Kirchhoff Yaklaşımı İntegralinin Radon Dönüşümü Yorumu ile Zaman Uzayında Belirlenmesi Üzerine

Abstract

Bu çalışmada, düzlemsel dalga ile aydınlatılmış, yumuşak ve sert saçıcılardan oluşan uzak alandaki akustik saçılmanın, Kirchhoff yaklaşımı (KY) ile zaman uzayında analizinde ortaya çıkan ışıma integralinin kapalı-formda belirlenmesi gösterilmiştir. Özel olarak KY ile ortaya çıkan ışıma integralinin, elektromanyetikteki eşdeğeri olan fiziksel optik (FO) yaklaşımı kullanıldığında oluşan ışıma integrali aynı olduğu gösterilmiştir. Sonuç olarak FO yaklaşımı için Radon dönüşümü yorumu ile geliştirilen kapalı-form ifade doğrudan KY için kullanılabilir. Kapalı-form ifadelerinin doğruluğu bir nümerik örnekle gösterilmiştir.

Keywords

• Akustik saçılma
• Kirchhoff yaklaşımı
• zaman uzayı analizi

On the Evaluation of the Kirchhoff Approximation Integral using Radon Transform Interpretation in Time Domain

Abstract

In this work, closed-form evaluation of the radiation integral to determine the time domain acoustic scattered fields at the far zone for soft and hard scatterers using Kirchhoff approximation (KA) under plane-wave illumination is presented. Specifically, it is shown that the radiation integral for KA is the same as the physical optics (PO) integral, which is the equivalent of KA in electromagnetics, for perfect electrically conducting scatterers. Consequently, the closed-form expression of the PO integral developed using Radon transform interpretation can be used in KA directly. The validity of the closed-form expression is demonstrated via a numerical example.

Keywords

• Acoustic scattering
• Kirchhoff approximation
• time domain analysis

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