Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

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hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

I am going to write down my attempt at quick and easy polar alignment in Singapore. Clear night skies are luxurious here and no one wants to waste extra time on polar alignment especially if you don't have a fixed telescope setup.

The purpose is not only to save myself (others alike) from the PA pains but also to denounce the disadvantages of EQ mount users in the equatorial regions.

The northern hemisphere amateurs are blessed with a bright polar star. A great deal of tools can pinpoint its exact location relative to the true north celestrial pole.

The southern hemisphere amtaeurs are less advantageous and they have to settle the alignment using a few faint stars in the Octans constellation. But, better than nothing.

Nothing in either celestrial polar fields is accessible to us in the equatorial regions for polar alignment. A usual get-around is to roughly align the mount and then resort to the drift alignment technique to precisely align the mount axis to the celestrial pole. Drift alignment is painstaking, even with tools like PhD2.

Adding to all these is the fact that every time I look at the electronics polar scope bundled with the mount, deciding whether to let it go (hey, who in the region wants it anyway?), or just to keep feeling very sorry about the beautiful but useless device?

This project aims to defy all this. The objective is to be able to align mount+scope reasonably well to below 10arcmin or down to 1~2arcmin level without drift alignment.

The basic idea is as simple as this: instead of using bright stars for reference, let's use fixed terrestrial objects -- at least hundreds of meters away in the direction of the pole.

(to be continued)
Last edited by hhzhang on Sat May 23, 2020 9:55 pm, edited 3 times in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

Before I move on to writing the theory and practices, let me report on the first night test on May 20, on the roof of an HDB block with a nice unblocked view towards the north pole.

It was smoother than expected when I set up and aligned the gears. After two adjustments using Acturus and Spica, the GOTO became fairly accurate -- not spot on but OK.

And then I checked the alignment using PhD2 drift alignment --- my first-time use of the tool actually. The initial drift report showed an ~10' error for Azimuth -- I was quite happy with that. After two rounds of adjustment -- it came down to ~1' error -- that trend line looked pretty flat.
Then I moved on to drift the Altitude. Without any adjustment, it was already as low as ~1' error!

Then I returned the mount to the zero position, retook and compared the polar scope image with the one from before drift alignment (i.e. just using GOTO based alignment), the image was shifted by 12px and 3px.

This indicates my simple quick GOTO-based alignment just missed 6' in Az and 1.5' in Alt, in the initial test by a newbie.

Not bad a start!
Last edited by hhzhang on Fri May 22, 2020 10:39 am, edited 3 times in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

As mentioned earlier, the idea is as simple as aligning the EQ mount with reference to terrestrial objects instead of a celestial one.
This logically leads to the questions:

How do we determine (measure) where my EQ mount is pointing?
How do we determine (measure) where the celestial pole is with reference to the terrestrial object?

To answer the two questions, we need to examine all the parts in the system and how they relate to the questions.

Here goes the list.
1 An equatorial mount with a RA axis and a DEC axis
2 A polar scope (electronics, i.e. with a camera) attached to the mount’s RA axis
3 An OTA sit in the saddle/attached to the mounting plate of the mount
Keep in mind that
 All three parts have their respective axes pointing at different directions.
 The polar scope and the equatorial mount are bounded and have a fixed angle from each other. OTA is a different story and can ride on the mount at any angle.

To tackle the two questions above, we are going to break down our solution to a sequence of tasks.
1. To precisely determine the angle between the mount’s axis and that of the polar scope (one-time only)
2. To align the OTA with the mount axis using the computed mount axis position in the polar scope view, while (this is important) keeping the RA in the level position (every time you set up the system)
3. To align the mount axis direction with a star using GOTO and the OTA (one-time only for a new site)
4. To capture the ZERO-POSITION polar scope view for future references (one-time only for a new site)
5. Optional: to refine it using drift alignment and re-capture the ZERO-POSITION polar scope view for future references (one-time only for a new site)

While we are staying in the low altitude regions, the disadvantage of the inaccessibility of the celestial pole region can be turned into the advantage of the pole direction associated with particular terrestrial object/feature/image pixels.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

Precision is all about fighting errors here and there. So here is a quick check on some of the errors I can measure/estimate on my system.

