  The advisability of the use of the Fresnel number as the measure
(characteristic) of the ratio of diffraction and focusing properties for
ultrasonic transducers and its radiated beams is proposed and demonstrated.
Althought this characteristic is more habitual in optics, in acoustics the
equivalent (mathematically although not fully in its physical meaning)
parameter of linear gain is used as a rule. However, the preference and the
more accuracy of the Fresnel number use is demonstrated here on the basis that
the usual determination of the linear gain parameter ceases to correspond to
the real value of the gain for low Fresnel number acoustic beams. It connects
with the linear effect of axial maximum pressure shift from the geometrical
focus towards the transducer. This effect is known for a long time, but here
the analytical formulas describing this shift with a high accuracy for
arbitrary Fresnel numbers are presented. As a consequence, also the analytical
dependence of the real gain on the Fresnel number is obtained.
