Optics: measuring and testing – By polarized light examination – With birefringent element
Reexamination Certificate
2000-06-16
2004-02-17
Font, Frank G. (Department: 2877)
Optics: measuring and testing
By polarized light examination
With birefringent element
Reexamination Certificate
active
06693710
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention is directed toward systems for measuring materials properties such as strain, crystallinity, thickness, purity, composition, and the like of samples; or for observing structures in transparent materials; or, for measurement of strain in models constructed for that purpose. It is more narrowly directed toward measuring systems that utilize polarized light for such measurements. It may be used in applications including scientific research, industrial measurement, quality control, forensics, and medical imaging.
2. Description of the Related Art
Polarization interference is a well-known way to observe birefringence or retardance in a sample. Birefringence is an intensive property of a sample whereby light polarized along different axes will experience different indices of refraction. The axis along which the index is lowest is termed the fast axis, and that along which the index is highest is termed the slow axis; these are necessarily perpendicular to one another. The optical indices are termed n
f
and n
s
.
Retardance is an extensive quantity measuring the total optical path difference experienced in passing through a sample, so for a uniform sample at normal incidence
R
=(
n
s
−n
f
)*
d
[1]
where n
f
and n
s
are the optical indices for light polarized along the fast and slow axes, respectively, and d is the thickness of the sample. More generally, in a sample where the values of n
s
and n
d
may vary along the line of sight due to e.g. inhomogeneities, but the fast axis orientation is constant, R is the integral of index difference over distance.
When a birefringent object is viewed through parallel or crossed linear polarizers, a pattern of colored fringes is seen. If the orientation of the slow axis varies across the face of the part, the fringe pattern will change as the polarizers are rotated. Alternatively, one may illuminate the sample in left-hand circularly polarized light and view it with a left-hand circular polarizer. This eliminates the dependence on polarizer orientation, while preserving the location and color of the fringes. These colored fringes (which simply appear light and dark when viewed in monochromatic light) are termed the set of isochromes, the lines consisting of the locii of points that share a given value of &dgr;.
Another set of crucial patterns is the isoclines, being the locii of points which are completely extinguished when the sample is viewed between crossed polarizers. The isoclines change when the polarizers are rotated relative to the sample, and indicate those points where the principal optical axis in the sample is parallel to one of the polarizers. The isoclines are often used to determine the crystal orientation, or a stress distribution, throughout a sample. But observations of this type alone do not reveal which is the fast axis and which the slow axis.
There is a large literature describing apparatus and methods for determining the retardance in a sample. These are typically based on the intensity of the interference pattern of the isochromes, given by:
I=I
0
cos (&dgr;)
2
[2
a]
for a sample placed between parallel polarizers, or
I=I
0
sin (&dgr;)
2
[2
b]
when between crossed polarizers, where
&dgr;=&pgr;
R/&lgr;
[3]
and I
0
is the intensity of the incident light, which is monochromatic with wavelength &lgr;. Polychromatic light may be analyzed as a sum or integral of various wavelength components.
Equations [2a] and [2b] do not specify a unique value of &dgr; for a given observed intensity I, because the sin( ) and cos( ) functions are periodic. Typically, these equations are solved to yield a value &dgr;
0
in the range [0, &pgr;/2], which is related to the actual &dgr; by either
&dgr;=
m&pgr;+&dgr;
0
[4a]
or
&dgr;=
m&pgr;−&dgr;
0
[4b]
where the indeterminacy between [4a] and [4b ] arises from the fact that cos( )
2
for either of these two arguments yields the same answer; this is also true of sin( )
2
. Simply measuring the pattern of isochromes between crossed or parallel polarizers does not provide enough information to specify which case applies, and combining crossed and parallel measurements gives no further data, since sin( )
2
and cos( )
2
are inherently complementary. Then there is the further indeterminacy of the order m. So, in attempting to relate a retardance to an observed intensity between polarizers, one must overcome the uncertainty in order, m, and also determine whether the sample is described by equation [4a] or [4b].
In analogy with the description of &dgr;
0
as the apparent phase, one may speak of the apparent retardance R
0
which is defined to lie in the range [0, &lgr;/2] and is related to the actual retardance R by
R=m&lgr;+R
0
[5a]
R=m&lgr;−R
0
[5b]
Except when the actual retardance is known to be less than &lgr;/2, one must use [5a] or [5b] together with a determination of the order, m, to calculate the actual retardance.
Some hardware used for polarization interference measurements provides additional data through the use of additional sensors, polarizing elements, waveplates, photoelastic modulators, and the like.
Oldenbourg et. al. U.S. Pat. No. 5,521,705 teaches how to unambiguously identify the slow axis and value of &dgr; for a retarder. This method uses an imaging detector and variable retarders, but it only functions for &dgr; in the range [0, &pgr;/2]. It is unable to determine the order, m.
Mason U.S. Pat. No. 5,917,598 teaches how to identify the fast axis using circularly polarized illumination and multiple linear polarizing analyzers with different orientations. This system appears to resolve phase &dgr;
0
over the range [0, &pgr;/2] for monochromatic light, or over a wider range of &dgr;
0
for broad-band light analyzed with a spectrometer. The determination of order, m, is only possible when broad-band light is used, and comes from analysis of the spectral distribution. But the requirement for a spectrometer to analyze the content of light passing through the sample means that system is limited in practice to measuring a single point in the sample at a time.
Croizer et. al. U.S. Pat. No. 4,914,487 determine isochromic fringes and then calculate absolute retardance by presuming stress levels at the end points of the sample, and integrating spatially across the sample using a finite-element stress equation. Since stress is related to birefringence by the stress-optic tensor, the stress equation provides additional information about birefringence levels that is said to allow unambiguous determination of &dgr; from &dgr;
0
, provided that the birefringence in the sample is entirely due to stress rather than e.g. crystallinity or other internal structures. Further, it requires one to spatially oversample, i.e. have a pixel scale that is considerably finer than any of the structures present, in order to perform the integration accurately. In practice, this approach is slow because of the need for the calculation step, and has proven unreliable when applied to real-world samples.
Others have observed samples at multiple wavelengths in an attempt to determine retardance in excess of &lgr;/2.
Young uses a linear polarizer to illuminate a single point in a sample, which is analyzed by a quarter-wave plate whose angle is keyed to that of the entrance polarizer, followed by a final rotating linear polarizer used as an analyzer. This last element is rotated to seek maximum extinction, and the angle of maximum extinction is noted. This is performed while the sample is illuminated at two wavelengths in turn. From the combinations of the polarizer setting angles, retardances in excess of &lgr;/2 are identified. But the system is inherently point-
Cambridge Research & Instrumentation Inc.
Cohen & Pontani, Lieberman & Pavane
Lee Andrew H.
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