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How does moving sideways change the view of a holographic image?

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When you move sideways while viewing a hologram, the perspective of the image changes because the virtual image produced by the process possesses the property of parallax.

Unlike a standard two-dimensional photograph, which remains static regardless of your viewing angle, a hologram recreates the original optical field. This allows you to see around the sides of objects within the image as you shift your position, providing a realistic sense of three-dimensionality.1