INTERFEROMETER TUNABLE IN A NON-MECHANICAL MANNER BY A PANCHARATNAM PHASE

INTERFEROMETRE SYNTONISABLE DE MANIERE NON MECANIQUE PAR PHASE PANCHARATNAM

English Abstract

The object of the invention is to create an
improved interferometer which does not require a drive
mechanism for moving a reference surface or test specimen in
order to tune the interferometer and which can be tuned in
virtually vibration-free manner, thereby preventing
measuring errors. For this purpose, the interferometer (10)
comprises at least one light source, a reference
surface (40), a test specimen (50) and at least one beam
splitter (30). For vibration-free tuning, the
interferometer (10) further contains an apparatus (60, 70)
for the polarization of the.interference beams such that, at
the output of the interferometer (10), they have different
polarization states with respect to each other; and an
analyzer (80), disposed at the output of the
interferometer (10), with a polarization state variable in
predetermined manner, said analyzer (80) - depending on its
polarization state - introducing a defined Pancharatnam
phase into the interference beams for tuning the
interferometer (10).

French Abstract

L'invention concerne vise à mettre au point un interféromètre perfectionné ne nécessitant pas de mécanisme d'entraînement pour déplacer une surface de référence ou un objet à mesurer, en vue de sa syntonisation et pouvant être syntonisé pratiquement sans entraîner de vibrations, ce qui permet d'éviter les mesures imprécises. A cet effet, l'interféromètre (10) comprend au moins une source lumineuse, une surface de référence (40), un objet à mesurer (50) et au moins un séparateur de faisceau (30). Pour une syntonisation n'entraînant pas de vibrations, l'interféromètre (10) contient en outre un dispositif (60, 70) permettant de polariser les rayons à interférer de manière qu'ils présentent à la sortie de l'interféromètre (10) un état de polarisation différencié les uns par rapport aux autres, ainsi qu'un analyseur (80) à état de polarisation modulable de manière prédéterminé, qui introduit en fonction de son état de polarisation une phase de Pancharatnam définie dans les rayons à interférer, afin de syntoniser l'interféromètre (10).

Claims

9
CLAIMS:
1. A tunable interferometer, in particular for the
measurement of optical surfaces, comprising:
at least one light source,
a reference surface and a test specimen and at least one
beam splitter,
an apparatus for the polarization of the interference beams
such that, at the output of the interferometer, they have
different polarization states with respect to each other;
and
an analyzer, disposed at the output of the interferometer,
with a polarization state variable in predetermined manner
for tuning the interferometer, the analyzer being physically
separate from the interferometer.
2. The interferometer according to claim 1, wherein
the interferometer is a two-beam interferometer; and
linearly polarized light is present at the input of the
interferometer; and
the polarization apparatus comprises a first .lambda./4 retardation
plate, associated with the reference surface or with the
test specimen, and a second .lambda./4 retardation plate,
positioned before the analyzer.
3. The interferometer according to claim 1 or 2,
wherein the analyzer is a rotatable linear analyzer.
4. The interferometer according to claim 1 or 2,
wherein the analyzer comprises an electrically tunable
liquid-crystal element with a linear polarizer.

Description

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Interferometer
The invention relates to an interferometer, in
particular for the measurement of optical surfaces.
A conventional two-beam interferometer is used to
measure optical surfaces in that it generates at the output
an interference fringe pattern of the optical surface and
supplies said pattern, for example, to a video camera for
further processing. The light reflected by the optical
surface, known also as a test wave field, contains
aberrations because of lens errors and surface roughnesses
at the surface being measured, said aberrations being imaged
by the interference fringe pattern. The local position of
the deviations of the interference fringe pattern from an
ideal fringe pattern (e. g. parallel fringes) correlates with
the local position of the aberration in the test wave field
and thus with the deviations of the optical test surface,
for example, with respect to an ideally flat surface. Such
a displacement of the interference fringe pattern because of
aberrations may have a considerably adverse effect on the
measuring sensitivity, because the fringe deformation, e.g.
in the pattern maxima and minima, is not able to image the
deformation of the test wave field as accurately as in the
regions with high intensity gradients. Therefore, it is
desirable to be able to displace the interference fringe
pattern in a defined manner in order to improve the
measuring accuracy. For this purpose, the reference surface
or the test specimen itself has hitherto been moved or
tilted in order to introduce an additional phase gradient
into the interference beams and thus into the interference
fringe pattern. In this manner it is also possible to
obtain unambiguous information about the aberration of the
test wave field, this subsequently allowing the elimination
of errors e.g. in a flat test surface. However, the

