Notes: [1] All modules.  [2] All except eSFR ISO.  [3] Checkerboard and SFRplus.  [4] Checkerboard-only. [A] arctan/tan and 3rd order models are inadequate for measuring wave (mustache) distortion. A minimum of a 5th order polynomial is required.

Pincushiondistortion

Distortion formulas – Modules – TV Distotion and Field of View – Image, Geometry, Distortion, FoV display Radial distortion plot – Distortion Contour plot – Compare results – Links

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Imatest 5.1+ allows you to select between traditional TV distortion (now a part of several ISO standards, including ISO 16505) and SMIA TV distortion. You can make the selection on the left side of the Options II window (button on the lower-right of the Imatest main window). The selection affects only graphic displays (ISO TV distortion = SMIA TV distortion ⁄ 2). Both results are included in CSV and JSON results (for all modules that calculate distortion).

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Pincushiondistortion in optics

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Notes: the third order calculations (Distortion and SFRplus) are less accurate than the fifth order and arctan/tan calculations (i.e., they cannot be as good a fit to the actual distortion.) The green line (SMIA TV Distortion) in the Dot Pattern figure cannot be compared with the other figures.

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Distortion in opticscalculator

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Distortion in opticsformula

Lens distortion and coefficients for correcting it are calculated in the Checkerboard module, which calculates 3rd order, 5th order and tangent/arctangent distortion model along with sharpness and several other factors, Dot Pattern performs CPIQ-compliant distortion measurement. SFRplus measure distortion with almost as much detail as checkerboard. SFRplus distortion results are in the Image, Geometry, Distortion, FoV and Radial distortion plots.  eSFR ISO measures distortion with slightly less precision than SFRplus.

SMIA TV distortion is twice as large (2X) as traditional TV distortion, now included in several standards. The traditional definition, shown on the right, 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).

Progressive Scan. A scanning method in which the sensor scans each lines of the field sequentially (rows 1, 2, 3, 4..., etc.). All image data is recorded in a ...

Distortion is worst in wide angle, telephoto, and zoom lenses. It often worse for close-up images than for images at a distance. It can be easily corrected in software.  For more details see Distortion: Methods and Modules.

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An image display is available in most modules that calculate distortion. In Rescharts it contains a large amount of information (not all distortion-related). Here is an example showing arrows and lines to the corrected image, available for Checkerboard-only. (The arrows & lines can be turned on or off in the More settings window.)

Distortion in opticsexamples

*N is the index of the distortion calculation dropdown menu in More settings. N = fovcalc in ini files for the above modules. It is displayed by the INI File Monitor. N = fovcalc = 5 is for no distortion (no FoV) calculation. 4 is for the best of 1-3. 7 is for the best of 3, 6.

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Imagedistortion inradiography

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Contrast definition: To set in opposition in order to show or emphasize differences.

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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.

The radial distortion plot is available in modules that calculate distortion. This plot has four display options:  1. Delta-r, or 2. Lens Geometric Distortion (LGD), 3. r undistorted (ru), or d(LGD)/d(ru). LGD is shown below.

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SMIA* TV Distortion is calculated from the distortion model equation (and the Distortion parameters for pre-distorted charts).  [*SMIA is the now-defunct “Standard for Mobile Imaging Architecture”, started by Nokia and STMicroelectronics in 2004.]

Barreldistortion

In the equations which apply to several modules, rd is the distorted (measured) radius normalized to the center-to-corner distance. ru is the undistorted radius. r is normalized to the center-to-corner distance.

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A Siemens star is a device used to test the resolution of an Optical instrument. It consists of a pattern of bright "spokes" on a dark background that ...

Field of view (FoV) is calculated for SFRplus, Checkerboard, and eSFR ISO by applying the distortion model equation to the top, side, and diagonal (always r = 1) of the image. In order to calculate FoV in units of distance (cm) a chart geometrical distance has to be entered into the Rescharts More settings window.

The solid lines show results for correction formulas: ru = rd + k1 rd3 (3rd order polynomial; blue); ru = rd + h1 rd3 + h2 rd5 (5th order ploynomial; green); or the arctan/tan equations (red). The best fit (5th order in this case) is shown in bold. With these equations |Δr| often increases as a function of r(distorted), i.e., it tends to be largest near the image corners. The selected value (or the one with the least error, err) is shown in boldface.

At Imatest we have traditionally used the SMIA definition, which has been widely adopted in the mobile imaging industry, because it is self-consistent. In the traditional definition, TV distortion is the change (Δ) of the center-to-top distance divided by by the bottom-to-top distance. In the SMIA definition, both A and B are bottom-to-top distances.

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Algorithm: SMIA TV Distortion is not actually calculated from the upper and lower bars, whose locations can vary considerably in different images. Instead it is calculated from the distortion coefficients using the selected equation, and using virtual horizontal lines located 1% of the image height below the top and above the bottom of the image.

The Measure Tool shape is like a tape measure for your Visio diagram. Use it to precisely measure distances between two points or shapes.

Lens (optical) distortion is an aberration that causes straight lines to curve near the edges of images. It can be troublesome for architectural photography and photogrammetry (measurements derived from images). The simplest approximation is the 3rd order equation, ru = rd + krd3 where rd is the distorted and ru is the undistorted radius. Depending on the sign of k, it can be either “barrel” (shown on the right) or “pincushion.” A mixture known as “mustache” distortion may occur for complex lenses which are better described by a 5th order approximation (ru = rd+ h1rd3+ h2rd5) .

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Opticaldistortionmeaning

Image Quality Factors for Cameras and Displays Sharpness Noise Dynamic range Color accuracy Distortion Uniformity Blemishes ISO Sensitivity Chromatic Aberration Stray Light (Flare) Moiré Artifacts Compression Losses Dmax (Maximum Density) Color gamut  Texture Detail Summary table — corresponding test charts and modules

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A set of images for comparing different Imatest distortion calculations can be downloaded by clicking on distortion_comparison_barrel_pin.zip. These images were created by the Test Charts module, converted to bitmaps of equal size, then equally distorted. The zip file includes barrel and pincushion-distorted images for Distortion, Checkerboard, Dot Pattern, SFRplus, and eSFR ISO. As the Lens Geometrical Distortion figures for the modules show, agreement is excellent. The Dot Pattern module uses the algorithm specified in the Camera Phone Image Quality (CPIQ) specification, but the other modules produce equivalent results.

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