Hinds Instruments PEM-100, Руководство пользователя

Страница: 82 / 100

Appendix A: Calibration
70 PEM 100 User Manual
Bessel Function Zero Methods
An examination of equation 2 suggests a method for precise setting of certain values
of retardation.
Note, for example, the “DC” term in equation 2. For certain values of
0
A
(e.g. 2.405
radians),
( )
0
0 0
=
A J
, and therefore the DC term becomes a constant, independent of
the birefringence B. The DC intensity also becomes independent of many other
changes which could be made to the optical system, such as the angular position of
the second polarizer. The DC intensity can therefore be used for “normalization” of
the AC signals, by forming the ratio
DC AC
V V
. This is now independent of
fluctuations in intensity in the light source, changes in optical transmission, etc.
To establish precisely the controller setting for which
0
0
=
J
, graphs of
DC
V
vs
controller setting were made for several different angular positions of the second
polarizer. A typical set of graphs is shown in Figure A.8. Notice that the graphs
should intersect at one particular controller setting for which the Bessel function
0
J
vanishes.
V
DC
Controller Setting
Polarizer
Orientation
Angle
Figure A.8 Determining the Controller Settings for which J
0
= 0
If a lock-in amplifier is available, and if the modulator is capable of providing
adequate peak retardation, then the AC signals can provide similar retardation
calibration points. Consider the second harmonic signal, at twice the modulator
frequency. At a peak retardation or amplitude of
136 . 5
0
=
A radians,
( )
0
0 2
=
A J .
This setting can be established with great accuracy using a lock-in at frequency 2f.