This article shows a methodology to adjust the tilt of the sensor of the camera. Is a quantitative method so it is objetive and not influenced by a visual inspection, that can lead to a lack of accuracy. This methodology is based on an article found on this web.
I noticed that something was wrong with my stars during the processing of the images taken during an astrophotography session. The stars on the center of the image were well focussed…
…but the stars on the corners seemed to be out of focus.
I started to investigate what happened. I tried several things (that I will not describe in this article, to not no make it too much dense) and finally I concluded that the sensor of my camera was tilted.
I selected and isolated 1 star from the center and each corner to evaluate their shape. They sufferend from some comma, as expected, but in addition I noticed that each of them had a different amount of defocus related to the central star. This gave me the hint that the sensor could be tilted.
To confirm this, I centered a star in the FOV’s center and focused it with a bahtinov mask, then I moved the telescope to put the star on every corner.
An analysis with FWHMEccentricity tool of Pixinsight confirms that there’s a problem on the lef-bottom corner.
In addition, a curvature analisys with CCD Inspector gives a value for this tilt:
So, this is the starting point, but before explaining how this tilt can be fixed, it is important to know what it is. This will help us to understand the results of the measurements and to know what we can expect of the resulting images once fixed.
Tilt is a concept easy to understand. Basically means that the sensor of the camera is not perfectly squared to the optical axis of the telescope.
When this error is present in the optical train, it is not possible to achieve a perfect focus on the entire sensor surface. In the diagram above I have assumed a perfectly focused star on the center of the image therefore the stars on the left corner will be extrafocal and the stars on the right, intrafocal.
Unfortunatelly the focus plane is not a plane, but a curved surface.
That means that, even with a perfectly squared sensor, it is not possible to achieve perfectly focused stars on the whole surface of the sensor. So assuming that the curvature is symmetrical along the field of the optical element, the best result that we can achieve is to achieve the same amount of defocus on the four corners while keeping the center perfectly focused.
There’s some admisible tolerance due to the deep of field present on any objective (it is called Critical Focus Zone (CFZ) in astromony).
This CFZ depends on how fast is the optical system and on the wavelenght of the incoming light. In my case I assumed the CFZ of my fastest telescope, the Borg 101ED f/4 that has a Critical Focus Zone of 30 microns (=0.03mm).
Note how much critical is the focusing (and the tilt tolerance also) in a fast focal optics. As an example, the thickness of a common sheet of paper is 0.15mm aprox, 5 times thicker than the focusing tolerance. It is extremely critical, so the adjustments will be very critical also (in my particular case).
So, once we know what can we expect of a tilt adjustment, and how much accurate it has to be, we can describe how to proceed to achieve a good result.
As mentioned, the objetive is to achieve a perfectly focused star in the center of the image and keep the same focus difference between the center of the image and the corners.
To achieve this we are going to use a bahtinov mask to focus a star in the center of the image and then move the star to the corners (without refocus) and measure the focus difference.
Note that the the four corners are out of focus (and intrafocal). This is the expected result even when the sensor is adjusted, and is produced by the field curvature as explained before.
The usual situation with a tilted sensor is to have some corners intrafocal, and some extrafocal. Which of them and how they are affected depends on the tilt’s orientation and its amount.
The following example shows my starting point:
It is obvious that the left bottom corner is more out of focus than the other corners. In addition, note that the left corners are out of focus in one way (the vertical spike’s offset is to the left) while the right corners are out of focus in the opposite direction.
To make a qualitative analisys I built a focus map that shows different amount of defocus. My focuser is an helical one and is indexed in 80 micron steps.
It is obvious that it’s difficult to evaluate the degree of defocus by a simple visual inspection and there’s no quantitative measurement of it. This would make the adjustment process to be trial and error and can be really difficult.
