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Three-flat test with plates in horizontal posture
Maurizio Vannoni1, Giuseppe Molesini
1Consiglio Nazionale delle Ricerche, Istituto Nazionale di Ottica Applicata, Largo E. fermi 6, Firenze, Italy. maurizio.vannoni@inoa.it
Applied Optics
|April 22, 2008
Summary
Gravity causes measurable sag in horizontally positioned optical flats. This study provides a mathematical model for bending and demonstrates an iterative algorithm to accurately recover deformation terms from interferometric measurements.
Area of Science:
- Optical Engineering
- Metrology
- Gravitational Effects on Materials
Background:
- Interferometric measurement of optical flats is crucial for precision optics.
- Gravity-induced sag can significantly affect horizontal measurements of flatness.
- Accurate characterization of deformation is essential for high-performance optical systems.
Purpose of the Study:
- To analyze the effects of gravitational sag on interferometer measurements of horizontal optical flats.
- To develop a mathematical model for the bending of a three-point supported plate.
- To validate an iterative algorithm for processing interferometric data and recovering deformation terms.
Main Methods:
- Detailed analysis of interferometric measurements of flats in horizontal and upright postures.
- Derivation of a mathematical expression for plate bending under gravity.
- Application of a three-flat measuring procedure to recover azimuthal deformation terms.
- Utilizing an iterative algorithm for data processing and analysis.
Main Results:
- A mathematical expression for gravitational bending of a three-point supported plate was derived.
- Azimuthal deformation terms were successfully recovered using a three-flat measurement.
- Pure radial terms were found to be estimable but not fully recoverable.
- The iterative algorithm proved effective for processing interferometric data.
Conclusions:
- Gravitational sag must be accounted for when measuring optical flats horizontally.
- The developed method allows for the recovery of azimuthal deformation, improving measurement accuracy.
- The iterative algorithm offers a robust approach to analyzing interferometric data for precise flatness assessment.
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