Two-frame phase-shifting interferometry for testing optical surfaces.

Standard phase-shifting interferometry (PSI) generally requires collecting at least three phase-shifted interferograms to extract the physical quantity being measured. Here, we propose the application of a simple two-frame PSI for the testing of a range of optical surfaces, including flats, spheres, and aspheres. The two-frame PSI extracts modulated phase from two randomly phase-shifted interferograms using a Gram-Schmidt algorithm, and can work in either null testing or non-null testing modes. Since only two interferograms are used for phase demodulation and the phase shift amount can be random, requirements on environmental conditions and phase shifter calibration are greatly relaxed. Experimental results of three different mirrors suggest that the two-frame PSI can achieve comparable measurement precision with conventional multi-frame PSI, but has faster data acquisition speed and less stringent hardware requirements. The proposed two-frame PSI expands the flexibility of PSI and holds great potential in many applications.

[1]  Werner P. O. Jueptner,et al.  Fourier transform evaluation of interference patterns: demodulation and sign ambiguity , 1992, Other Conferences.

[2]  Pramod Rastogi,et al.  Fringe analysis: Premise and perspectives , 2012 .

[3]  Tao Wei,et al.  Demodulation of a single-image interferogram using a Zernike-polynomial-based phase-fitting technique with a differential evolution algorithm. , 2011, Optics letters.

[4]  John E Greivenkamp,et al.  Iterative reverse optimization procedure for calibration of aspheric wave-front measurements on a nonnull interferometer. , 2004, Applied optics.

[5]  J Antonio Quiroga,et al.  Two-step demodulation based on the Gram-Schmidt orthonormalization method. , 2012, Optics letters.

[6]  John E Greivenkamp,et al.  Design of a nonnull interferometer for aspheric wave fronts. , 2004, Applied optics.

[7]  James H. Burge,et al.  Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres , 2009, Optical Engineering + Applications.

[8]  Shengchun Liu,et al.  Demodulation of two-shot fringe patterns with random phase shifts by use of orthogonal polynomials and global optimization. , 2016, Optics express.

[9]  James H. Burge,et al.  Optical testing with computer generated holograms: comprehensive error analysis , 2013, Optics & Photonics - Optical Engineering + Applications.

[10]  Xuefeng Chen,et al.  Modal wavefront reconstruction in radial shearing interferometry with general aperture shapes. , 2016, Optics express.

[11]  Maciej Trusiak,et al.  Optically-sectioned two-shot structured illumination microscopy with Hilbert-Huang processing. , 2014, Optics express.

[12]  M. Trusiak,et al.  Two-shot fringe pattern phase-amplitude demodulation using Gram-Schmidt orthonormalization with Hilbert-Huang pre-filtering. , 2015, Optics express.

[13]  D. Whitehouse,et al.  REVIEW ARTICLE: Surface metrology , 1997 .

[14]  Maciej Trusiak,et al.  Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis. , 2016, Optics express.

[15]  J Vargas,et al.  Two-step self-tuning phase-shifting interferometry. , 2011, Optics express.

[16]  J Antonio Quiroga,et al.  Two-step interferometry by a regularized optical flow algorithm. , 2011, Optics letters.

[17]  Tao Wei,et al.  Nonnull interferometer simulation for aspheric testing based on ray tracing. , 2011, Applied optics.

[18]  Chao Tian,et al.  Implementation of dispersion-free slow acoustic wave propagation and phase engineering with helical-structured metamaterials , 2016, Nature Communications.

[19]  D Hansen,et al.  Hubble Space Telescope primary-mirror characterization by measurement of the reflective null corrector. , 1993, Applied optics.

[20]  D. J. Brangaccio,et al.  Digital wavefront measuring interferometer for testing optical surfaces and lenses. , 1974, Applied optics.

[21]  L G Seppala,et al.  Experimental comparison of a Shack-Hartmann sensor and a phase-shifting interferometer for large-optics metrology applications. , 2000, Applied optics.

[22]  Qian Kemao,et al.  Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations , 2007 .

[23]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  Christof Pruss,et al.  Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces. , 2014, Optics express.

[25]  James C Wyant,et al.  Computerized interferometric surface measurements [Invited]. , 2013, Applied optics.

[26]  J C Wyant,et al.  Using computer generated holograms to test aspheric wavefronts. , 1972, Applied optics.

[27]  Krzysztof Patorski,et al.  Highly contrasted Bessel fringe minima visualization for time-averaged vibration profilometry using Hilbert transform two-frame processing. , 2013, Optics express.

[28]  J. Marroquín,et al.  Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique. , 1997, Applied optics.

[29]  Qiaofeng Tan,et al.  Phase extraction from interferograms with unknown tilt phase shifts based on a regularized optical flow method. , 2013, Optics express.

[30]  Wolfgang Osten,et al.  Evaluation of absolute form measurements using a tilted-wave interferometer. , 2016, Optics express.

[31]  Yongying Yang,et al.  Generalized data reduction approach for aspheric testing in a non-null interferometer. , 2012, Applied optics.

[32]  Tomoyuki Matsuyama,et al.  Nikon projection lens update , 2004, SPIE Advanced Lithography.

[33]  Zhaoyang Wang,et al.  Two-dimensional continuous wavelet transform algorithm for phase extraction of two-step arbitrarily phase-shifted interferograms , 2014 .

[34]  S. Sutton,et al.  National Ignition Facility laser performance status. , 2007, Applied optics.

[35]  Dong Liu,et al.  Regularized frequency-stabilizing method for single closed-fringe interferogram demodulation. , 2010, Optics letters.

[36]  Bongtae Han,et al.  Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms. , 2004, Optics letters.