How does an image change in a 3D hologram depending on angle of viewing?

 A Hologram is made by taking a single coherent beam, usually from a LASER, and splitting it into two beams.

One of the beams called a reference beam, directly hits a photographic plate where as other is reflected off an object (whose image needs to be stored in the Hologram). The interference pattern of these two beams is stored as Hologram.

When light is focussed on this Holographic plate, it reflects off the plate, but after mixing with the stored pattern.

 So if the original light beam that was used is directed at the corrected angle, it cancels out the component corresponding to reference beam and we see the object.

However, in a typical room, Light hits hologram from all angles and is also reflected back in all angles. Hence, there will be a beam that will fall on plate at same angle as that of reference and reflect the image of the object. If our eye happens to be in the path of the reflected beam then we can see the stored object.

If two interference patterns were stored simultaneously with different reference beam, we can see two different images depending on the angle of viewing. Because the light reaches each eye is not exactly the same, the 3D effect or perception of depth is produced.