How the computer reconstruction works
Understanding-oriented. The trickiest idea in the topic, told without heavy maths.
You've recorded a hologram — a pattern of fine rings that doesn't look like anything (see What is a hologram?). Now the computer turns it into a sharp picture. How?
The "proper" version of this involves Fourier transforms, complex numbers, and double integrals — first-year university material. We're going to skip all of that and build the right mental picture instead. If you want the real formulas, they're in the Münster thesis and in Parts and parameters.
Step 1: light waves keep travelling — so we can "rewind" them
Here's the key insight. The hologram on the sensor is a frozen snapshot of a light wave at the moment it hit the camera. But light waves obey simple, predictable rules as they travel. If we know what a wave looks like in one plane, we can calculate what it looked like a few millimetres earlier — back where the sample actually was.
That's the whole job of reconstruction: take the wave the camera recorded and run it backwards through space, numerically, until it snaps into focus at the sample plane. This is called back-propagation.
Think of it like rewinding a video of ripples spreading on a pond. The ripples on the sensor are blurry and spread out; rewind them and they collapse back into the sharp little splash that made them — your sample.
backpropagation-pond.svgShow: A "rewinding ripples" metaphor — spread-out rings on the right (sensor), an arrow labelled "back-propagate" pointing left, and a sharp point/object on the left (sample plane). Optionally a real before/after reconstruction underneath.
Step 2: the sound analogy (this is the important bit)
To rewind the wave efficiently, the computer first sorts the hologram into its spatial frequencies — its fine details versus its coarse details. This sorting is done by a tool called the Fourier transform (the fast version is the "FFT"). It sounds abstract, so borrow an example from your own ears.
When a friend sings a single note, the air carries a messy jumble of vibrations. Inside your ear, the cochlea sorts that jumble out: different tiny hairs respond to different pitches, so your brain receives the note split into a low fundamental tone plus its higher overtones. Your ear is running a Fourier transform on sound, all day, automatically.
The FFT does the same trick on an image instead of a sound:
- A sound is split into its musical frequencies (low hum + high overtones).
- An image is split into its spatial frequencies (broad smooth areas + fine repeating details).
Once the hologram is sorted this way, "running the wave backwards" becomes easy: each spatial frequency just gets nudged by a small, known amount that depends on the distance, the wavelength, and the pixel size. Then the computer reassembles the frequencies back into a picture — and that picture is your focused sample.
Rewinding the wave directly, pixel by pixel, would take a computer ages. Sorting into frequencies first turns a gigantic calculation into a quick one. It's the same reason sorting your laundry by colour first makes the whole job faster.
Step 3: the distance dial — refocusing after the photo
Here's the part that feels like magic. You tell the computer how far to rewind. In the
software this is the dz distance slider (the propagation distance — see
Parts and parameters).
- Set
dztoo small or too large → the sample looks blurry. - Land on the right
dz→ the sample snaps into sharp focus.
Because you choose the focus distance after the hologram is recorded, you can refocus a photograph that was already taken — and even focus on objects at different depths in the same shot. An ordinary camera can never do this; once it presses the shutter, the focus is locked forever. The hologram kept the wave, so the focus stays adjustable.
dz-refocus.gifShow: A short loop of the reconstruction sharpening and blurring as the dz slider is
dragged — ideally a screen recording of the ImSwitch inline-holography widget refocusing a
real sample.
Step 4: why the ghost stays
You'll often see a faint halo around your reconstructed sample — the twin image from What is a hologram?. It's there because the camera recorded only brightness and lost the phase, so the computer genuinely can't tell the real image from its mirror twin. Both come into focus together. Removing it cleanly needs more advanced methods; seeing it and knowing why it's there is already a real understanding of the physics.
The whole pipeline in one breath
The sensor records a ringy interference pattern → the computer sorts it into spatial frequencies (FFT) → nudges each frequency to "rewind" the wave by a distance you choose → reassembles them into a sharp image of the sample. Drag the distance dial to refocus.
That's reconstruction. No calculus required.
Ready to do it for real? → Your first hologram