# Why is it difficult to differentiate between interference and diffraction?

Why is it difficult to differentiate between interference and diffraction? Is it because we don't clearly understand how both of these phenomenon takes place?

My thoughts: From an answer to one of my earlier question here I could understand that light waves behave differently when it strikes a slit which is of several times bigger than its wavelength and when it strikes a slit of size comparable to it its wavelength.In the former case the different points on the slit acts as wave-front sources producing circular wave fronts which interfere to form the diffraction pattern but in the later case plane wave-front striking a slit after passing through it forms circular wave-fronts and two such wave-fronts from two different slits interfere to form the interference pattern. But, I'm not satisfied by that because I don't get any intuition about points on the slit acting as wavefront sources. So, what is actually happening?

• You seem to have misunderstood jinawee's answer to your previous question. He's got everything in the right place. There is always interference, and diffractive effect change the interfence pattern that you observe. – dmckee Oct 8 '13 at 3:05

It's difficult to differentiate between the two phenomena because they are fundamentally the same phenomenon. It's common to use the term "interference" in a more general sense, where the interfering optical fields may not have the same source, or where a beam was split and is interfering with itself after being recombined. Diffraction is more commonly used when talking about the way a single optical field evolves as it propagates. Ultimately, we use the exact same mathematical tools to describe both, because they are really just different examples of wavelike behavior.

I'm going to take a different tack then Colin's, though I believe that he and I are getting at the same thing.

There is no difficulty in distinguishing the two phenomena as they are clearly distinct. It's just that the visible effects of diffraction are interference phenomena.

Diffraction happens when light interacts with an edge or with a gradient of optical parameters perpendicular to it's path. The result is a range of outgoing wave vectors that is not uniform over the face of the wave and these result in interference.

You should have no confusion what-so-ever.

• I think there might be a slight usage ambiguity amongst different physicists. Your definition is a good one: would you say that the idea is how a propagating light field, having encoded perturbations imposed on it at one transverse plane (i.e. orthogonal to the nominal propagation direction), and expresses these perturbations at another transverse plane ? I'd not have thought to write it down as you have: I'd be more inclined to express the ideas like Colin does (I know his and my training overlap somewhat) i.e. I think I'd have said they're fundamentally the same thing. – WetSavannaAnimal Oct 8 '13 at 8:24
• I'd consider your description to be of one of the common effects of diffraction of an optical field around an edge. The resulting fringe pattern is called "diffraction" by many. However, in optics we would say that any optical field propagates via diffraction, even in the absence of any obstruction. For example, if I shine a laser at the moon and I want to calculate how wide the beam would be when it gets there, I'd calculate the optical field at the moon due to diffraction propagation, using a Fraunhofer diffraction integral. – Colin K Oct 8 '13 at 22:28
• @ColinK Then I suppose I must bow to authority. That said, I'm sure you and I agree on the math (it is clear from Hyugen's principle that the whole of the wave front further back along the wave vector contributes to each point on the current wave front unless blocked), but I have always understood it as I expressed it here. Anyway, thanks. – dmckee Oct 9 '13 at 3:06
• @ColinK I of course agree with you (as in my answer), but I think dmckee's characterization is reasonable as a practical one - especially if taken abstractly. The whole point of doing diffraction calculations is to find out how structure (even if not imposed, but simply a known field configuration over a plane as in the spot defining the laser pointer output stipulated as a boundary condition) on transverse planes is mapped to other transverse planes or like geometrical objects e.g. how a focal plane field is mapped to a farfield spherical surface centred on the focus, in which case our ... – WetSavannaAnimal Oct 9 '13 at 13:12
• ...definitions are the same as dmckee's. Anyhow, as I said, I have never given the names much thought because I almost never come across them without some mathematical description in their neighbourhood, so all ambiguities are defined away. – WetSavannaAnimal Oct 9 '13 at 13:13

I must say I am like Colin and tend to think of the two phenomenons as overlapping and the way I would describe diffraction would be roughly as Colin does (which maybe isn't too surprising given that our backgrounds overlap). I must admit to never really having cared about the difference deeply - but now I read @dmckee 's definition, I think I like it because it is cleanly discriminating between the two and moreover when I think about it it does pretty much describe my own gut definition if I had to give one.

I think I can reword @dmckee 's diffraction definition as: "how a propagating light field, having encoded perturbations imposed on it at one transverse plane (i.e. orthogonal to the nominal propagation direction), and expresses these perturbations at another transverse plane".

