Two very similar diffraction patterns are shown, in patterns of green dots against a blue background. The left image is labelled "Kompressions-algorithmus", and the one on the right is labelled "Licht & Zweibelzellen".

Why Diffraction Gratings Create Fourier Transforms

January 27, 2026 by 9 Comments

When last we saw [xoreaxeax], he had built a lens-less optical microscope that deduced the structure of a sample by recording the diffraction patterns formed by shining a laser beam through it. At the time, he noted that the diffraction pattern was a frequency decomposition of the specimen’s features – in other terms, a Fourier transform. Now, he’s back with an explanation of why this is, deriving equations for the Fourier transform from the first principles of diffraction (German video, but with auto-translated English subtitles. Beware: what should be “Huygens principle” is variously translated as “squirrel principle,” “principle of hearing,” and “principle of the horn”).

The first assumption was that light is a wave that can be adequately represented by a sinusoidal function. For the sake of simplicity (you’ll have to take our word for this), the formula for a sine wave was converted to a complex number in exponential form. According to the Huygens principle, when light emerges from a point in the sample, it spreads out in spherical waves, and the wave at a given point can therefore be calculated simply as a function of distance. The principle of superposition means that whenever two waves pass through the same point, the amplitude at that point is the sum of the two. Extending this summation to all the various light sources emerging from the sample resulted in an infinite integral, which simplified to a particular form of the Fourier transform.

One surprising consequence of the relation is the JPEG representation of a micrograph of some onion cells. JPEG compression calculates the Fourier transform of an image and stores it as a series of sine-wave striped patterns. If one arranges tiles of these striped patterns according to stripe frequency and orientation, then shades each tile according to that pattern’s contribution to the final image, one gets a speckle pattern with a bright point in the center. This closely resembles the diffraction pattern created by shining a laser through those onion cells.

For the original experiment that generated these patterns, check out [xoreaxeax]’s original ptychographical microscope. Going in the opposite direction, researchers have also used physical structures to calculate Fourier transforms.

Continue reading “Why Diffraction Gratings Create Fourier Transforms” →

Double-Slit Time Diffraction At Optical Frequencies

October 18, 2024 by 11 Comments

The double-slit experiment, first performed by [Thomas Young] in 1801 provided the first definitive proof of the dual wave-particle nature of photons. A similar experiment can be performed that shows diffraction at optical frequencies by changing the reflectivity of a film of indium-tin-oxide (ITO), as demonstrated in an April 2024 paper (preprint) by [Romain Tirole] et al. as published in Nature Physics. The reflectivity of a 40 nm thick film of ITO deposited on a glass surface is altered with 225 femtosecond pulses from a 230.2 THz (1300 nm) laser, creating temporal ‘slits’.

Interferogram of the time diffracted light as a function of slit separation (ps) and frequency (THz). (Credit: Tirole et al., Nature Physics, 2024)
Interferogram of the time diffracted light as a function of slit separation (ps) and frequency (THz). (Credit: Tirole et al., Nature Physics, 2024)

The diffraction in this case occurs in the temporal domain, creating frequencies in the frequency spectrum when a separate laser applies a brief probing pulse. The effect of this can be seen most clearly in an interferogram (see excerpt at the right). Perhaps the most interesting finding during the experiment was how quickly and easily the ITO layer’s reflectivity could be altered. With ITO being a very commonly used composition material that provides properties such as electrical conductivity and optical transparency which are incredibly useful for windows, displays and touch panels.

Although practical applications for temporal diffraction in the optical or other domains aren’t immediately obvious, much like [Young]’s original experiment the implications are likely to be felt (much) later.

Featured image: the conventional and temporal double-slit experiments, with experimental setup (G). (Credit: Tirole et al., Nature Physics, 2024)

Creating Customized Diffraction Lenses For Lasers

August 23, 2024 by 3 Comments

[The Thought Emporium] has been fascinated by holograms for a long time, and in all sorts of different ways. His ultimate goal right now is to work up to creating holograms using chocolate, but along the way he’s found another interesting way to manipulate light. Using specialized diffraction gratings, a laser, and a few lines of code, he explores a unique way of projecting hologram-like images on his path to the chocolate hologram.

There’s a lot of background that [The Thought Emporium] has to go through before explaining how this project actually works. Briefly, this is a type of “transmission hologram” that doesn’t use a physical object as a model. Instead, it uses diffraction gratings, which are materials which are shaped to light apart in specific ways. After some discussion he demonstrates creating diffraction gratings using film. Certain diffraction patterns, including blocking all of the light source, can actually be used as a lens as the light bends around the blockage into the center of the shadow where there can be focal points. From there, a special diffraction lens can be built.

The diffraction lens can be shaped into any pattern with a small amount of computer code to compute the diffraction pattern for a given image. Then it’s transferred to film and when a laser is pointed at it, the image appears on the projected surface. Diffraction gratings like these have a number of other uses as well; the video also shows a specific pattern being used to focus a telescope for astrophotography, and a few others in the past have used them to create the illusive holographic chocolate that [The Thought Emporium] is working towards.

