Holography

Remarks

When $\abs{R}$ is constant on the plate, the term $\beta \abs{R}^2 O$ is a constant multiple of the object wave, so the object is seen as a virtual image. The term $\beta R^2 \overline{O}$ is the conjugate wave and forms a real image. The first term is the reference wave, modulated in amplitude. With an off-axis reference wave, these three parts leave the hologram in different directions and can be separated.

Example: let $O$ and $R$ be plane waves of equal amplitude $1$ with transverse wave vectors $k_O$ and $k_R$ in the plate. Then $I(x) = 2 + 2\cos((k_O - k_R) \cdot x)$, so the hologram is a sinusoidal grating. Lit by $R$, it diffracts a wave proportional to $O$ in the direction of the original object wave.

Non-example: a photograph records $\abs{O}^2$ alone, with no reference wave. The phase of $O$ is lost, and lighting the photograph does not reconstruct the object wave.