Use Eq. (7-14) for the superposition of two unequal beams to show that the irradiance patt...

Use Eq. (7-14) for the superposition of two unequal beams to show that the irradiance pattern of a Gabor zone plate (the hologram of a point source) is given approximately by

 I = A + D cos2(ar2)

where , , and a = π/(2sλ). Here, I1 and I2 are the irradiances due to the reference and signal beams, respectively, s is the distance of the object point from the film, and λ is the wavelength of the light. For the approximation, assume the path difference between the two beams is much smaller than s, so that we are looking at the inner zones of the hologram.

Figure 1