Polar Aligning your PANOPTES Unit!

What is polar alignment?

Polar alignment is the process of aligning the rotation axis of the equatorial mount with the rotation axis of Earth. The interactive plot below shows the path taken by stars on the celestial sphere. The axis of rotation is the line joining the North and South celestial poles.

(Clicking on the plot will take you to Python plotly studio, where you can interact with the plot)

cel_sphere_alldec

Polar alignment is accomplished by pointing the axis of rotation of the mount at the celestial pole (North celestial pole in the Northern hemisphere and South celestial pole in the Southern hemisphere). Once polar alignment is achieved, the mount will rotate along its axis (now parallel to Earth’s axis of rotation) in a direction opposite to Earth’s direction of rotation. Polar alignment helps to accurately offset the motion of the stars on the celestial sphere caused by the Earth’s rotation. The mount’s rotation opposite to Earth’s rotation is observed as the mount ‘tracking’ the stars in the night sky.

We now have a new approach using the drift method to polar align the PANOPTES unit, once it has been deployed and is fully operational with cloud storage set up.

The equatorial mount can be rotated on two axis for polar alignment, the altitude and azimuth. For polar alignment, the altitude adjustment knob on the mount has to be set to the latitude of your location. The azimuth knob has to be set to point towards true North.


Drift method

When mount in polar aligned: That is, the mount’s axis of rotation is perfectly aligned to the Earth’s axis of rotation, the mount can track the stars for very long durations of time without any drift.

Example: See plot shown below for a star at declination = 25 degrees. The mount is perfectly pointed to the North celestial pole (altitude error al = 0.00 deg, azimuth error az = 0.00 deg). The mount tracks a path on the celestial sphere (black line) that overlaps with the star’s path on the celestial sphere (colored points).

cel_sphere: dec 25.0, al  0.0, az  0.0

When mount in not polar aligned: When the mount’s axis of rotation is not aligned to the Earth’s axis of rotation, the misalignment can be in altitude, or azimuth, or both. This misalignment causes the mount to track the stars poorly. This difference in the star path and mount tracking path is observed as a star drifting in the PANOPTES observations. By observing and calculating the direction and magnitude of the drift in stars, we can estimate how much offset in polar alignment the PANOPTES mount has.

Example: See plot shown below for a star at declination = 25 degrees. The mount is misaligned in altitude by 15 degrees and in azimuth by 10 degrees. The mount tracks a path on the celestial sphere (black line) which is now different from the path taken by the star on the celestial sphere (colored points). This difference in path is observed as stars drifting in the PANOPTES observations.

cel_sphere: dec 25.0, al 15.0, az 10.0

The path traced by the mount on the celestial sphere can be computed from the observations taken by the PANOPTES unit, by measuring the magnitude and direction in which the stars appear to drift. This is then compared with models to determine the extent of misalignment in mount altitude and azimuth.


Python notebooks

The equations used for drift alignment and for making the plots shown above, are derived and explained in detail in Python notebooks available on this link. There are three Python notebooks to help understand and visualize the drift method:

  • Notebook 1: Model Derivation

    • Derive the equations necessary to predict the offset in the equatorial mount pointing on the celestial sphere, when it is misaligned in altitude and azimuth.
  • Notebook 2: Model Visualization

    • Using equations derived in Notebook 1, we see how stars would drift as seen by a PANOPTES unit when the equatorial mount is misaligned in altitude and azimuth.
  • Notebook 3: Fitting Model to Data

    • Fit the models derived in Notebook 1 to observations taken by your PANOPTES unit to compute the offset in the mount alignment in altitude and azimuth.
    • Then use the computed offsets to do the polar alignment of your PANOPTES unit.

Note: It is not critical to understand the equations derived in Notebook 1 and Notebook 2 to do the polar alignment of your PANOPTES unit. You only need to follow Notebook 3 to polar align your PANOPTES unit.


Example: Polar alignment of PAN022

Step 1: Python notebook 3

(Refer to the Python notebook for the complete code: PANOPTES - 03 Drift Observation Polar Alignment.ipynb)

  • Part I: Download drift rates from Google cloud for PAN022 observations

    • The metadata includes the drift rates (arcsecond per second) computed from the observations, which will be used to compute how much the mount is misaligned in altitude and azimuth.
    • The code downloads a file PAN022_sampledata.csv with all the metadata. The file in included in this link as sample data to practice the Python notebook with.
  • Part II: Import drift rates from the downloaded .csv file

The hour angle of a celestial object on the celestial sphere is measured similar to the right ascension, i.e. along the celestial equator from the observer’s local meridian, but, in the westward direction. While the right ascension is fixed for every celestial object, the hour angle continually as the celestial object rises and sets in the observer’s sky.
-90° ⇒ star is on the horizon, rising in East
0° ⇒ star is on the meridian, about to cross from eastern side to western side
+90° ⇒ star is on the horizon, setting in West

  • Part III: Create drift rate models and compute alignment errors
    • We create drift rate models for all the stars in PAN022_sampledata.csv
    • The model will help us predict how the observed stars(HA,dec) will drift for a range of alignment errors in the PANOPTES mount.
    • We will compare the model drift rates to observed drift rates to determine the error in mount alignment.
    • The errors computed will be used to polar align your PANOPTES unit.
    • The plot above shows the model drift rates (black line) that best fit our observed drift rates (colored points) for PAN022.
    • We find that PAN022 was misaligned in altitude by -1.05 deg and in azimuth by +0.75 deg. The +/- sign indicates the direction in which the mount is misaligned while the number indicate the magnitude of misalignment.
    • The plot above shows the position of North celestial pole on the sky for PAN022 site (blue circle) superimposed with the position where the mount’s axis is pointing (red open cross circle) to show the extent of misalignment.
    • The mount needs to be moved such that the red circle overlaps with the blue dot, this is the process of polar aligning the mount.

When misaligned in altitude, the mount is either pointing above or below the celestial pole.
When misaligned in azimuth, the mount is either pointing to the right (towards East) or to the left (towards West) of the celestial pole.

Step 2: Polar aligning PAN022

  • Now that we know the direction and magnitude to which PAN022 mount is misaligned, we polar aligned PAN022 in the daytime as shown in this video:

Step 3: Repeat Step 1 & Step 2!

  • Once polar aligned, we ran the unit again for a few more nights and took more observations.
  • We again downloaded the drift rates metadata for the new observations and determined the errors in mount alignment.
  • We polar aligned the unit again.
  • We repeated these steps 3 times in total for PAN022 until we minimised the observed drift rates.
  • The plot above shows the observed drift rates for PAN022 after it was polar aligned.
  • The minor drift rates observed do not fit the drift rate models and is dominated by mechanical flexures rather than by poor polar alignment.

Depending on how well you polar align the unit in each try, you might have to repeat the alignment process 2-3 times until the errors are minimised.


PAN022: Before & After

The videos below show the frames from a single observation obtained by PAN022, before and after the unit was polar aligned. The drifting of stars within a single observation is evident before polar alignment.

Before polar alignment:

After polar alignment:


Link to more information on polar alignment in the PANOPTES user guide:
https://projectpanoptes.gitbook.io/pocs-user-guide/deploying/deployment-guide/polar-alignment

Follow the instructions in the guide to polar align your unit.


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Nice analysis ! Thanks for sharing

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