This document proposes a technique called Automatic Dynamic Depth Focusing (ADDF) for phased array non-destructive testing. The technique estimates the geometry between the ultrasound array probe and test part using time-of-flight measurements from initial trigger shots. It then calculates a "virtual array" that operates as if in a homogeneous medium, avoiding complications from the real interface. Using the virtual array, it computes initial focusing parameters for real-time dynamic focusing during scanning. The overall procedure takes about 2 seconds, providing fully automated focusing faster than existing geometry-based calculators.

1. Automatic Dynamic Depth Focusing for NDT
Jorge Camachoa
, Jorge F. Cruzaa
, Carlos Fritscha
and José M. Morenoa
a
Instituto de Tecnologías Físicas y de la Información “Torres Quevedo”
Consejo Superior de Investigaciones Científicas (CSIC), Serrano 144, 28006 Madrid, Spain
e-mail: j.camacho@csic.es
Abstract. Automatic Dynamic Depth Focusing (ADDF) is a function currently not available in state of the art phased
array NDT instruments. However, it would be a valuable tool to inspect arbitrarily shaped parts or when the part-array
geometry is not accurately known. ADDF will avoid the burden of computing and programming focal laws, the
complications of CAD-based geometry descriptions and is an effective tool to adapt to changes in the probe-part
geometry during the inspection. Furthermore, the dynamic depth focusing feature will yield the best possible image
quality with phased array technology.
This work proposes an ADDF technique based on a procedure that automatically obtains the array-part geometry and sets
up all the required focusing parameters. The array-part geometry is estimated from the first echo time of arrival using a
few trigger shots. A virtual array that operates in the second medium only allows computing the initial values for a real-
time dynamic depth focusing hardware. This technique is well adapted to inspect parts of unknown or variable geometry,
or when the distance and/or the alignment of the array probe with the part changes during the inspection. The overall
procedure is relatively fast (about 2 seconds using standard computers), even faster than currently available geometry-
based focal law calculators.
.
Keywords: Autofocus, Dynamic Depth Focusing, Interfaces, Non-Destructive Testing, Phased Array
PACS: 43.60.+d, 43.58.+z
INTRODUCTION
Phased array ultrasound provides images of the interiors of the inspected parts. From these images many kinds of
flaws, like cracks, inclusions, voids, etc. can be analyzed for Non Destructive Testing and Evaluation (NDT). High
resolution images are required to accurately size defects and to improve sensitivity. Differently from the classic
mono-element inspections, the phased array technology allows to steer and focus the beam, in emission and in
reception, which improves image resolution. Beam steering and focusing are implemented by controlling the delays
applied to signals in emission and reception.
The best image quality is obtained with Dynamic Depth Focusing (DDF) where all the acquired samples are “in
focus”, that is, the beam steering and focusing delays (focal laws) have been set appropriately for their individual
spatial positions. The set of focusing delays required for a single focus (sample) can be obtained from the
differences on the time-of-flight from the focus to every array element. This is carried out from geometric
considerations with the knowledge of the sound propagation velocity and should be repeated for all the sample
positions to implement the DDF function.
For an N-element array and an image line with M-samples, the number of focusing delays in reception is N·M,
which must be computed with a resolution of a few nanoseconds. If the image has L lines, the number of focusing
delays for DDF is L·N·M. For example, if L=100 lines, N=64 elements, M=4K samples, the number of focusing
delays for the whole image is above 25·106
.
The large number of focusing delays required for DDF causes some problems. First, they must be accurately
calculated, which may be performed off-line, although with a high computational cost. Second, they must be stored
someway in the acquisition equipment to be applied in real-time during acquisition.
Furthermore, a good description of the array-part geometry is required to compute accurate focal laws, which is
easily achievable for “in contact” inspections, where the geometry is accurately defined by that of the transducer.
But, in water immersion, a deviation of only 0.1 mm yields timing errors of 130 ns, more than half the period of a 5
MHz signal, which impairs focusing. A probe misalignment of only 1º can produce important amplitude losses and
wrong localization of the flaw indications [1].

2. To obtain the correct focal laws, CAD-based geometry descriptions together with simulation and focal-law
computing software are commonly used [2], which increases inspection complexity and requires time to prepare it.
