Discussion with Rick Nowell - Sept 2017
William Smith
16 Posts
Thanks for the quick reply, Esko;
We have recent camera calibration info here (2016). I had to repair the camera since, but I don’t think I moved it much.
And the 2016 wSentinel software allows me to go into measurement mode
I can move a mouse pointer around the screen, and it gives me a readout of (Xpixel, Ypixel); Azimuth, Elevation
I can also overlay a grid.
Orientation:Camera sensor screen 640x480 pixels.
Centre of horizon symmetry: Pixel coordinates (330, 234)
Dr. Howell calculates the camera centre of view coordinates (320, 240) is tilted at 3 degrees to the North; and rotated 4.4 degrees to East. Our calibration beacons suggest it is tilted 2 degrees to North, and rotated 2 degrees East.
|
Centre of View |
x-pixel |
y-pixel |
elev (deg) |
azimuth (deg) |
|
Dr. Howell |
330 |
234 |
3N |
4.4E |
|
Rick |
330 |
234 |
2N |
2E |
Lens distortion: Zenith Radial Distance polynomial: 1st and 2nd order terms for variable r.
It's polar type (r, theta), from centre; except theta is assumed symmetrical, thus distortion given as only a function of r, and not a function of theta. R is in pixels.
Alt(rc - ro) = ar + br^2 (where rc is R corrected, and ro is centre of view, at sky zenith)
Alt(rc - ro) = 0.3210r + 2.142E-4 r^2
Elliptical Eccentricity: no correction, assumed circular.
My own estimate:
Radial scale: Alt(deg) = 0.3676 (r) + 20.6E-3 Cos (Bearing); where r is in pixels.
Eg. point on Western horizon at (575,235): Alt(deg)= 0.3676 (574-330)= 90.06
Elliptical horizon eccentricity: aspect (y/x) =(478-14pixels)/(577-87pixels)= 0.949 facing bearing -2deg.
Next Table shows calibration values generated by Dr. Andy Howell's calibration; compared with my own estimates beside. Dr. Howell requested 60 second composite star photos taken at hourly intervals over a night, and located bright stars with their Time, Az, Alt and pixel locations. Then he generated a radial pixel match curve with a RMS great circle error of 0.58 degrees.
|
|
x-pixel |
y-pixel |
elev deg |
azimuth deg |
dist m |
height m |
|
Woodtech |
310.716 |
10.104 |
1.73252 |
2.71848 |
|
|
|
(my estimate=) |
310 |
9 |
1.11 |
2.80 |
6031 |
1042 + 15 = 1057m |
|
TV Tower R |
498.750 |
90.750 |
3.93909 |
308.929 |
|
|
|
(my estimate=) |
497 |
89 |
3.76 |
309.04 |
5174 |
1251 + 28 = 1279m |
|
TV Tower L |
500.750 |
92.250 |
3.73855 |
308.296 |
|
|
|
(my estimate=) |
499 |
92 |
3.62 |
308.35 |
5160 |
1251 + 15 = 1266m |
MY REFERENCE POINTS:
Beacon Location:
Method: the Great Circle Orthodrome path for bearing angles and Haversine Great Circle method for distance, using the beacons GPS coordinates. Height of the towers was estimated since they are fenced off. GPS readings taken South and West of their bases and extrapolated to inside the fence. Overall, uncertainty in bearing should be around 0.02 degrees. Uncertainty in elevation about 0.2 degrees.
Meteor Camera coordinates are 49° 31' 03.18"N, 115° 44' 37.10"W, at an elevation of 940.0m (within 10cm). Enter 49.51755, -115.74363 into Google Maps and zoom in and you'll see the crosshair exactly on the college roof vent beside the camera. Double checked with GPS.
Woodtech Hill Beacon Calibration Point: I hiked up Woodtech Hill with a GPS for calibration purposes in 2013.
Tower base is at 49.57172ºN, -115.73954ºW, 1042m. Or: 49º 34' 18" -115º 44' 22"; Plus the tower height, which I estimate about 9 times my height of 1.7m=15.3m. So add 1042+15m= 1057m. So Vector from camera is 6.031km at azimuth 2.803 degrees and elevation (1.11 degrees plus/minus 0.01).
Refractive error in elevation for beacons just 6.03km away at 3.0 degrees elevation would be about 0.011 degrees.
