There exist well known methods of reconstruction of the 2D function g'(x,y) from the set of projections r(p,f). Back projection algorithm which we use is linear and stationary , which means that we can analyze the quality of reconstruction using 2D point spread distribution (PSD). The projection of a point d(x0,y0) gives a trace in a form of a sinusoidal line, therefore during the reconstruction we find the value for every point by integration along such lines.
, (5)
z  defocusing parameter,  echo scaled to the space domein,
For a point object we get the 2D PSD function of the setup (including reconstruction algorithm). Due to the rotational symmetry of the PSD , it is enough to calculate and show its crooss section. The shape of PSD depends on the defocusing z, and thus we get 3D

Figure 3a. good quality 
PSD. Now we can consider transversal and axial resolution of reconstruction in Reileigh's sense (a distance from the maximum to the first zero of PSD in p and z direction).
There are three examples of pulse responses in Figure 3. We have analyzed narrow band transducer, transducer with short pulse response and a signal after deconvolution.
Figure 3 shows that even using transducers of several periods per one pulse response we are able to

Figure 3b. poor quality 
obtain narrow central maximum of PSD, due to the suppression of side loops by the reconstruction
integral (5). The disadvantage of such transducer is that we can get also a false reconstruction for another defocusing parameter (Figure 3 (a)).
Deconvolution dramatically improves the pulse response of the setup, or the amplitude and phase of of the signal spectrum specially at the higher frequencies (Figure3(c)).

Figure 3c. poor quality transducer after convolution 
Figure 3. Examples of pulse responses h(p), its fourier transforms H(v) and crosssections of 2D PSD
depending on defocussing parameter z0, for electronic setup and transducers of:
good quality  (a), poor quality  (b), poor quality transducer after convolution  (c)