## Short Subjects

This area is intended to address topics that may be of interest to the photogrammetric community using Reports of Calibration produced by the Optical Science Laboratory (OSL) for a film mapping camera. We plan to discuss two to four new topics per year and will provide updates to existing topics about new procedures, new technology, or clarification of visitor questions. If anyone has a potential new subject for discussion, wants to change the way information is presented in the Report of Calibration, or wants to change the order of visiting the topics listed below, please provide feedback.

The list of topics, in order of incorporation, is as follows:

- Lens Distortion
- Extrapolating Beyond the Calibration Limits (in work)
- SMAC Math Model (in work)
- In Situ Validation of Calibration (in work)

**Lens Distortion**

The OSL is planning to include residual plots of symmetric radial, decentering distortion, and total lens distortions with each Report of Calibration. From two very recent calibration reports, the lens distortion parameters were used to generate sample plots of distortion corrections at the intersections of a regular grid. These vectors show the amount of correction that will be added to a measurement on a photo to minimize error due to lens distortion. This grid has a spacing of about one centimeter across the photographic area resulting in a 22- by – 22 matrix of distortion vectors. The matrix has been trimmed to those points falling within the boundaries defined by the fiducials and the calibration limit at the 40 degree field angle.

The distortions in a metric film camera lens are determined at the OSL by means of one of two software packages. For the 6-inch focal length lenses, the Simultaneous Multiframe Analytical Calibration (SMAC) package is used to produce two sets of calibration coefficients, commonly referred to as the Ks and Ps, and a table of corrections at various field angles for both types of distortions. The K-coefficients are used in a formula to compute symmetric radial distortion and the P-coefficients to compute decentering distortion at any point within the photo. For all other focal length (i.e., 3.5-inch, 8-inch, and 12-inch) lenses, the USGS package is used to produce a table of corrections at various field angles for symmetric radial distortion. There is no computation done for decentering distortion in this package.

For the symmetric radial distortion, there is a disjoint between the tabular values presented in Section II of the calibration report and the corresponding value computed by means of the K-coefficients (also in this Section II). They produce the same magnitude value, but the SMAC value must be added to an image measurement (when working in image space) and the tabular value must be subtracted (i.e., they have the opposite sign). Since both of these methods have been used in commercial packages for quite a few years, it does not make sense to change the way they are presented in the Report of Calibration. The burden then falls on the user to use the data correctly.

For the decentering distortions, the tabular values in Section II of the calibration report only provide an idea of the magnitude of the distortion since the actual distortion cannot be easily tabularized. Decentering distortion has a non-symmetric radial component and tangential component normal to the radial. It is the maximum unsigned tangential component at each of the field angles that is shown in the table. The maximum decentering radial component can be up to three times the magnitude of the maximum tangential component within the calibration limits of the photo.

To summarize, unless we get a lot of resistance to including residual plots along with the Report of Calibration, you will start seeing them this year. Also, please validate how your photogrammetric software package(s) handle the application of lens distortion data; it could be critical to your solutions. For instance, some commercial packages require the sign on the parameters to be reversed to make the distortion corrections apply properly within their software. It is imperative to understand how the software packages (homegrown or commercial) using these data apply the distortions and thus ensure the best possible photogrammetric solutions. Finally, just because the tabular decentering value in the Report of Calibration may seem small, do not automatically disregard its usage since the maximum distortion correction can be more than three times that value.

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