aRE: [EXTERNAL] Re: [apgto] Tilt plate with digitial readout
Nathan Myhrvold
It is simple geometry, so the correlation is essentially perfect. But you are correct that it is not a simple multiple.
 The key assumption is that the sensor is a flat plane. But even if it isn’t this will work as well as one can hope. HF effectively figures out the equation of the plane in 3dimensional space that makes as much of the frame as possible sharp. The equation of the plane is expressed as an offset at four points. Each point is a corner of the frame.
If we call the center of the frame coordinate (0, 0), then for a full frame sensor, one corner is at (18, 12) – in this case the dimensions are in millimeters. The others corners are at (18,12), (18, 12) and (18, 12). But HF averages over 1/9 of the sensor. So the actual corner measurement for the corner which is nominally (18, 24) is actually computed at (12, 8), and so forth for the other points.
If we call that the (x,y) coordinates, then the HF values gives you (x,y,z) – each of the 4 positions gets a zvalue.
That defines a plane – actually you only need 3 of the points to define a plane – but anyway you have the equation of a plane a*x + b*y+ c*z + d = 0 for numbers a, b, c, d. It’s a simple formula to go from offset numbers to the coefficients a, b, c, d.
So now you need to measure where your screws are in the same coordinate system. I don’t have the exact numbers in front of me, but here is a sample – for my adapter the corners would be at (37.7, 37.7) mm and then the same pattern of those numbers with (+,), (,), (,+) for the other points.
To get the exact offset at each of those positions you plug in the x, y of each screw into the plane equation and then solve for the z value.
That will be exact – meaning that much offset at each screw will give you the correct z value at the x,y of each sensor section.  That is the basic story, but here are some details.
The dial indicators are not exactly at the screw positions – they are as close as a practically could get them. So really what I will calculate is not the coordinates of the screw positions – I will calculate at the coordinates of the dial indicator feet. But that is a very tiny difference.
Some adapters let you shift the sensor in x, y. That would change the coordinates of the screws. But you can center and then measure the coordinates.
Some adapters let you rotate the sensor in the same place you do tilt and centering. That would also change the coordinates of the screws relative to the sensor. I am not using that degree of freedom because I have a rotator on the other side of the adapter.
But if you did have centering and rotation, there is a way to easily figure that out. George (the author of Hocus Focus) is planning on putting that into HF. Basically, what you do is take a measurement, then deliberately move two of the screws (a long a diagonal) a bunch, then measure again – you can recover the parameters you need from the difference.
This means you need to measure where your screws are, or have the vendor give you a diagram. But either one is straightforward. Since there are not that many tilt adapters out there, HF will just have a list that knows the dimensions – it’s just another configuration setting.
An optical detail is that the field is never flat, but the approach that HF takes is to find the best fitting plane, which is all you can hope to adjust with a tilt adapter. What you will get from HF is the tilt plane that optimizes sharpness across the corners of the sensor – which might conceivably not be what you want for your application and that is fine.  Note that this assumes that HF is giving you the correct numbers.
As per other email we’ve exchanged, one might say HF is not giving you the best tilt. Which is fair enough, but it is a separate point. The screw calculation is this  the offsets measured from the focus sweep give you the equation of the plane. That equation tells you the exact offset at the screw positions.
As you may have seen on a thread on CN, I am not a fan of averaging tilt over 1/9 of a frame  it is fundamentally less accurate. The HF “sensor model” mode is theoretically better in some ways but it has some robustness issues. But George has a fantastic attitude and is currently working on several ways to improve what HF outputs. 
The next obvious evolution is to make this be motorized, just like we focus is motorized. In that case rather than me fiddling with an allen wrench while looking at the dial indicator one would have a stepper motor on the screw, which is either calibrated, or where you have a sensor that tracks the offset. This might make sense for a remote observatory. I thought that I would try the digital display first.
Nathan
From: main@apgto.groups.io <main@apgto.groups.io>
On Behalf Of Chris White via groups.io
Sent: Wednesday, March 29, 2023 7:26 PM To: main@apgto.groups.io Subject: [EXTERNAL] Re: [apgto] Tilt plate with digitial readout
[Edited Message Follows] Nice work, Nathan! It's cool idea to quantify the adjustments.


ROBERT WYNNE
Nathan I am working through this mornings emails and am about half way through. I responded first to your earlier message only to find other messages had followed. I find this one so far as I've read the most succinct analysis of the problem and various rabbit holes one can get lost.
I believe a laser leveling system coupled to a digital DAQ system w/ display ought to be in the works for this level of precision guidance. Mechanical devices are simply not up to the task at hand. Our laser lab had digital micrometers accurate to .00001 and that was a few years ago. Matters must have improved since.
Best,
Robert


Nathan Myhrvold
On 10 meter professional telescopes they do use laser alignment, and precision metrology. Indeed, some like the Keck have segmented mirrors that also need to be aligned and so forth. But for an amateur scope that would be a lot of overhead.
Lasers are great but it is just one kind of light source. They have some nice properties, but it turns out we already have perfectly good light sources to measure our tilt – the stars. Measuring the diameter of the stars on an image is an easy image processing task, and you can generally measure diameter and center (centroid) to within a small fraction of a pixel, so easily within 1 micron.
That is the input data for Hocus Focus or other autofocus and tilt adjustment applications. If we can measure diameter to much less than one pixel, we have more than enough precision to estimate the tilt of the sensor to within the tolerance needed to make a good astrophoto. Which is a key point – we only need to measure the tilt well enough to get a good photo, which means that lack of precision due to the diffraction limit for the OTA, or the pixel size or the sensor flatness pretty much cancel out. If the tilt produces a variation in the size of the stars smaller than we can measure with image processing, then by the same token you’ll never see it in a photo.
I don’t think that a laser is fundamentally any better – although it would have the advantage of being able to work during the day.
150 years ago Foucault made parabolic mirrors figured to within a fraction of a wavelength of light using a candle and a knife edge. We can do this more easily today with laser light sources for the measurements, but it’s a good reminder that optics by its very nature is a precision measurement game.
Nathan
From: ROBERT WYNNE <robertwynne@...>
Sent: Thursday, March 30, 2023 12:37 PM To: main@apgto.groups.io; Nathan Myhrvold <nathanm@...> Subject: Re: aRE: [EXTERNAL] Re: [apgto] Tilt plate with digitial readout
Nathan I am working through this mornings emails and am about half way through. I responded first to your earlier message only to find other messages had followed. I find this one so far as I've read the most succinct analysis of the problem and various rabbit holes one can get lost.
I believe a laser leveling system coupled to a digital DAQ system w/ display ought to be in the works for this level of precision guidance. Mechanical devices are simply not up to the task at hand. Our laser lab had digital micrometers accurate to .00001 and that was a few years ago. Matters must have improved since.
Best, Robert

