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A New Method for Compensating for Periodic Nonlinearity in a Heterodyne Interferometer

A New Method for Compensating for Periodic Nonlinearity in a Heterodyne Interferometer. May 28, 2012 Kyuman Cho Department of Physics, Sogang Universit y. OVERVIEW. Introduction Heterodyne I/Q-Interferometer Nonlinear Periodic Error New Method for Compensating NPE

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A New Method for Compensating for Periodic Nonlinearity in a Heterodyne Interferometer

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  1. ANewMethod for Compensating for Periodic Nonlinearity in a Heterodyne Interferometer May 28, 2012 Kyuman Cho Department of Physics, SogangUniversity

  2. OVERVIEW • Introduction • Heterodyne I/Q-Interferometer • Nonlinear Periodic Error • New Method for Compensating NPE • Experimental Results • Application • Summary

  3. Heterodyne I/Q-Interferometer • Can measure the phase and amplitude change induced on the probe beam simultaneously. Ideally, , • No need for feedback control to maintain optimum • sensitivity. • Can be used for various applications: • Scanning microscopy which can map the local complex reflectance variations  Ideal for surface diagnostics, • Linear & non-linear susceptibility measurements, • Displacement sensors, etc. • Resolution is limited by periodic nonlinearity. • Dynamic range is limited by the 2-ambiguity.

  4. Periodic Nonlinear Error • Nonlinear error caused by imperfect laser, optics, and demodulator. • Small ellipticity on polarization eigen modes of a stabilized, dual-frequency, dual-polarization laser. • Phase error of a demodulator. • Residual birefringence induced by imperfect optics. • Parasitic or ghost reflections at the optics • Various compensation methods have been proposed. • Post processing of data. Not appropriate for a real-time measurement. • Polarization independent interferometer which can minimize cross talk between polarization modes. • Phase compensation using a rotating polarizer, and so forth. • We are proposing new compensation method with wide dynamic range.

  5. Simple Analysis • As a simple model, nonlinear error can be represented by , : effective periodic nonlinear error (sinusoidal function of ) • Effect of nonlinear periodic error on phase measurements , then . If , then If • Effect of nonlinear periodic error on amplitude measurements

  6. New Method for Compensating NPE • Keep phase difference between the signal and reference arm at a fixed value in which periodic error is negligible. • Interferometer can provide high sensitivity during measurements. • Since the phase remains at constant value amplitude can also be measured without periodic error. • Because of real time tracking of phase, a displacement can be measured without-ambiguity • This new interferometer scheme has been designed for • Scanning interferometer • Biosensor applications, • Vibrometer, • and the other high sensitivity and wide dynamic range measurements in both academic and industrial applications • May be eligible for monitoring seismic noise and/or positioning the test mass in the gravitational wave detector

  7. Heterodyne I/Q-Interferometer for POP

  8. Experimental Results • Measurements of periodic nonlinear error in phase. • Test mirror was linearly displaced over entire rang of the PZT. • Measured phase values were subtracted by the best fit.

  9. Experimental Results • Measurements of periodic nonlinear error in amplitude. • Test mirror was linearly displaced over entire rang of the PZT. • Measured amplitudes were subtracted by the average value.

  10. Experimental Results Periodic Amplitude and Phase Nonlinearity

  11. Experimental Results Phase Stability Before and After Phase Locking

  12. Experimental Results Temporal Responses

  13. Experimental Results Measurements of Abrupt Phase Changes

  14. Experimental Results FFT of the Phase Signals W/ and W/O Constant Phase Scheme

  15. Experimental Results FFT of Amplitude Signals W/ and W/O Constant Phase Scheme

  16. Experimental Arrangement High Resolution Scanning Microscope

  17. The Wide Dynamic Range I/Q-Interferometer [Conventional scheme] Scan axis In focus Out of the focus [Constant-phase scheme] ∆z Feedback control In focus In focus

  18. Summary • A new heterodyne interferometer scheme has been introduced. • By keeping the phase difference between two arms at constant value where the periodic nonlinear error is negligible, • PNL can be eliminated for both phase and amplitude measurements • Dynamic range is improved • Various applications of this new interferometer scheme will be researched

  19. Thank You Very Much for Your Attention!!!

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