Current commercial height profile measuring instruments, e.g. the confocal microscope and, the white light
interferometer, are widely used in both research institutes and industry. The systematic error of such instruments can be
the same order of magnitude as features on the surface to be measured, if care is not taken with calibration. Instrument
error in most cases depends on the surface slope. Thus, calibration of the instrument is important. The random ball test,
proposed by Parks et al, is a self calibration technique for transmission sphere calibration in phase shift interferometry.
The idea is, by measuring a collection of random patches on the surface of a sphere and then averaging the results, the
contributions from the ball go to zero leaving only the systematic biases due to the instrument. This paper shows it can
also be used to calibrate slope-dependent errors in profilometers such as the scanning white light interferometer (SWLI).
This will be demonstrated with both simulation and experimental results. For example, with a commercial SWLI
measurement with a 20X objective, our random ball test indicates that the height error can be as large as 250 nm at a
slope value of 2.9 degrees when using the envelope peak algorithm for analysis. Similarly, with a confocal microscope
measurement using a 50X objective, the height error can be as large as 800 nm at a slope value of 12.1 degrees. These
slope-dependent errors can be used to compensate future sloped-surface measurements.