Wiesław Bicz

A discussion paper about the possibility of using acoustic holography
 for the visualisation of three dimensional objects within a structure. 
The paper proposes some new ideas.
  

Optical holography has found many applications, not only for the creation of images with very good stereoscopic properties, but also for showing vibrations and displacement of diverse objects. There have been fewer applications of acoustic holography. In the main applications that have been used employ a synthetic aperture and view slices of the object under observation. Occasionally the phase of the scattered wave has also been used, but seldom has the whole of the information about changes in the wave as it propagates through the object been used.

This paper will show that it is possible to use acoustic holography more effectively and will discuss some of the difficulties that may be anticipated.

It is assumed that the reader already knows that holography is based on the recording of information contained in the whole wave front that has passed through the object and been scattered and diffracted by it. The recorded information allows a reconstruction to be made of the object. In optical holography the reconstruction is made with a reference beam and photosensitive material.

Acoustic holography doesn't allow this possibility since there is no material that is sensitive to acoustic waves similar to photosensitive materials. Also, a reference beam is unnecessary; an electronic reference will be good enough. Most acoustic transmitters can be treated as coherent.

Most applications to date use a moving transducer or a transducer array to scan the acoustic field (Fig 1).

Fig 1.

It is proposed to make this measurement simpler by using only one annular array or transducer moving in a circular path instead of using a single transducer scanning the whole surface or a large array. Figure 2 illustrates the idea using a moving transducer and Figure 3 using an annular array.
 

Fig 2.

Fig 3.

The easiest way to make these measurements would seem to be by using a transducer that moves in a circular path. Such a technique has been used successfully in a device developed by Optel for fingerprint visualisation. Although this device was aimed at obtaining a hologram for a two dimensional surface, the aim was achieved with high accuracy.

This paper aims to show that it is also possible to obtain holograms of three dimensional objects using the same method. Before doing this it is useful to summarise the methods that have been used in classical ultrasonic imaging.
  

The simplest method used employs one transducer that moves along a defined path (linear, circular etc) and sends an ultrasonic beam that should be as narrow as possible. The beam is directed towards the object to be investigated and the returning echoes are collected to produce an image of a slice through the body. Best results would be obtained from a narrow beam of high intensity and short pulse length, similar to a laser beam. Since this is not possible using normal transducers, only low resolution images can be produced.

A more complicated method uses many transducers (an array) and a synthetic aperture. The literature describes several options:

• Transmitters can be excited simultaneously or with differing delays
• Received signals are composed with differing delays to build the image of a slice of the object.
• Transducers can be used in different configurations.
• In most cases synthetic focusing is used.

In all cases where a synthetic aperture is used there is a fundamental problem in that each transducer produces a wave field that is independent of the others. Furthermore there are differences between transducer behaviour. As a result a kind of noise field is created that impairs resolution. Even with large numbers of transducers and complicated mathematical processing it is not possible to make this noise field small enough to produce good resolution.

It can be said that in all cases of acoustic imaging, with synthetic aperture or holographic methods, it is necessary to find answers to the following questions:

• How many transducers should be used?
• Where should they be placed?
• How should they be controlled?
• What should be done with the received signals?

Classical ultrasonic imaging uses linear arrays employing rectangular shaped transducers that are used for both transmitting and receiving. In most cases these transducers have a beam that is wide in one plane and relatively narrow in another. Sometimes the narrower plane is focussed. As a result a relatively thick slice of the object is produced.

To achieve a three dimensional image with this method it is necessary to move the array and the data collected from different positions assembled to produce the 3-D image. It can be seen that this procedure cannot produce an image in real time.

It could also be possible to work with a two dimensional array. Such a device would allow the ultrasonic beam to be controlled in three dimensions. However this would be both complicated and expensive to produce.

 
Following the work by Optel on fingerprint visualisation, an alternative approach to 3-D imaging is envisaged. Figure 3 illustrates one transmitting transducer in the centre of the device producing a very strong pulse with a perfect spherical phase and gaussian amplitude distribution. A circular array of receiving transducers collects the scattered waves from the object being examined. The echoes can be collected sequentially or in parallel, they can be sampled with a frequency high enough to see the whole data and processed by computer. It is considered to be possible to achieve a resolution of around 0.1mm using a receiver array of 300 elements.

Acoustic holography is believed to have the following advantages:

• Real time 3-D images could be obtained (even multiple images per second)
• The resolution compared to classical imaging can be improved due to the absence of phase noise and the presence of only one limitation (diffraction).
• The device would not be more expensive than classical devices. 

Many of the anticipated problems in developing this technology have been solved in the fingerprint project; however, some problems remain to be solved for the 3-D application.

The most important of the remaining problems seems to be the visualisation of the collected data. The ideal solution would be to show this data in the form of an optical hologram but no holographic display exists at the moment. Showing the data in the form of slices as in classical imaging techniques is not ideal, but may be possible.

There are many ways to show how the use of only one circle can be enough to collect sufficient information.

The simplest way takes into account the fact that, if a series of holograms is made using different frequencies, the only difference between them will be the size (magnification). If we take only a part of a hologram (allowing us our circular array of sensors) but use many frequencies, the result will be similar to a scan of the whole hologram. Effectively it is the same situation as using many circular arrays of different diameters. The frequency would have to be changed within the bandwidth that is equivalent to the spatial frequency of the object. The best method would be to use a pulse with enough bandwidth. The use of bursts is also a possibility and in some cases might prove to be even better. Either way, it would be necessary to use transducers with a large bandwidth.

The main assumption is that the object should scatter in all directions with about the same amplitude. This would be true for most biological objects and some others. Where the assumption is not true, it would not be possible to collect enough information with just one circle because scatter moving in another cone would be lost.

There is an open question over the possibility to assemble a reconstruction of the object in classical form as slices. It can be shown it is only possible for relatively simple objects using just one circle. The natural visualisation of ultrasonic holography would be holographic visualisation, but this causes problems.

• The object will be visible as a kind of transparent 3D structure and this is not a familiar presentation at the moment. People using such a device would need to learn how to interpret this new way of looking at a body.
• The best way to show the images would be to use a holographic display but there is no such display existing or proposed currently. Optel have a concept of how such a display could be made, but to realise the concept would require a dedicated development project.

In the absence of a developed holographic display, it would be possible to show images from ultrasonic holography using a normal computer display or to produce classical optical holograms (synthetic). It is also possible to produce images of slices through the object similar to classical B-scan images. In this case it would probably be better to combine data from many positions in one circle or to use more than one circle and more than one sender.

It would be possible to develop a device that would produce 3D images of high resolution based on the described ideas and on Optel's fingerprint experience. Such a device could be used for both medical and industrial applications. It would be necessary to develop software for the visualisation or a holographic display.

 

I have decided to publish this paper, because I think, that this could be the best way to find partners, interested in possibilities of this technology.

Wiesław Bicz

03.05.2002