Facilitating soil-and plant-water research through the use of TDR

The development of TDR for measurement of soil water content and electrical conductivity has resulted in a large shift in measurement methods for a breadth of soil and hydrological characterization efforts. TDR has also opened new possibilities for soil and plant research. Five examples show how TDR has enhanced our ability to conduct our soil- and plant-water research. (i) Oxygen is necessary for healthy root growth and plant development but quantitative evaluation of the factors controlling oxygen supply in soil depends on knowledge of the soil water content by TDR. With water content information we have modeled successfully some impact of tillage methods on oxygen supply to roots and their growth response. (ii) For field assessment of soil mechanical properties influencing crop growth, water content capability was added to two portable soil strength measuring devices; (a) A TDT (Time Domain Transmittivity)-equipped soil cone penetrometer was used to evaluate seasonal soil strengthwater content relationships. In conventional tillage systems the relationships are dynamic and achieve the more stable no-tillage relationships only relatively late in each growing season; (b) A small TDR transmission line was added to a modified sheargraph that allowed shear strength and water content to be measured simultaneously on the same sample. In addition, the conventional graphing procedure for data acquisition was converted to datalogging using strain gauges. Data acquisition rate was improved by more than a factor of three with improved data quality. (iii) How do drought tolerant plants maintain leaf water content? Non-destructive measurement of TDR water content using a flat serpentine triple wire transmission line replaces more lengthy procedures of measuring relative water content. Two challenges remain: drought-stressed leaves alter salt content, changing electrical conductivity, and drought induced changes in leaf morphology affect TDR measurements. (iv) Remote radar signals are reflected from within the first 2 cm of soil. Appropriate calibration of radar imaging for soil water content can be achieved by a parallel pair of blades separated by 8 cm, reaching 1.7 cm into soil and forming a 20 cm TDR transmission line. The correlation between apparent relative permittivity from TDR and synthetic aperture radar (SAR) backscatter coefficient was 0.57 from an airborne flyover. These five examples highlight the diversity in the application of TDR in soil and plant research.

Modeling diffraction and imaging of laser beams by the mode-expansion method

We present a new method of modeling imaging of laser beams in the presence of diffraction. Our method is based on the concept of first orthogonally expanding the resultant diffraction field (that would have otherwise been obtained by the laborious application of the Huygens diffraction principle) and then representing it by an effective multimodal laser beam with different beam parameters. We show not only that the process of obtaining the new beam parameters is straightforward but also that it permits a different interpretation of the diffraction-caused focal shift in laser beams. All of the criteria that we have used to determine the minimum number of higher-order modes needed to accurately represent the diffraction field show that the mode-expansion method is numerically efficient. Finally, the characteristics of the mode-expansion method are such that it allows modeling of a vast array of diffraction problems, regardless of the characteristics of the incident laser beam, the diffracting element, or the observation plane. (C) 2005 Optical Society of America.