Central lobe

The spectral frequency range covered by the central lobe of this sinc fiinction increases as the piilselength decreases. For a spectrum to be undistorted it should really be confined to the middle portion of this central lobe (figure B 1.12.2). There are a number of examples in the literature of solid-state NMR where the resonances are in fact broader than the central lobe so that the spectrum reported is only effectively providing infonnation about the RF-irradiation envelope, not the shape of the signal from the sample itself... 

The effect of DP-2) is to produce a virtual pulse whose length is the width of the central lobe. Of course, this is never completely perfect since it does have side-lobes, but waveforms have been described for which the performance in this respect is excellent. DP-3) means that the Doppler frequency shift is being sampled at a discrete set of time points. If the sampling rate is faster than the Nyquist of the Doppler frequency shift, then the Doppler can be unambiguously extracted. 

By integrating the dirty data cube over wavenumber one can extract the spatial features of the sky, because the dirty beam ripples at different frequencies or wavenumbers cancel and hence the ratio between the power of the central lobe and the secondary lobe increases. However, this is only useful if the sources on the sky have similar size and power. 

The exact structure of the replay field distribution depends on the shape of the fundamental pixel and the number and distribution of these pixels in the hologram. The pattern we generate with this distribution of pixels is repeated in each lobe of the sine function from the fundamental pixel. The lobes can be considered as spatial harmonics of the central lobe, which contains the desired 2D pattern. For example, a line of square pixels with alternate pixels being one or zero (i.e. a square wave) would have the basic replay structure seen in Fig. 1.4. 

When an arbitrary pattern is generated by the FT of a hologram, it is contained within a sine envelope based on the dimensions of the smaller or fundamental pixel. For each lobe in the sine there is an associated replication of the pattern. There is also a replication of the pattern at each zero in the sine, even though the central value of the pattern is suppressed by the zero. With holograms, we are only interested in the central lobe of the sine function. The other orders or lobes merely repeat the desired pattern in the replay field and waste the available intensity which can be placed into that desired pattern. The area of interest in the replay field must be limited to half of the area of the central lobe to prevent overlap of orders. As the pixel pitch decreases, the central lobe of the sine envelope broadens, easing the restrictions that are placed on the replay field pattern. 

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