Moreover, in many cases, this approach is unpractical due to manufacturing process tolerances (casting material,
molded components, non-rigid parts or with varying shape, soft curved plates, weld-caps, etc.), which turns CAD
descriptions useless. Also, the geometry becomes unknown when the relative positions of the array probe and the
part change during the inspection in an unpredictable manner.
Another aspect is the requirement for the phased array instruments to store the large amount of focal laws and
handle them in real time. In many cases, a single focus is set up in emission as well as in reception, with the
corresponding losses in image resolution, sensitivity, etc. at regions apart from the focus. Sometimes, a few foci are
set in every scan line [3]. However, strict focusing at every sample of every scan line is desired to keep the
maximum image quality. Techniques that code in a single bit per focus the information required for dynamic
focusing have been proposed [4], reducing the storage requirements.
Computing the focal laws is simple when the N-element array probe is in contact with a homogeneous part of
known propagation velocity c. The time-of-flight from an array element at (xAi, zAi) to a focus at (xF, zF) is:
Ni
c
zzxx
iT FAiFAi
AF 1,
)()(
)(
22
(1)
The focusing delay for element i and a single focus is:
)](min[)()( iTiTi AFAF (2)
However, when a coupling medium is inserted between the array probe and the part (water immersion, plastic
wedge, etc.), refraction at the interface complicates this task. In these cases there are not closed formulae to compute
the time-of-flight of array elements to foci. Instead, approximate numerical techniques must be used.
The more often applied method is based on the Fermat’s principle, searching for the path of minimum time-of-
flight. To this purpose, the interface is first finely sampled and rays are traced from the array element to the interface
samples and to the focus. Propagation time along these rays takes into account the propagation velocities in the
coupling medium (c1) and in the part (c2). Although simple, this technique may require long searches and computing
time [5]. An improvement can be achieved with a fast focal law calculator [6] but, for DDF, computing can take
several minutes.
Simulation tools are also frequently used to compute the focal laws and to estimate the acoustic field distribution
in the Region of Interest (ROI). These tools are commercially available and provide means to predict sound
trajectories and field intensities [7]. However, they demand a strict knowledge of the probe-part geometry and also
require a significant amount of processing time.
In recent years there have been some attempts to automatically adapt the inspection parameters (focal laws, etc.)
without prior knowledge of the actual probe-part geometry. One technique uses special flexible phased array probes
where every element is independently spring loaded to adapt to the part surface [8]. These non-conventional probes
basically operate in contact, where the focal laws are easily computed from (1) and (2) as long as the individual
position of the elements is known with the required accuracy.
Another method, called SAUL, automatically produces a wave-front parallel to the interface that makes the
ultrasound penetrate with normal incidence [9]. This technique requires several trigger events with full-parallel
reception and provides unfocused images because the geometry is not estimated. This technique is suited to inspect
laminated structures where a high lateral resolution is not as essential.
Some other techniques based on the Time-Reversal Mirror, automatically provide a focus to the strongest
reflector. This concept has been extended with iterative processes to focus into the ROI [10]. However, these
techniques require non-conventional electronics and also have a high computing load.
In this work we address the above problems by proposing a new technique that performs auto-focusing using
standard phased array probes, modified phased array instruments and software procedures. Our auto-focusing
technique does not require any prior knowledge of the array-part geometry, so that, CAD-based descriptions are
avoided. It provides Dynamic Depth Focusing at every acquired sample, and hence, the maximum image quality is
automatically obtained. The operator is released from the task of deciding the location of the foci. Finally, the
overall procedure is very fast, about 2 seconds using standard computers. This is even faster than state-of-the-art
software-based focal law computing tools.

3. The proposed auto-focusing function performs in three steps: 1) Estimation of the array-part geometry, 2)
Calculation of a virtual array that operates in a homogeneous medium, 3) Computing and setting the initial values
for a real-time focusing hardware. Step 1 adapts the subsequent processing to the current array-part geometry. The
virtual array avoids the complications of refraction at the interface and, together with the real-time focusing
hardware, has been patented and incorporated into a first-time commercially available auto-focus phased array
technology [11].
FIGURE 1. Points Pi at the interface are located at distances Ri from the array elements. The interface is defined
by the envelope of N circumferences with radius Ri and centers at the array elements.
