Lens profiling - trying to understand the process

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So, I’ve read a few tutorials on how to profile your lens to obtain distortion correction parameters for lensfun. Following a combination of these approaches ([1], [2], [3] and [4]), I got reasonable results. However, the values for a, b and c that I got have me puzzled (table below is WIP using Hugin following Wilson Bronger’s method):

Tamron SP 70-200mm f/2.8 Di VC USD G2 (A025)
distortion(70mm)  =  0.00184, -0.01278,  0.00975  
distortion(80mm)  = 
distortion(90mm)  = -0.00071,  0.00153, -0.00562 
distortion(100mm) = -0.00041,  0.00236, -0.00521 
distortion(110mm) =  0.00222, -0.00626,  0.00578 
distortion(120mm) =  0.00016,  0.00052, -0.00192 
distortion(122mm) = -0.00621,  0.02526, -0.03134
distortion(125mm) =  0.00228, -0.00547,  0.00444
distortion(135mm) =  0.00018,  0.00296, -0.00539
distortion(150mm) =  0.00348, -0.01066,  0.01289
distortion(160mm) = -0.00114,  0.00703, -0.00778

My assumption was that my lens has a gradual (physical) change in its distortion upon increasing the focal length, and that this would reflect in a gradual change of the distortion parameters. However, the values of a, b and c are all over the place. They can even differ quite a bit if I redo a calibration in Hugin. Is this okay? Wouldn’t this lead to potentially strange interpolations for intermediate focal lengths?

I haven’t delved into the source code of Hugin to figure out in what way the distortion parameters are estimated, but I assume there is some optimization method going on. Could it be that this method, for example, only finds a local minimum? Would it help to increase the number of ‘straight lines’ that I indicate in Hugin? Should I include vertical lines too? Diagonals?

Or am I simply doing something wrong? I thought that using a photo like below would be able to give me a highly accurate estimation of the lens distortion, but maybe I am wrong. This is taken by placing my camera and lens perpendicular to my pc screen while showing a grid pattern.

_DSC4902
_DSC49026024×4024 4.55 MB

And as an aside: would it be possible to automate the determination of the lens distortion parameters by analyzing the image above and doing some least squares analysis of the lines by comparing it with a reference grid?

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Is there anyone with any thoughts on this? I would really like to clear up my understanding of the methods for lens profiling…

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I know nothing about this. A few question arise:
– How do you know that the sensor+lens is perpendicular to the screen?
– Would it be better if you printed out the grid?

Out of curiosity:
– Do any of the glass elements in a lens ever rotate? (I want to know in general.)
– Does lens profiling have a top, left, right and bottom? I would assume so.

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In many lenses: yes. But lenses (the single glass elements) should be rotationally symmetric, so it doesn’t matter.

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here are the distortion coefficients graphed, as you can see even if the numbers buzz wildly around the zero point, the graph of the distortion still behaves in very sane manner - going from negative distortion to positive distortion as the lens is zoomed.

distortion-coeffs-70to160mm

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I’ve worked on improving and documenting the lens profiling steps. My work in progress is here:

The last comment links to the tutorial I’m working on. I’m also trying to understand the gnuplots for TCA and vignetting …

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