E(arcsec)= 16.3 (L P/T2)(0.0342 + dT/dh)/COS q;
L= dist in metres; P= pressure(mB)=905@940m; T(kelvin)=273+20=293; q= angle from horizon in degrees; assume moist air at dT/dh = 5 degrees/ 1000 m.
Although stars at the greater distance outside the atmosphere (L=200km) would appear 0.23 degrees higher.
Curvature of Earth over 6.03km; at 940m elevation: Subtract 0.03 degrees.
If L= distance in km, r is radius of Earth (6371km), s is surface drop; then
L2= 2 r s + s2; then s= 0.00285km.; or a 2.9 metre dropoff, or Arctan(2.9/6031)= 0.028 degrees.
TV towers site. Circles mark the two towers which are 70m @ 31deg apart.
The Left TV/Cell Tower beacon at 309 degrees relative to camera, measures by GPS: [49.54633N, 115.79972W, 1251m]= 49° 32 47N, 115° 47 59W; Distance 5.160km at bearing 308° 21’ 02”= 308.3506°. Left Tower base altitude (road): 1251m= 4104 ft (the ground is 100 feet higher than the 4000 ft marked on the topo map).
Establish a baseline scale to estimate tower height in the next photo:
The Green vector points to the college camera view at 308deg. The red line joins the Left Tower (0m,0m) to the Right Tower (36m,60m)= 70m@59° degrees. Bearing (90-59)=31°. For apparent separation, project the actual 70m separation vector onto a plane 90° degrees to the college view (308°+90°)=38°. 70m COS(38-31°)= 69.5m. Our view is within 7 degrees of a right angle, so there isn’t much difference in apparent spacing. .
In the next photo, the height of the towers can be estimated since we know they are separated by 70 m. For the Right Tower this will establish a scale of 19/47; height is thus 28m above the road at Left Tower. By similar method, Left Tower would be (10/47)*70 or 15m. Thus top of Left Tower at 1251m + 15m= 1266m. Since college elevation is 940m, then Tower Angle= Arcsin [(1266- 940m)/5160] = (3.62 +- 0.01) degrees.
The Right Tower with double beacons, lit up: GPS: 49.54684N, -115.79933W, 1192m (3911 ft) = 5.174km at 309° 02' 11” (309.0364°).
The base of Tower 2 sits 59m down the hill, lower, and 70m @ angle of 31 deg apart. However, it can be simply described as 28m higher than the road at Left Tower. Thus top of Right Tower at 1251m + 28m= 1279m.
Elevation= Arcsin [(h- 940)/5174] = 3.76 degrees.
Refractive Error: Distance 5.174km; angle up from horizon 3.76°
E(arcsec)= 16.3 (L P/T2)(0.0342 + dT/dh)/COS q; Assume summer moist air lapse rate at dT/dh = 5 degrees/ 1000 m
E= 16.3 (5174m 905mB/2932) (0.0342 + .005) COS 3.76°= 34.8 arcsec; 34.8 arcsec/3600= 0.0097 degrees.
Curvature of Earth over 5.174km; at 940m elevation would be -0.0232°: If L= distance in km, r is radius of Earth (6371km), s is surface drop; then
L2= 2 r s + s2; then s= 0.00210km.; or a 2.1 metre dropoff. Angle is Sin A= (2.1m/5174m). A= ArcSin (2.1/5174)=0.0232° down.
A few years ago, I compared the TV towers bearing against a visually close star (Elnath) in Auriga, that checked as bearing 309.25 degrees at elevation of 3.0 degrees. But the superimposed photograph/starmap method was only good to about 0.2 degrees, even though refraction was allowed for. I averaged it to the centre point.
This used a starmap generated by Meade Autostar Suite Astronomer's Edition 3.19, in high precision topocentric mode, which compensates for elevation, refraction, aberration, precession, nutation. The starmap was scaled to overlay the Nikon camera photograph, then merged.
Rick
From: andyho49@gmail.com <andyho49@gmail.com> on behalf of Andy Howell <andyho@mindspring.com>
Sent: May 21, 2016 3:29 PM
To: Nowell, Rick
Cc: admin@goskysentinel.com
Subject: CRITICAL UPDATE - Re: Allsky Camera calibration Cranbrook BC
Rick,
Do the below numbers look better? I looked into the issue. It turns out that WSentinel’s V.1.2.1 assumption that optical center = (320, 240) is the probable reason for the discrepancy in azimuth. The upcoming release of WSentinel incorporates the true optical center (AKA “center of projection”). It turns out that the true center is located at (324.69304, 233.55940), as found by the calibration algorithm.
