Application of the random ball test for calibrating slope-dependent errors in profilometry measurements

Area of Science:

• Metrology
• Optical Engineering
• Surface Science

Background:

• Optical profilometers like scanning white light interferometers and confocal microscopes are crucial for high-resolution surface topography measurements.
• Slope-dependent systematic errors in these instruments can be significant, comparable to the surface features being measured.

Purpose of the Study:

• To introduce and validate a self-calibration technique, the Random Ball Test (RBT), for addressing slope-dependent errors in optical profilometers.
• To enable compensation for future measurements of spherical geometries, such as refractive microlenses.

Main Methods:

• Development and simulation of the Random Ball Test (RBT) for calibrating slope-dependent errors.
• Experimental demonstration of the RBT on a 50× confocal microscope.
• Investigation of factors like drift and ball radius uncertainty on calibration uncertainty.

Main Results:

• The RBT effectively calibrates slope-dependent errors within practical limits, as confirmed by simulations.
• A significant, monotonically increasing surface slope-dependent bias was observed on the confocal microscope, reaching ~800 nm at a 12° slope.
• Calibration uncertainty was found to be less than the measured bias, primarily limited by random noise.

Conclusions:

• The Random Ball Test (RBT) provides an effective method for self-calibrating slope-dependent errors in optical profilometers.
• The technique allows for the compensation of measurement biases, enhancing the accuracy of surface topography measurements, particularly for microlenses.
• Further investigation into error sources like drift and ball radius uncertainty is important for refining calibration accuracy.