In Focus: Bahtinov Masks

A Bahtinov mask is a highly effective, yet easy to use, focussing tool for astronomy and astrophotography. But who came up with the design, and how does it work?

In this article I take a deeper look into the history and physics behind the mask.

The Invention

When I first researched Bahtinov masks a few years ago, I was surprised to find that they are a relatively recent invention.

In September 2005, Pavel Bahtinov posted a new thread on the Russian astronomy forum Astronomy.ru [1] to propose an improvement that he had devised for an existing mask design. The existing mask that some astronomers were using at the time made use of two triangular holes (see Figure 1), to create a diffraction pattern in a telescope which was visible when a bright star was viewed with the mask fitted.

Figure 1 - Bahtinov's first mask design is on the right. Credit: Pavel Bahtinov - Astronomy.ru

The diffraction pattern that this mask creates appears asymmetric when viewed through an out-of-focus telescope. This means that to achieve perfect focus, the masked telescope can be adjusted until the diffraction pattern becomes symmetric (similar to Figure 3).

Although these triangles do create a pattern useful for focusing, Bahtinov found that the diffraction rays created were too dim, and too wide, for the method to be useful on all but the brightest stars, such as Vega. If a similar mask could be devised which created a stronger pattern, it would be easier to use, and also could be used with less bright stars if needed.

The diffraction is caused by the edges of the triangles, so to make the effect stronger the perimeter of the triangles would need to be increased. Bahtinov's insight was that the triangles themselves weren't so important - the key was to increase the total length of edges. Or in his words:

Intuitively, in order to increase the energy "ejected" from the central spot into the rays, it is necessary to increase the perimeter of the rectilinear edges of the triangles. But it will not be possible to do this by simply increasing the size of the triangles: firstly, the secondary mirror (dotted line in the figure) interferes, and even without it, according to the meaning of the method, the triangles should be located as far apart as possible. In order to overcome this contradiction and "develop" the perimeter while maintaining the small overall dimensions of the holes, I came up with the idea to try to make a mask in the form of a lattice.

Pavel Bahtinov, Astronomy.ru (translated)

Figure 2. Example of a Bahtinov Mask made by Astro Printer.

How the Bahtinov Mask works

Bahtinov's lattice-based mask design produces a strong diffraction pattern of three intersecting spikes, which form an "Ж" shape, as shown in the photographs in figure 3.

Figure 3. Perfect focus is shown in the central image: the other two are slightly off-focus. Credit: Geoastro.co.uk [2]

As the telescope focus is moved, the central spike will appear to move sideways relative to the other two. The angles between the spikes are equivalent to the angles of the lattices on the mask, at around 20 degrees - an angle which was chosen "purely intuitively" by Bahtinov.

Because this acute angle is used, a slight sideways movement of the central spike relative to the others can be detected fairly easily. This means that even a small deviation from perfect focus will be visible, and the astronomer can adjust their telescope's focus until the pattern becomes symmetrical, indicating that perfect focus has been reached.

The Physics

The key to how a Bahtinov mask works is that light diffracts when it passes an edge.

Figure 4. Extract from a NASA infographic explaining diffraction in a telescope. Credit: NASA.

In the case of a Newtonian telescope, this already occurs in two places: firstly when light passes the struts holding the secondary mirror, and secondly at the edge of the primary mirror. Figure 4 shows an extract from a NASA infographic [3] that illustrates very clearly how this effect works.

Just like the struts holding a secondary mirror, any other bar or slit placed in front of a telescope mirror will also create a diffraction spike, which will be perpendicular to that bar or slit.

Multiple parallel edges will create parallel diffraction lines, which then get focussed into a single, brighter line by the mirror. This is why the grid design of the Bahtinov mask is particularly effective at creating a strong, easily visible pattern. In fact, the last pattern illustrated at the bottom of figure 4 is very similar to the pattern a Bahtinov mask creates: but in this case, only one bar in each direction has been used to create the diffraction spikes. In theory this shape could also be used like a Bahtinov mask, but the effect would be much dimmer.

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Thanks for reading - if you have any thoughts or questions, please leave a comment!

References / Further reading

[1] https://astronomy.ru/forum/index.php/topic,10421.0.html (via Google translate from Russian) - this is the original forum post where the design was first published.

[2] http://geoastro.co.uk/bahtinov.htm - this is an article on Bahtinov masks which I found very helpful, and it includes some great illustrations.

[3] webb-diffractionspikesinfographic-stsci-01g6933bg2jkatwe1mgt1tcpj9-1500w.png (1500×7297) (nasa.gov) - the full NASA infographic that figure 4 is taken from.