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Holographyis a two steps technique. In the first step, the interference pattern of the object wave (ψobj) and the reference wave (ψref) is calculated, recording necessary information (amplitude and phase) for reconstructing ψobj . In the second step, the 11 interference pattern is multiplied by ψref to reconstruct the object wave. This technique is developed in Eq.(1) to Eq.(3) .
2 I = ψre f + ψob j (1)
ψtrans = I ψsec (2) ×
2 2 2 ψtrans = ψre f ψre f + ψob j ψre f + ψob∗ jψre f ψre f + ψre f ψre f (3)
Although four waves are generated in Eq.(3), the first three w aves are not expected to exist in the visible region. The last 2 term represents the object wave ψob j ψre f . After doing a few calculations, Eq.(4) is obtained from Eq.(3). According to Eq.(4), the holographic interference pattern is purely amplitude while it contains the phase information of the interfered waves11.This equation represents the mathematical hologram, so the problem is with the practical realization of the hologram. In10, the utilization of artificial impedance surfaces with modulated dimensions is proposed to solve this problem. Prior to employing the artificial impedance surfaces, it is vital to provide a mathematical relation between the interference pattern and the impedance surface. This is done by defining Eq.(5)4:
2 2 I = ψre f + ψob j + 2ℜ ψob jψre f (4)