A New Method for Compensating for Periodic Nonlinearity in a Heterodyne

Interferometer

May 28, 2012

Kyuman ChoDepartment of Physics,

Sogang University

OVERVIEW Introduction

Heterodyne I/Q-Interferometer

Nonlinear Periodic Error

New Method for Compensating NPE

Experimental Results

Application

Summary

Can measure the phase and amplitude change induced on the probe beam simultaneously. Ideally,

Heterodyne I/Q-Interferometer

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.

cossin

I

Q

v Av A

1tan /Q Iv v I Qv v A ,

Periodic Nonlinear ErrorNonlinear 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.

Simple Analysis

Effect of nonlinear periodic error on phase measurementssin( ) sin coscos( ) cos sin

Q

I

vv

0 Q

I

vv

/ 2 Q

I

vv

If , then If , then.

2 2 1 2 sin 2 (1 sin 2 )I Qv v A A

Effect of nonlinear periodic error on amplitude measurements

, if 0, / 2(1 ), if / 4 AA

cos( )Iv A sin( )Qv A

,

: effective periodic nonlinear error (sinusoidal function of )

As a simple model, nonlinear error can be represented by

New Method for Compensating NPEKeep 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 forScanning interferometerBiosensor 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

Heterodyne I/Q-Interferometer for POP

Experimental ResultsMeasurements 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.

Experimental ResultsMeasurements 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.

Periodic Amplitude and Phase Nonlinearity

Experimental Results

Experimental Results Phase Stability Before and After Phase Locking

Experimental Results Temporal Responses

Experimental Results Measurements of Abrupt Phase Changes

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

Scheme

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

Scheme

Experimental Arrangement High Resolution Scanning Microscope

The Wide Dynamic Range I/Q-Interferometer

[Constant-phase scheme]

Feedbackcontrol

∆z

Scanaxis

[Conventional scheme]

In focus Out of the focus

In focus In focus

SummaryA 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 measurementsDynamic range is improved

Various applications of this new interferometer scheme will be researched

Thank You Very Much for Your Attention!!!