Applicability of effective medium theory to wood density measurements using terahertz time-domain spectroscopy
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The use of an effective medium theory is important when accurately measuring wood density using millimeter and terahertz wave techniques. To confirm the applicability of this theory to the evaluation of wood density, the relative permittivity and dielectric loss of oven-dry flat-sawn specimens of 11 different wood species were measured in a frequency range of 0.15–1.2 THz using a transmission measurement system for terahertz time-domain spectroscopy. A mixture model based on the effective medium theory well explained the density dependence of relative permittivity over the entire frequency range, while it did not fully explain that of dielectric loss, especially for higher frequencies. This indicates that wood scatters the terahertz wave with a wavelength close to the transverse sectional dimensions of the pores in wood in the same way as Mie scattering. It was found from the dielectric loss spectrum of wood substance that the frequency around 0.23 THz was preferable for the nondestructive evaluation of wood.
KeywordsOven-dry wood Effective medium theory Dielectric mixture THz-TDS Density evaluation
Wood is a natural material and there are fluctuations in its physical properties, such as its moisture content, grain direction, and density, and thereby it should be evaluated nondestructively to promote its wide usage in industry . The fluctuation of density in wood is especially important in determining the strength of wood .
Terahertz and millimeter wave techniques, which use electromagnetic waves with frequencies of 0.1–10 and 0.03–0.3 THz, respectively, have been developed so that the waves that penetrate through and reflect from a wood specimen can be detected with low noise [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. These techniques have attracted notice as new tools for the nondestructive evaluation (NDE) of wood density because they are contact-free, noninvasive and safe, and can provide higher resolution images [6, 7, 8] than the microwave techniques [15, 16, 17, 18, 19, 20, 21].
The method to evaluate density while using these techniques is generally based on effective medium theory [22, 23, 24], in which wood is regarded as a mixture of pores (air in the cell lumina) and wood substance (cell wall) [3, 11] and responds to electromagnetic excitation as if it were homogeneous . This theory, however, has a lower wavelength limit and the following rule of thumb is often employed : “the size of an inclusion in the mixture must not exceed a tenth of the wavelength in the effective medium”. In general, wood has many pores of transverse sectional sizes ranging from about 10 to 200 μm, and thereby the lower wavelength limit for wood is to be about 100–2000 μm or 0.15–3 THz in frequency. Therefore, to correctly evaluate wood density using the terahertz and millimeter wave techniques, it is necessary to examine the validity of the effective medium theory in this frequency range.
In our other paper, which was submitted to the Journal of Wood Science and is currently under review, the effect of pores on wood dielectric anisotropy was examined with the assumption that the effective medium theory is applicable to the relative permittivity of oven-dry wood obtained by terahertz time-domain spectroscopy (THz-TDS) at 0.15 THz. The purpose of this paper is to examine the applicability of the effective medium theory to the density evaluation of wood over a frequency range of 0.15–1.2 THz. The complex permittivity along the longitudinal axis of flat-sawn oven-dry specimens of 11 different wood species was measured using a THz-TDS transmission measurement system. The fitness of a mixture model based on the effective medium theory to the measured relative permittivity and dielectric loss was examined, and the relationships of the averages and standard deviations of the dielectric parameters of wood substance to the frequency were also examined.
Flat-sawn specimens, 25 mm square and 3 mm thick, were prepared from softwoods: hinoki (Chamaecyparis obtusa), sugi (Cryptomeria japonica), and akamatsu (Pinus densiflora); ring-porous hardwoods: kiri (Paulownia tomentosa), kuri (Castanea crenata), and keyaki (Zelkova serrata); diffuse-porous hardwoods: kusunoki (Cinnamomum camphora), tochinoki (Aesculus turbinata), buna (Fagus crenata), and isunoki (Distylium racemosum); and radial-porous hardwood: shirakashi (Quercus myrsinaefolia). Five specimens were prepared from each species. All specimens were dried to a constant weight at 105 °C.
THz-TDS transmission measurement
Results and discussion
Relation between dielectric parameters and density of wood at a low frequency
Dielectric properties of wood substance
The standard deviation of ε′WS slightly increased with f, while that of ε″WS significantly increased with f (Fig. 3b). This indicates that the applicability of effective medium theory is inferior at a higher frequency or at a shorter wavelength, especially for dielectric loss.
Effect of frequency on relation between dielectric parameters and wood density
To examine the applicability of an effective medium theory to the evaluation of wood density in the terahertz frequency range, the complex permittivity along the longitudinal axis of flat-sawn oven-dry specimens of 11 wood species was measured in a frequency range of 0.15–1.2 THz using a transmission measurement system for THz-TDS. The effective medium theory explained the density dependence of relative permittivity for the entire frequency range, but did not explain that of the dielectric loss for a higher frequency range. This indicates that the terahertz waves are more scattered at higher frequencies. It was concluded from the dielectric loss spectrum of wood substance that a frequency of approximately 0.23 THz is preferable for the NDE, since a high gain of the detected signals was obtained. A quantitative evaluation of the effect of the scattering on the dielectric loss should be examined in the future.
The authors would like to express their gratitude to Motoki Imamura and Akiyoshi Irisawa (Advantest Corporation, Japan) for their technical support.
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