Relative error in out-of-plane measurement due to the object illumination.

Area of Science:

• Optical Metrology
• Interferometry
• Speckle Interferometry

Background:

• Electronic speckle pattern interferometry (ESPI) is a non-contact optical measurement technique.
• The sensitivity vector dictates the direction and magnitude of displacement measurable by an interferometer.
• Accurate characterization of the sensitivity vector is crucial for reliable displacement measurements, especially in out-of-plane configurations.

Purpose of the Study:

• To analyze the sensitivity vector for collimated and divergent oblique illumination in an out-of-plane arrangement.
• To develop a geometric model for evaluating the sensitivity vector components.
• To predict displacement measurement errors based on illumination conditions.

Main Methods:

• Theoretical analysis of the sensitivity vector components for collimated and divergent illumination.
• Development of a geometric model for sensitivity vector evaluation.
• Experimental validation using an out-of-plane electronic speckle pattern interferometer on an aluminum plate.

Main Results:

• Sensitivity vector components were analyzed for collimated and divergent oblique illumination.
• A geometric model was proposed and used to evaluate the sensitivity vector.
• For collimated illumination, sensitivity was predominantly along the pulling direction, with other components being small.
• Displacement was measured primarily along the pulling direction.

Conclusions:

• The sensitivity vector's behavior was characterized for different illumination types in an out-of-plane setup.
• The proposed geometric model aids in understanding and evaluating the sensitivity vector.
• Considering a constant sensitivity vector allows prediction of displacement measurement errors for both divergent and collimated illumination.