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movement of large and heavy test specimens or reference
surfaces introduces further inaccuracies into the
interferometer.
Embodiments of the invention, therefore, create an
improved interferometer which does not require a drive
mechanism for moving a reference surface or test specimen in
order to tune the interferometer and which can be tuned in
virtually vibration-free manner, thereby preventing
measuring errors.
Accordingly, in one aspect of the present
invention, there is provided a tunable interferometer, in
particular for the measurement of optical surfaces,
comprising: at least one light source, a reference surface
and a test specimen and at least one beam splitter, an
apparatus for the polarization of the interference beams
such that, at the output of the interferometer, they have
different polarization states with respect to each other;
and an analyzer, disposed at the output of the
interferometer, with a polarization state variable in
predetermined manner for tuning the interferometer, the
analyzer being physically separate from the interferometer.
In some embodiments, the interferometer is a two-
beam interferometer; and linearly polarized light is present
at the input of the interferometer; and the polarization
apparatus comprises a first ~/4 retardation plate,
associated with the reference surface or with the test
specimen, and a second ~/4 retardation plate, positioned
before the analyzer.
In some embodiments, the analyzer is a rotatable
linear analyzer.

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2a
In some embodiments, the analyzer comprises an
electrically tunable liquid crystal element with a linear
polarizer.

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In some embodiments, the analyzer is physically
separate from the interferometer.
The principal idea behind the invention consists
in making available a tunable interferometer without it
being necessary for the reference surface or test specimen
to be moved in order to tune the interferometer. Usually,
the tuning of an interferometer means changing the optical
path of one of the arms of the interferometer by moving or
tilting the reference surface or test specimen, this
introducing a defined phase into the interferometer. In
contrast thereto, tuning in the sense of the invention means
that a defined phase, the so-called Pancharatnam phase, is
introduced into the interferometer, there being, however, no
change in the relative position between the reference
surface and the test specimen. The phenomenon of the
Pancharatnam phase is known and is described in detail in
the paper "Pancharatnams Phase in Polarisation Optics",
published in Advanced Electromagnetism, T. Barratt et al.,
Editors Singapore, pages 357-375 by W. Dultz et al.
The interferometer comprises at least one light
source, a reference surface and a test specimen as well as
at least one beam splitter. The interferometer further
contains an apparatus for the polarization of the
interference beams such that, at the output of the
interferometer, they have different polarization states.
Disposed at the output of the interferometer is an analyzer
with a polarization state variable in predetermined manner
for tuning the interferometer. Depending on the
polarization state of the analyzer, an additional phase, the
so-called Pancharatnam phase, is introduced into the
interference beams of different polarizations, the result
being that the interference fringe pattern, imaging the test
specimen, is displaced by a predetermined distance.

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A linear relationship between the degree of
displacement of the fringe pattern and the position of the
analyzer is obtained if, in a two-beam interferometer, the
interference beams are polarized orthogonally with respect
to each other. This is achieved in that, first, a linearly
polarized light, preferably laser light, is present at the
input of the interferometer, and in that the polarization
apparatus comprises a first ~/4 retardation plate,
associated with the reference surface or with the test
specimen, and a second ~/4 retardation plate, positioned
before the analyzer.
The first retardation plate ensures that the light
beams reflected by the reference surface and by the test
specimen are polarized orthogonally with respect to each
other. The second retardation plate converts the two beams
into a left-circularly polarized beam and a right-circularly
polarized beam.
The analyzer may be a rotatable linear analyzer or
an electrically tunable liquid-crystal element with a linear
polarizer.
In order to afford the interferometer additional
protection against vibration during tuning, the
interferometer and the analyzer may be physically separate,
i.e. even installed in different locations.
Herein below, the invention is described in
greater detail with reference to an example embodiment in
connection with the drawing.
The drawing shows a two-beam interferometer 10 at
the input of which is a linearly polarized laser light which
has previously passed through a linear polarizer 20. The
linear polarizer 20 is followed by a known beam splitter 30

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which splits the incident light into at least two
components. In the present example, a reference surface 40
is placed in the optical path which passes the beam
splitter 30. With respect to the light beam which passes
5 through the beam splitter 30, there is an optical test
specimen 50 after the reference surface 40. Let it be
assumed that the reference surface 40 is a flat glass plate
of such properties that it transmits 950 of the incident
light and reflects 50 of the incident light back to the beam
splitter 30. In the present example, the test specimen 50
is likewise represented by a glass plate which, in turn,
reflects 50 of the incident light and transmits 95o thereof.
Disposed between the reference surface 40 and the test
specimen 50 is a ~/4 plate 60, referred to below, for the
sake of simplicity, as retardation plate 60. Let it be
emphasized that the described relative position between the
reference surface 40, the retardation plate 60 and the test
specimen serves merely as an example. A second ~/4
plate 70, referred to below, for the sake of simplicity, as
retardation plate 70, is disposed in the interferometer 10
in such a manner that the light beams reflected by the
reference surface 40 and the test specimen 50 and deflected
by the beam splitter 30 are able to pass through the
retardation plate 70. A rotatable linear analyzer 80 is
positioned after the retardation plate 70, with the result
that the interference beams which pass through the
retardation plate 70 strike the analyzer 80. The
analyzer 80 is followed, for example, by a video camera (not
shown) which records the interference fringe pattern
supplied by the interferometer 10 at the output.
In the following, the operating principle for
tuning the interferometer 10 is described in greater detail.
Let it be emphasized once again that conventional

