Desensitising a polarisation-based speckle
interferometer for the polarisation direction of incoming
scattered light
P A A M Somers and N Bhattacharya
Delft University of Technology, Lorentzweg 1, NL-2628 CJ Delft, the
Netherlands
P.A.A.M.Somers@TUDelft.nl; N.Bhattacharya@TUDelft.nl
Abstract. A polarisation-based shearing speckle interferometer requires the incoming
scattered light to have proper characteristics: for highest modulation the interfering
beams should have the same intensity. Most surfaces scatter linearly polarised light
randomly, providing equal intensities for the interfering beams on average. However,
when a diffusely reflecting metallic surface is illuminated by a linearly polarised laser
beam, the polarisation direction of the illuminating beam is retained to a large extent in
the scattered light. As a result light entering the interferometer will not be randomly
polarised, which may lead to low modulation due to unbalanced object and reference
beams. Applying a polariser or a half wave plate in an appropriate direction to adjust
polarisation direction or a combination of both can solve the problem. These solutions
have disadvantages: loss of light and dependency on the orientation, which may
require frequent adjustments to accommodate experimental conditions. An alternative
solution that handles the problem effectively without these drawbacks is presented. It
consists of a quarter wave plate oriented at 45°, positioned in front of the
interferometer. It is shown that the unfavourable predominant polarisation state
encountered with metallic surfaces will be converted into a favourable one, thereby
obtaining well balanced object and reference beams, irrespective of the polarisation
direction of the incoming light.
1. Introduction
Polarisation based shearing speckle interferometers make use of a polarisation sensitive
element to create two orthogonally polarised beams, one of them sheared, both originating
from the object of interest. Within the interferometer the beams travel along a common
optical path, outside the interferometer the optical path is almost common, giving this type of
interferometer its intrinsic stability against disturbances. The beams interfere at a CCD
sensor after passing an analyser. Possible implementations for the polarisation sensitive
element are a Wollaston prism [1], a Savart plate [2], a bi-refringent wedge [3], or another
beam splitting device such as a polarising beam splitter cube, used with two mirrors in a
Michelson configuration [4]. One of the mirrors can be tilted to produce a variable shearing
angle between the two beams.
When the two speckle patterns interfere, the intensity I at a given pixel at the camera is
given by the interference equation:
I  I o  I r  2 I o I r cos  ,
(1)
where Io and Ir are the intensities of the object and reference beams and  is phase
difference between the two interfering beams at that particular location. The modulation term
I M  2 Io Ir
(2)
reaches it highest value when the interfering beams have equal intensities. Modulation is
zero if one or both of the interfering beams have zero intensity.
2. Problem description
Since the intensity distributions of both interfering speckle patterns have their maximum at
zero intensity, modulation is zero or low at many locations, resulting in poor signal to noise
ratios. Low modulation can also occur due to unbalanced interfering beams, caused by
unfavourable polarisation conditions. It is therefore desirable that the polarisation state of
incoming light is well defined, for instance by taking care that incoming linear light is
polarised at 45° upon entry.
The interferometer acquires speckle patterns that are generated by a scattering object
illuminated by a uniform beam. The polarisation state of the illuminating beam, often linearly
polarised, is not preserved in the scattered field for many materials, producing randomly
polarised beams that enter the interferometer. Although not ideal, this situation is acceptable
when the average intensities of the interfering beams are the same. Metallic materials
however show very low levels of depolarisation [5]. As a result the scattered field has a
predominant polarisation state, depending on the polarisation of the illuminating beam.
There are a number of measures that can be taken to solve this problem. First of all the
polarisation state of the illumination could be altered, for instance by rotating the polarisation
direction when it is linearly polarised, or by converting the light to circular. When using more
than one illumination system, this should be done for every single system. A second
approach could be a change of the polarisation state of the scattered light, just before it
enters the interferometer. A polariser oriented at 45° ensures that a 1:1 relation between
horizontal and vertical polarisation is established, at the expense of losses for other
polarisation directions, in particular for -45°. In addition there are absorption losses when
using a polariser. Another solution without substantial absorption losses is an adjustable half
wave plate that can be given the best position to obtain mainly 45° polarised light, when the
depolarising properties of the object are not sufficient to provide random polarisation. This
approach requires re-adjustment of the half wave plate whenever the polarisation state of the
scattered light makes it necessary. In addition it is desirable to have available some
measurement system that can determine the optimum setting during adjustments.
3. Polarisation state conversion
We have chosen another way of conditioning the light before it enters the interferometer that
does not require re-adjustment and associated measurements, thus simplifying the
operational use of the interferometer. Although for this system there are also polarisation
states that are unfavourable after conversion, this solution provides considerable
improvements in most practical situations, in particular when the scattered light coming from
an object that is illuminated by a linearly polarised beam is not fully depolarised, and the light
has largely linear properties in a possibly unfavourable orientation.
A perfectly scattering object illuminated by a uniform beam with linear polarisation reflects
light in all directions with all polarisation states: for coherent illumination the polarisation state
of the scattered light is random. Coherent light with random polarisation can be described as
the combination of a horizontally and a vertically polarised wave, both with arbitrary
amplitude, with an arbitrary constant phase difference between them. An object that not fully
depolarises the incoming light preserves its polarisation state to some extent: that state
becomes predominant in the scattered light, which can be unfavourable for a polarisationbased interferometer.