ASSISTED MEASUREMENTS – BAHTINOV GRABBER
To achieve a more accurate measurement and quantify the amount of defocus, I used use the bahtinov grabber software. It is capable to recognize the pattern of the bahtinov mask in real-time, and measure the amount of defocus. It is freeware and can be downloaded from the author’s website.
In the image above we can see a screenshoot of the software working. There are several measurements. I used 2 of them for my analysis.
- The calculated absolute focus error tells us how much offset distance has the sensor to the focus point. It has the advantage to be measured in microns, in this case, 20 microns. However this value varies in real time and is influenced by the seeing so it’s difficult to decide which is the central value. As a tip, try to use the longest exposure time possible for your system (without focus or tracking drifts). This will decrease the amount of variance of this value over the time.
- The 15s average parameter is an average of the last values over 15s, so it’s a very stable value. The counterpart is that is measured in pixels, not microns, but can be used anyway as we are only going to «balance» the values of our measurements.
I’ve been reported that there are other software alternatives that can manage multiple measurements at the same time. @focus3 is a plug-in for The Sky that does it. This would be an interesting improvement in terms of accuracy and would be a faster workflow. The counterpart, in the case of @focus3 is that is not freeware, as the bahtinov grabber, and it’s not a standalone software.
I strongly suggest to use some kind of visual notation to represent the values obtained, to help to imagine what’s happening to the sensor. I used the notation showed below:
- The rectangle represents the sensor and the outside notation (TL TR BL BR) in gray, corresponds to the name of the corners (Top-Left, Top-Right, Bottom-Left, Bottom-Right).
- The values in black are the amount of defocus on each point in microns (the calculated absolute focus error). Note that the value of the center hasn’t been writen. The reason is because it will always be 0 as we always start the analisys by focusing a star in the center of the image.
- Below them, in gray, there are the corresponding 15s average values in pixels, as mentioned before.
- The outer values in red are the gauge applied, in milimeters.
- The delta value is the difference from the previous step (that means, how much gauge has been added or removed)
So, after focusing a star on the center and measuring the defocus on each corner, this is the initial state:
It is obvious that there’s a significant tilt on the Bottom-Left to Top-Right direction (let’s abbreviate as BL-TR). 70um from corner to corner, with BL at extra focus. In addition, the opposite corner has a slightly tilt too, less noticeable, 15um corner to corner, in that case with BR at extra-focus.
- BL-TR = 70um (2.82px)
- BR-TL = 15um (0.43px)
TR is the most intra-focus point so I have to put gauges in the other 3 corners. I putted two gauges of 0.52mm on BL and BR, and one gauge of 0.26mm on TL.
- BL-TR = 30um (1.05px)
- BR-TL = 5um (0.35px)
Now the difference, or slope, from BL to TR is less, 30 microns, but can be improved, so I added 0.11mm more.
The slope TL-BR is 5 microns, really close, so I considered it as good enough.
- BL-TR = 5um (0.27px)
- BR-TL = 0um (0.02px)
Now the slope BL-TR is 5 microns, very close, but is reversed (TR is more that BL), so I tried to go back as fine as possible and removed only one layer of gauge, 0.03mm. The TL-BR slope has become surprisingly 0, perfect!
- BL-TR = 5um (0.17px)
- BR-TL = 0um (0.00px)
The slope BL-TR remains 5 microns and reversed again, so it is not possible more improvement with this gauges. In fact, to try to go further than 0.03mm of adjustment is not really feasible, in my opinion, at least with my setup configuration. The distance is so small than many other factors can vary it.
Once the adjustment is done, I recommend to make an analysis of the resulting collimation. I suggest to take a serie of images and average them in order to reject any variance caused by the seeing, tracking issues, etc…
Again, a FWHMEccentricity analysis in Pixinsight reveals a big improvement.
CCD Inspector shows a noticeable improvement on the tilt values(the starting point was X=-0.7″ / Y=0.7″), as expected. There’s some residual error on the X axis, that I have to investigate.
And finally, a corrected image, that is what we really want.