Continue reading “Creating Customized Diffraction Lenses For Lasers” →

How To Get Your Diffraction Grating 3D Prints Right The First Time

February 24, 2022 by 2 Comments

Diffraction gratings are beautiful things, bending transmitted and reflected light and splitting it into its component wavelengths to create attractive iridescent rainbow patterns. It’s the same effect you see on the bottom of a CD!

You can 3D print a functional diffraction grating, too, with the right techniques, as it turns out! The average 3D printer can’t recreate the tiny-scaled patterns of a diffraction grating directly; a typical diffraction grating may have up to 1000 lines per mm. Instead, by 3D printing onto an existing diffraction grating, the print can pick up the texture on its base layer. It’s a great way to add iridescence and shine to a print.

We’ve seen similar work before, but the guide from [All3DP] goes into greater detail on how to get the effect to work just right. Getting the bed as close to perfectly level is key here, as is the first layer height. This is because the first layer of plastic has to meld perfectly with the diffraction grating to pick up the pattern. Too high and the grooves won’t transfer to the plastic, and too low, and it’s likely you’ll just melt the grating itself. Setting the Z-offset appropriately can help here.

Choosing the right bed temperature is also important to ensure the molten plastic is able to flow into the grooves of the grating. Again, the temperature at which the diffraction grating itself can survive is important to take into account; going above 90 degrees can be risky here. The guide also shows two methods of achieving the goal: one can either use an off-the-shelf grating, or one can prepare a no-longer-wanted CD into a suitable print surface.

Naturally, removing the print must be done delicately, lest one disturb the delicate structures key to generating the iridescent effect. [All3DP] recommends using a freezer to help separate the parts from the grating surface. It also bears noting that the print won’t survive excessive handling, as the grating structures will get damaged by physical touch.

It’s a great in-depth guide on how to get diffraction grating prints right. Meanwhile, consider diving deeper into the world of 3D printed optics!

 

Iridescent Rainbow Chocolate, Just Add Diffraction Grating!

May 23, 2021 by 15 Comments

Chocolate plus diffraction grating equals rainbow chocolate

Here’s a great picture from [Jelly & Marshmallows] that shows off the wild effects of melted chocolate poured onto a diffraction grating. A diffraction grating is a kind of optical component whose micro-features act to disperse and scatter light. Diffraction gratings are available as thin plastic film with one side that is chock full of microscopic ridges, and the way light interacts with these ridges results in an iridescent, rainbow effect not unlike that seen on a CD or laserdisc.

It turns out that these micro-ridges can act as a mold, and pouring chocolate over a diffraction grating yields holo-chocolate. These photos from [Jelly & Marshmallows] show this effect off very nicely, but as cool as it is, we do notice that some of the letters seem a wee bit hit-or-miss in how well they picked up the diffraction grating pattern.

Fortunately, we know just what to suggest to take things to the next level. If you want to know more about how exactly this effect can be reliably accomplished, you’ll want to check out our earlier coverage of such delicious optics, which goes into all the nitty-gritty detail one could ever want about getting the best results with either melted sugar, or dark chocolate.

Delicious Optics, A Chocolate Diffraction Grating

April 16, 2018 by 12 Comments

Diffraction gratings are curious things. Score a series of equally spaced tiny lines in a surface, and it will cause reflected or transmitted light to bend and separate into its component wavelengths. This ability gives them all manner of important applications in the field of optics, but they’re also fun to play with. [Tech Ingredients] has done the hard work to find out how to make them out of candy!

The video starts with a basic discussion on the principles of diffraction gratings. The basis of the work is a commonly available diffraction grating, readily available online. It’s a plastic sheet with thousands of microscopic ridges scored into the surface. The overarching method to create a candy version of this is simple — coat the ridged surface in liquid chocolate or sugar syrup, to transfer the impression on to the candy surface when it solidifies. However, the video goes further, explaining every step required to produce a successful end result. The attention to detail is on the level of an industrial process, and shows a mastery of both science and candy processing techniques. If you’ve ever wondered how to properly crystallize chocolate, this video has the knowledge you need.

It’s not often we see candy optics, but we like it — and if you fail, you can always eat your mistakes and try again. If you’re wondering what you can do with a diffraction grating, check out this DIY USB spectrometer.

I, Integrated Circuit

February 4, 2026 by 63 Comments

In 1958, the American free-market economist Leonard E Read published his famous essay I, Pencil, in which he made his point about the interconnected nature of free market economics by following everything, and we mean Everything, that went into the manufacture of the humble writing instrument.

I thought about the essay last week when I wrote a piece about a new Chinese microcontroller with an integrated driver for small motors, because a commenter asked me why I was featuring a non-American part. As a Brit I remarked that it would look a bit silly were I were to only feature parts made in dear old Blighty — yes, we do still make some semiconductors! — and it made more sense to feature cool parts wherever I found them. But it left me musing about the nature of semiconductors, and whether it’s possible for any of them to truly only come from one country. So here follows a much more functional I, Chip than Read’s original, trying to work out just where your integrated circuit really comes from. It almost certainly takes great liberties with the details of the processes involved, but the countries of manufacture and extraction are accurate. Continue reading “I, Integrated Circuit” →