Methods and apparatuses for obtaining a calibration for a substrate topography measurement and methods and apparatuses for determining a topography of a substrate using the calibration

A method of obtaining a calibration for a substrate topography measurement, for each of a plurality of locations on a calibration substrate the method comprising:

• obtaining a calibration substrate height reference value at a location of the plurality of locations;
• obtaining a plurality of calibration substrate height measurement values at the location, each calibration substrate height measurement value corresponding to a measurement of a surface of the calibration substrate at the location, wherein a total number of the plurality of locations is greater than a total number of the plurality of calibration substrate height measurement values obtained at each location;
• and
• using the plurality of calibration substrate height measurement values and the calibration substrate height reference values obtained for each location to determine a plurality of calibration terms for the calibration substrate height measurement values.

An apparatus configured to obtain a calibration for a substrate topography measurement, the apparatus comprising:

• a support configured to support a calibration substrate;
• a projection unit configured to direct a beam of radiation onto a location on the calibration substrate;
• a movement mechanism operable to adjust the support and/or the projection unit to move the location on the calibration substrate at which the beam of radiation is directed onto the calibration substrate;
• a detection system configured to detect the radiation after reflection by the location on the calibration substrate and configured to determine a calibration substrate height measurement value corresponding to a measurement of a surface of the calibration substrate at the location;
• and
• one or more controllers configured to operate the movement mechanism such that the beam of radiation is incident on a plurality of locations on the calibration substrate and configured to, for each of the plurality of locations on the calibration substrate:
• receive a calibration substrate height reference value at the location, and
• receive a plurality of calibration substrate height measurement values from the detection system,
• wherein a total number of the plurality of locations is greater than a total number of the plurality of calibration substrate height measurement values received at each location, and
• wherein the one or more controllers are further configured to determine a plurality of calibration terms for the calibration substrate height measurement values using the plurality of calibration substrate height measurement values received for each location, and the calibration substrate height reference values received for each location.