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Evaluating the lunar observations on July 31^st 2023 at Calanais I

Introduction

On tis web page, the ground proofing of the 3D scenery of Calanais I site within Stellarium will be done at only three levels:

• Determining the azimuth (rotation of vertical axis) of the 3D laser scan
  
• Determining the tilt (rotation of East-West axis) 3D laser scan to give the apparent altitude
  
• Determining if the whole 3D laser scan has to be vertically and East-West transformed with respect to Cnoc and Turso's DSM.

These three levels are hopefully enough to get a good South viewing skyline (from the end of the avenue: near stone 8 and 19). More rotations/transformations could be needed, but that cannot be determined with the present camera location.

Steps to ground proof the Calanais I 3D scenery

On July 31^st 2023 some 23 photos were taken (by E. Rennie) to record the Moon going over/through the Calanais I site. These photos are being used to ground proof the Calanais I 3D scenery in Stellarium using the three mentioned levels.

The following steps have been used for the preparation

• Camera
• FUJIFILM; Digital Camera X-T3
  
• Geotagging (aka GPS Date/Time) works only through the Fuji App, which is on the smartphone. The timing is though all over the place, so it can't be used.
  
• The EXIF data (Create Date and Shutter Speed) of the photos has been used to calculated: a photo's Average time (= [EXIF Create Date] + Offset + [EXIF Shutter Speed]/2).
• Times are in EXIF not defined properly (is it before the shutter is opened or after: see Section Time Tags). As the Shutter speed was relative long (in many cases around 20sec) it is important to know the definition of the EXIF Create Date. It has been verified that for a FUJIFILM E510 and FUJIFILM X-T3 the EXIF Create Date is the moment the camera button is pressed.
  So the average time is half the Shutter speed after the EXIF Create Date (assuming the photo has been averaged over the whole exposure).
  
• Photo taking workflow
• The clock on the camera is checked (to determining the Offset) just before the photo session with a Windows 10 system (which had just been synced using NTP). The Offset is found by taking a photo of the Windows time/clock screen (including seconds!).
• Place camera on tripod as near as possible near stone 8 and facing towards the circle. Zoom, so that the whole site is in the photo (around 50deg FOV). Keep zoom and position of camera during the whole session the same.
• Take photos at discrete positions of the Moon: left, middle or right of a certain stone contour (also left, middle or right).
  
• The clock on the camera is checked (checking again the Offset) just after the photo session with a Windows 10 system (which had just been synced using NTP). The check is done by taking a photo of the Windows time/clock screen (including seconds!).
• Timing
  
• For each photo, with its Average time, the Moon's azimuth is calculated: azimuth_EXIF.
• Tools
  
• The 3D scenery of Calanais I (version: callanish1_Readjusted_20230505, including Cnoc an Turso) in Stellarium (version 23.2) has been used.
• ARCHAEOCOSMO (with Swiss Ephemeris and Excel) has been used to calculate the Moon's apparent position (azimuth).
  
• PSP (Coral Paint Shop Pro X9) was used to layer Stellarium screen grabs on the photos
• Animated gif files were used to show the matching of a photo with Stellarium screenshot.

Aligning the azimuth

• The camera location (part of View in Stellarium) needs to be found in the 3D scenery. This can be determined iteratively by mapping the stones in a photo over the stones in the 3D scenery (using PSP).
  
  
• Method 1: Discrete Moon positions (the taking of photos was also planned at such positions)
  
• Stellarium was used to determine the azimuths of the 3D scenery's discrete stone-features in relation to the discrete position of the Moon (left edge, right edge, or middle): azimuth_Dis
• The azimuth_Dis and azimuth_EXIF were compared (azimuth_EXIF - azimuth_Dis), producing difference Rot_VertDis.
• Method 2: Continuous Moon positions
  
• In Stellarium the time was determined when the Moon was at a similar position as in the photo. The Average time was used to determine the Moon's apparent position: azimuth_Con.
• The azimuth_Con and azimuth_EXIF were compared (azimuth_EXIF - azimuth_Con), producing difference Rot_VertCon.
• Method 1 is expected to be less accurate as it uses only discrete Moon and stone positions, Method 2 really looks at the real positions od Moon and stones in the photo. But the two methods should provide similar averages; the standard deviation (1σ) of Method 1 might be somewhat larger (due to the courser discrete Moon and stone position) than of Method 2.
  
