Date of Award

1999

Degree Name

Physics

College

College of Science

Type of Degree

M.S.

Document Type

Thesis

First Advisor

Dr. James O. Brumfield

Second Advisor

Dr. Ralph E. Oberly

Third Advisor

Dr. R. Elwyn Bellis

Fourth Advisor

Dr. Leonard J. Deutsch

Abstract

An optical Fourier transform represents the interference of wavefronts produced as light passes through multiple slits. Theoretically, any image containing periodic structure causes diffraction. The cellular arrangement of a plant leaf and the regularity in venation are ideal conditions for diffracting light. As light passes through columns of cells, its path is altered according to the distance and orientation present.

A photograph or slide of a leaf or the leaf itself may be used to produce a diffraction pattern by either optical or digital means. Optically, a laser beam directed through a slide is refracted by a converging lens and focused onto a piece of film at the transform plane. Digitally, software such as ER Mapper processes a scanned image using the Fast Fourier Transform (FFT) algorithm that closely approximates the mathematical analysis by summing the sine and cosine functions, referred to as the real and imaginary bands, respectively. Due to the flexibility and resolving capabilities, the digital method was utilized to acquire and to analyze transforms.

The Fourier transforms were analyzed qualitatively according to venation. High spatial frequency in the veins and veinlets did not determine the amount of detail in the transform. The transforms from the top surface of a leaf had very high order information, but the bottom of the leaf exhibited only a central maximum, characterized by low frequency. Veins are apparent on both sides of the leaf; however, cells are ordered on the top of the leaf and more random underneath. Fourier transforms are produced by even higher spatial frequency resulting from the cellular arrangement at the top of the leaf, independent of the venation.

To quantitatively analyze the Fourier transforms, the patterns were measured to determine the spacing between successive maximum orders. Using the “cell values” and “cell coordinates" features of ER Mapper, the maximum interference values were located and the distance between the central maximum and each order were measured. The calculated cell dimensions ranged from 15 to 45 microns.

Transforms from leaf layers photographed at 400X magnification suggest that the palisade cells and the cell walls both diffract light. Cellular dimensions predicted by the Fourier transform appear to result from the sum of the palisade diameter and the cell wall thickness for a total width of 14.5 to 16.5 microns. A correlation between Fourier transforms produced by individual leaves may be compared quantitatively to those arising from an entire tree to accurately represent patterns of plant physiognomy and cellular dimensions.

Subject(s)

Fourier transform optics.

Plant physiology.

Different patterns.

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