One of the first things I need to know in order to design the OTA is the distance from the rear lens to the focal plane. It is shorter than the focal length because the entrance pupil of the objective lies somewhere inside the 3 element group.
Fortunately, there is a simple trick to measuring distance to the focal plane. It uses a technique called autocollimation. If you place a mirror in front of the objective and place an illuminated slit at the focus, the light from the slit will pass through the lens, reflect off the mirror back through the lens and form an image at the slit. The beauty of this arrangement is that in passing the light through the lens first, a parallel beam then hits the mirror and is reflected back to form the image. Light from effectively infinity, such stars, enters as a parallel beam. So the focus of this setup is the same as the focus at infinity.
Here is my optically benchless autocollimation setup.
Yes, the slit is in a Chinet paper plate and the mirror is my wife’s hand mirror but it works! I measured 883mm from the rear element surface to the image of the slit on the paper plate. This agrees very well with data on another objective from the same production run. I’m happy.
I want to know how long to cut the tube. To figure that out I need to know how much space or back focus each component stuck on the end of the tube takes up. This is a simple matter of measurement, with the exception of the Apex ED. It’s back focus is a function of the objective’s focal length. In this case it is:
There is another factor to consider with the Apex and that is that, like all reducers, it shifts the focal plane towards the objective.
Getting back to simple measurement the focuser at one third out focus is the following:
And the back flange to attach it to the tube is:
So putting it all together I get the tube length.
My next problem is baffling. Literally. If I want to ensure the highest possible contrast in my images, then I have to prevent extraneous light from getting to the imaging sensor. If light enters the objective well off-axis it won’t impact the sensor directly but it might well illuminate the tube wall and scatter. Bad news for contrast as it can hit the sensor.
A common solution is to paint the inside of the tube black. But unless you have access to VantablackTM some light will still scatter. A better solution is to prevent the wall from being visible to the sensor in the first place. And then paint it black to boot!
Baffles can block the view of the wall from the focal plane — but where to place them and how many are needed? To answer those questions I need to know what the un-vignetted field diameter is. I chose the following:
The un-vignetted field diameter for the Apex ED is only 30mm so why choose 44mm? The answer is future-proofing. The larger field will encompass a full-frame sensor (36 x 24mm). Who knows what cameras lie in my future???
The next piece of the puzzle to solve for is the angle of the light cone for the un-vignetted field.
With the above I can make a calculation of the diameter of the light cone at the rear element of the objective.
I also need to know where that problematic wall is.
In order to simplify the calculations I defined the distance from the objective to the field as z and the height above the lower tube wall as y. Therefore we get the following:
Given the above coordinates, I calculated the slope of the light cone or field of view (FOV).
The slope is very useful to estimate the height of the cone at any point along the z axis. I defined a function to help calculate the height of the lower edge of any baffle given the z location.
But where the z should the baffles be? The following diagram helped to get my head around the problem.
The objective end is to the left and the focal plane is to the right. The green dotted lines show the FOV and the red ones the cutoff for each baffle. It was immediately clear that the height and location of each baffle corresponded with the intersection of the FOV lines and the cutoff as drawn from the base of the preceding baffle. To ensure the cutoff for the first baffle includes the lens cell mount I will place the first baffle up against the mount ring allowing for the baffle thickness.
Then I get the height using previously defined function.
To solve for the next intersection I needed to know the slope of next cutoff line.
Solving for z:
And then for y:
Viola! The second baffle is defined! Repeating the process yields the other 2 baffles.
Since the tube is only 634mm there isn’t room for another baffle. I was surprised that only 4 baffles would do the job. In the reflector world such baffling is generally not possible as the entrance beam must travel all the way to the bottom of the tube and it is more or less parallel to the tube wall. Score one more for the refractor!
I now have all of the dimensions of the OTA defined. The next step is drawing the needed parts and then machining them.