This representation of the Doppler signal is often referred to as a Doppler sonogram. In clinical applications of Doppler ultrasound, the spectral velocity information is calculated in real time on a time/frequency grid and shown in a display with time along the horizontal axis and frequency (or velocity) along the vertical axis. This is the basis of a pulse measurement technique called frequency-resolved optical gating (FROG).
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Consequently, to obtain the full intensity and phase of a pulse from its spectrogram requires an iterative 2D phase retrieval algorithm. Unfortunately, the intensity profile is not as readily measurable as the pulse spectrum. The time domain phase together with the intensity of the pulse, I( t, provides the full intensity and phase of the pulse. Thus, if a narrow time gate is used, the time domain phase is obtained. The spectrogram is experimentally much easier to obtain than the sonogram however, the measured quantity is not quite as mathematically useful as the sonogram because the time slicing of the pulse occurs in the time domain. Rather than determining the time arrival of spectral slices of a pulse, a spectrogram is obtained when the spectrum of time slices of the pulse are measured.
However, a method called 2D phase retrieval, discussed in the next section, can alleviate many of these issues.Ī spectrogram is a relative of the sonogram. In addition, for a given frequency, the sonogram may have two or more peaks in time, that is, the group delay may not be a function. If the spectral phase is not well behaved, the filtered pulse may not be much longer than the original pulse. The main difficulty of the Chilla–Martinez method is that the frequency gate must be very narrow, reducing the filtered pulse energy significantly, which greatly reduces the measured signal strength. The other pulse is cross-correlated with the spectrally filtered pulse to determine the time arrival. One replica is spectrally filtered using a tunable filter. The pulse is split into two replicas using a beamsplitter. Measuring a sonogram requires determining the time arrival of spectral slices of the pulse.
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