Nondestructive Testing of Live Trees
using Microwave Radiography
Finding ways of testing the soundness of live trees is a topic of international interest. For example, see V. Bucur, "Techniques for high resolution imaging of wood structure: a review", Measurement Science and Technology, 14 (2003) R91-R98. Measuring the soundness of high-value trees such as Black Cherry could have economic significance since such trees are often bargained for individually. X-ray tomography of logs is useful in sawmills but is cumbersome and does not as yet appear to have attracted sufficient research capital to be applied to trees standing in forests. Microwave tomography is relatively undeveloped but requires much less capital expenditure to investigate. Microwave imaging has the potential to detect decay in live trees. Microwave equipment is lightweight and involves no dangerous ionizing radiation. However, its application presents new challenges. Compared to light and x-ray, microwaves are big waves. Consequently, the straight-line geometric approach that works for x-ray tomography is inadequate because the microwaves can flow around the flaws being examined reducing their visibility and creating diffraction artifacts; imaging calculations must take into account the wave nature microwave illumination -- an interesting challenge. Another challenge comes from the impractability of wrapping a goniometer around a tree. This mechanical challenge may be solved by extending some new design ideas now incorporated into aircraft inspection tools. A third challenge comes from the high absorbtance of trees for microwaves. This challenge may also lead to discovery since the biological activities of trees have strong effects on absorption and polarization of microwaves. This is what my colleague, Hashim Yousif and I are now studying.
Wood, especially living wood, is a very effective polarizing medium for microwaves. In the 3 cm band being studied, the electric vector must be perpendicular to the grain for significant propagation to take place. Consequently, the magnetic vector, the H vector, runs more or less parallel to the grain. In practice there often appears to be some rotation of polarization on transmission through wood. Transmissivity is strongly affected by water content since water strongly absorbs microwaves.
Work in Progress: Wave Propagation Measurements on Wood
We have estimated and measured the complex dielectric constants of tree trunks and their components. The structure of wood and cambium is fiberous. The electrical connectivity along the fibers, phase 1, is here presumed to be continuous while the interfiber connectivity is presumed nil at this preliminary stage. The fibers are contained in a cellulose matrix, phase 2. The fibers are presumed to be a mixture of cellulose salt and water. The initial model follows that developed for artificial dielectrics made out of conducting fibers in an insulating matrix. [T. Teshirogi and T.Yoneyama, 1999]. The analytical result depends strongly on the amount and properties of the water and salts.Both models an measurements confirm that the real dielectric constant for tree trunk components is low. Conseqently the index of refraction is low, about 1.4. Thus little reflection takes place at the surface and bark roughness is relatively unimportant. The absorption due the the imaginary dielectric constant is very significant by comparison. Our current measurements are being made at 9.5GHz.Here is a summary of our preliminary tests.
MATERIAL POLARIZATION of E ATTENUATION ALPHA
reciprocal inchesBlack Cherry sapwood perpendicular 1.1 Black Cherry sapwood parallel very large Black Cherry bark perpendicular 0.04 Black Cherry bark parallel 0.89 Maple, waterlogged perpendicular 1.2 Maple, decayed parallel very large Maple bark perpendicular 0.04 Maple bark parallel 0.89 Douglas Fir lumber perpendicular 0.46 Douglas Fir lumber parallel 0.89 Commercial Flakeboard arbitrary 0.49
Regarding Absorption
The feasibility of microwave tomography or any form of microwave imaging as a means for the nondestructive testing of live trees depends on the technology's ability to cope with the low signal strengths expected for the received signals. A back of the envelope estimate can be based on assuming that absorption outweighs all other effects. Commercial microwave receivers can cope with signals as small as -80 dBm. This amounts to an input power of about 1E-11 watt. Given a source power of about 100mW, we obtain a limiting product of thickness times alpha of 23. For alpha ranging between 1.1 and 1.2, the corresponding limiting diameter of tree is 19 to 21 inches. Improvement can be obtained by skillful detector design and increasing the input power. However, too little is known about the other factors that could degrade this estimate.
Because of the high attenuation constants for live wood, internal voids in trees should be easy to detect. Similarly, the water content of tree trunks can probably be mapped and areas of nonfunctional cambium identified. The limiting resolution for this technique would probably be about 1/2 the wavelength or about 1.6 cm. under the best of conditions short of phase contrast methods. Tree trunks smaller than those commercially harvested would be easier to examine. Time and experimentation will determine what diagnostics may be obtained from this new technique to assist the cultivation of trees.
Acknowledgement: Thanks to Bradford Forest Products for samples of Black Cherry.
An Initial Transmission Image
We have obtained a one-dimensional transmission image of a bolt (section of tree trunk) having an internal void. A cross-section of the bolt is shown at left. Its projection is centrosymmetric and consequently its Fourier transform is real. The image, obtained as the inverse Fourier transform of the diffraction pattern is shown below. The bolt acts as a thick cylindrical lens. Consequently, the Fraunhofer diffraction pattern of the central (source) plane containing the void appears at distance approximately equal to twice the focal length of the bolt. The Fraunhofer diffraction pattern is the square of the norm of the complex Fourier transform of the transmittance of the source plane.
(The data were collected in physics laboratory of the University of Pittsburgh, Bradford by Larry Lawson and Hashim Yousif using apparatus designed and built by Larry Lawson. The Fourier image processing was performed at Umbrage house by Larry Lawson.)
4.2.2006