The polar scope. I have measured the pixel size and determined that each pixel is about ~32.73". Roughly half of arcmin. This seems quite good (using advanced techniques we can measure sub-pixel shift -- but that is beyond the scope of the work)

The leveling of the RA. I don't have any precision device but just a 3 dollar spirit level. I checked how sensitive I could tell if it is tilted a tiny bit. With a few pieces of paper of measured thickness going in and out of the end of the device, I determined that I could tell a tilt as small as 2.4' to 4.8'. OK, this looks something we need to pay special attention to. Either we go get a precision level device (someone at 5-arcsec sensitivity!), or we can think of how to compensate this error in alignment techniques -- after all, this is highly possible since the tilt from perfect level will produce a consistent shift in RA only (if the mount axis is perfectly aligned) wherever you point your scope using GOTO (assuming accurate GOTO slew).

For the time being, let me just use this cheap level. It then will only get better!

What else? The OTA may not be a limiting factor -- my scope at 805mm FL and a flattened focal plane can provide arcsec level precision. An overkill.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

Now let's get started with determining the mount RA axis in the polar scope.

Get ready some handy tools: a tubular spirit level (mine is a cheap $3 one and when combined with my mediocre vision, produces >2.4arcmin sensitivity to tilt), and of course a computer.

Before you move on, make sure the screws are tightened so that mount will not move/tilt however you rotate RA. I have learned a hard lesson from my mistake here and wasted lots of time and brain cells to figure out what went wrong.

Then I like to align the polar scope level to the mount level. You will definitely feel much better after this– although theoretically this is not necessary. After all, we are obsessed with precision and beautiful alignment.

For this, I first level the tripod using the spirit level and confirm the mount top surface (which stays stationary when you rotate RA or DEC) is leveled at the same time. Next I level the mount RA by placing the level on the saddle top -- of course Alt and Az adjustments are irrelevant here and I just use the RA move. Finally, let's carefully turn the polar scope (after removing the cap and screws, …) to make the image leveled too -- for that I resorted to some long horizontal features in the distance I trust.

Rotate the RA to a few positions and take a picture at each.

Now it’s image analysis time.

To understand how this is done, we can visualize the scope – attached to the RA axis, revolving around RA. That means there is one pixel (or subpixel) on which the image feature stays stationary however you rotate RA. In other words, you are trying to locate the rotation axis in the images.

This is a typical image registration problem and can be readily resolved if you have the proper software. I don’t bother to use them – anyway this just needs to be done one-time.

So my technique is simple and can be implemented using a calculator--- although Python or Matlab comes very handy and much preferred.

The principle is this. When an image feature (an object) rotates around an unknown axis from one position to another, the line connecting the positions is perpendicular to the line that goes from the middle of the connection to the rotation axis.

The solution is straightforward. Compute the line functions (those going through the rotation axis), and compute where they intersect with each other. Well, due to errors here and there, the intersect would drift a little bit from a pair of lines to another.

On my scope, I selected three image features and computed the intersect points of those through-axis lines. The standard deviation of the intersect location is just about a pixel (after removing a couple of measurements seemingly corrupted).

The polar scope cam captures images at 1280x960px resolution. The position of the rotation axis is [634,496]. So the above measurement means that the true rotation axis is [-8, 16]px away from the centre of the image.

I used the estimate of some object’s physical size in the view and Google maps for distance estimate, and used its image size to compute the pixel scale. It is 32.7’’/px. So that means the above error is [4.36’, 8.72’].

This tells us, if we are naive and use the centre of the image for granted as the mount’s axis direction, we would be wrong by 9.75'!

By the way, my mount is CEM40. Non-EC.

Now I know this. For northern hemisphere users of mounts of the same grade, if the error of the polar scope direction is not compensated/corrected, their mount's RA axis aligned using the scope could deviate from the true pole direction by nearly 10'!
Last edited by hhzhang on Sat May 23, 2020 10:55 pm, edited 2 times in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

We need to stay reasonable when expecting precision target.

Is 1-arcsec precision a reasonable target?

I doubt it. 1-arcsec is a mere ~4.5mm lateral distance across the view at a distance of 1KM. Would your scope be able to stay spot on such a small visual/image feature? Considering there are atmosphere turbulence and shaky images at a high magnification needed for such precision.

And there is flex in the mount and OTA. A consumer-level portable setup is likely not sufficiently solid to stay within 1-arcsec from the target when you rotate RA and DEC to different positions.

If you have a trusty autoguiding solution, you may relax the precision to multiple arcmin level.

If you do unguided imaging, then it depends on your imaging scale/pixel size and sub-explosure length.

For something as a reference, I recommend a handy online tool: http://celestialwonders.com/tools/polarErrorCalc.html

Playing with different inputs, here are some interesting result.

