Hinds Instruments PEM-100, Руководство пользователя

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Appendix A: Calibration
72 PEM 100 User Manual
A sample calculation is given below for quarter-wave retardation. The required
Bessel functions are:
For half-wave:
( )
485 . 0
2
=
π
J
For quarter wave:
( )
250 . 0 2
2
=
π
J
The required setting for quarter-wave retardation is:
( )
( )
( )






=
2
2
4
2
2
2
2
λ
π
π
λ
f f
V
J
J
V
(7)
( )
515 . 2
2
=
λ
f
V
( )
2
2
λ
f
V
(8)
( )
2
2
λ
f
V
is the lock-in reading for half-wave retardation, as set by the oscilloscope.
Parallel Polarizer Calibration at a Single Wavelength
The primary calibration technique discussed in “Calibration Using an Oscilloscope” is
observation of the waveform at half-wave retardation. This gives calibration only at
half-wave retardation or integral multiples of half-wave retardation. Other methods
such as the Bessel function zero method give retardation only at specific values of
retardation (e.g. 3.877 radians or 5.136 radians). Another method of accurately
measuring retardation at arbitrary values of V
Control
is much desired.
Calculating the ratio of V
2f
/V
DC
is in principle a good approach. However, if
calibration is being done with the PEM between crossed polarizers at 45º there are
problems, especially at low retardation levels. From theoretical analysis of the
resulting waveforms we learn that:
DC
V
α
( )
0 0
1 A J
−
(9) and
f
V
2
α
( )
0 2
2 A J
(10)
If one plots the ratio V
2f
/V
DC
the graph shown in Figure A.9 is obtained.