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Paraxial speckle-based metrology systems with an aperture
Damien P Kelly1, Jennifer E Ward, Bryan M Hennelly
1School of Electrical, Electronic and Mechanical Engineering, College of Engineering, Mathematical and Physical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.
Summary
This study demonstrates a single optical system for surface motion analysis using linear canonical transforms (LCT). By adjusting illumination, researchers can measure motion magnitude and direction, simplifying metrology design.
Area of Science:
- Optics
- Metrology
- Surface analysis
Background:
- Digital speckle photography combined with optical linear canonical transform (LCT) analyzes surface motion.
- Optical fractional Fourier transforms (OFRTs) previously enabled simultaneous measurement of motion magnitude and direction using two optical systems.
Purpose of the Study:
- To extend OFRT analysis to more general LCT systems with a single limiting aperture.
- To demonstrate the benefits of an LCT approach for metrology design.
- To enable motion estimation using a single optical system and varied illumination.
Main Methods:
- Derivation of a generalized Yamaguchi correlation factor to examine the effect of a limiting aperture in LCT systems.
- Utilizing varying curvature of the illuminating field to change the output domain within LCT systems.
- Experimental validation of the theoretical analysis.
Main Results:
- The study extends OFRT analysis to general LCT systems with a single limiting aperture.
- A generalized Yamaguchi correlation factor is derived for LCT systems.
- Varying the illuminating field's curvature effectively changes the output domain.
Conclusions:
- The LCT approach simplifies metrology design by allowing motion estimation with one optical system and adjustable illumination.
- This technique offers a practical and efficient method for analyzing surface motion.
- Experimental results confirm the theoretical framework for LCT-based metrology.
