
3.1.10 Statistical Analysis of Retardance Measurements
Jack C.M. Wang Statistical Engineering Division, CAML
Paul A. Williams
Kent B. Rochford
Alan H. Rose Optoelectronics Division, EEEL
Optical communication, data storage, ellipsometry, sensor and other
optoelectronic systems often use linear retarders to control or analyze
optical signals. Often these systems require retarders with specific
and/or accurately known values of retardance. NIST is developing a
quarterwave linear retarder designed to have a retardance stable within
over a variety of operational and environmental conditions.
Three methods are used to measure retardance. One of the methods uses
a modified version of standard polarimetric measurements and uses
rotating polarizers.
Linearly polarized light, with known orientation, is incident on
the retarder and the light emerges with an elliptical polarization.
The intensities of the perpendicular and parallel states of the
emerging light are measured.
Measurements are made as the input polarizer rotating from to
with increments of
.
Let
,
be the ith orientation of
the input polarizer, and R_{i} be the square root of the ratio of
the measured perpendicular intensity to the measured parallel intensity
at angle .
Define
,
a model relating
Y_{i} and
is given by
where are random noise, and are parameters to be estimated. In particular, is the retardance parameter.
Many (112) experiments were run to determine the retardance
of 5 rhombs. A brief summary of the findings is given below.
Figure 10: The top figure displays the measurement results of intensity ratio vs. polarizer orientation for a typical experiment. The dotted line is the leastsquares fit of the model. The bottom plots the rotation and residual errors for each experiment. It shows, for most cases, the residual error is smaller than the rotation error, indicating that the model is adequate for the data.
Date created: 7/20/2001 