With this important change, we get the following AZ-EL values of the beacons, which are in much better agreement with what you said:
Woodtech Beacon
Enter px = 310.716
Enter py = 10.104
elev = 1.73252
azim = 2.71842
TV Beacon #1
Enter px = 498.750
Enter py = 90.750
elev = 3.93909
azim = 308.929
TV Beacon #2
Enter px = 500.750
Enter py = 92.250
elev = 3.73855
azim = 308.296
Does this look right now?
J. Andreas (Andy) Howell
Gainesville, FL 32605
o: 352-389-4903
m: 352-359-1539
On Sat, May 21, 2016 at 12:32 AM, Nowell, Rick <NOWELL@cotr.bc.ca> wrote:
Hi Andy;
Thanks, I entered those values. Switched grid on. Images are attached of grid on and calibration settings.
Using mouse cursor, I clicked on those two beacons and got:
Woodtech beacon at 2.8 degrees N, reads (309,10) Az 358 El 1.85
TV beacon at 309 degrees N reads (305,58) Az 305.58 El 4.68
Strange. This contradicts my own calibration references. Is there a minus sign error somewhere? It looks backwards. East is left, right?
Woodtech should be at (310, 9) Az 2.78 El 1.0 (no refractive adjustment for El)
TV beacon at (498,90) should be at Az 309.1 El 3.0
You estimate the camera is tilted at 3 degrees to the North then; and rotated 4.4 degrees to East
You mentioned: “chip center at coordinates (320, 240) is not on the camera’s optical axis”
Check, I get (330, 234) for my centre of horizon symmetry.
Zenith Radial Distance polynomial: 1st, 2nd and 3rd order terms. I assume you are using order like “degree”, the power of the variable r.
I assume it's polar type (r, theta), from centre; except theta is assumed symmetrical, thus distortion only a function of r, not a function of theta.
(rc - ro) = ar + br^2 + c r^3 (where rc is R corrected, and ro is centre, sky zenith)
= 0.3210r + 2.142E-4 r^2 + 0 r^3
Anyhow, there seems to be an error here somewhere.
Rick
From: andyho49@gmail.com <andyho49@gmail.com> on behalf of Andy Howell <andyho@mindspring.com>
Sent: May 19, 2016 10:30 PM
To: Nowell, Rick
Cc: admin@goskysentinel.com; Dwayne Free
Subject: Re: Allsky Camera calibration Cranbrook BC
Hi Rick,
Thanks for the images. Here are the parameters to plug into WSentinel:
|
Rotation (deg) |
-1.06 |
|
Degrees per pixel 1 |
0.3210 |
|
Degrees per pixel 2 |
2.142E-04 |
|
Degrees per pixel 3 |
0.0000000 |
|
Apparent latitude |
52.39432 |
|
Apparent longitude |
-111.35202 |
|
True latitude |
49.51750 |
|
True longitude |
-115.74360 |
The calibration used 80 calibration points (stars) from the two nights of data you sent. The RMS great circle error is 0.58 degree, which is the size of the typical difference between the actual and modeled star positions. Now you can click on any pixel in the scene to read the pixel's AZ-EL directly from WSentinel. Also, the calculated AZ-EL of meteor tracks will be much more accurate.
A characteristic of WSentinel model fits is that AZ error is virtually zero at 45 degrees elevation. Below 10 degrees, however, the maximum azimuth error increases to +/- 1.5 degrees or perhaps larger. Using this calibration model, it will be interesting to see how the calculated azimuths of the radio towers compare to their expected values.
If the camera were vertical, then the apparent lat/lon should equal the true lat/lon. The fact that they do not equal each other reflects a combination of two factors: (1) The camera is not perfectly vertical, and / or (2) the chip center at coordinates (320, 240) is not on the camera’s optical axis. You also indicated that the image is slightly oval, which the WSentinel model doesn’t take into account, because it assumes azimuthal and radial symmetry.
"Degrees per pixel 1, 2 and 3" are the coefficients of the 1st, 2nd, and 3rd order terms in the polynomial model of zenith (radial) distance. In general, the 3rd order term doesn’t improve the model fit, which is why it’s set to zero.
It does seem camera gain is set too low, because most 1st magnitude stars (e.g., in the Big Dipper) were not visible. Still, the calibration turned out quite well with a “typical” error of just 0.58 degree.
- Andy
J. Andreas (Andy) Howell
Gainesville, FL 32605
o: 352-389-4903
m: 352-359-1539
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