• Method 2 is the preferred method.
  
• The standard deviation (1σ) provides an idea of the accuracy one can reach using photos and EXIF data.
  
• If the median difference (Rot_VertCon) is zero, the 3D scenery is correctly aligned in Stellarium.
  If not, one needs to rotate the 3D scenery in the vertical axis with the median difference: using convergence_angle ~ from_grid - Rot_VertCon in scenery3d.ini. This needs to be iteratively repeated (start again at the first bulletin in this section) until the 3D scenery is properly aligned in azimuth.

Aligning the apparent altitude

When the azimuth of the 3D scenery is aligned, the apparent altitude of the 3D scenery needs to be aligned:

• First one needs to make sure that the height of the camera location (part of View in Stellarium) is correct.
  
• This can be checked best where nearby stones (e.g. stone 7, 6, 5 and 4) and far away stones are overlapping (e.g. stone 30)
  
• When the height of the camera (in View of Stellarium) is correct, we use a photo where a specific part of the Moon (e.g. bottom rim) just touches a top of (far away) stone (e.g. stone 27). This gives Rot_EW.
  
  
• If the Moon does not touch that stone properly in 3D scenery (e.g. DSCF8622), one will need to rotate the 3D scenery in the East-West axis with Rot_EW.

Positioning the whole 3D laser scan

In the photos the Cnoc an Turso's skyline can be seen and this must be aligned with the Cnoc an Turso's skyline constructed by its DSM. In Stellarium one can determine the angle difference: Cnoc-XXXangle.
This can be transformed into a vertical transformation using:

Trans_vert = DistanceCnoc * tan(Cnoc-Vertangle)

with DistanceCnoc around 175m.

This can be transformed into a East-West transformation using:

Trans_EW  = DistanceCnoc * tan(Cnoc-EWangle)

Transforms in East and North direction are positive numbers.

Remember this displace is due to general height error of the 3D laser scan and the resolution of the Cnoc an Turso 25cm DSM.

First iteration

This first iteration (based on callanish1_Readjusted_20230505) will derived the results for azimuth, apparent altitude and height of whole 3D laser scan. Hopefully this first iteration gives for all three adjustment a value of (close to) zero.

Azimuth

The distribution of Rot_VertCon and Rot_VertDis are derived for different convergence_angles.

convergence_angle=from_grid (-4.03255°)

We started the analysis with the default convergence angle (from_grid) and this gave the following results:

convergence_angle=-4.21667°

After doing a few iterations the best convergence_angle was -4.21667°.

This gives an median Rot_VertCon of around 0deg (with a standard deviation of 0.1deg) for Method 2. As expected, the standard deviation has not changed much compared to other convergence_angle.

Apparent altitude

Positioning whole 3D laser scan (transform)

Derived data from photos

Here is the azimuth related information (convergence_angle = -4.21667°) from the taken photos (click below picture to see it larger):

Findings first iteration

Initial adjustments (at the point of stone 8) for the Calanais I 3D laser scan (and keeping the Cnoc an Turso DSM the same) are:

• Aligning azimuth (Rot_VertCon): a vertical axis rotation of some -0.184deg (due to lacking georeferencing of Calanais I).
  Its standard deviation is relatively large (0.1deg, equivalent to 30sec), and this is due to the Method's inaccuracy of visual inspecting the photos. Observations with binoculars and stopwatch might produce more precise values.
  
• Aligning altitude (Rot_EW): an East-West axis rotation of some -0.118deg (due to lacking georeferencing of Calanais I).
• Aligning with Cnoc an Turso (Trans_vert): a vertical transform of some -44cm (due to lacking georeferencing of Calanais I and DSM resolution of Cnoc an Turso). This value does looks too large.
  In general, this transformation might not be fully correct (certainly for positions closer to Cnoc an Turso).
  

These three adjustments might need an iterative process (as things might be depending on each other). The resultant scenery is: callanish1_Readjusted20230817.

