Calibration of numerical aperture effects in interferometric microscope objectives.

Area of Science:

• Metrology
• Optical Engineering
• Surface Science

Background:

• Microscope objective numerical aperture (N.A.) influences surface profile measurement accuracy.
• High N.A. objectives tend to underestimate measured surface heights.
• Calibration is crucial for reliable nanoscale surface metrology.

Purpose of the Study:

• To experimentally calibrate the effect of numerical aperture (N.A.) on surface profile measurements.
• To quantify the N.A. scaling factors for objectives ranging from 0.1 to 0.95 N.A.
• To validate Ingelstam's theoretical model for N.A. effects in optical profilometry.

Main Methods:

• Utilized a computer-controlled interferometric optical profiler with phase-measurement interferometry.
• Employed four traceable step height standards for calibration.
• Conducted experiments across a range of objective N.A. values (0.1-0.95).

Main Results:

• Measured N.A. scaling factors demonstrated strong agreement with Ingelstam's theory.
• Determined N.A. scaling factors with an uncertainty of +/- 1% for N.A.s <= 0.5.
• Achieved an uncertainty of +/- 2% for N.A.s >= 0.9.

Conclusions:

• The study successfully calibrated N.A. effects in surface profile measurements.
• Experimental results confirm the validity of Ingelstam's theory for N.A. scaling.
• The established calibration provides accurate surface height measurements for various N.A. objectives.