Here's my own understanding. I think of diffraction mostly as:

A wavefront scrambling process arising from the divergence of a light field's constituent plane waves

Consider a field on a plane, say $z = 0$ and split it up using Fourier decomposition of the field variation over the plane $z=0$ into constituent plane waves, which are "modes" of Maxwell's equations insofar that their propagation description is simply that the fields become phase delayed by a simple scale factor $\exp(i\,\mathbf{k}\cdot\mathbf{\Delta r})$ under the action of a translation $\mathbf{\Delta r}$. Each constituent plane wave has a different direction defined by the wavevector $\left(k_x, k_y, k_z\right)$ with $k^2 = k_x^2 + k_y^2 + k_z^2$ (i.e. the Fourier space equivalent of Helmholtz's equation), that is, all the wavevectors have the same magnitude but different directions. So, when we ask what the field looks like at a different value of $z$, we build the field up from our plane wave constituents at this point (use an inverse Fourier transform). However, now, because the wavevectors are all in different directions, the plane waves have all undergone different phase delays in reaching the new value of $z$ (even though their phase advances by $k$ radians per unit length in the direction of the respective wave vector). Therefore, the field's configuration gets scrambled by all these different phase delays. I sketch this idea in a drawing below:

To illustrate this idea further, we think of a one-dimensional problem, so we have a uniformly lit slit of some finite width $w$ modeling the laser output; in this simplified system that there are only 2D wave vectors. The screen with the slit is in the $z = 0$ plane and the one orthogonal direction is the $x$ axis. All the Cartesian components of the fields fulfil the same (Helmholtz) equation, so we can discuss the principles by just looking at one scalar field $\psi$ (say, the electric field's $x$-component). Each plane wave has the form $\psi(k_x) = \exp\left(i \,(k_x\, x + k_z\, z)\right)$ The Fourier transform of the field output from the slit is then (I'll leave out factors of $2\pi$ in the unitary FT because scale factors don't affect the following):

$$\frac{\sin\left(\frac{w\, k_x}{2}\right)}{k_x} \quad\quad\quad(1)$$

where $w$ is the slit width, and unless the slit is very wide, the Fourier transform has a wide spread of frequencies. This means that for $z = 0^+$ ("immediately downstream" of the slit's output) the field is the superposition

$$\int\limits_{-\infty}^\infty \frac{\sin\left(\frac{w\, k_x}{2}\right)}{k_x} \exp\left(i\, (k_x\, x + k_z\, z)\right) \mathrm{d} k_x\quad\quad\quad(2)$$

When we plug $z = 0$ in, the integral is simply the inverse FT of (1) and we get our original slit field. But now put some nonzero value of $z$ in: because $k_x^2 + k_z^2 = k^2$, we have $k_z = \sqrt{k^2 - k_x^2}$ (assuming the field is running in the $+z$ direction), we get

$$\int\limits_{-\infty}^\infty \frac{\sin\left(\frac{w\, k_x}{2}\right)}{k_x} \exp\left(i\, (k_x\, x + \sqrt{k^2 - k_x^2}\, z)\right)\, \mathrm{d} k_x\quad\quad\quad(3)$$

You can see the "scrambling", $k_x$-dependent phase factor $\exp(i\, \sqrt{k^2 - k_x^2}\, z) = \exp\left(i\, k\, \cos\theta_x\,\right)$ (where $\theta_x$ is the angle that the plane wave with wavevector $(k_x, k_z)$ makes with the $z$-axis) will yield the complicated scrambling you see as "diffraction".

A phenomenon I would definitely have preferred to call "interference" rather than "diffraction" would be multipathing: i.e. the splitting of a beam of light into two distinct beams e.g. for interferometry and the patterns of "interference" one gets when the beams are brought back together again.

To look at a common "ambiguous" situation: one speaks equally of "single slit interference" or "single slit diffraction" for the same thing: given what I have said above, I would rather call this "diffraction".

Lastly: Ultimately diffraction can be thought of as a special case of interference. Instead of spatially separated beams interfering, however, we take heed that the diffracted wavefront arises from the interference between the separate plane waves that make up a light field and because the pathlength for these interfering "beams" depends on propagation direction, you get the wavefront "scrambling" I spoke of.

• Sir, I'm just a high school student so, I don't know much of your math or Fourier decomposition etc. – Rajath Krishna R Oct 8 '13 at 11:24
• Dear @RajathKrishnaR I am REALLY sorry about that. I had been browsing a few of your questions and I got the impression you were a uni student at least. I'll have a think about some better words for you. Does the diagram make any sense?: the point being that you can always split a light field up into a set of plane waves going in different directions, so in going from z1 to z2 each plane wave is going to undergo a different number of periods $\Delta z\, \cos\theta$ depending on its direction, so the wavefront gets "scrambled". – WetSavannaAnimal Oct 8 '13 at 13:21
• @RajathKrishnaR I just added the last paragraph to my answer. One can think of diffraction as a special case of interference, as explained there. – WetSavannaAnimal Oct 11 '13 at 3:22
• @ WetSavannaAnimal aka Rod Vance Sir, in this Wikipedia link en.wikipedia.org/wiki/File:Doubleslit3Dspectrum.gif I see how the waves interfere in double slit interference but why does the plain wavefront become spherical when it passes through the slits? – Rajath Krishna R Oct 11 '13 at 9:02
• @RajathKrishnaR Pretty simulation! In that picture, the slit is so small that the diffraction sidelobes can be seen only in the field propagating at very high angles to the plane wave direction. The slit is a wavelength or less wide, so it behaves pretty much as a point source, which yields spherical waves. SPherical waves from a slit are also a special case of diffraction: there is still a wide diversity of plane wave directions in the superposition. – WetSavannaAnimal Oct 11 '13 at 9:11