Design of the phase-shifting algorithm for flatness measurement of a mask blank glass

Yangjin Kim; Kenichi Hibino; Naohiko Sugita; Mamoru Mitsuishi

doi:10.1117/12.2045319

2 April 2014 Design of the phase-shifting algorithm for flatness measurement of a mask blank glass

Yangjin Kim, Kenichi Hibino, Naohiko Sugita, Mamoru Mitsuishi

Proceedings Volume 9050, Metrology, Inspection, and Process Control for Microlithography XXVIII; 90501W (2014) https://doi.org/10.1117/12.2045319
Event: SPIE Advanced Lithography, 2014, San Jose, California, United States

Abstract

Nonlinearity and non-uniformity of phase-shifts significantly contribute to the error of the evaluated phase in phase-shifting interferometry. However, state of the art error-compensating algorithms can counteract the linear mis-calibration and first-order nonlinearity associated with the phase-shift. We describe an error expansion method that is utilized to construct a phase-shifting algorithm that can compensate the second-order nonlinearity and non-uniformity of phase-shifts. The conditions for eliminating the effect of second-order nonlinearity and non-uniformity of phase-shifts are given as a set of linear equations for the sampling amplitudes. We developed a novel 11-sample phase-shifting algorithm that can compensate for the second-order nonlinearity and non-uniformity of phase-shifts and is robust up to a 4^th harmonic. Experimental results show that the surface shape of a transparent plate could be measured with a precision of 1 nm, over the 120-mm-diameter aperture.

Citation Download Citation

Yangjin Kim, Kenichi Hibino, Naohiko Sugita, and Mamoru Mitsuishi "Design of the phase-shifting algorithm for flatness measurement of a mask blank glass", Proc. SPIE 9050, Metrology, Inspection, and Process Control for Microlithography XXVIII, 90501W (2 April 2014); https://doi.org/10.1117/12.2045319

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