Simulation for digital holograms on tilted planes

Please refer to Optica Article for more details.

The angular spectrum method is widely used in hologram calculations. However, the conventional angular spectrum method is limited to propagation between parallel planes. This work introduces a method for optical propagation between tilted planes by employing coordinate transformations, as shown in Fig. 1.

Figure 1. Schematic

Correspondly, the optical wave progating after a distance is

is the spectrum of the object at . We then rotate the wave vector coordinates , where .

Consider 3D rotation matrix (clockwise rotation):

Figure 2. Rotation Matrix Image

We can get the rotated wave vector components:

Substituting into the expression:

Therefore,

Before applying the inverse Fourier transform, the grids have to be mapped into a uniformly spaced frequency grid using interpolation methods.

Finally,