An out of plane optical sensitive configuration for pulsed digital holography was used to detect biological tissue inside solid organic materials like gels. A loud speaker and a shaker were employed to produce a mechanical wave that propagates through the gel in such a way that it generates vibrational resonant modes and transient events on the gel surface. Gel surface micro displacements were observed between the firing of two laser pulses, both for a steady resonant mode and for different times during the transient event. The biological tissue sample inserted approximately 2 cm inside the gel diffracts the original mechanical wave and changes the resonant mode pattern or the transient wave on the gel surface. This fact is used to quantitatively measure the gel surface micro displacement. Comparison of phase unwrapped patterns, with and without tissue inside the gel, allows the rapid identification of the existence of tissue inside the gel. The results for the resonant and transient conditions show that the method may be reliably used to study, compare and distinguish data from inside homogeneous and in-homogeneous solid organic materials.
©2004 Optical Society of America
Some areas in science and technology have devoted a great amount of time to study inhomogeneities in solids and semisolid materials. Anomalies within materials are the cause of ruptures, cracks and even deadly illnesses in humans, among many other problems. Theoretically it can be predicted that a mechanical wave travelling through an object will behave differently when this object is homogeneous and when it is inhomogeneous. Experimentally, it is very difficult to detect the resulting difference that the inner object inhomogeneity has on the mechanical wave, a perturbation that creates a rather different, as compared to an homogeneous object, surface micro displacement.
Non invasive methods in optics have played a central role in the detection of these defects in materials mainly because of their ability to detect displacements in the order of micrometers. Conventional holography, i.e., using photographic material, has been used to detect anomalies in human breast tissue [1,2]. This implies the use of a wet process to develop the photographic plates and the qualitative interpretation of the data making the whole procedure a lengthy one. The invention of coherent pulsed lasers, high resolution CCD cameras used with very fast PCs, created the non-invasive optical method called pulsed digital holography. It may be used as an alternative to conventional holography and well known methods used in medicine to differentiate healthy from defective tissue. Pulsed digital holography has been widely and successfully applied in many fields [3–7], including the measurement of deformations on biological tissues . The latter studied a pig leg with an incrustation of a metal rod 3 mm beneath the surface of its skin. Here, it should be pointed out that this metal rod was easily seen as a protuberance on the pig leg, however the experiment helped to show the feasibility and potential of pulsed digital holography to detect anomalies just beneath the skin. The present paper offers a further application of pulsed digital holography that contrasts the previous reported work in that it is now possible to detect human breast tissue inserted deeply into semisolid non-transparent gel, i.e., the tissue sample could not be seen and did not create a protuberance on the gel surface. The final goal is to apply the method in the near future to study inhomogeneities in human organs, e.g., the breast.
A frequency doubled single pulsed Nd:YAG laser (SPECTRON Laser Systems, Model SL404/SL804, Rugby, England), was used to illuminate the gel that was modelled to acquire the shape of a medium size breast. Healthy and unhealthy human breast tissue and glass marbles were incrusted at arbitrary locations deep into the gel. A loudspeaker placed some millimetres away was used to produce the natural resonant frequencies of the gel without incrustations, resulting in a characteristic phase map corresponding to the surface micro displacements. As expected due to the alteration in the propagation of the mechanical wave through the gel when an inhomogeneity is present, the resonant mode is affected and therefore this phase map suffered alterations. These surface displacement alterations are well suited to be studied with optical non invasive methods such as the one used here. The loudspeaker was also used to produce a transient event in the gel with and without the incrustation. Upon comparison of these phase maps, for two laser pulses and for both a steady resonant mode and different times during the transient event, it is readily observed without a doubt that the gel has an inhomogeneity within itself. All the results presented here show that pulsed digital holography is an optical non-invasive method that can be applied to detect human breast tissue in semisolid materials.
2. Experimental method and results
Figure 1 shows the out of plane sensitive optical setup for pulsed digital holography.
The coherent laser delivers single pulses of 15 ns width at 60 Hz, 10 mJ/pulse and λ=532 nm, illuminating the object which is a plastic semi spheric container holding a mixture of an opaque commercial gelatine or gel, with dimensions of 4 cm height and 9 cm diameter.
