Fraunhofer diffraction and Fresnel diffraction are two regimes that describe how a diffraction pattern changes with distance from the aperture. Picture a car headlight: up close you see the detailed shape of the bulb and reflector — that is near-field, Fresnel diffraction. A kilometre away the headlight is just a bright point — that is far-field, Fraunhofer diffraction. The transition between them is not a hard boundary. It is set by a single number: the Fresnel number. Here is what each regime means, how to calculate which one you are in, and why it matters.
Think of the aperture like a garden hose nozzle. Close to the nozzle, the water spray has a complex, changing pattern — individual streams, gaps, and pulses. That is the Fresnel regime. Far away, the spray smooths into a steady cone. That is the Fraunhofer regime. The physics of the water leaving the nozzle is the same — only the viewing distance changes what you see.
What is Fraunhofer diffraction?
Fraunhofer diffraction, named after the German optician Joseph von Fraunhofer, is the far-field regime. The key condition: both the light source and the observation screen are effectively at infinite distance from the aperture.
What this means in practice:
- Wavefronts are planar. Because the distances are so large, the curvature of the spherical wavefronts is negligible. The incident and diffracted waves can be treated as plane waves.
- The pattern depends only on angle, not distance. Move the screen further back and the pattern gets larger but keeps the same shape. The intensity as a function of angle is fixed.
- The mathematics is simpler. The Fraunhofer diffraction integral reduces to a Fourier transform of the aperture function. This is why most textbook diffraction patterns — single-slit, double-slit, circular aperture (Airy disc), diffraction grating — are treated in the Fraunhofer regime.
The formal condition for Fraunhofer diffraction is that the Fresnel number N_F is much less than 1:
N_F = a² / λL ≪ 1
Where a is the aperture size, λ is the wavelength, and L is the distance from the aperture to the screen.
For a typical classroom setup — a 0.1 mm slit, 1 m from the screen, with red laser light (632.8 nm) — N_F ≈ 0.016. That is firmly in the Fraunhofer regime. Any standard single-slit experiment in a physics lab is Fraunhofer diffraction.
What is Fresnel diffraction?
Fresnel diffraction, named after the French physicist Augustin-Jean Fresnel, is the near-field regime. The source or the screen (or both) is at a finite distance from the aperture.
What this changes:
- Wavefronts are curved. The incident and diffracted waves are spherical or cylindrical, not planar. The curvature matters in the calculation.
- The pattern changes with distance. Move the screen closer or further and the pattern changes shape and size, not just scale. Fringes appear and disappear as you scan through the near field.
- The mathematics is more complex. The Fresnel diffraction integral contains quadratic phase terms that do not simplify to a Fourier transform. The integral is often evaluated numerically or using special functions (Fresnel integrals).
The Fresnel condition: N_F ≳ 1.
The same 0.1 mm slit at 1 cm from the screen gives N_F ≈ 1.6 — Fresnel regime.
The pattern on a screen 1 cm behind the slit looks completely different from the Fraunhofer pattern at 1 m.
The Fresnel number: the decision rule
The Fresnel number N_F is the most useful tool for deciding which regime applies.
N_F = a² / λL
- a = characteristic size of the aperture (or obstacle)
- λ = wavelength of the light
- L = distance from the aperture to the observation screen
| Fresnel number | Regime | Wavefronts | Pattern |
|---|---|---|---|
| N_F ≪ 1 (≤ 0.1) | Fraunhofer (far-field) | Planar | Stable, depends only on angle |
| N_F ≈ 1 | Transition | Slightly curved | Changes with distance |
| N_F ≳ 1 | Fresnel (near-field) | Spherical/cylindrical | Changes shape with distance |
The boundary is not sharp. At N_F = 0.1 the Fraunhofer approximation is good to about 1% accuracy. At N_F = 1 you need the full Fresnel treatment.
Fraunhofer vs Fresnel: comparison table
| Feature | Fraunhofer diffraction | Fresnel diffraction |
|---|---|---|
| Also called | Far-field diffraction | Near-field diffraction |
| Source distance | Effectively infinite | Finite |
| Screen distance | Effectively infinite | Finite |
| Incident wavefront | Plane (parallel rays) | Spherical or cylindrical |
| Diffracted wavefront | Plane | Spherical or cylindrical |
| Pattern stability | Fixed shape, scales with distance | Changes shape with distance |
| Lenses needed in lab | Yes (to create plane waves) | No (natural spherical waves) |
| Mathematical tool | Fourier transform | Fresnel integrals |
| Fresnel number | N_F ≪ 1 | N_F ≳ 1 |
| Computational difficulty | Easy (closed form for most shapes) | Harder (often numerical) |
Real-world examples of each
Fraunhofer diffraction occurs in:
- Single-slit and double-slit experiments with lasers. The screen is metres away; the slit is micrometres wide. N_F is tiny.
- Diffraction gratings in spectrometers. The grating is at the focal plane of a collimating lens, ensuring Fraunhofer conditions.
