We propose a new matrix method for calculating geometric image rotation, taking into account the effects of the geometric and dynamic phases in a nonplanar optical layout. In order to describe the propagation of light in this system, the algebra of two-dimensional Jones polarization vectors and matrices in two-dimensional space is extended to three-dimensional space. We give practical examples of nonplanar layouts of polarization nulling interferometers for application in astronomy and precision wavefront analysis.
Similar content being viewed by others
References
A. V. Tavrov, “Physical principles of achromatic nulling interferometry for stellar coronagraphy,” Zh. Eksp. Teor. Fiz., 134, No. 6(12), 1103–1114 (2008).
A. V. Tavrov, “Increased spatial coherence of an extended source in sequential rotational shear interferometers for achromatic stellar coronagraphy,” Zh. Eksp. Teor. Fiz., 135, No. 6(12), 1109–1124 (2009).
A. V. Tavrov, “Technical principles of achromatic interferometry for stellar coronagraphy,” Zh. Tekh. Fiz., 80, No. 3, 83–92 (2010).
Yu. V. Kolomiitsev, Interferometers [in Russian], Mashinostroenie, Leningrad (1976).
A. Ya. Karasik, B. S. Rinkevichius (ed.), and V. A. Zubov, Laser Interferometry Principles, CRC Press, New York (1995).
A. Tomita and R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett., 57, 937–940 (1986).
D. N. Klyshko, “Berry’s geometric phase in oscillatory processes,” Usp. Fiz. Nauk, 163, No. 11, 1–18 (1993).
D. W. Swift, “Image rotation devices – a comparative study,” Opt. and Laser Technol., 175–188 (August 1972).
R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light [Russian translation from English], Mir, Moscow (1981).
E. F. Ishchenko and A. L. Sokolov, Polarization Optics [in Russian], Izd. MEI, Moscow (2005).
H. Jiao et al., “Two topological phases in optics by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev., A39, 3475–3486 (1989).
A. Tavrov et al., “Generalised algorithm for the unified analysis and simultaneous evaluation of geometrical spinredirection phase and Pancharatnam phase in a complex interferometer system,” J. Opt. Soc. Am. A (JOSA A), 17, No. 1, 154–161 (2000).
P. Hariharan, “The geometric phase,” in: Progress in Optics, Vol. 48, (2005), pp. 194–201.
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers [Russian translation], Nauka, Moscow (1974).
ZEMAX: Software for Optical System Design, http://www.zemax.com, accessed April 10, 2010.
A. Tavrov et al., “Common-path achromatic interferometer-coronagraph: nulling of polychromatic light,” Opt. Lett., 30, 2224–2226 (2005).
A. Labeyrie, S. G. Lipson, and P. Nisenson, An Introduction to Optical Stellar Interferometry, Cambridge University Press, Cambridge (UK) (2006), p. 325.
P. Hariharan, Optical Interferometry, Academic Press, Sydney (2003), p. 236.
E. J. Galvez, “Achromatic polarization-preserving beam displacer,” Opt. Lett., 26, 971–973 (2001).
Complex Index of Refraction Look-Up Utility/Extinction Coefficient, http://www.ee.byu.edu/photonics/opticalconstants.phtml, accessed April 10, 2010.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izmeritel’naya Tekhnika, No. 9, pp. 31–37, September, 2010.
Rights and permissions
About this article
Cite this article
Tavrov, A.V., Orlov, D.A. & Vinogradov, I.I. Phase calculation for image rotation in a nonplanar polarization nulling interferometer. Meas Tech 53, 1011–1020 (2010). https://doi.org/10.1007/s11018-010-9612-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11018-010-9612-9