Automatic Estimation of the Probe-Part Geometry
Frequently, the inspection of arbitrarily shaped parts is performed by water immersion or with a wedge coupled
to the part surface. 1D array probes are often used to obtain linear or sector images. Here it is assumed that the
interface geometry between the two media is unknown.
The first step for a fully-automated auto-focus algorithm is the estimation of such geometry to take into account
refraction effects. To this purpose, using conventional phased array equipment, a set of interface points is obtained
by performing a pulse-echo linear scan with an active aperture of 1 element. The first-echo time of arrival Ti to
individual elements, 1≤ i ≤ N is recorded. These times define a set of N circumferences tangent to the interface (Fig.
1), whose radius are:
2
1 i
i
Tc
R (3)
where c1 is the propagation velocity in the coupling medium. Assuming that radius Ri and Ri+1 are parallel, the angle
φi (φ1 is shown in Fig. 1) is given by:
)(
2
sin 1
11
ii
ii
i TT
d
c
d
RR
(4)
where d is the array element pitch. Then, if the coordinates of element i are (xAi, zAi), the coordinates of points Pi are:
φ1
R1
R2
1 2 3 N
P1
P2
P3
PN
R3
RN
z
x
d
interface

4. iiAiPi
iiAiPi
Rzz
Rxx
cos
sin
(5)
The assumption of parallelism among Ri and Ri+1 is easily met if the curvature radius of the interface is large in
relation to d. In fact, the above expression is exact for a plane interface. A set of N-1 interface points is obtained
using equations (3) to (5) with N trigger events.
The set of coordinates {(xPi, zPi)} is input to a curve fitting algorithm that yields an analytical representation of
the interface. For example, a 2nd
to 4th
degree polynomial or spline fit can be used for soft curved interfaces of
arbitrary geometry, which allows for convex and concave parts. The curvature radius of a concave part must be large
enough to provide points Pi whose abscise increases with the element number, following the conventions of Fig. 1.
A fitting to a circle or a straight line can be made if the part shape is known to be of this kind. A simple interpolation
between the detected points can be used as well.
The analytical representation of the interface allows its extension at both sides of the detected points by
extrapolation. The range covered by the detected points is enough for normal incidence (0º steering angle) but may
be not sufficient for other angles.
Alternatively, a lower number of measurements can be performed. If the degree of the polynomial is q, the
minimum number of trigger events must be S=q+1. These measurements should be taken with array elements
separated dM = [N/S] (where [·] indicates rounding to the nearest integer) and d should be substituted by dM in (4).
However, this has the risk of increasing the geometric errors due to larger deviations of parallelism among
consecutive ray paths.
Furthermore, the curve fitting process robustness depends on the first-echo time of flight measurement accuracy,
the absence of outliers and the number of points used by this algorithm. To increase robustness it is advisable: a) to
acquire, at least, a number 2S of time-of-flight measurements, b) to use the highest sampling frequency available or
perform interpolation to increase time resolution and c) to include some outlier detection and rejection algorithm.
Most outliers are due to the pulser tail, to weak interface echoes or to noise spikes. All these effects must be
considered and their measurements ignored by the curve fitting process.
Virtual Array and Dynamic Depth Focusing
The first idea behind this objective is quite simple: finding a “virtual array” that operates in the second medium
only and yields approximately equivalent time-of-flight to foci in the ROI. It is a key concept for the DDF auto-
focusing algorithm that avoids the complications of refraction at the interface (Fig. 2).
FIGURE 2. Representation of a real array element A, the entry-point G of the ray to the focus F and the position of
the corresponding virtual array element V.
A
V
G
F
interface
c1
c2

5. For a given real array element A at (xA, zA) and a focus F at (xF, zF), the true time-of fligth A to F is tAF. This is
the sum of two terms: tAG from A to G with sound velocity c1, and tGF from G to F with sound velocity c2. From the
Fermat’s principle, G is located at the interface point that makes minimum tAF = tAG + tGF.