For a drift rate of 2.5arcsec/min, the PA error needs to be 9.55arcmin.

For a drift rate of 1arcsec/min, the PA error needs to be 3.82arcmin.

I think it's reasonable to assume the seeing condition here would have a bigger impact than the PA error under similar conditions. And the mount's RA accuracy (so called PE) is also a bigger limiting factor.

My conclusion: 10arcmin precision will be good enough for subexposures of 1-min length each.

But I am still aiming for <5arcmin error in PA. Obsession, maybe.
Last edited by hhzhang on Sat May 23, 2020 9:56 am, edited 1 time in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

Before moving on to quick and easy GOTO-based alignment, let's examine the theory and assumptions.

This is clear: your GOTO will be absolutely accurate provided all the three things are absolutely accurate at the same time
A. Your leveled RA zero position
B. The GOTO function
C. Your PA alignment

The RA zero position gives the GOTO function the crucial reference position to which the gears slew. As mentioned earlier, we may expect a couple of arcmin error down to a few arcseconds depending on your access to either low-quality or high-precision instrument.

The GOTO function basically computes the apparent coordinate of the star for the present observation site at the present time, and convert the coordinate to the angles that RA and DEC need to move across, and slews RA and DEC accordingly. The first step is about the astro algorithm and I don't want to question its accuracy for our amateur use, the second is straightforward. The question is really about the 3rd step which is electrical-mechanics motion. I have no idea how precise that could be. But I think it is reasonable to assume it is 1-arcmin or below accuracy level unless you have a really bad unit. I mean I choose to stay optimistic and have some trust in my lovely, beautifully engineered mount.

Most likely during our adjustment towards 10 (5) arcmin accuracy PA, the PA misalignment itself is the overwhelming error factor here in the overall GOTO error. Only when it goes down to a few arcmin error region, the other two factors might speak relatively aloud in the overall effect (error). In that case, if we choose to omit the factor B, as said earlier, the factor A might still possibly be compensated in a certain way during the GOTO-based PA process. Just at this time I don't bother to work out and validate a solution -- perhaps in the future when I am more obsessed with the PA precision I will try to settle it.

Now the question is, how to use GOTO and OTA to correct the PA alignment error.

From the above discussions, we assume the PA alignment error itself is the dominant source of the GOTO error. And through the OTA we will observe how much the OTA direction (more precisely, the mount axis direction in the OTA view -- most likely not at the exact centre) deviates from the target object.

A simple mind is this: if we carefully turn the alt/az screws to bring the mount axis direction onto the target object, would it at the same time bring the ZERO POSITION mount axis direction to the celestial pole?

The answer is yes. Unfortunately the thing is not always simple. It depends on the location of the object.

Hopefully this is the last round of correction here

I think there are only two+1 regions we need to pay attention to (I mean to avoid).

The (Alt=90 or 270, Dec=0) regions: the PA's alt error would have very trivial effect on the object's shift in alt (i.e. GOTO error in alt) for small PA error.

At the exact point of Alt=90 or 270, Dec=0, the effect is zero. Thus you cannot recover the alt error information from the GOTO error.

Oh, don't forget to avoid the zenith. The AZ is indefinite at that point or imprecise in the vicinity. You can hardly link the GOTO error to the PA error in AZ.

Further away from the three regions, you are ok: the GOTO error is far more sensitive to the PA error in both AZ and ALT.

Hey, are you thinking of the best possible region for the GOTO target? It is the point most distant from all the three regions at the same time. Yes you are absolutely right, it is no other than the pole itself!

No. We are not back to zero. No, we cannot access the pole star fields from the equatorial regions. But, we can make use of plenty of other regions.

So there are three regions to avoid. Choose a star from out of these regions and GOTO slew to it. Align the mount RA axis (in the view through OTA) to the star using Alt and AZ screws. Now if you slew back to ZERO POSITION, your mount RA axis should point at the true pole if all the other sources of error are naught.

The above is a bit intuitive. Oh, I think I need to provide some proof using simple reasoning. I always prefer something intuitive to equations.

First, assume the object is not in that three spots/regions so the GOTO error is sensitive to the PA error and there is no apparent ambiguity. (An ambiguity example is that if the object is near zenith and you raise the RA axis in atl, it will cross over from the north of the zenith to the south; even though there is no Az motion itself, the AZ measurement has changed dramatically)

Imagine you have corrected the GOTO position. You slew back to ZERO POSITION. Are you sure it is the true pole?

