Holography: Recording Light as Interference Fringes

Why a photograph is not enough

A camera sensor measures |E|² — the time-averaged intensity of the electromagnetic field at each pixel. That single number throws away the phase of the light wave, and phase is exactly what carries depth: two points at different distances scatter light that has travelled different path lengths, so their waves arrive with different phase shifts. A photograph flattens a scene into one viewpoint; nothing about it changes if you tilt your head. A hologram does, because it stores the phase too, and phase is what encodes the direction each wavefront came from.

The only practical way to record phase is to make it visible as intensity — and that means interference. Two overlapping waves produce bright and dark fringes wherever their phase difference varies, and a photographic emulsion can record those fringes just fine. The trick is arranging for the interference pattern to encode the entire object wave.

Coherence: the one hard requirement

Stable fringes only form if the two interfering waves keep a fixed phase relationship for the whole exposure — they must be coherent. Ordinary light sources are incoherent after a path difference of a few micrometres, which is why sunlight or a lightbulb never produces a usable interference pattern. Laser light, by contrast, stays coherent over metres, sometimes kilometres, which is long enough for a real optical setup with beam splitters and mirrors.

Dennis Gabor demonstrated holography in 1948, years before the laser existed, using a filtered mercury arc lamp — the fringe contrast was poor and the idea stayed a curiosity for over a decade. It was Emmett Leith and Juris Upatnieks who combined the technique with laser light in 1962, and their off-axis reference beam — splitting the laser at an angle so the reconstructed image separates spatially from the undiffracted light — became the configuration behind every modern display hologram.

Recording: two beams, one plate

A single laser is split into a reference beam, which travels directly to the film, and an object beam, which illuminates the subject and scatters off it in every direction — every point on the object becomes a secondary source carrying its own phase shift. Where the object wave and reference wave overlap at the film, they interfere and create a submicrometre-scale pattern of bright and dark fringes. A silver-halide emulsion records that pattern as varying density after development.

Writing the reference beam as a plane wave R = A·e^(iφ_R) and the object wave at the film as O, the recorded intensity is:

I = |R + O|²  =  |R|² + |O|² + R*O + RO*
              =  |A|² + |O|² + A·e^(-iφ_R)·O + A·e^(iφ_R)·O*

The first two terms are just background brightness. The cross terms R*O and RO* are the ones that matter: R*O is the object wave multiplied by the reference conjugate, which is a diffraction grating encoding both the object's amplitude and its phase. Because every object point contributes fringes across the whole plate, even a small fragment of a hologram still contains information about the entire scene — at reduced angular resolution, but not missing content, which is the single fact that most distinguishes holograms from photographs.

Reconstruction: reading the wave back out

To reconstruct the scene, illuminate the developed plate with the same reference beam R. The transmitted light is R·I:

R·I  =  R(|R|² + |O|²)  +  |R|²·O  +  R²·O*

The third term, |R|²·O, is exactly the original object wave, just scaled. It radiates from the plate as if the object were still behind it, so a viewer sees a genuine 3D virtual image at the object's original position — move your head sideways and parallax reveals surfaces that were hidden a moment before. The fourth term, R²·O*, produces a conjugate real image, which is related to the phase-conjugate mirrors used in nonlinear optics to time-reverse light and correct atmospheric distortion in laser systems.

Transmission, reflection and beyond

A transmission hologram stores fringes roughly perpendicular to the plate and needs laser light passed through it to view — sharp and high-contrast, but tied to the recording wavelength. A reflection hologram, developed independently by Yuri Denisyuk in 1962, stores fringes parallel to the surface, so the plate acts as a wavelength-selective mirror that reflects only the recording colour out of ordinary white light — this is the type used in museum displays and, in embossed mass-produced form, on credit cards, passports and banknotes. A computer-generated hologram skips optical recording entirely: the interference pattern is calculated numerically and printed at submicron resolution, letting any virtual 3D scene be encoded — the approach behind near-eye displays such as HoloLens.

Beyond display, the same physics drives holographic data storage — multiple holograms can be superimposed in one volume by varying the reference beam angle, a technique called angular multiplexing, with theoretical densities near 1 TB/cm³ — and holographic tomography, which reconstructs 3D refractive-index maps of living cells without staining them.

Frequently asked questions

Try it live

Change the angle and wavelength of the reference and object beams in Holography and watch the interference fringes form, then reconstruct into an image. Everything runs client-side in your browser.