For every real element, a corresponding virtual element V is assumed at (xV, zV). The time-of-flight from V to F,
tVF, is computed in the second medium only with sound velocity c2. To achieve the equivalence between virtual and
real elements, the time-of-flight tVF plus a constant term tK is made equal to tAF:
AFKVF ttt (6)
The constant term tK is given by:
2
2
2
1
1
c
c
tt AGK (7)
where tAG is the time-of-flight from real element A to entry-point G, computed by numerical methods.
To find the coordinates (xV, zV) of the equivalent virtual element (two unknowns), two equations are required.
They are obtained from (6) by computing, by numerical methods, the time-of-flight to two foci FA and FB, located at
the beginning and the end of the ROI at (xFA, zFA) and (xFB, zFB), respectively:
AFBK
FBVFBV
AFAK
FAVFAV
tt
c
zzxx
tt
c
zzxx
2
22
2
22
)()(
)()(
(8)
Solving these equations for (xV, zV), the virtual element that corresponds to the real element at (xA, zA) is obtained.
Note that tVF is computed in the second medium only (propagation velocity c2), so that refraction effects are taken
into account by the constant tK term only.
The virtual element, operating in the second medium only, provides exact times of flight for FA and FB, where
they are solutions of (8), and approximate for foci between FA and FB.
FIGURE 3. a) A typical application, showing the real array, the virtual array, the interface and a focus in the main ray
(dimensions in mm) ; b) Time-of fligth errors (ns) in the normalized range 0 to 6·(R/D).
Figure 3a) shows a typical application, where a 32-element real array is used to perform the inspection of an
arbitrarily shaped part, with c1=1.5 mm/μs and c2= 6.2 mm/μs. It is also shown the corresponding virtual array
computed as explained above.
Focus F is located at a normalized distance RF/D = 0.85 from the interface, where D is the aperture size (D=N·d).
The ray from the first real array element A to focus F enters the interface at G. This point practically coincides with
the intersection of the straight-line ray from V to F.
Reference foci FA and FB to solve (8) were located at RFA/D = 0.5 and at RFB/D = 4, respectively (not shown).
Times of flight from the real array and from the virtual array to foci in the main ray at normalized ranges 0 to
-20 -15 -10 -5 0 5 10
-25
-20
-15
-10
-5
0
5
0 1 2 3 4 5 6
-6
-4
-2
0
2
4
6
R/D
ns
Real array
Virtual array
interface
F
a) b)
V
A
main ray
G

6. 6·(R/D) were computed. The former were obtained by numerical methods based on the Fermat’s principle with a
finely sampled interface. The latter were obtained using the following equation:
K
FVFV
VF t
c
zzxx
t
2
22
)()(
(9)
where tK was obtained from (7).
The differences ε=tAF-tVF are considered timing errors and are shown in Fig. 3b). It can be appreciated that they
remain within ±4 ns in the whole range, a quite acceptable value for a high focus quality, even for 10 MHz arrays.
At the ranges of FA and FB timing errors are zero.
The virtual array can be used to obtain the focal laws, using (9) to get the equivalent time-of-flight and, then,
applying (2) with tAF substituted by tVF. This is a much faster procedure than any numerical method based on a
search for the minimum time-of-flight path.
But the virtual array allows a step ahead that does not require computing any focusing delay. This is achieved by
using some of the known dynamic focusing circuits available in the literature that operate in a single, homogeneous
medium [12]. In our case, we have developed a focusing circuit that has several advantages: requires setting less
parameters, the time resolution can be freely chosen and a single circuit can be shared among several channels using
state-of-the art FPGAs [13].
Once initialized for a given steering angle, which requires setting 2 values/channel, the focusing circuit operates
in real time by incrementally computing the sampling instant that corresponds to the next sample. In general, the
sampling instant is composed of a coarse delay, expressed in sampling periods, and a fine delay that can be a
fraction (v-1)/v of the sampling period obtained by interpolation, where v is an arbitrary integer greater than unity
that sets the time resolution.
The received signal is first delayed by the coarse delay and then sampled at intervals determined by the focusing
circuit that automatically determines the next sampling instant. The circuit keeps the overall focusing delay error
below ±1/2v, thus achieving an effective Dynamic Depth Focusing.
