Overview
This lecture explains the physics, recording process, and mathematics behind holography, demonstrating how a 2D film can store and reconstruct a 3D scene using the principles of light interference.
What is a Hologram?
- A hologram is a 2D film that, when properly illuminated, creates the illusion of a 3D scene.
- Unlike ordinary photos, holograms encode information from every possible viewing angle, storing the entire light field of a scene.
- Holography was discovered by Dennis Gabor in 1947 and became practical with the invention of lasers.
How Holograms are Recorded
- Ordinary photography captures light intensity (amplitude) from one direction only.
- Holography aims to record both the amplitude and phase (position in the wave cycle) of light.
- Two laser beams are required: the object wave (light reflected from the scene) and the reference wave (direct laser).
- The two beams interfere at the film, creating a complex pattern that encodes phase differences.
- The exposure pattern depends on the square of the wave amplitude, revealing phase through interference fringes.
- The process is extremely sensitive to motion; even tiny vibrations can disrupt the pattern.
Reconstruction of the Image
- Illuminating the developed film with the original reference beam recreates the object wavefront, making the scene appear in 3D.
- Each small piece of holographic film contains information about the whole scene; cutting the film still shows the entire object from various angles.
- The pattern is analogous to a diffraction grating, where interference causes light to form images at specific angles.
Physics and Math of Holography
- For a single point, the exposure pattern on the film is a Fresnel zone plate (concentric rings).
- The diffraction equation: d·sin(θ) = λ relates fringe spacing (d), angle (θ), and wavelength (λ).
- The reconstructed beam travels along the same direction as the original light from the object.
- Three main beams result: reference (zeroth order), real image (first order), and conjugate image (mirror/reflected artifact).
- Higher order beams are suppressed if the film's opacity varies smoothly (sinusoidally).
- The process generalizes to multiple points and full scenes by superposing many zone plates.
Advanced & Practical Considerations
- High-resolution film (thousands of lines/mm) is required to accurately record fine interference patterns.
- Reflection holograms and computer-generated holograms allow viewing with ordinary light or from digital models.
- Holography connects to interferometry, which measures minute displacements using wave interference.
Formal Explanation Using Complex Numbers
- Light waves are modeled as complex numbers, encoding amplitude and phase.
- The exposure pattern is proportional to |R + O|², where R = reference wave and O = object wave.
- Algebra shows that reconstructing with the reference beam reproduces the original object wave and its conjugate.
Key Terms & Definitions
- Hologram — 2D film encoding a 3D scene using light interference.
- Reference Wave — Laser beam directly illuminating the film.
- Object Wave — Light reflected from the scene onto the film.
- Phase — Position within the cycle of a wave, crucial for recording 3D info.
- Diffraction Grating — Pattern that splits light into beams at specific angles.
- Zone Plate — Concentric ring interference pattern for a point source in holography.
- Conjugate Image — Mirror/reversed artifact created during hologram reconstruction.
- Interferometry — Technique measuring small distances by analyzing wave interference.
Action Items / Next Steps
- Review Gabor’s Nobel Prize lecture for further historical and technical context.
- Practice deriving interference and diffraction equations.
- Experiment: try observing diffraction patterns with simple gratings (e.g., CDs, DVDs) and lasers.