Language: English, Japanese

A Tri-Bahtinov Mask for Aiding Collimation and Focusing of Schmidt Cassegrain, Ritchey Chretien and Newtonian Telescopes

Introduction

In my opinion, the Bahtinov mask is one of the most useful inventions for astrophotography. The traditional use of a Bahtinov mask is for focusing a telescope only and is not used for collimation of reflector type telescopes like SCTs, RCs and Newtonians. For collimating a reflector, the method that is commonly used is the Airy disk method. I have found this method to be quite onerous because

• due to atmospherics at my observation location, I have never been able to see a really clear diffraction pattern of the defocused star or Airy disk.
• when I adjust the collimating screws to centre the doughnut hole, my judgement is rather arbitrary and not as objective as it should be. I think my overly optimistic judgement of the diffraction pattern makes this method a collimation challenge for me.

And thus, these two reasons motivated me to create a less judgemental way for collimation.

The idea

Since the standard Bahtinov mask is such a useful tool for focusing, I thought that there must be a way to use it for collimation as well. My idea when applied to an SCT is as follows:

For an SCT, that is well collimated, I would expect that the path length travelled by light rays from the primary mirror reflected to the secondary mirror and then reflected to the image plane should all be the same. However, if the SCT is not collimated then the light rays do not all have the same path lengths. The effect is that focus can only be established at one location on the image plane, while focus is not achieved at other locations.

Therefore, for an uncollimated SCT, while I can achieve perfect Bahtinov diffraction spikes with one orientation of the Bahtinov mask, the diffractions spikes will not be perfect for other orientations. Thus, in my opinion, the most natural way to simultaneously measure the focus for different orientations of the Bahtinov mask is to make a mask that has multiple orientations already built in.

Tri-Bahtinov mask

For an SCT, the secondary mirror has three adjustment screws. Therefore, the most obvious way to me is to have three Bahtinov masks designed into the mask. Thus, my idea of a Tri-Bahtinov mask that has three Bahtinov masks arranged in a 3-fold symmetric fashion. This symmetry should produce a diffraction pattern that is also 3-fold symmetric. To check this hypothesis, I generated the diffraction pattern using the program Maskulator. The diffraction pattern from such a Tri-Bahtinov mask is shown below for the design where the smallest angle between the diffraction spikes is 10 degrees. This simulation confirms my hypothesis that a Tri-Bahtinov produces a diffraction pattern that has three orientations for checking the focus.

Implementation

I have made a Tri-Bahtinov mask for my 8" LX200 classic which I show below

The Tri-Bahtinov mask is mounted on my LX200 is shown below I have mounted thumb screws on the mask so that when I use it, I orient these screws to align with the collimation screws on the secondary mirror. I can then mask one of the three Bahtinov sub-masks to determine which collimation screw to adjust.

Improved Tri-Bahtinov mask invented by S. Takagi

S. Takagi has improved the original mask which can be found here. This improved mask is more sensitive to any focus errors than the original mask.

Although I don't show the results of the improved mask here, the method for using the mask that is outlined in the wiki is still applicable.

Results

My as found diffraction pattern when I point my LX200 at Polaris, magnified 400x and integrated for 0.5 seconds for the diffraction pattern of the defocused star and 4 seconds for the Tri-Bahtinov are shown below It is clear that my LX200 is badly mis-collimated from the diffraction pattern. For the Tri-Bahtinov diffraction pattern, I can get two directions that are close to focus but in one Bahtinov spike orientation, indicated in the picture, is clearly not in focus. In fact, this orientation is in the same direction that the donut shadow that is also off-centered.

After using the collimation screws to move the diffraction pattern to the center and using the Tri-Bahtinov mask to fine tune each orientation, I got my LX200 to be very well collimated (might still be a smidgen off from perfection)

Thus, my collimation exercise with the Tri-Bahtinov mask allowed me to achieve collimation with minimal arbitrariness. This is the goal that I wanted!

Use on RCs and Newtonians

The contribution from the community at Cloudy Nights has been tremendous! I had only thought of using the Tri-Bahtinov on my SCT, but users like Richard (alias "frantolmy") and Satoru Takagi (alias "Psittacula") have shown that the Tri-Bahtinov also works on RCs and Newtonians. Please see their posts here

Tri-Bathinov Grabber

K. Evans' has created a Tri-Bahtinov Grabber program to objectively help with focusing and collimation.

Directory structure

• ponoko My Tri-Bahtinov mask that can be sent to Ponoko to be laser cut.
• other_formats My Tri-Bahtinov mask in other formats so that you can print it out or edit it.
• pics Image files for this repository.
• maskulator_movie directory that contains the avi movie from maskulator that shows how the Tri-Bahtinov diffraction pattern changes when the focusing changes.
• python My python script for generating my Tri-Bahtinov mask for any telescope. Please see the README.md file in that directory for instructions how to install the required python libraries in order for generate.py to work.
• releases For most users, you will download the executables for Mac OS X and Windows in the releases directory.
• cover_generator The cover generators written in python that are useful when used in conjunction with K. Evans' Tri-Bahtinov Grabber program.
• pre-made There are pre-made masks in svg format for some popular telescopes.
• translations Documents translated into languages other than English are stored.

How to use the mask

I have written the instructions for using the mask in the wiki.

Satoru Takagi has posted instructions for collimating a Newtonian here. I have reproduced his instructions in the wiki.

Discussion group

There is an active discussion group that the I monitor. You can post to Cloudy Nights::Equipment::A Tri-Bahtinov mask for SCT collimation and focusing to get community help.

A Tri-Bahtinov mask generator on the web

Here's the link to a Tri-Bahtinov mask generator that is written by Satoru Takagi:

Satoru Takagi's Tri-Bahtinov mask generator

Thanks to Satoru Takagi, you can use his webapp to generate the mask rather than download and install my program to do this.

Acknowledgements

I would like to thank Satoru Takagi (25 Jul 2017) for his contributions for improving generate.py. His contributions added the following options for the user:

• setting the stem width
• setting the ratio between the slit and stem widths.

Satoru has also invented an improved version of the Tri-Bahtinov which can be found here.

Ever since publication of the Tri-Bahtinov mask, the support from the community has been fantastic. For example, K. Evans has created a Tri-Bahtinov Grabber program to objectively help with focusing and collimation. As part of the support for this program, I have written python cover generators for both the original and improved Tri-Bahtinov masks.

Copyright

All the documentation, pictures, movies and design that I have here is copyright 2016 C.Y. Tan and released under Creative Commons Attribution-ShareAlike 3.0 Unported License.

All software is released under GPLv3