Correcting for stage error motions in radius measurements

Area of Science:

• Optical Engineering
• Metrology

Background:

• Traceable radius of curvature measurements are crucial for precision optics manufacturing.
• Optical bench measurements are repeatable and suitable for low-uncertainty applications.
• Stage motion errors introduce bias in radius measurements, complicating uncertainty estimation.

Purpose of the Study:

• To develop a new mathematical definition for the radius measurand.
• To intrinsically correct radius measurements for error motion biases.
• To provide a framework for incorporating other uncertainty sources like figure error and calibration.

Main Methods:

• Developed a novel mathematical definition of the radius measurand.
• Utilized a figure measuring interferometer to identify cat's eye and confocal positions.
• Characterized and estimated uncertainties of stage error motions.

Main Results:

• The new definition intrinsically corrects for systematic biases from stage error motions.
• The formalism allows for the inclusion of figure error, wave-front aberration biases, and displacement gauge calibration.
• Precision radius measurements can be performed with lower-quality optical benches if error motions are characterized.

Conclusions:

• A new mathematical definition simplifies traceable radius of curvature measurements.
• This approach reduces the need for high-quality optical benches by accounting for errors.
• Accurate and traceable radius measurements are achievable with characterized, repeatable error motions.