[Article] Introduction to Mobile Money in Developing by Jane K Winn, Louis de Koker

By Jane K Winn, Louis de Koker

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After propagation through a distance z behind the hologram, the complex field is transformed according to the Fresnel diffraction formula. Note that because the field is converging, it will contribute to a real image. Explicitly, the field can be written as ψ pr ðx, yÞt rel1 ðx, yÞ Ã hðx, y; zÞ ! jk 0 − jk 0 2 2 ¼ ψ pr ðx, yÞt rel1 ðx, yÞ Ã expð− jk 0 zÞ exp ðx þ y Þ 2πz 2z & ' & ' − jk0 jk 0 2 2 2 2 / exp ½ðx − bÞ þ y Š exp ½ðx − h=2Þ þ y Š 2l2 2R & ' ! 1], we perform the integration by writing the functions involved with new independent variables x0 , y0 and (x − x0 , y − y0 ).

The situation is shown in Fig. 7. Points 1 and 2 are shown in the figure as a reference to show the original image locations. Points 10 and 20 are reconstructed real image points of object points 1 and 2, respectively, due to the reconstruction wave from point r. We notice there is a translation between the two real image points along the x-direction. The translational distance Δx is given by Δx ¼ x1 − x2 , where x1 and x2 are the locations previously found [see below Eqs. 24)]. 7 Translational distortion of the reconstructed real image.

The restored complex field preserves the entire parallax and depth information much like the original complex field and is interpreted by our brain as the same three-dimensional object. 2 Hologram as a collection of Fresnel zone plates The principle of holography can be explained by recording a point object since any object can be considered as a collection of points. 1 shows a collimated laser split into two plane waves and recombined through the use of two mirrors (M1 and M2) and two beam splitters (BS1 and BS2).

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