Accounting for focal shift in the Shack-Hartmann wavefront sensor

Area of Science:

• Optical Metrology
• Wavefront Sensing
• Diffraction Optics

Background:

• Shack-Hartmann wavefront sensors (SHWS) use lenslet arrays to measure wavefront aberrations.
• Accurate wavefront slope measurement relies on precise image centroid localization on a sensor.
• Partial or non-uniform illumination of lenslets introduces image centroid bias, compromising SHWS accuracy.

Purpose of the Study:

• To investigate the root cause of image centroid bias in SHWS under partial/non-uniform illumination.
• To demonstrate the relationship between lenslet Fresnel number and focus shift.
• To propose a method for determining the correct geometrical focus to mitigate bias.

Main Methods:

• Analysis of diffraction focus shifts caused by low Fresnel numbers in lenslets.
• Empirical determination of the geometrical focus by minimizing centroid bias in partially illuminated lenslets.
• Experimental validation of the proposed focus finding method.

Main Results:

• Image centroid bias in SHWS is attributed to the diffraction focus shifting away from the geometrical focus due to low Fresnel numbers.
• A method to empirically locate the geometrical focus by minimizing bias in partially illuminated lenslets was successfully demonstrated.
• This method allows for accurate wavefront slope measurements even with non-ideal illumination conditions.

Conclusions:

• The low Fresnel number of lenslets is the primary cause of focus shift and subsequent centroid bias in SHWS.
• Empirically finding the geometrical focus by minimizing bias provides a practical solution for improving SHWS accuracy.
• This technique enhances the reliability of Shack-Hartmann wavefront sensing in challenging illumination scenarios.