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374 Chapter Eleven
possible. In practice, for femtosecond-duration pulses it is difficult to
satisfy the narrow time-gate approximation, so that iterative recon-
struction algorithms are needed to deconvolve the response functions
of these filters. Given the current state of technology, this class of direct
devices is not practical for pulses of duration less than several tens of
picoseconds.
11.3.4.2 Shearing Interferometry
Shearing interferometers consist of a time-nonstationary linear phase
filter and a time-stationary linear phase filter in parallel, followed by
an amplitude-only filter. The action of linear phase filters is to shift
the electric field in either time or frequency. For instance, consider the
spectral linear phase modulator of Eq. (11.64). The action of this filter
is a translation of the pulse in time, which can easily be obtained with a
nondispersive delay line. Likewise, imparting a temporal linear phase
ontheinputfieldisequivalenttoatranslation,orshift,ofthefrequency
axis. The resulting interferogram contains information about an entire
section of the correlation function, as opposed to sampling a single
point of the function, as is the case with the two-slit types.
In spectral shearing interferometry, the amplitude-only filter fol-
lowing the in-parallel linear phase filter arrangement is a spectral filter
(see Fig. 11.7g). Since the spectral filter is a time-stationary device, the
key filter is the time-nonstationary linear temporal phase modulator
that provides a shift, or shear, of the spectrum of one replica of the
input pulse. 79,80 The detected signal is a function of the linear tempo-
ral phase modulator parameter as well as the center frequency of
t
the spectrometer C ,
7
A P
D({ , C ; }) = d ˜ S ( − C ) d ˜ N ( − , ) ˜ E( )
t
L
t
;
2
P
+ ˜ S ( , ) ˜ E( ) (11.82)
L
where the temporal linear phase filter’s response function and the
spectral linear phase filter’s transfer function inherently depend on
the variables and , respectively. Therefore, the detected signal
t
is also a function of the amount of spectral phase modulation ,
although this dependence plays a secondary role which will be de-
scribed below. It is easy to see from Eq. (11.61) that the transfer function
of the temporal linear phase modulator is
P
˜ N ( , ) = ( − ) (11.83)
l t t
Again the spectral filter is taken to have a passband much narrower
than the spectrum of the input pulses. Upon substitution of the