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interferometers are tuned in that the reference surface 40
or the test specimen 50 has to be moved or tilted. However,
the interferometer 10 according to the invention can be
tuned without it being necessary to move the reference
surface 40 or the test specimen. In other words, the
relative position between the reference surface 40 and the
test specimen 50 remains unchanged. This is achieved by the
invention in that the interference beams - i.e. the beams
reflected by the reference surface 40 and the test
surface 50 - have different polarization states. Let it be
assumed that the light passing the linear polarizer 20 is
polarized in the direction of the arrow, i.e. vertically.
The vertically polarized light strikes the beam splitter 30
and half of it, for example, is reflected to the outside,
the other half passing through the beam splitter 30. The
vertically polarized light first strikes the reference
surface 40, on which 50 of the light is reflected. The
proportion that penetrates the reference surface 50 passes
through the retardation plate 60, as a result of which the
vertically polarized light undergoes right-circular
polarization. If this light strikes the test surface 50,
the reflected light is left-circularly polarized. The light
reflected from the test surface 50 passes the retardation
plate 60 again. Having again passed the retardation
plate 60, the light once again has a linear polarization
which, however, is orthogonal with respect to the
polarization of the light reflected from the reference
surface 40. The two reflected interference beams with
polarizations orthogonal with respect to each other strike,
in turn, the beam splitter 30, which deflects half of the
light intensity to the retardation plate 70. In the
retardation plate 70, the two interference beams undergo
circular polarization, one of the beams being right-
circularly polarized and the other left-circularly

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polarized. Owing to this polarization state of the
interference beams and the rotatable linear analyzer 80,
there is a linear relationship between the displacement of
the interference fringe pattern at the output of the
interferometer 10 and the rotation angle of the linear
analyzer 80. In order to tune the interferometer 10, the
linear analyzer 80 is simply rotated in a predetermined
manner, as a result of which the so-called Pancharatnam
phase is introduced into the interferometer 10, said
Pancharatnam phase causing the linear displacement of the
interference fringe pattern. The rotation angle by which
the linear analyzer 80 has to be rotated in order to cause a
predetermined displacement of the interference fringe
pattern can be accurately determined if use is made of the
Poincare sphere, which is known. The polarization states of
the interference beams are on the poles of the Poincare
sphere, the linear analyzer 80 moving on the equator when it
is rotated. The phase which is in this manner inserted into
the interferometer 10 is y=~ ~(A, R, L, P) when ~ is the
spherical excess of the spherical lune A, R, P, L, A on the
Poincare sphere. Therein, A is the linear polarization
state of the light at the input of the interferometer 10.
R and L, respectively, stand for the right- and left-
circular polarization states of the two interference beams.
The right- R and left- L circular polarization states of the
two interference beams are achieved, as already mentioned,
by the retardation plates 60 and 70. The right- and left-
circularly polarized light (R, L) is, as already mentioned,
present at the output of the retardation plate 70. With the
aid of the rotatable linear analyzer 10, the Pancharatnam
phase y, which is proportional to the rotation angle of the
analyzer 80, is introduced between the left- and right-
circularly polarized beams at the output of the
interferometer. Through the defined rotation of the

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analyzer 80, the Pancharatnam phase is changed in
predetermined manner and the interference fringes, recorded
by the video camera, are displaced as if the reference
surface 40 or the test surface 50 had been displaced.
Instead of a rotatable linear analyzer 80 it is possible to
employ a known electrically tunable liquid-crystal element
with a linear polarizes. Particularly preferred is an
electrically rotatable ~/2 retardation plate of the kind
producible using modern liquid-crystal techniques. With
such retardation plates which operate very quickly, the
axial orientation is rotated with the electric voltage.
The interferometer 10 can be tuned with all
processes in which the two beams are differently polarized.
However, the tuning is only linear, i.e. predictable, if the
polarizations of the beams reflected from the reference
surface 40 and the test specimen 50 are orthogonal and if
the analyzer moves on the symmetrically intermediate great
circle on the Poincare sphere.

Representative Drawing