- Telescope and camera resolution. The Airy disc from a circular aperture is a Fraunhofer pattern. Stars are so far away that the incoming wavefronts are effectively planar.
- X-ray crystallography. X-rays diffracting off atomic planes meet Fraunhofer conditions because the crystal is effectively a 2D grating in the far field.
Fresnel diffraction occurs in:
- Poisson spot. Shine a laser at a small circular obstacle. In the centre of its shadow, directly behind the obstacle, there is a bright spot of light. This is a Fresnel diffraction effect — it disappears in the Fraunhofer regime.
- Shadow edges. The soft, fuzzy edge of a shadow cast by a nearby point source is Fresnel diffraction. Move the screen far enough away and the edge sharpens into the Fraunhofer regime.
- Fresnel zone plates. A specially designed pattern of alternating transparent and opaque rings that focus light by Fresnel diffraction. They act as lenses without refractive material.
- Near-field microscopy. Techniques that capture Fresnel diffraction patterns close to a sample can achieve resolution below the diffraction limit by recording the near-field information before it propagates to the far field.
Extra: the transition regime and Fresnel zone plates
Most textbook discussions stop at the comparison table. But the transition regime between Fresnel and Fraunhofer is where some of the most useful optics lives.
Fresnel zone plates are a beautiful application. A zone plate has alternating transparent and opaque rings whose radii follow r_n = √(nλf), where f is the focal length. Light passing through the transparent rings arrives in phase at the focal point because each ring is exactly one wavelength further from the focus than the previous one. The zone plate acts like a lens, but by diffraction rather than refraction. Zone plates are used in X-ray microscopy where refractive lenses are impractical because X-rays pass straight through most materials.
The zone plate operates in the Fresnel regime (N_F ≳ 1) and transitions to Fraunhofer at large distances. It is a rare case where the intermediate regime is the useful one.
For the full introduction to diffraction, start with our guide on what is diffraction. To see how the single-slit Fraunhofer pattern works with real numbers, read the single-slit diffraction equation guide. For how diffraction gratings (always Fraunhofer) split light into spectra, see the diffraction grating article.
The HyperPhysics Fraunhofer diffraction page gives a clear comparison of the two regimes with interactive calculators. The Wikipedia Fresnel diffraction article provides the full mathematical derivation including Fresnel integrals. The Wikipedia Fraunhofer diffraction article covers the Fourier transform approach and its applications in imaging.
Frequently Asked Questions
What is the difference between Fraunhofer and Fresnel diffraction?
Fraunhofer diffraction (far-field) occurs when both the source and screen are effectively at infinite distance from the aperture, so the wavefronts are planar and the pattern is stable. Fresnel diffraction (near-field) occurs when the source or screen is at finite distance, so the wavefronts are curved and the pattern changes with distance. The Fresnel number N_F = a²/λL determines which applies: N_F ≪ 1 is Fraunhofer, N_F ≳ 1 is Fresnel.
What is the Fresnel number?
The Fresnel number is a dimensionless quantity N_F = a²/λL, where a is the aperture size, λ is the wavelength, and L is the distance from the aperture to the screen. When N_F ≪ 1, the Fraunhofer approximation is valid (far-field). When N_F ≳ 1, the Fresnel approximation must be used (near-field). It quantifies how curved the wavefronts are at the observation point.
What is Fraunhofer diffraction?
Fraunhofer diffraction, also called far-field diffraction, occurs when both the light source and the observation screen are effectively at infinite distances from the diffracting aperture. The incident and diffracted waves are treated as plane waves. The pattern is stable with distance and depends only on angle. Most textbook diffraction patterns — single-slit, Airy disc, diffraction grating — are Fraunhofer patterns.
What is Fresnel diffraction?
Fresnel diffraction, also called near-field diffraction, occurs when the source or the observation screen is at finite distance from the aperture. The wavefronts are spherical or cylindrical rather than planar. The pattern changes with distance and includes edge effects that are absent in Fraunhofer diffraction. Examples include the shadow of a coin with a bright spot at the centre (Poisson spot) and the soft edge of a shadow in sunlight.
What are examples of Fraunhofer and Fresnel diffraction?
Fraunhofer diffraction examples: a laser beam passing through a single slit onto a distant wall, the Airy disc pattern of stars in a telescope, and a diffraction grating spectrum. Fresnel diffraction examples: the bright spot in the centre of a circular obstacle shadow (Poisson spot), the fuzzy edge of a shadow cast by a point light source, and the diffraction pattern from a knife edge in near-field.
How can I tell if a setup is Fraunhofer or Fresnel?
Compute the Fresnel number N_F = a²/λL. If N_F ≪ 1 (less than about 0.1), you are in the Fraunhofer regime. If N_F ≳ 1, you are in the Fresnel regime. For example, a 0.1 mm slit at 1 m from the screen with red light (632.8 nm) gives N_F ≈ 0.016 — firmly Fraunhofer. The same slit at 1 cm gives N_F ≈ 1.6 — Fresnel regime.
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