Distortion analysis

This feature requires the Analyze-License

General
Display the radial distortion as profile
Display the tangential distortion as profile
Display the distortion as grid

General

Verzeichnungs-Analyse

With the tab-control you can select between three different graphical representations of the distortion data:

  1. Radial distortion profile
  2. Tangential distortion profile
  3. Distortion grid

In addition the following buttons are available:

Export view ...: Saves the displayed diagram as a Tiff-file with a resolution of 1600 * 1200 pixel.
Distortion profile ...: Saves the entire distortion profile as ssv-file, which can be imported into any conventional spreadsheet application.
The data correlates to the curves of the diagram "Radial distortion profile" and "Tangential distortion profile".
See below for further information.
Distortion grid ...: Saves the distortion (in pixel) as a grid over the image area.
The data correlates to the curves in the diagram "Distortion grid".
See below for further information.
Close: Closes the analysis window.

The two check boxes affect the representation of the indicated curves:

Fixed Range: If checked, all distortion- and vignetting-curves are drawn in the same coordinate range. This simplifies the optical comparison between different graphs.
Smooth Curve: The curves are not only drawn by the calculated knots, but also by spline interpolated values, what results in a smoother curve shape.

Display the radial distortion as profile

Radial distortion profile

The graph shows the distortion factor shapes for 20 different directions, originating from the distortion center. The distortion factor is the factor, by which the vector between the distortion center and the undistorted point must be multiplied scalarly, so that it points to the appropriate, radially distorted, position.

By using the direction control


the curve, which corresponds to the adjusted direction, is highlighted in the chart. Drag the mouse with pressed button to move the direction pointer. The 0° angle shows to the right and the positive rotation direction is counter clockwise.

Example:

We have the above distortion curve (selected direction: 0°) and the distortion center (997 / 773).

For a distortion-free image we want to know the location on the distorted image, from which the point (1700 / 773) shall obtain its color-value.

The vector, which points from the center to the point (1700 / 773) is calculated as follows:
(1700 - 997 / 773 - 773) = (703 / 0)
Consequently its length is 703 pixel.

The corresponding radial distortion factor can be read off from the red curve: ~0.9872

Thus the vector from the center to the distorted point is:
(703 * 0.9872 / 0 * 0.9872) = (694.00 / 0.00)

Transformed to the image coordinate system (with the origin in the top left corner), the vector is approximately:
(694.00 + 997 / 0.00 + 773) = (1691.00 / 773.00)

Note that this calculation did not consider the tangential distortion.

The data, which corresponds both to this representation, and the representation of the tangential distortion profile, can be found in the ssv-table "Distortion profile ...".


Display the tangential distortion as profile

Tangential distortion profile

The graph shows the tangential distortion portion as rotation around the distortion center in degree. A positive angle means a counter-clockwise rotation. According to the radial distortion profile, the values are read off dependent on direction (selectable with the direction control) and distance to the distortion center.

Example:

We have the above tangential distortion curve (selected direction: 0°), and the distortion center (997 / 773).

We want to know the tangential distortion portion for the point (1700 / 773), for which the radial distortion portion was already determined in the previous example.

The vector, which points from the center to this point, was determined to (703/0), with the length of 703 pixels.

Based on the red curve the appropriate rotation angle can be read off: ~0.02°

A vector with the polar coordinates length = 703, angle = 0.02° has the cartesian coordinates
X = 703 * cos 0.02° ~ 703.00
Y = 703 * sin 0.02° ~ 0.25

Transformed to the image coordinate system, the tangential distorted position results in approximately:
(703.00 + 997 / 0.25 + 773) = (1700.00 / 773.25)

If the combination of the tangential and the radial distortion of one point is requested, it is recommended to likewise use the polar coordinate system for the calculations.

The data, which corresponds both to this representation, and the representation of the radial distortion profile, can be found in the ssv-table "Distortion profile ...".


Display the distortion as grid

Distortion grid

This representation illustrates the distortion with the help of two grids put over the photo surface. The undistorted variant is drawn in black, whereas the distorted variant is drawn in red color. Thus strength and kind of the distortion can be estimated on a view. In addition this representation shows the distortion center marked by a small cross.

The data, which corresponds to this representation can be found in the ssv-table "Distortion grid ...".


Save distortion profile in ssv-table

With the button "distortion profile..." the complete distortion data of the current calibration set is saved in a ssv-table (Semicolon Separated Value).

A ssv-table is a text file, in which the columns are separated by semicolons (in contrast to a csv-table, where the columns are separated by commas). For viewing and processing the contained data any conventional spreadsheet application is suitable, like e.g. OpenOffice Calc or Microsoft Excel.

In order to import the ssv-table into OpenOffice for example, proceed as follows:

  1. File >> Open ...
  2. If necessary select the file type All files (*.*)
  3. Select and confirm the requested ssv-table
  4. Filter selection: "Text CSV" and confirm
  5. Select the character set "Unicode (UTF-8)" and exclusively check "Semicolon" under separator options and confirm

The file contains following data:

  • Calibrations-Set name
  • Resolution of the calibration-pictures
  • The distortion center for each focal-length
  • The maximal and average residue distortion for each focal-length
  • One table with the radial, and one table with the tangential distortion values (in 20 different directions and 24 distances from the center) for each focal-length

Save distortion grid in ssv-table

Note: Please read in the previous section "Save distortion profile in ssv-table", how to import ssv-tables into OpenOffice or Excel!

The distortion grid table contains the data, which corresponds to the above representation of the distortion grid. For each focal length exists both a table for the point shift in X and a table for the point shift in Y-direction. Therefore the distortion for certain locations on the image area can be read off directly with this dataset.

If possible, the distortion grid data should be preferred to the distortion profile data, since the accuracy of the grid data is sometimes higher (this data is also used in the HQ-mode). The reason is that it mainly forms the calculation basis for the distortion profile.

Continue with "Analyze vignetting"