R1 Calibration for the Canon 15mm on a Canon EOS 5D, diagonally
Finally I have done the calibration for the Canon 15mm lens on a Canon EOS 5d slanted diagonally by 33.7 degrees. The calibration is done for an angle of 60 degrees (i.e. 6 pictures around). I haved used the method described by John Houghton at http://www.johnhpanos.com/epcalib.htm  3. A DIRECT APPROACH  FOR SLRs ONLY.
Tilt angle (t) 
Correction (c) 
7.5 
0.7 
5 
1.0 
0.0 
1.65 
2.5 
1.95 
7.5 
2.55 
10.0 
2.85 
The straight line is described by c = 1.629333 0.1232 * t
The correlation coefficient is r = 0.9998688
This is a very good correlation.
So there are two more calculated values:
Tilt angle (t) 
Correction (c) 
12.5 
0.09 
15 
3.48 
Viele Gr?º?üe
Carsten
Re: R1 Calibration for the Canon 15mm on a Canon EOS 5D, diagonally
R1 Calibration for the Canon 15mm on a Canon EOS 5D  Theoretical Considerations
The correction of the R1, when tilted, can be described by a simple trigonometrical formula. In Fig. 1 you can see a camera on the R1 tilted by 10 deg.
http://www.freiburgpanorama.com/material/fig1a.jpg
Let us have a closer look at the triangle in Fig. 2. The lens was calibrated at 0 degrees. So at 0 degrees the NPP (to be more precise  the Least Parallax Point) is located directly above the center of tilt rotation, i.e. the point around which the lens is tilted. Now d is the distance between the center of tilt and the NPP. In the vertical the NPP is located in the center of the lens.
http://www.freiburgpanorama.com/material/fig1b.gif
When the lens is tilted counterclockwise by alpha degrees, then the NPP dislocated from the vertical line and is no longer directly above the center of tilt. To compensate this dislocation, one needs to move the lens by x to the right.
Now d can be measured and alpha is the value of tilt you chose at the R1. From those two values, x can be calculated:
x = d * tan(alpha)* (1)
The factor 1 is used as the unit is moved counterclockwise. When using excel, make sure that alpha is converted to radian instead of degrees.
With this x you can now calculate the corrections at different tilt angles. Simply add x for each tilt angle to the correction value (c) that you have determined at 0 degrees.
For my lens (Canon 15mm) I have determined the correction at tilt angle 0 degrees to c = 1.65 cm.
For my lens I have determined d = 6.9 cm  from this I will calculate x1.
Nick Fan was so kind to send me the precise value of d for my lens as d = 7.226 cm  from this I will calculate x2.
alpha 

x1+c 

x2+c 

measured 
15 

3,499 

3,586 


10 

2,867 

2,924 

2,85 
7,5 

2,558 

2,601 

2,55 
2,5 

1,951 

1,965 

1,9 
0 

1,650 

1,650 

1,65 
5 

1,046 

1,018 

1 
7,5 

0,742 

0,699 

0,7 
12,5 

0,120 

0,048 


As you can see, for both cases, x1+c and x2+c, the calculated values differ less than 1 mm from the experimentally determined values.
Yes there is a difference in the values and I would like to quote a caveat, that Nick Fan has posted to me, when sending his value d:
"The height is 72.26mm. This is a theoretical value. It assumes the lens barrel is perfectly cylindrical, lens ring mount and lens are perfectly concentric etc. The NPP value derived from trigonometry should be used as a guide as starting point of NPP calibration."
Now with an error below 1 mm, the trigonometrical calculation is quite an acceptable starting point for the calibration. This also shows how precise a unit the R1 is! (And how nicely I have attached to lens ring to the lens :wink: )
I have loaded a little excel sheet on my website http://www.freiburgpanorama.com/mat...ection.xls.zip
Simply enter your values for d and c  both values are lens specific  and you will get the correction values to start with in the column x+c.
Viele Gr?º?üe
Carsten
Re: R1 Calibration for the Canon 15mm on a Canon EOS 5D, diagonally
Hi Carsten,
Thanks for working out the equation. I have been too relying on CAD software. Most of time I just measure required values in the software directly. But it is much more efficient to use your equation.
Nick
Re: R1 Calibration for the Canon 15mm on a Canon EOS 5D, diagonally
Hi Carsten.
A quick question.
How did you decide on the 33.7 degrees and how did you position the lens with that kind of accuracy?
Well i guess its 2 questions, sorry
Jim
Re: R1 Calibration for the Canon 15mm on a Canon EOS 5D, diagonally
Hello Jim!
The sensor of the Canon EOS 5D is sized 4368 * 2912 pixel, the ratio is 3/2. I now want to have the widest view going vertically. Thus I have to rotate the Camera so that the diagonal of the sensor is running exactly vertically. With the EOS 5D and the 15mm lens this means that the view from top to bottom covers round about 180 degrees.
To calculate the angel of rotation, some trigonometry is needed. The ratio of the triangle is 2/3  the arcus tangens is 0,588 ind radians, in degrees this is 33,69 degrees.
For an camera with a ratio of 3/4, the arcus tangens is 0,6435 ind radians, in degrees this is 36,87 degrees.
How did I position the lens? I did use my iPhone with the application "iHandy Level". Holding it to the bottom of the camera, you will get the precise angle of rotation.
Viele Gruesse
Carsten