Can we reverse time? – scientific blog

---

The title question is definitely not new and, depending on the context, it may have different answers. This article shows an engineering perspective on the problem. As we all know, engineers are very creative people (especially those at AGH UST!) who can find solutions to the problems they encounter; sometimes very unconventional solutions.

 

One of the problems that arises in many engineering applications is the need to focus energy in space and time. Examples include the focusing of ultrasonic waves for material testing, in urology for the fragmentation of kidney stones, and many others.    

 

Non-destructive testing (NDT) is the field of engineering that deals with the evaluation of defects inside materials without damaging them, i.e. non-destructively. There are many NDT techniques, some of them were already discussed in this blog [1]. Currently, the most commonly used NDT techniques are based on the propagation of ultrasonic waves. Ultrasonic testing is based on a principle that elastic waves within an ultrasonic frequency range are sent into the material, typically using piezoceramic transducers, and the resultant wave propagation field is analysed. Typically, linear wave features like a change in wave amplitude or a phase shift are used to detect a damage, and to determine its location and size. Sometimes, however, the damage present in the material is too small (e.g. micro-cracks) to cause an observable change in either the amplitude or phase of the ultrasonic waves. In such a case, the damage remains undetected in ultrasonic testing. An alternative testing approach, based on non-linear wave features, can be applied to deal with such problems. The condition under which non-linear ultrasonic testing can be applied is to deliver a sufficiently large wave amplitude to the material to observe a non-linear response. This is, however, not an easy task as the commonly used ultrasonic transducers operate at low amplitudes, not sufficient for non-linear testing. To solve this problem the concept of Time Reversal has been introduced.

 

How to reverse time – what is Time Reversal? 

 

Probably the most illustrative example of the Time Reversal principle is the one with a stone thrown into a pond. Touching the surface of water, the stone creates waves that propagate radially from the location of the impact. The process is illustrated in Figure 1. The energy of the impact is initially (at time t0) focused around the impact point, and as the time goes by (from t1 to t3), it is carried away from the source by the propagating waves. The desired goal is to reverse this process and to focus the energy again at one point (i.e. go back from t3 to t0).

 

But how can we force waves to go back in time and focus in a point?   

 

An engineering solution to this problem works in the following way: let us consider a block of material with attached piezoceramic transducers (marked as PZT1 and PZT2 in Figure 2). Each of the transducers generates sequentially ultrasonic waves driven by the same input signal. Typically, this would be a wave packet of a given central frequency (e.g. 100 kHz) as it is shown in the bottom left side of the figure. The wave propagation field has to be measured at a given location on the surface. This can be done with a laser vibrometer, which is a device which enables very precise vibration measurement in a non-contact manner. This way we obtain two time signals, marked as “measured signals” in the figure. The operation that has to be performed at this point is to reverse those signals in time, that is to perform the  t = – t mapping, as shown in the figure. Time reversed signals are used as input signals for the piezoceramic transducers that now generate waves working simultaneously. As a result, ultrasonic waves propagating in the material focalise at the measurement location in a given point of time! The waveform of the focalised signal is shown in the top right side of the figure. What is more important in the context of non-destructive testing, the focalised wave amplitude is much greater than the amplitudes obtained from piezoceramic transducers working individually. In addition, a high amplitude is obtained only at the focal spot location, which is another advantage for NDT applications. 

 

Following the Time Reversal process, we obtain a great tool for non-linear testing of materials using the same hardware as we would normally use for linear ultrasonic testing. Thanks to the spatial and temporal focusing of the wave field, we can probe the material locally and evaluate its condition. Augmenting this technique with a scanning procedure allows to probe material non-linearity and detect damages on a larger area.

 

 

The use of Time Reversal for damage detection in composites 

 

One of the tasks that we are working on at the AGH UST Department of Robotics and Mechatronics is damage detection in composite materials. A typical kind of damage found in laminated composites, commonly used in aircraft industry, is delamination. This type of damage results from a blunt force impact on a composite component (like a wing or fuselage of an airplane). This is typically due to a collision with ground service equipment (e.g. during cargo loading or stairs delivery), a collision with birds or runaway debris during take-off or landing. This type of damage is very difficult to detect as it develops in the volume of the material and leaves virtually no sign on the surface.    

 

The Time Reversal technique can be used to detect this type of damage. One of possible test scenarios is to focus ultrasonic waves, according to the procedure described above, on a grid of points on the surface of a tested component. In this way we can obtain a two dimensional map of damage. In addition, we will focus the energy at two different signal amplitudes – low amplitude (x) and high amplitude (e.g. 2x). If the material in the probing location is undamaged, we expect it to behave linearly. This means that the difference between the signal measured at amplitude 2x and the rescaled (in this case multiplied by 2) signal measured at amplitude x will be zero. This is in analogy to a linear spring where duplicating the tensile force results in the duplication of spring elongation. Because damage introduces non-linearity to the material, this relation is no longer true and we can identify its presence and location. In literature, the measurement technique is known as the Scaling Subtraction Method or SSM. In real experimental data, the difference between the signals will not be equal to zero due to the measurement noise, but the values in damaged locations will be much greater than the noise level, and easily detectable.

 

The Time Reversal SSM technique has been applied to find a barely visible impact damage in a laminated carbon/epoxy pre-preg plate. Eight piezoceramic transducers were used to focus ultrasonic energy, and a scanning laser vibrometer was used to measure vibration responses on a grid of points. A schematic diagram of the measurement configuration is shown in Figure 3.   

 

The measurement result is shown in Figure 4a. The characteristic butterfly-shaped delamination can be clearly seen around the impact point that is located in the centre of the figure. For comparison, the same plate was investigated with the vibrothermography technique. The measurement result is shown in Figure 4b. As it can be seen, the location and shape of damage are very similar, showing that both techniques can effectively be applied to evaluate impact damage in composites.  

 

Summary 

 

The Time Reversal technique can be applied to many fields of engineering, including the non-destructive testing of materials, presented in this article. The technique, allowing to focus energy in both time and space, can also be applied to focus acoustic waves. One can imagine an application where an acoustic signal can be transmitted to a specific person in a room and, at the same time, remain inaudible to other people, or a car audio system that allows to play different music for each passenger in a car! The Time Reversal technique is also applied in underwater acoustics, in geophysics to localise earthquake sources, in medicine to focalise ultrasonic energy in a human body (e.g. to fragment kidney stones or to destroy cancer cells), or in defence systems to monitor unauthorized nuclear weapon tests. There are also concepts to apply Time Reversal to create a wireless mobile phone charger that could charge a device located anywhere inside a room, to locate and destroy tapping devices, to send ‘encrypted’ information over long distances, or to create haptic interface that could be used in smartphones.  

 

Author: Łukasz Pieczonka

 

The presented research has been carried out in collaboration with the Los Alamos National Laboratories, NM, USA. Financing was provided by the Foundation for Polish Science within the scope of the WELCOME programme no. 2010-3/2.

---