Near field calculation and beam divergence are well known for conventional transducers. For a phased array probe, we need to treat the active and the passive axes separately.
The passive axis is the axis that is not controlled by the phased array delay. This can be considered an unfocused rectangular element. The near field is therefore the square of the transducer elevation X probe frequency/4 X wavelength. For example, assuming a 10 MHz transducer ( 10 mm elevation) in immersion inspecting an aluminum block with a 75 mm water column, we get:
N in water = 10mm x 10 mm * 10,000,000 Hz/4 X (1460/100000) = 171 mm
As the formula is for a circular probe, we use a correcting factor of 1,35 leading to N = 230 mm. Adjusting for the water column, and the speed of sound in Aluminum, we obtain of 36 mm.
In the active direction, the size relates to the aperture used and if focusing is used. The formulae are adapted to each scenario based on conventional ultrasonic calculations.
Beam divergence in the passive direction, is given by:
sin Î±/2 = 0,44 c / fD = 0,44 6200000/10000000*10
which lead to divergence equal to approximately 1 degree.