The reference beam is conveyed to the sensor of the CCD camera (PCO SENSICAM) via single mode fiber optics whose length helps matching the optical paths of reference and object beams. The camera has a high resolution sensor of 1280 by 1024 pixels, and 12 bit resolution, with a capability of acquiring images at a maximum rate of 7 frames per second. The CCD sensor receives an image of the flat gel surface, and is combined in the usual way with the reference beam. A low price loudspeaker is placed at about 10 mm away from the bottom part of the container and is driven with a low amplitude frequency generator. In order to find the resonant frequencies of the gel an accelerometer, whose trace could be seen on an oscilloscope, was placed in contact with the container, and frequencies were scanned from a few tens of Hz up to 1 KHz. For the model in question two resonant frequencies were found at 44 Hz and 810 Hz. The gel was prepared in a quantity such that several equal containers were filled at the same time and put to solidify for the same length of time. Only one container had no inhomogeneities and the rest of them with various types of them. These were: a) human healthy and unhealthy tumors approximately 6 mm in diameter, all surrounded by fat making their final sizes about 20 mm and with no definite shape, and b) glass marbles of three diameter sizes, 1.34 cm, 1.61 cm and 2.1 cm. All inhomogeneities were inserted in the gel at different locations around the geometrical centre of the model approximately 2 cm above the container bottom, prior to gel solidification. The inhomogeneities were not seen from the outside and did not create a protuberance on the gel surface. Care was taken to position the gel containers exactly at the same place in the experimental set up. The typical experimental procedure for digital holography was followed, see for instance reference , however for the first time applied to the kind of research reported here. The phase maps containing the information for the displacement of the gel surface are obtained for two laser pulses. The CCD camera shutter was independently opened in such a way that the laser pulses were separated 142 ms, so the resonant mode was captured at arbitrary amplitude displacements. This is possible because the resonant condition is a stationary one.
For the transient event, the same loudspeaker was used but now excited with a shaker amplifier that provided a 4 ms width pulse. This pulse produced a travelling mechanical wave on the gel surface that was observed at different propagating times from 4 ms up to 90 ms. An electronic synchronizing device designed specifically for the experiment was used to acquire the images at these times, and also is used to divide in two signals the electric signal coming from the Q-switch device of the 60 Hz single pulse laser: one that triggers the shaker amplifier whose signal goes to the loudspeaker, and the other goes to the CCD card controller. The circuit has the ability to time delay both signals and to control the image acquisition: the first image is taken at an arbitrary time, for the undisturbed object and for one single laser pulse, while the second image is captured after a time delay set by the electric impulse coming from the shaker amplifier, time used to open the camera shutter that acquires the disturbed object illuminated with another single laser pulse. In other words, the CCD camera captures a first image of the undisturbed object at any time (e.g., laser pulse 1) and the second image some ms (multiples of 16.7 ms) after the loudspeaker electric impulse disturbs the object, i.e., after several laser pulses, time in which the mechanical wave travels through the gel and reaches its surface and becomes observable, i.e., the surface micro displacements may now be observed with this optical method. Briefly, in mathematical terms the process may be expressed designating R(x,y) to be the smooth reference wave and U(x,y) the object wave. The intensity recorded on the CCD-detector for each image hologram is given by
where xH and yH are the coordinates at the hologram (detector) plane and the asterisk denotes the complex-conjugate amplitude. The last two terms of Eq. (1) contain information that corresponds to the amplitude and the phase of the object wave, data which is retrieved using the Fast Fourier transform method. Digital holography data was processed in the usual manner, e.g., .
Figure 2 shows the unwrapped phase map for the resonant mode at 44 Hz of the gel surface, without inhomogeneities.
Figures 3(a) and (b) shows for the same frequency, the unwrapped phase map of a gel with a tumor and a 2.1 cm marble, respectively. On comparison of Figs. 2 and 3 the difference is readily observed as the resonant mode is modified when the inhomogeneity is present, a feature that is reflected as a dark area in the images.
Furthermore, the size and object material can be differentiated between images a and b in Fig. 3. Figure 4 is the unwrapped phase map for the transient event with a 60 ms time delay and a marble in the gel. For other time delays, before and after this time, the inhomogeneity is seen but not as remarkably clear as shown here.
In Fig. 5 a plot is shown of a line through the central portion of the phase maps with and without inhomogeneity, but with a transient pulse in both. It is clearly seen the effect produced by the presence of the marble inside the gel: the line through the homogeneous gel shows a surface displacement around 6 µm, while the other shows a surface displacement between 0 and 10 µm.
The mechanical wave on the gel surface travels along it producing a displacement shown in the black line when the marble is absent, but it seems that this mechanical wave is obstructed to reach the surface when the marble is inserted producing an effect shown in the blue line.
Theoretically it can be predicted that a mechanical wave travelling through an object will behave differently when this object is homogeneous and when it is inhomogeneous. Experimentally, it is very difficult to detect the resulting difference that the inner object inhomogeneity has on the mechanical wave, a perturbation that creates a rather different, as compared to an homogeneous object, surface micro displacement. The results presented here showed that pulsed digital holography is an optical non-invasive method that can be applied to detect inhomogeneities in semisolid materials. Phase maps for a particular resonant mode could differentiate from a homogeneous gel and one containing inhomogeneities. At this time it was not possible to distinguish the type of material in the gel, but only if it was of a different size. Results with the transient loudspeaker pulse showed remarkably the presence of an inhomogeneity within the gel. It is believed that this transient pulse may be used to investigate the type of material within the gel, since tumors have different mechanical properties compared to marbles as seen in Figs. 3(a) and (b), a topic that will be pursued by the authors. Also, in the near future the research will be focused to find the 3D location of the inhomogeneities within the material. It is envisaged that when the present work is extended to study real cases the resonant modes and the mechanical transient waves for human organs will be different, but will use the facts found in this research for human breast tissue.
References and links
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