**Appendix**

#### **Prototype design considerations**

Since the active imaging system depicted in Figure 5 in section 4 above is required to produce a direct acoustic image which is made visible by synchronised stroboscopic light (Schlieren or other acoustooptical modulation technique), the design parameters for NDT applications were determined both by theoretical simulations and experimentation. For the construction of the transducer arrays, bearing in mind the tight requirements for elemental uniformity, number of parameters for a selected centre frequency of 2 MHz were determined which included [15]:


**•** Element width-to-gap ratio

it produces sector images formed by overlapping zones, but each zone requiring only one pulse to produce a complete zone image, thus gaining by far the highest speed of sector scanning

Furthermore, the clarity and contrast of the images are high as the stroboscopic image mapping results in gating out many artefacts, problems due to reverberations and noise, to a high degree. Since the image reconstruction, by design, is based on coherent summation of signals in amplitude and phase corresponding to true targets satisfying the sonoptical focusing require‐

The typical results shown with the hybrid imaging system is applicable at present only to structural NDT for which it was designed. In order to produce true B-mode images for medical applications requires further work on the design of transducers and the sonoptical geometry to satisfy the conditions necessary for body tissue imaging, while accommodating the required dynamic range. In particular, it should be noted that the technique of image reconstruction is based on amplitude and phase integrity of signals; thus the inter-element uniformity of transducer elements and channels are crucial. In the case of medical imaging, the transducer element spacing is much smaller compared to NDT applications for any given frequency. For the above NDT system, the arrays were constructed using ordinary PZT transducer material. This is unlikely to be satisfactory in the case of medical transducers utilizing the above imaging techniques, since the requirements of transducer specifications are different and much tighter compared to conventional imaging to achieve good performance. Hence, transducers with piezo-composites or PVDF material may have to be developed for this application. Although the present system is designed to produce imaging in 2-D, extension of this technology to 3-D imaging in real-time is a distinct possibility which needs to be explored. This work and the development of dynamic compensation hardware will be taken forward in the next phase of

Since the active imaging system depicted in Figure 5 in section 4 above is required to produce a direct acoustic image which is made visible by synchronised stroboscopic light (Schlieren or other acoustooptical modulation technique), the design parameters for NDT applications were determined both by theoretical simulations and experimentation. For the construction of the transducer arrays, bearing in mind the tight requirements for elemental uniformity, number of parameters for a selected centre frequency of 2 MHz were determined which included [15]:

ments, random noise gets suppressed without the need for further processing.

compared to conventional methods.

290 Advancements and Breakthroughs in Ultrasound Imaging

**6.1. Future work**

development.

**Appendix**

**Prototype design considerations**

**•** Estimation of number of channels (30 for the initial design)

**•** Transducer element spacing (2 mm for the initial design)

**•** Physical size, shape and transducer material

The primary aim was to obtain an idea of the sharpness of the images and the extent of artefacts that may be formed in a given image space. Since the transducer backings were conductive, maintaining a low level of electrical cross-coupling was required for the size of the backing thus the element gap spacing was kept around 0.3mm. For visualisation of the acoustic image formed in the modulating medium, the requirements for channel characteristics were then determined. These included practical determinations of number of parameters including:


#### **Acoustooptical design considerations**

As mentioned in section 4 above, as opposed to conventional image reconstruction, the passive DUVD system had some ideal properties for ultrasonic imaging namely, image linearity and isochronicity. Maintaining the same properties in the active system was therefore important. The requirement for image linearity as determined by Hansted [12] for the DUVD is given below.

#### **Maintaining image linearity**

Figure 19 shows the two-lens system of the DUVD.

Using paraxial ray analysis, it can be shown that in order to maintain image linearity through‐ out the image field, the only requirement is to make the focal point of the two acoustic lenses coincident. This however changes the lateral magnification as given in equation 10, but since this is a constant it does not affect linearity or image quality and can be easily compensated if necessary.

#### **Maintaining isochronicity**

As stated in section 4 above, iscochronicity means that when the test object is insonified with a short acoustic pulse, all the echoes from the different targets, irrespective of their special distribution within the object field, arrive simultaneously at their respective image points thus giving the system its ability to display the whole image at once.

