How To: Design a Bahtinov Mask

A focusing mask is a device placed over the aperture of a telescope to aid achieving perfect focus. All focusing masks operate by the same principle; the mask geometry causes the incoming light to diffract which generates a diffraction pattern at the eyepiece. This diffraction pattern is sensitive to the telescope focus, so you focus the telescope by adjusting the focus until the pattern takes the specific form which indicates that perfect focus has been achieved.

The Bahtinov Mask

The Bahtinov mask is the most popular type of focusing mask, first proposed by Russian amateur astronomer Pavel Bahtinov in 2005 (you can find his original forum post here). There are also other kinds of masks, such as the Hartmann and Carey masks, however these are less popular and are typically not sold commercially.

This article will outline how to design your own Bahtinov mask which is optimised for your specific telescope. All of the diffraction patterns were simulated using software I wrote called Diffraction Simulator. You can download it and use it to test out your Bahtinov mask design before committing to fabricating it.

Bahtinov Mask Generator

To design your own Bahtinov mask, I strongly recommend using the Bahtinov Mask Drawings Generator created by Satoru Takagi.

Tri-Bahtinov Mask

In 2016, a forum user known as cytan299 created the Tri-Bahtinov mask, a modified version of the original Bahtinov mask which produces many more diffraction spikes. Although it can still be used for focusing, the primary advantage it has over the original Bahtinov mask is that it can also be used for collimation. Satoru Takagi has also created an online generator for the Tri-Bahtinov mask, which can be found here. Although this tutorial will focus on the design of a regular Bahtinov mask, the design principles are also applicable to the Tri-Bahtinov mask if you wish to make one.

Bahtinov Mask Design

To begin designing a Bahtinov mask for your telescope, head over to the Bahtinov Mask Drawings Generator. I will explain each of the parameters and how they affect the mask. I will be designing a mask for the Skywatcher 10 inch Collapsible Dobsonian telescope. This telescope has a focal length of 1200 mm, a primary mirror diameter of 254 mm, a central obstruction diameter of 40 mm, and the aperture has an outer diameter of approximately 290 mm.

Setup for telescope geometry

To begin, we need to enter some parameters specific to the telescope for which we want to design the Bahtinov mask. First off, under ‘Focal Length’ enter the focal length of your telescope. Next, under ‘Outer Diameter’ enter the outer diameter of your telescope aperture. Note that this is not the diameter of the primary mirror, as the mask needs to be big enough to fit over the front aperture of your telescope. Lastly, under ‘Inner Diameter’ enter the diameter of the central obstruction of your telescope. If you’re using a telescope without a central obstruction (such as a refractor), just enter zero in this field.

Stem to Slit Ratio

The next setting to consider is the “StemWidth : SlitWidth” ratio. The ‘stems’ are the structural part of the mask, while the ‘slits’ are the gaps through which light passes. The effect of this setting was simulated and is shown in the diffraction patterns below. Wider slits mean the final image is brighter (as more light is let through). However, as the slits get wider (or as the stems get smaller), the light becomes more concentrated in the central region of the diffraction pattern, and the visible length of the diffraction spikes decreases. Personally, I prefer the diffraction spikes to be longer as I find it makes them easier to use when focusing. I would keep this ratio at 1:1 as a good trade-off between the length of the spikes and image brightness.

Bahtinov Factor

The next setting is called the ‘Bahtinov Factor’. This is defined as the focal length of your telescope, divided by the spatial period of the grating (sum of the gap and stem widths). For example, if your focal length 1200 mm, gap width is 5 mm, and stem width is 5 mm, then the Bahtinov factor is 1200/(5+5) = 120. The simulated diffraction patterns are shown below. Increasing the Bahtinov factor increases the strength of the diffraction spikes and is generally considered a good thing. However it also increases the spacing of the two horizontal spikes in the center.

3rd Order Spectrum

To the right of the stem to slit ratio you’ll see a checkbox marked ‘Use 3rd order spectrum’. Enabling this multiplies the focal length by 3 before calculating the Bahtinov factor. This uses the 3rd order diffraction spikes for the diffraction pattern. This option is useful if you are designing a mask for a large focal ratio telescope (such as a refractor), as trying to achieve a Bahtinov ratio of 150 may result in stems which are too thin to be structurally sound. By enabling the 3rd order spectrum, the stems will be three times as thick and will be much more robust. A comparison of the 1st and 3rd order diffraction patterns is shown below. In the 3rd order case, the light is spread out much further from the center of the diffraction pattern, providing long distinct spikes. Even if you are not designing for a large focal ratio telescope, you may still want to use 3rd order diffraction anyway as the stronger spikes make it easier to focus.

Rounding

The next option you’ll see is a small checkbox labelled ‘Rounding’. Enabling this fillets the corners of the slits with semicircles. A comparison of squared and rounded corners is shown below. The difference is very subtle, but rounding suppressed the two horizontal spikes in the middle of the diffraction pattern by slightly reducing their length. It is a small difference but I would recommend it when designing your own mask.

Conclusion

With the existence of online mask generators, designing your own Bahtinov mask is not difficult. I hope that the guide above has explained what each setting does so that you can design the optimal focusing mask for your telescope system.