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Imatest Documentation except for its autofocus. Mine doesn't autofocus as reliably as Canon lenses, but it works beautifully on manual. The autofocus problem is plainly visible when working with the distortion chart. Main figure showing modest pincushion distortion The Sigma has modest amounts of pincushion distortion at 125 mm and barrel distortion at 18mm, its widest angle setting. Corrected vertical lines are deep magenta; horizontal lines are blue. The following results are displayed on the left below the image. TV Distortion from the SMIA specification, §5.20. Referring to the image on the right, SMIA TV Distortion = 100( A-B )/B ; A = ( A1+A2 )/2 The box on the right is described in the SMIA spec as "nearly filling" the image. Since the test chart grid may not do this, Distortion uses a simulated box whose height is 98% that of the image. Note that the sign is opposite of k1 and p1. SMIA TV Distortion > 0 is pincushion; < 0 is barrel. SMIA vs. traditional TV distortion Thanks to Mark Butterfield for pointing out that SMIA's distortion definition differs from the traditional TV industry definition by a factor of two. The traditional definition is shown in the illustration on the right, which has been adapted from the publication "Optical Terms," published by Fujinon. The same definition appears in "Measurement and analysis of the performance of film and television camera lenses" published by the European Broadcasting Union (EBU). SMIA TV distortion is double the traditional TV distortion definition. SMIA TV Distortion 352 of 451
Imatest Documentation Imatest will continue to use the SMIA definition, which has been widely adopted in the mobile imaging industry. We prefer it because it is self-consistent. In the traditional definition, TV distortion is the change (∆) in the centerto-top distance divided by by the bottom-to-top distance. In the SMIA definition, both A and B are bottom-to-top distances. Although any number in this list can be used as a measure of distortion, SMIA TV distortion may be the best choice because it's the easiest to visualize. Coefficient k1 from the equation, ru = rd + k1 rd 3 where r is normalized to the center-to-corner distance. k1 = 0 for no distortion; k1 < 0 for pincushion distortion; k1 > 0 for barrel distortion. Coefficients h1 and h2 from the fifth-order equation, ru = rd + h1 rd 3 + h2 rd 5 . The selected area must contain at least five horizontal and vertical lines. The Lens Distortion correction coefficient and scale factor for Picture Window Pro. The sign is the same as k1. The scale factor is the value that includes as much as possible of the original image without including areas outside the image. It is less than 1 for barrel distortion and greater than 1 for pincushion. The calculation used for plotting the corrected lines. Selected in the input dialog box. 3rd order, 5th order, and Picture Window Pro are the choices. Picture Window Pro uses a tangent/arctangent model of distortion, which works well for a variety of lenses, including fisheyes. ru = tan(10 p1 rd )/ (10 p1 ) ; h1 > 0 (barrel distortion) ru = tan -1 (10 p1 rd )/ (10 p1 ) ; h1 < 0 (pincushion distortion) Where p1 is the correction coefficient. Using Taylor series, we can show that it is similar to the third-order model, tan(x) = x + x 3 /3 +2x 5 /15 + ... ; tan -1 (x) = x - x 3 /3 + x 5 /5 - ... ( x 2 < 1) ; ru = x + 100 p1 2 x 3 /3 + ... (barrel); ru = x - 100 p1 2 x 3 /3 + ... (pincushion) , k1 ≈ sign( p1)*100 p1 2 /3 for small values of k1 and p1. k1 and p1 diverge for large values. The plot includes arrows that illustrate the change in radius when distortion is corrected. Distortion was too low on the above plot to make the arrows visible. They are illustrated in the plot below for a large amount of simulated barrel distortion. You can try different line display calculations to see the difference. 353 of 451
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