Answer is this: if it is not true pole, you slew back to the same object and it will move along the same arc -- just backward, but wait, if you move the same CORRECT RA and DEC angles but from the true pole, it will also reach the same CORRECT spot? Would that be possible? Note that mount is assumed perfect level: RA zero position absolutely accurate, and the PA error is small.

That is impossible. Draw the great circle arcs and you will understand.
Last edited by hhzhang on Sat May 23, 2020 9:42 pm, edited 13 times in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

I probably spent too much time on the writing here. Just wished it could be of help to some of the other equatorial-region users of EQ mounts.

But with all the above posts, it has become straightforward to implement the techniques in the PA practices. So it is time to just quickly revisit the steps already written in the 3rd post. Slightly amended.

1. To precisely determine the angle between the mount’s axis and that of the polar scope (one-time only)
2. To align the OTA with the mount axis using the computed mount axis position in the polar scope view, while (this is important) keeping the RA in the level position (every time you set up the system)
For me, I identify a prominent terrestrial object/feature in the polar scope view and bring that to the identified mount axis position using Alt/Az. Then I slew DEC to bring OTA view to be exactly aligned with that feature in the vertical (alt) direction. And I take note of the bias from the centre of the view -- you may choose to use OTA camera for more precise alignment,

DON'T forget to set it the ZERO POSITION for the mount now.

3. To choose a bright star, GOTO, and use Alt-Az to bring the mount axis direction to the star (one-time only for a new site)
4. To slew to ZERO POSITION and capture the scope view for future quick references (one-time only for a new site)
5. Optional: to refine it using drift alignment and re-capture the ZERO-POSITION polar scope view for future references (one-time only for a new site)

On a site revisit, the PA would be super easy: we just position the leveled mount and align the polar scope image with the reference image (from Step 4 or better, from Step 5). For this, I have written a simple Python script that blinks the two images.

The same site, I mean the same tripod position. If you shift the tripod-mount 27cm lateral and your reference terrestrial object is 1KM away, you will be 1 more arcmin off.
Last edited by hhzhang on Sat May 23, 2020 10:56 am, edited 3 times in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

# Don't know how to attach a file. So here goes the py script.

# !!! The forum automatically removes the indent spaces for the code lines :(( Be aware. You need to add those spaces back for the script to run properly.

# -*- coding: utf-8 -*-
# Image blinking for quick alignment of scope view with a reference image
# You need to install opencv for python:
# pip install opencv-contrib-python
# You may need to create your own reference image 'refimg'
# You may need to tune your explore

import numpy as np
import cv2

import sys
import time

refimg = cv2.imread(cv2.samples.findFile("iPolarCamView_AftPhd2DriftAlign.png"))
if refimg is None:
sys.exit("Could not read the image.")

refgray = cv2.cvtColor(refimg, cv2.COLOR_BGR2GRAY)
refshape=refgray.shape

cv2.imshow('frame',refgray)
time.sleep(0.5)

cap = cv2.VideoCapture(1)
# you may need to manual set the exposure or choose to use auto exposure
cap.set(cv2.CAP_PROP_GAIN,512)
cap.set(cv2.CAP_PROP_AUTO_EXPOSURE,0.25)
cap.set(cv2.CAP_PROP_EXPOSURE,0)


if(not cap.isOpened()):
print('cannot open camera')
cap.release()
cv2.destroyAllWindows()
sys.exit()

while(True):
# Capture frame-by-frame
ret, frame = cap.read()

frame=cv2.resize(frame,(refshape[1],refshape[0]))

# Our operations on the frame come here
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
cv2.putText(gray,'Live View',(0,25),20,1,0)

# Display the resulting frame
cv2.imshow('frame',gray)
k=cv2.waitKey(500)

if k & 0xFF == ord('q'):
break
cv2.imshow('frame',refgray)
if cv2.waitKey(500) & 0xFF == ord('q'):
break

# When everything done, release the capture
cap.release()
cv2.destroyAllWindows()
Last edited by hhzhang on Sat May 23, 2020 9:35 am, edited 1 time in total.

hhzhang
Posts: 21
Joined: Sun May 10, 2020 4:11 pm
Favourite scope: 115mm APO

Re: Towards Quick and Easy Polar Alignment for Equatorial-Mount Users in Equatorial-Regions

Post by hhzhang »

Job done.

Wish for clear night skies.

Sadly the wet weather persists and I seem to miss the galaxies season totally.

Not a fan of nebulosity, what shall be my targets for the summer?

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