The task of a device that must reduce the dependency of the interferometer on the
polarisation direction is then to convert the unfavourable predominant polarisation state into a
favourable one. The unfavourable polarisation state for a system with vertically polarised
illumination used on a metallic scattering surface is vertical. This unfavourable state
becomes the favourable one if the light is converted to circular. A quarter wave plate oriented
at 45° in front of the interferometer fulfills the task. Linear light in arbitrary direction will be
converted to elliptical light by the quarter wave plate. Special cases of the ellipse are circles
for vertical or horizontal input, or straight lines for linear input at -45° or +45°. The axis of the
ellipse is oriented at 45°, ensuring that the split-up after the polarising beam splitter will be
1:1 for incoming linear light in any direction. The plate will not affect the most favourable
input state without conversion: linear light at 45° will remain linear. Circular states however
will be converted to either vertical or horizontal, which implies a degradation for these states.
Other states, in general all elliptical states, will be less affected: since elliptical light can be
considered as a combination of linear light and circular light, only the circular portion gets the
unfavourable vertical or horizontal state after passing the quarter wave plate. The linear
portion is converted to the ideal circular state.
4. Experimental
Experiments were carried out to evaluate the properties of the interferometer before and after
modifying it by adding a quarter wave plate oriented at 45° in front of it. An overview of the
interferometer is presented in figure 1. Light entering the interferometer is split by polarising
beam splitting cube PBC1. Horizontal light is transmitted to fixed mirror M2, and reflected
back towards the beam splitter. A quarter wave plate oriented at 45° attached to the beam
splitter takes care of conversion to vertical light, that is reflected to the exit of the cube.
Similarly vertical light entering the interferometer is reflected towards shearing mirror M1,
reflected back and converted to horizontal by another quarter wave plate. Mirror M1 is
slightly tilted to obtain a sheared image. At the exit now two orthogonally polarised beams
propagate into a channel splitter section that splits the beam pair into two channels to allow
for a phase step in one of the two channels. As a result two speckle interferograms are
available side by side on a single CCD camera, with a mutual phase step of /2. The
interferometer and its alignment system are described in more detail elsewhere [4,6].
First of all a measurement was carried out on a metallic object demonstrating the problem.
The object, coated by a thin primer layer, was illuminated by vertically polarised light. The
polarisation state was measured using an analyser in different angular positions. Although
coated, the metallic object still scatters light with predominant vertical polarisation as figure 2
clearly shows. A matt white painted object also illuminated by vertical light shows almost no
dependency on analyser angle.
L1
Object
CCD
Left image
Right image
Intermediate image
L3
Piezo controls
L2
BC1
BC1
M4
M1
PBC2
¼ wave plate
Phase stepper
PBC1
M2
M3
P1
Beam splitter
Beam combiner
Shearing unit
Figure 1 Polarisation-based shearing speckle interferometer.
Trace A
Trace B
Figure 2 Intensity of a scattered
beam as a function of analyser
angle. Trace A: light scattered
by a metallic surface covered
with a thin primer layer. Trace B:
light scattered by a surface
covered with white matt paint.
Another result is shown in figure 3. Here the interferometer itself is used as measuring
device. Either mirror M1 or M2 is blocked and the average intensity of the speckle pattern on
the CCD is measured as a function of the orientation of a half wave plate, positioned in front
of the interferometer. The tracks for mirror M1 and M2 presented in figure 3 show large
fluctuations, due to the mainly vertical polarisation of light scattered by the metallic object.
Figure 3. Intensity of a beam
scattered by a metallic object,
measured by the interferometer
with either mirror M1 or M2
blocked, as a function of the
polarisation
direction
of
incoming light. Polarisation is
changed by adjusting the
orientation of a half wave plate
in front of the interferometer.
After insertion of a quarter wave plate oriented at 45°, results have considerably improved,
as figure 4 shows. Again the interferometer is used to measure average intensities as a
function of the orientation of the half wave plate, when either one of the mirrors M1, M2 is
blocked. Some dependency remains, possibly caused by imperfect alignment.
Figure 4 Intensity of a beam
scattered by a metallic object,
measured by the interferometer
with either mirror M1 or M2
blocked, as a function of the
polarisation
direction
of
incoming light. Polarisation is
changed by adjusting the
orientation of a half wave plate
in front of the interferometer.
The interferometer is modified
by adding a quarter wave plate
oriented at 45° in front of it.
Finally some experiments have been carried out on a component with an artificial defect,
before and after the modification. The component, a Fokker 100 speed brake containing an
artificial defect was thermally loaded to induce local deformation at the defect area. The
object was observed with the interferometer during cooling down, using vertical shearing,
and the intermediate phase differences for a series of measurement intervals were
accumulated to obtain an unwrapped final phase difference map. Figure 5 shows the results.
An estimate of the improvement was obtained by calculating the ratio between measured
maximum phase difference over a vertical cross-section at the defect area and the average
noise level for that cross-section. Before modification this ratio was 5.83, after adding the
quarter wave plate it was 7.39.
(a)
(b)
Figure 5 Indication of a defect in a Fokker 100 airbrake, after thermal loading.
Results are shown before (a) and after (b) modifying the interferometer.
5. Conclusions
A polarisation-based shearing speckle interferometer has been modified in order to convert
the predominant unfavourable vertical polarisation state encountered when a metallic
scattering surface is illuminated by a vertically polarised beam. As a result linear light in any
direction is converted to circular, providing well balanced object and reference beams for
these cases. Average modulation has thus been increased, yielding better S/N ratios for
measurement results.
Acknowledgements
This research was supported by the Technology Foundation STW, applied science division
of NWO and the technology program of the Ministry of Economic Affairs.
References
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