All of the content presented here is inspired by the 3Blue1Brown video. The explanations are a paraphrasing of the video, written in my own words based on my understanding of the material.
The video begins with a demonstration of what a hologram is. A laser illuminates a photographic film, and when the developed film is later illuminated and viewed from different angles, it recreates the original scene with changing perspectives. Unlike a normal photograph, the image appears three-dimensional, responding naturally as the viewer moves. This idea was developed by Dennis Gabor, who was awarded the Nobel Prize in Physics in 1971.
The video proceeds in three stages: first an overview of the process, then a simple example, and finally a more general mathematical description.
The key distinction between a hologram and a standard image is the information being recorded. In ordinary imaging—such as a pinhole camera—the film only records the intensity (amplitude squared) of incoming light from a single viewing direction. This collapses the full light field into one perspective. In contrast, a hologram aims to record the entire light field, meaning both the amplitude and the phase of the light arriving at the film.
This raises a fundamental problem: photographic film can only record intensity, not phase. The solution is to introduce a second, known wave called the reference wave. When light from the object interferes with this reference wave at the film, the resulting interference pattern converts phase differences into measurable intensity variations. In this way, the phase information of the object’s light becomes encoded in the recorded amplitude pattern.
This process requires coherent light, which is why lasers are essential for holography. After the film is developed, illuminating it again with the same reference wave causes the interference pattern to diffract the light in such a way that the original light field is reconstructed. As a result, the viewer sees a three-dimensional image of the original scene.
A striking consequence of this process is that every small region of the hologram contains information about the entire scene. If part of the hologram is blocked or cut out, the full image can still be seen through the remaining piece, albeit with reduced resolution. Each portion of the film acts like a window into the original light field.
To build intuition, the video first considers the simplest case: a single point source of light. The reference wave is taken to be a plane wave perpendicular to the film. The interference between the spherical wave from the point source and the plane reference wave produces a pattern of concentric fringes on the film. This pattern is mathematically equivalent to a Fresnel zone plate.
The video then introduces a short detour into diffraction gratings. For a grating made of many evenly spaced slits, the light immediately after the grating appears complicated. However, far from the grating, the light organizes itself into distinct beams, known as diffraction orders. These occur at angles where light from each slit interferes constructively, determined by the slit spacing and the wavelength.
Returning to the hologram example, the recorded interference fringes act like a diffraction grating. The spacing of adjacent fringes is such that when the reference beam shines on the hologram, one of the diffracted beams travels exactly in the direction of the original point source. This reconstructs the wave that originally came from that point.
Another diffracted beam appears in the opposite direction, producing what is called the conjugate image, which is a mirrored version of the reconstructed scene. In practice, higher-order beams are suppressed because the interference pattern is smoothly varying (closer to a sinusoidal pattern rather than a sharp, binary grating).
By imagining the object as a collection of many point sources, each recording its own interference pattern, we can see how a full three-dimensional scene is encoded in a single holographic plate. Although this explanation is qualitative and not fully rigorous, it provides strong intuition for how holography works.
Finally, the video notes that when this process is described using complex numbers and wave superposition, the mathematics becomes surprisingly clean and shows explicitly how the recorded pattern reconstructs the original light field.