# Difference Between Fraunhofer and Fresnel Diffraction

What is the difference between Fraunhofer diffraction and Fresnel diffraction? I mean diffraction is just bending of light waves or waves in general around a point. So how can there be two types of diffractions?

If Diffraction means something else in this context, then please explain the difference between these two types of diffraction.

## 4 Answers

You are right in that there is only one set of physical things going on in diffraction. The reason people talk about two different kinds, is because there are two natural limits in a diffraction problem.

The intensity of light you see at any point is the contribution from all of the points at the aperture, where the contribution from any point decreases as the distance, and every contribution accumulates phase given its path. It is the differences in the path length from the various parts of our aperture to a point of interest that lead to the interesting interference phenomenon associated with diffraction.

Consider an aperture with a characteristic size $a$, and imagine trying to figure out the diffraction at a point roughly in line with the aperture at some distance $d$ from the point at the aperture's center. We can estimate the relative phase difference from the point at the aperture's center and a point near its edge, namely

$$\Delta \phi = k ( d_{\text{edge}} - d_{\text{center}})$$ where $k$ is the wavenumber of our light. We can estimate this difference in length using some simple trig.

$$\Delta \phi = k \left( \sqrt{ d^2 + a^2 } - d \right) \sim \frac{ k a^2 }{ 2 d }$$

So, there is a natural trade off in our problem, between the size of our aperture and the distance we are from it. In particular, we can separate the problem into two limits, one where $d \ll ka^2$ where we expect large differences in phase contribution ($\Delta \phi \gg 1$) and $d \gg k a^2$ where we expect little difference in phase contribution ($\Delta \phi \ll 1$). These are the Fresnel and Fraunhofer regions respectively. I've included a little picture for illustration. As you can imagine, these two limits have very different qualitative phenomenon, and so that's why people talk about them as two different kinds of diffraction. In the Fresnel limit you have mostly geometric optics type cast shadows, with perhaps some wiggly bits near the edges of your shadow, whereas in the Fraunhofer region, our wave has spread out over a large region and starts interfering with different parts of the cast image. This leads to the observed behavior of Fraunhofer diffraction corresponding to a Fourier transform of the aperture.

In the case of visible light, this characteristic distance is quite large, $$ka^2 \sim \left( \frac{ a }{ 1 \text{ cm}} \right)^2 \frac{ 2 \pi }{ 550 \text{ nm} } \sim 1 \text{ km } \left( \frac{ a }{ 1 \text{ cm}} \right)^2$$ so that the Fraunhofer diffraction cannot be seen directly. This is why you commonly see Fraunhofer diffraction associated with the use of a lens, as a converging lens allows you to view this far field pattern much more practically.

### Reference

Applications of Classical Physics by Roger D. Blandford and Kip S. Thorne - Chapter 8 - Diffraction

• "Mostly geometric optics with some wiggly bits" misses the best part: Poisson's spot - a bright point that appears in the center of the "shadow" of a circular obstacle. Predicted by Poisson as an "absurd result that proves diffraction theory is wrong", it was soon observed and named after him... – Floris Jun 29 '14 at 13:50
• "In the Fresnel limit you have mostly geometric optics type cast shadows, with perhaps some wiggly bits near the edges of your shadow, whereas in the Fraunhofer region, our wave has spread out over a large region and starts interfering with different parts of the cast image." This part is confusing. There should be lot's of variation in the diffraction pattern during propagation in the near-field, whereas in the far-field limit only the size of the image should change, right? – Ross G Feb 28 '19 at 18:34

Fresnel's diffraction: It means that source of light and screen at finite distance from the obstacle. In this case no lenses are used for making rays parallel. The wavefront is either spherical or cylindrical.

Fraunhofer diffraction: In Frensel's diffraction the source and screen are finite distance to obstacle, but in this case the source of light and screen placed infinite distance from obstacle. In this case parallel rays and plane wavefronts are produced because of using lens.

Fraunhofer diffraction is far field diffraction where the plane wave approximation applies and the patterns do not depend on distance between source and aperture.

This is different from Fresnel diffraction (near-field) that occurs when a wave diffracts in the near field, causing any diffraction pattern observed to differ in size and shape, depending on the distance between the aperture and the projection.

• What do you mean by near field? – Isomorphic Sep 29 '13 at 19:03
• The different terms for these regions describe the way characteristics of an electromagnetic (EM) field change with distance from the charges and currents in the object that are the sources of the changing EM field. (en.wikipedia.org/wiki/Near_and_far_field) – mcodesmart Sep 29 '13 at 20:01

In optics, Fraunhofer diffraction (named after Joseph von Fraunhofer), or far-field diffraction, is a form of wave diffraction that occurs when field waves are passed through an aperture or slit causing only the size of an observed aperture image to change due to the far-field location of observation and the increasingly planar nature of outgoing diffracted waves passing through the aperture.

It is observed at distances beyond the near-field distance of Fresnel diffraction, which affects both the size and shape of the observed aperture image, and occurs only when the Fresnel number $$F \ll 1$$, wherein the parallel rays approximation can be applied.

On the other hand, Fresnel diffraction or near-field diffraction is a process of diffraction that occurs when a wave passes through an aperture and diffracts in the near field, causing any diffraction pattern observed to differ in size and shape, depending on the distance between the aperture and the projection. It occurs due to the short distance in which the diffracted waves propagate, which results in a Fresnel number greater than 1 ($$F > 1$$). When the distance is increased, outgoing diffracted waves become planar and Fraunhofer diffraction occurs.