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Optical System to Correct Nonlinearity in Heterodyne Interferometers

IP.com Disclosure Number: IPCOM000101510D
Original Publication Date: 1990-Aug-01
Included in the Prior Art Database: 2005-Mar-16
Document File: 5 page(s) / 175K

Publishing Venue

IBM

Related People

Bobroff, N: AUTHOR [+2]

Abstract

Attainable accuracy with heterodyne interferometers is limited by periodic nonlinear errors that arise from improperly phased beat signals at the detector. These errors can be cancelled by a correcting optical system that uses two g/4-plates and two polarizers to introduce compensating sine and cosine quadrature amplitudes.

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Optical System to Correct Nonlinearity in Heterodyne Interferometers

       Attainable accuracy with heterodyne interferometers is
limited by periodic nonlinear errors that arise from improperly
phased beat signals at the detector.  These errors can be cancelled
by a correcting optical system that uses two g/4-plates and two
polarizers to introduce compensating sine and cosine quadrature
amplitudes.

      Heterodyne polarization interferometers are widely used in
precision instruments.  Such systems consist of a Michelson
interferometer with polarizing beamsplitter, a two-frequency laser
head, and a mixing polarizer that interferes with the two frequencies
upon recombination at a detector.  In an ideal system the phase of
the beat signal varies linearly with changes in the length of the
measurement arm.  A phase detector locked to the beat frequency then
provides a linear measure of the longitudinal displacement of a
target mirror or retroreflector.  A typical configuration for this
prior art is shown in Fig. 1.

      These interferometers suffer from a systematic error that has
become known as "nonlinearity".  Often nonlinearities prove difficult
to control, in part because their detailed origin has been difficult
to establish. However, in a general way nonlinearities are known to
originate from imperfections in the optical system and laser source
which cause improper mixing of the two laser frequency states, giving
rise to beat signals at the detector which have the wrong phase.  In
cases of greatest interest, the position error is proportional to the
component error as measured in amplitude units, rather than intensity
units.  This increased sensitivity adds to the difficulty in
correcting the nonlinearity. For example, a polarizing beamsplitter
with a rejection ratio of 400 in intensity units will still pass 5%
amplitude in the wrong frequency state, which in some interferometer
configurations will give rise to a position error of 0.05/2f fringes.
(As it happens, beamsplitter leakage will not give rise to a first
order nonlinearity with most interferometer configurations.)  There
are many sources of nonlinearity, and the total in a typical system
is usually of the order of 5%.

      Such nonlinearities can be analyzed in a phenomenological way
using the scalar interferometer equation.  Consider the case in which
a small fraction b of the reference arm frequency follows an improper
path through the interferometer, and propagates down the measurement
arm.

      It can be shown that the phase measured by the system will be:

                            (Image Omitted)

                øMeas = øTrue  -b sin øTrue .
      (1)

      The dominant phase term in eq. 1, øTrue, is the desired
measurement signal, proportional to displacement of the target
mirror.  The second phase term, b sin øTrue, is the nonlinear error,
and is proportional to the contamina...