Second iteration

The first iteration (based on callanish1_Readjusted_20230505) did not provide the correct azimuth, apparent altitude and height of whole 3D laser scan. The following sections provide the results of version callanish1_Readjusted20230817.
Hopefully this second iteration gives for all three adjustment a value of (close to) zero.

Azimuth

Rot_VertCon = +0deg

Apparent altitude

Rot_EW = +0.03deg

This unexpected difference could be related to the fact that an up-down rotation (azimuth) of 0.26deg (in first iteration) will also change the apparent altitude (around 0.029deg). This 0.029deg is close enough to the above 0.03deg.

Positioning whole 3D laser scan

Trans_vert = +31cm, but transform adjustments will be postponed to following iteration, as there exist some uncertainty of the method:
Trans_vert = +0cm

Trans_EW  = +0cm
Trans_NS  = +0cm

Third iteration

The second iteration (based on callanish1_Readjusted20230817) did not provide the correct apparent altitude. The following sections provide the results of version callanish1_Readjusted20230818.

Azimuth

Rot_VertCon = +0deg

Apparent altitude

Rot_EW = +0deg

The above match is good enough, we need to remember that stone 27 also has an artefact (the 3D laser scan does not fully match the photo), which needs to be solved first.

Positioning whole 3D laser scan

Fourth iteration

The third iteration (based on callanish1_Readjusted20230818) did not provide the correct apparent altitude of Cnoc an Turso. The following sections provide the results of version callanish1_Readjusted20230818-2.

Azimuth

Rot_VertCon = +0deg

Apparent altitude

Rot_EW= +0deg

Positioning whole 3D laser scan

Trans_vert = +0cm (for now this is ok-ish).

This 10' could be a transform into the East-West direction of:

Trans_EW = -50cm at the end this was changed to Trans_EW = -30cm
TransNS  = +0cm

Fifth iteration

The fourth iteration (based on callanish1_Readjusted20230818-2) did not provide the correct east-west transform of Cnoc an Turso. The following sections provide the results of version callanish1_Readjusted20230818-3.

Azimuth

Rot_VertCon = +0deg

Apparent altitude

Rot_EW = +0deg

Positioning whole 3D laser scan

Trans_vert = +13cm

An extra 4' could be a transform into the West direction of Trans_EW  = -20cm, but this will mesh up the rest of Cnoc an Turso's skyline. So no Trans_EW = +0cm

Summary of results of fifth iteration

• there sometimes are thin brown borders (smaller than 1arcmin) on the right sides of stones (e.g. stone 42 and 29). So there is not a 100% match between the 3D scenery and the photo. This is thus within an accuracy of around 1 arcmin.
  
• Nearby stones (e.g. 7, 6, 5, 4) are just as well positioned in the 3D scenery (compared to photo) as more far away stones (e.g. 32, 43, 41, 29).
• The Moon's azimuth is on average ok (sample of 23 photos), but it has a large standard deviation of around 6arcmin. So Rot_VertCon is ok, but its standard deviation not. This is too large; see conclusions for some remedies.
• The Moon touches top of stone 27 nicely (within 1 or 2 arcmin) in the 3D scenery. So Rot_EW is ok.
  
• The overall Cnoc an Turso's skyline (light green) in 3D scenery is still some 3arcmin too high compared to the photo's (darker green). A Trans_vert = 13cm (3D laser scan higher up) would possibly be needed.
  
• Cnoc an Turso's peak near stone 26 is in the 3D scenery some 4arcmin too much to the West compared to the photo. The rest of both Cnoc an Turso's skylines peaks and dips look to match ok-ish. This could be due to the 25cm resolution of the Cnoc an Turso's DSM, so no additional Trans_EW.
  

Sixth iteration

The fifth iteration (based on callanish1_Readjusted20230818-3) did not provide the correct vertical and east-west transform of Cnoc an Turso. The following sections provide the results of version callanish1_Readjusted20230818-4.

Azimuth

Rot_VertCon = +0deg

Apparent altitude

Rot_EW = +0deg

Positioning whole 3D laser scan

Trans_vert = +0cm
Trans_EW  = +0cm
Trans_NS  = -18cm (this amount would result in an 0.5arcmin reducing the seen width of far away stones).

Some findings:

• There are larger brown borders around stones than in the fifth iteration, so less good matching. Could this be due to the Trans_NS?
  
