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Phased Array AND TOFD principles
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Active apertura

The Active Aperture is the total probe active length

A => Active aperture.

g => Gap between two adjacent elements

e=> Width of a single piezocomposite element, its typical value is ≤ λ/2.

n => Number of elements.

λ => Wavelength.

p (pitch) => It is the elementary distance between the centers of two adjacent elements.

W => Passive aperture is the element length or width. It determines the focal length on y-axis.

Fmin – Fmax => Maximum and minimum focal depths.


The near field depends on the aperture size.

A => Active aperture.

No => Near field.

Beam width

The beam width depends on the focal depth  and the active aperture size.

zfoco => Focal depth.

κBW  => Constant that depends on width criteria:

κBW => 1 (Rayleigh criteria)

κBW => 1.22 (FWHM - Full Width at Half Maximum - criteria)

κBW=> 1.33(Sparrow criteria)

Δx => Lateral resolution is defined by the beam width.

Δz => Axial resolution is given by

ΔT-20dB - Echo duration at a -20dB drop-off.

V=> Sound velocity in the test material.

Focus depth

For a given aperture (A), the focus length (L)  DECREASES as the focal distance (zfoco) DECREASES.

The maximum focal distance (zfoco(MAX)) must be inside the near-field No.

A => Active aperture.

V => Velocity of propagation.





The DDF dynamically changes the focal distance as the signal returns to the phased array probe. It significantly increases the depth-of-field, resolution and SNR.

Calculation of emitting focal law – angular sweep

DLE => Emission delay time.

DLR => Reception delay time.

θ => Steering direction.

xi => Position of the element “i”.

FE => Distance from the array centre to the emitting focal point in polar coordinates (RE,θ).

FR1, FR2, FR3, ...=> Distance from the array centre to the reception focal point “n”.

rin => Distance from the reception focal point “n”   to the element “i”  - round-time-of -flight

VM=> Ultrasound velocity in the test material.

Max. steering angle

Maximum steering angle depends on the element size

θSTmax => Maximum steeering angle at -6dB.

e => Width of a single array element.

λ => Wavelength.

Grating lobes

Grating lobes are generated by sub-sampling across the probe elements. Grating lobe amplitude depends on pitch size, number of elements, frequency and bandwidth.

βGrating => Location of grating lobes.

p => Pitch.

λ => Wavelength.

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