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The problem of a guided wave obliquely incident on a grating etched in a thin film guide is considered. Two-dimensional coupled wave equations for the incident and reflected beams are derived for the cases of TE-TE, TE-TM, and TM-TM coupling. Two methods, a ray optic approximation and a coupled beam method, are proposed for the numerical solution of the coupled wave equations. Both methods are illustrated by a number of calculated examples.

Background Because of technical limitations, most experimental studies on the energy-absorbing properties of ballistic fabrics are limited to discrete evaluations based on impact and residual velocities. Consequently, the continuous interaction between a projectile and a target material is still commonly assessed with analytical models or numerical simulations, the validation of which is based on the aforementioned discrete values. Objective The present document aims at describing and validating a new experimental method to make it possible to evaluate the continuous evolution of the projectile velocity during penetration into a fabric material. The method is based on the Doppler effect and a specific and complex nonstationary signal treatment. Methods A high-frequency continuous-wave Doppler radar was adapted to assess the continuous evolution of the velocity of a projectile penetrating a fabric material. Based on two ballistic-grade fabric configurations, a perforating and a nonperforating case were described and evaluated. The instantaneous Doppler frequency was extracted based on the Hilbert-Huang transform. A validation of the proposed method was performed based on high-speed camera images, giving the displacement of the apex of the deformation pyramid of the fabric with time. Additionally, a Weibel® Doppler radar was used to measure the impact velocity. Results Based on instantaneous frequencies deduced from the high-frequency radar signal analysis, Doppler theory and highspeed camera images, velocity-time and displacement-time plots were obtained. Additionally, the evolution of the fabric deformation (pyramid morphology) was recorded from the high-speed camera images. Conclusions Comparisons between the data assessed with the high-frequency Doppler radar and those deduced from the highspeed camera indicated that good agreement exists between the two methods. The new Doppler radar method seems to be a promising complementary tool for measuring the continuous interaction between a projectile and a fabric target material.

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A computer program has been written which permits us to do aberration calculations on holographic optical elements based on ray tracing.In this article we first examine the diffraction phenomena which leads to a simple method for defining light ray deviation. Because most optical systems with holographic optical elements have no circular symmetry it was necessary to give appropriated definitions for the Seidel-aberrations.The structure of the computer program is given and a practical example is worked out.When ,after development, this hologram is illuminated by one of the two recording light beams, the other is reconstructed. This is based on the Bragg diffraction theory. 316 Ray tracing program for holographic optical elements. J. Van RoeyState University Ghent, Lab. electromagnetism and acoustics Sint Pietersnieuwstraat 41, AbstractA computer program has been written which permits us to do aberration calculations on holographic optical elements based on ray tracing. In this article we first examine the diffraction phenomena which leads to a simple method for defining light ray deviation. Because most optical systems with holographic optical elements have no circular symmetry it was necessary to give appropriated definitions for the Seidel-aberrations.The structure of the computer program is given and a practical example is worked out.

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