• IMHO there is not enough information to base Trans_NS on.
  
• Cnoc an Turso's skyline has overall the right apparent altitude (comparing green with light green), so Trans_vert is now correct
• Cnoc an Turso's peak near stone 26 (light green) could still be somewhat more to the left in the 3D scenery. But we leave this, as it will mesh up the rest of Cnoc an Turso's skyline (possibly due to 25cm resolution of Cnoc an Turso's DSM).

Seventh iteration

The sixth iteration (based on callanish1_Readjusted20230818-4) did not provide the correct vertical and east-west transform of Cnoc an Turso. The following sections provide the results of version callanish1_Readjusted20230821.

Azimuth

Rot_VertCon = +0deg

Apparent altitude

Rot_EW = +0deg

Positioning whole 3D laser scan

Trans_vert = +0cm
Trans_EW  = +0cm
Trans_NS  = +0cm

Overview of iterations

Experiences

Overall accuracy

We have been able to position the 3D laser scan properly within the 3D scenery. The accuracy is around 1 or 2 arcmins (the Moon's azimuth looks to have somewhat lager standard deviation: 6arcmin. this is due to inaccurate timing).

Sequencing of adjustments

The best sequence of adjustments, by reducing interdependencies, of rotations and transforms is:

• 3D laser scan Rot_Vert
• 3D laser scan Rot_EW
• Cnoc an Turso DSM Trans_EW
  
• Cnoc an Turso DSM Trans_vert
  

1. An exposure time of less than 1 sec would give more crisp touch, vanish, reappear and release moments of stone and Moon (less movement blur of Moon); exposure time must be such that the Moon's contour is just visible against stone contours. Zoom-in in such a way that there are some 10 stones visisble (FOV~10deg). Clear skies also make crisp photots, but we don't have that in hand. Use binoculars to determine the touch/vanish/reappear/release moments.
   
2. A video (with timestamp in picture), this would be some 60 minutes of continuous video (not over-exposed for the Moon).
3. Using binoculars (as a kind of theodolite) and a stopwatch (on a sync-ed phone); will make sure one gets the touch and release moments of stone and Moon more accurately. 
4. Other?

Method 1 will be utilised in the next Moon path.

Determining remaining rotation and transform

Of course there are still a transform (Cnoc an Turso's DSM in North-South direction: Trans_NS) and rotation (3D laser scan around North-South axis: Rot_NS) possible; these are not yet investigated as these can't really be determined using the camera location at stone 8. One would need a camera location at stone 33 or 23 (and times of resp. set or rise events of a celestial object).
A realistic Trans_NS can't really be determined (as the effect of this is marignal on celestial directions).
The rotation Rot_NS will not have effect on the Cnoc an Turso's DSM, more on the positioning of 3D laser scan with the celestial object.

Artefacts in the 3D laser scan

A few stones in the 3D laser scan have some triangulation artefacts (these were found as they were handy for aligning the celestial object: red areas); stone 32 (error some 2arcmin: due to possibly wrong normal of some triangles); stone 26 (error some 2 to 3arcmin: missing left side top and small bit on the right side top); stone 27 (error some 2 to 3arcmin: missing left side top); and stone 28 (has a mushroomed top).

These errors make up a part the accuracy of the whole 3D scenery (expected to be around 1 arcmin), so they are not that serious except if these missing stone contours are used for defining 'touching' moments. Upto now no stone contour that were missing, were used.

Position of stone 33A (resolved)

A check needs to be done about the position of stone 33A in the 3D laser scan (by making a photo of the east row of stones: 33A to 30). The position of that stone does not map the skyline made by Ponting (1981, Fig. 2.10) and looks not to match sometimes between the 3D scenery and a skyline photo. A photo check (DSCF8791, FOV 53deg and stones 33A to 30 in the middle of photo) has been done and the locations of stones 33A to 30 are mapping the 3D scenery's.

Replace skyline in direction of View B (resolved)

A SRTM 1" based skyline is not accurate enough in the direction of View B. A DSM for that skyline has been included with good results. Permission has been gotten (Oct. 2nd, 2023) from bluesky to utilised this DSM.

Acknowledgments

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