Rigorous decision of the excess fraction method in absolute distance interferometry

Il'ya P. Agurok

doi:10.1117/12.279134

1 November 1997 Rigorous decision of the excess fraction method in absolute distance interferometry

Il'ya P. Agurok

Proceedings Volume 3134, Optical Manufacturing and Testing II; (1997) https://doi.org/10.1117/12.279134
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Absolute distance interferometry is a promising technology for comprehensive investigation of optical component parameters, including measurement of radii and thicknesses. In special interferometric schematics, it is applicable to measuring parameters of surfaces after grinding and can simplify null corrector design or eliminate its implementation for final testing aspherical surfaces. A universal method for precision length measurement, called 'excess fractions,' was proposed at the end of the last century to calibrate gauges. In this method, the interferometer compares an unknown distance with magnitudes of several wavelengths. The array which consists of the remainders of integer parts of the phase shift between the reference branch of the interferometer and the measuring distance, will be obtained. The proposed consideration of the 'excess fraction' method is based on the Chinese Remainder Theorem. It will be shown that the confidence interval of the obtained distance is equal to the confidence interval of the fractions. Consideration of the finite precision will make the method independent of which units will express, and provides the intervals of unambiguity of the method.

Citation Download Citation

Il'ya P. Agurok "Rigorous decision of the excess fraction method in absolute distance interferometry", Proc. SPIE 3134, Optical Manufacturing and Testing II, (1 November 1997); https://doi.org/10.1117/12.279134

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available