The above capability is in stark contrast to the need for line serial scanning in conventional imaging, giving the system its speed - the highest theoretically possible speed of imaging as it

D D <sup>=</sup> 1 3 2 *u v*

> = <sup>1</sup> 4

*f*

1 2

Using paraxial ray analysis, it can also be shown that when satisfying the above necessary conditions, the maximum object distance (Umax) and maximum image distance (vmax) can be

> æ ö = + ç ÷ ç ÷ è ø 1 2 max 1 3

æ ö = + ç ÷ ç ÷ è ø 3 4 max 4 2

where, f1 & f2 are the focal lengths of the first lens defined by medium velocities v1 v2, and f3 &

Thus the necessary and sufficient conditions for linearity and Isochronicity for the acoustic

**•** The external focal lengths must be related in accordance with that given in equation (7)

Using paraxial ray analysis taking also into account the conditions necessary for Isochronicity, it can be shown that there is however lateral image magnification (as mentioned above) such

Where, MA and ML are axial and lateral magnifications respectively. This does not affect image

f4 are that determined by the 2nd acoustic lens.

**•** The internal focal points must be coincident

linearity and can be compensated if necessary.

that:

written as:

imaging system are:

that:

where, Δu is the axial separation of the objects in the object medium and Δv is the axial separation of the respective image points in the image medium. In terms of respective focal lengths in object and image media (f1& f4) the condition depicted in equation (6) is achieved for this lens combination with a common focus in the medium v2 when f1 & f4 are related such

*V V* (6)

http://dx.doi.org/10.5772/56378

293

Breaking Through the Speed Barrier — Advancements in High-Speed Imaging

*<sup>f</sup>* (7)

*f f U f <sup>f</sup>* (8)

*f f v f <sup>f</sup>* (9)

= 2 *M M A L* (10)

**Figure 19.** Maintaining image linearity

**Figure 20.** Requirements for maintaining Isochronicity

produces images with a single pulse practically within the time of flight of the pulse echoes in the object and image media. The conditions required for iscochronicity as determined by Hansted for his DUVD system with reference to Figure 20 is given below.

It can be clearly seen that the necessary and sufficient condition for the images of two objects in the object medium with velocity v1 to be brought to focus at the same instant of time in the image medium with velocity v2 could be given as:

Breaking Through the Speed Barrier — Advancements in High-Speed Imaging http://dx.doi.org/10.5772/56378 293

$$\frac{2\Delta\mu}{V\_1} = \frac{\Delta v}{V\_3} \tag{6}$$

where, Δu is the axial separation of the objects in the object medium and Δv is the axial separation of the respective image points in the image medium. In terms of respective focal lengths in object and image media (f1& f4) the condition depicted in equation (6) is achieved for this lens combination with a common focus in the medium v2 when f1 & f4 are related such that:

$$\frac{f\_1}{f\_4} = \frac{1}{\sqrt{2}}\tag{7}$$

Using paraxial ray analysis, it can also be shown that when satisfying the above necessary conditions, the maximum object distance (Umax) and maximum image distance (vmax) can be written as:

$$\mathcal{U}\_{\text{max}} = \left(\frac{f\_1 f\_2}{f\_3}\right) + f\_1 \tag{8}$$

$$w\_{\text{max}} = \left(\frac{f\_3 f\_4}{f\_2}\right) + f\_4 \tag{9}$$

where, f1 & f2 are the focal lengths of the first lens defined by medium velocities v1 v2, and f3 & f4 are that determined by the 2nd acoustic lens.

Thus the necessary and sufficient conditions for linearity and Isochronicity for the acoustic imaging system are:

**•** The internal focal points must be coincident

produces images with a single pulse practically within the time of flight of the pulse echoes in the object and image media. The conditions required for iscochronicity as determined by

It can be clearly seen that the necessary and sufficient condition for the images of two objects in the object medium with velocity v1 to be brought to focus at the same instant of time in the

Hansted for his DUVD system with reference to Figure 20 is given below.

image medium with velocity v2 could be given as:

**Figure 20.** Requirements for maintaining Isochronicity

**Figure 19.** Maintaining image linearity

292 Advancements and Breakthroughs in Ultrasound Imaging

**•** The external focal lengths must be related in accordance with that given in equation (7)

Using paraxial ray analysis taking also into account the conditions necessary for Isochronicity, it can be shown that there is however lateral image magnification (as mentioned above) such that:

$$M\_A = \sqrt{2}M\_L\tag{10}$$

Where, MA and ML are axial and lateral magnifications respectively. This does not affect image linearity and can be compensated if necessary.