Experimental Verification
The Automatic Dynamic Depth Focusing instrument performs in 3 steps that are carried out by pressing on a
single button “Autofocus”:
1. Estimation of the probe-part geometry by measuring the first echo time of arrival, as explained.
2. Evaluation of a virtual array for every steering angle, carried out as presented.
3. Computing and setting the initial values for the focusing circuit (focusing parameters).
This process is carried out in a relatively short time using standard computers (about 2 seconds for 100 scan lines
and 128-element arrays), which is less than the time involved on computing and setting focal laws for DDF with
other methods. Furthermore, the focusing parameters are automatically adapted to the actual probe-part geometry.
Steps 1 and 2 are omitted for “in contact” inspections.
Figure 4a shows a typical experimental arrangement. A 90º aluminum sector of 100 mm radius with several rows
of side drilled holes (SDH) is inspected in water immersion with a 5 MHz, 128-element array transducer, d= 0.6
mm. The array was arbitrarily located at about 20 mm from the part surface. A sector scan from -45º to +45º relative
to the normal to the interface was programmed for imaging at 1º steps, with active apertures of 23 elements in
emission and 96 elements in reception.
Figure 4b shows the linear scan performed with an active aperture of 1-element to estimate the probe-part
geometry. Only the first interface echo is of interest, but note that there are many other preceding indications
resulting from the pulser tail. These echoes are ignored by means of a suppression gate marked by a straight line at
about 400 sampling periods.
After canceling the pulser tail artifacts, Figure 4c shows the position of the interface echoes received by every
element (black dots), obtained with the procedure of Eqs. (3) to (5). Fitting these points to a 3rd
degree polynomial,
the estimated interface was extrapolated and shown in the same figure (in gray). The coordinates are automatically
set relative to the first array element, with the x-axis running parallel to the array length and the z-axis to the sound
propagation direction. Since it is known that the part has a circular interface, fitting the points to a circle could have
been also used, although it yields indistinguishable results in this case.

7. Figure 4d shows the resulting sector image, where two rows with 4 SDHs each are clearly seen. Their locations
and resolution correspond with the expected ones.
The RMS error of the interface detected points was 30 μm, a value that corresponds to the time resolution of the
first-echo time of arrival, acquired with a sampling frequency of 40 MHz. More accurate results had been obtained
using a higher sampling frequency or interpolating the received A-scan. However, for most applications, the
averaging effect of the fitting algorithm compensates for these errors, which remains low enough to achieve a good
image quality.
FIGURE 4. a) Experimental arrangement: array probe arbitrarily positioned 20 mm apart from the part surface; b) Linear scan
with a single element active aperture (horiz: mm, vert: samples); c) Detection of the interface and extrapolation; d) Obtained
image where all the SDH are correctly located and focused (horiz and vert axis in mm).
Conclusions
The proposed auto-focusing technique operates with a coupling medium in three steps: a) estimates the probe-
part geometry, b) computes an equivalent virtual array that operates in the second medium only and c) performs
Dynamic Depth Focusing with a specialized hardware in real time. If the array probe is in contact with the part, only
step c) is required.
This new technique, which has been patented, avoids the operator all the complications of computing and setting
the appropriate focal laws. Neither CAD-based geometric descriptions nor prior knowledge of the part shape are
required. Auto-focus will adapt to the actual geometry.
The geometry is estimated by a series of pulse-echo measurements from individual elements and using closed
formulae to obtain a set of interface points. These points are interpolated and/or fitted to a polynomial to extend the
interface at both sides of the detected points.
Avoiding the refraction effects with the virtual array provides a fast method for computing the focal laws.
However it is here used to calculate the initialization parameters of a real-time focusing hardware that sets a focus at
every sample with an arbitrarily high resolution.
a) b)
c)
d)

8. The auto-focusing technique has been experimentally verified, producing phased array images with the
resolution expected for DDF. The data acquisition process to estimate the geometry and the computations to obtain
the virtual array and the focusing parameters are carried out typically in 2 seconds, using a standard computer.
The new method, which operates with conventional phased array transducers, has proved to be quite robust for
soft curved interfaces (convex or concave), as long as techniques to detect and reject outliers are included in the
algorithm that acquires the interface points.
ACKNOWLEDGMENTS
This work has been funded by project DPI 2010-17648 of the Spanish Ministry for Science and Innovation.
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