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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Analytical Jacobian and its application to tilted-wave interferometry.

Ines Fortmeier, Manuel Stavridis, Axel Wiegmann

|October 17, 2014

Summary

Tilted-wave interferometry (TWI) enables precise measurement of aspherical surfaces. Analytical Jacobian matrix calculation significantly reduces TWI processing times for faster optical metrology.

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Area of Science:

Optical Metrology
Interferometry
Surface Metrology

Background:

Aspherical surfaces require advanced measurement techniques.
Tilted-wave interferometry (TWI) is a novel method for aspherical surface measurement.
Perturbation methods are essential for wavefront and surface reconstruction in TWI.

Purpose of the Study:

To develop a faster and more exact method for calculating Jacobian matrices in TWI.
To reduce the overall calculation time for TWI.
To optimize the design and application of TWI systems.

Main Methods:

Analytical calculation of Jacobian matrices using optical perturbation methods.
Determining Jacobian matrices based on the nominal optical path.
Applying methods of optimal design for surface positioning.

Main Results:

Significantly reduced calculation times for TWI.
Enabling faster and more efficient optical metrology.
Demonstrated an improved TWI procedure with optimized surface positioning.

Conclusions:

Analytical Jacobian matrix calculation is crucial for practical TWI implementation.
The developed method considerably speeds up TWI data processing.
This advancement is essential for optimal design and application of TWI.