Ground penetrating radar by D J Daniels; Institution of Electrical Engineers

By D J Daniels; Institution of Electrical Engineers

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30). 4 What is the meaning of conjugated wave? 5 Verify Eq. 37) by differentiating Eq. 36). 6 A Fresnel lens has a focal length of 10 cm. Calculate the diameter of the 1st and 100th ring (λ = 600 nm). 27 Holography Gerhard K. Ackermann and Jürgen Eichler © 2007 WILEY-VCH Verlag GmbH & Co. 29 3 Fundamental Imaging Techniques in Holography The recording of a hologram is performed by bringing object and reference wave to interference. The information of the object wave is completely contained in the resulting interference pattern.

6 Fourier hologram. (a) exposure, (b) reconstruction, (c) calculating a Fourier hologram (see text). That means the square of R(ξ, η ), the intensity, is constant and just 1. Both waves interfere. The resulting intensity at the plane of the holographic plate is given by I = {O(ξ, η ) + R(ξ, η )}2 I = 1 + O(ξ, η )2 + O(ξ, η ) · R∗ (ξ, η ) + O∗ (ξ, η ) · R(ξ, η ). 3) The resulting amplitude transparency of the holographic plate again is a linear function of intensity as assumed already in Eq. 21).

Therefore o∗ ( x, y) is also a plane wave. If o( x, y) has the angle of incidence δ0 (see Fig. 5), Eqs. 26) can be written as u−1 = βτr2 oei 2π λ x (sin(− δ0 )+2 sin δ ) . 27) Here the relation e a eb = e a+b was used. 27) represents a wave with the angle of incidence δ−1 with sin δ−1 = sin(−δ0 ) + 2 sin δ. 28) As already stated the conjugated image with δ0 = 0◦ (object wave impinging perpendicular on the hologram) appears at an angle of sin δ−1 = 2 sin δ; δ is the angle of the reference and reconstruction wave.

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