182 Chapter 8
Measurement Theory
Time Domain Phase Derivative
The time domain phase derivative plot is the derivative of the phase of the impulse
response with respect to time. Note that the time derivative of phase is the definition
of optical frequency, so this derivative can be scaled as a wavelength. For a device
with a distributed impulse response, the time domain phase derivative shows the
wavelength distribution as a function of time for an infinitely short pulse as it is
dispersed by the device. Another way to think of the time domain phase derivative
is it represents the “wavelength” of the device under test. It is therefore especially
meaningful for wavelength conditioning devices and filters.
In terms of the impulse response
h
˜
j
defined above, the time domain phase derivative,
PD
j
, is defined
as
2π
c
∆
t
=
-------------
,
PD
j
-----------------
∗
ar
g ( h
˜
j +
1
h
˜
j
)
where c is the speed of light in a vacuum and ∆t is the difference in time between
index j and index
j + 1 .
8
Figure 8-7. Phase Derivative of the time domain response of a fiber Bragg grating.
Time Domain Magnitude Difference
This parameter allows the user to display the difference in magnitude between Trace
A and the Reference Trace in the time-domain.
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