to correction via mapping include those due to leadscrew cumulative error, leadscrew periodic error, Abbé error, nut backlash, cosine error, and deviations from orthogonality in multiple axis systems. Essentially, mapping consists of measuring and recording the actual position of a stage, for later use in returning to that point. In most cases, the measuring instrument is used only to acquire data on the stage, and is not present during actual operation. Common calibration sources include laser interferometers and precision glass grid plates. The positioning system must have sufficient resolution to implement a corrective move to the desired degree of accuracy. As an example, consider a single-axis positioning table with 1 micron resolution. Nominally, a 100 mm move would require 100,000 steps. In this case, due to a cumulative leadscrew error, 100,000 steps actually results in a 100.013 mm move. Programming a move of 100 / 100.013 x 100,000 = 99,987 steps, will produce the desired 100 mm move.
Mapping is especially effective when a relatively small number of positions are required; in this case, a unique measured value can be used for each location. In other cases, one or more points can be recorded, and subsequent points inferred, or “interpolated” from the nearest measured values. In the above example, a 50 mm move would require 49,994 steps, under the assumption that the screw error is linear. Compensation for leadscrew periodic error requires several points for each revolution, substantially increasing the storage requirements. In leadscrew based systems, thermal expansion often sets a limit on the level of accuracy worth reducing by mapping techniques. Systems with linear encoders and/or linear motors are better suited to high accuracy mapping techniques.
Single-axis stages are mapped with the use of a laser interferometer and automated data acquisition software. X-Y tables require the use of a two axis laser with an L-mirror assembly, or a precision grid plate, with the latter technique being easier to implement on production stages. At DOVER, we have devoted significant resources to the acquisition of very high precision grid plates. We currently have plates of dimensions 190 x 190 mm, 300 x 300 mm, and 600 x 600 mm. These plates were exposed on one of the world’s most accurate photoplotters, and the two smaller plates are fabricated on Zerodur, a glass-ceramic with nearly zero thermal expansion. The gridplates consist of 12 micron wide chrome lines on a uniform grid every 10 mm, and are mounted in a fine adjustment tip-tilt-yaw stage, which is in turn placed on the X-Y stage under test. The stage is mounted on a large granite surface plate, under a bridge with a centrally mounted, precision Z-axis focusing stage. A long working distance 100X microscope objective, infinity corrected optical system, and machine vision camera and software complete the system. This mapping station allows us to provide a file of stage X-Y errors, and permits numerous error sources to be compensated. The net result is an improvement in X-Y accuracy of from ten to twenty times that of an unmapped stage.