I'm writting you from Spain, with respect to your camera Ultracam XP. I am not a end-user of the camera myself but, as the provider of technical support for an aerotriangulation program, I have had access to several aerotriangulations of projects flown with the XP camera. I, together with a customer of mine, have found a systematic distortion in the camera. Its main component is an asymmetric radial one, the one which I call c5 in my model. It is not part of the usual decentring distortion. Its form is:

DR=c_5scos(2theta),   s=r/r_max,

the value of the c_5 coefficient has proven to be somewhere between 7.5 and 9 (its units are microns), and its mean quadratic value all over the photograph is 3.5 microns. The form of this component of distortion can be seen in the image attached. As will be made clear in the examples that follow, this component is so conspicous in the Ultracam XP mostly because of the distortions in the y photo coordinate on the middle-top and middle-bottom areas of the photograph.

Of the several flights to which I have had access, here are for instance the results of one of them comprised of 450 photographs, computed with (SC) and without (NC) self-calibration. All the values are microns.

    A posteriori standard deviations of photo coordinates:
        (NC): 2.5
        (SC): 1.9

    Mean values of the residuals in each area of the photograph:

        (NC)
                                          x       y

                             area 0:     0.2    -1.5
      |-----|-----|-----|    area 1:     0.4     2.9
      |  0  |  1  |  2  |    area 2:    -0.3    -0.3
      |-----|-----|-----|    area 3:     0.1     0.4
      |  3  |  4  |  5  |    area 4:     0.1    -0.3
      |-----|-----|-----|    area 5:    -0.1    -0.1
      |  6  |  7  |  8  |    area 6:    -0.0     0.6
      |-----|-----|-----|    area 7:     0.3    -3.7
                             area 8:    -0.5     0.9


        (SC)
                                          x       y

                             area 0:    -0.2    -0.1
      |-----|-----|-----|    area 1:     0.5    -0.1
      |  0  |  1  |  2  |    area 2:    -0.3     0.3
      |-----|-----|-----|    area 3:    -0.3     0.3
      |  3  |  4  |  5  |    area 4:     0.2    -0.3
      |-----|-----|-----|    area 5:     0.1     0.1
      |  6  |  7  |  8  |    area 6:     0.0     0.4
      |-----|-----|-----|    area 7:     0.1    -0.4
                             area 8:    -0.2     0.1

Note specially the values of the mean y residuals in areas 1 and 7. Here is the same pattern exhibited for another flight, on this occation of 101 photographs:

        (NC)
                                          x       y

                             area 0:     0.1    -1.1
      |-----|-----|-----|    area 1:    -0.2     3.2
      |  0  |  1  |  2  |    area 2:    -0.2    -1.2
      |-----|-----|-----|    area 3:     0.2    -0.5
      |  3  |  4  |  5  |    area 4:     0.1     0.2
      |-----|-----|-----|    area 5:    -0.2     0.3
      |  6  |  7  |  8  |    area 6:     0.0     1.5
      |-----|-----|-----|    area 7:     0.3    -3.1
                             area 8:    -0.4     0.8

        (SC)
                                          x       y

                             area 0:     0.1    -0.2
      |-----|-----|-----|    area 1:    -0.2     0.4
      |  0  |  1  |  2  |    area 2:    -0.0    -0.2
      |-----|-----|-----|    area 3:    -0.3    -0.5
      |  3  |  4  |  5  |    area 4:     0.3     0.2
      |-----|-----|-----|    area 5:     0.1     0.2
      |  6  |  7  |  8  |    area 6:    -0.1     0.2
      |-----|-----|-----|    area 7:     0.4     0.0
                             area 8:    -0.4    -0.2

In this case the a posteriori deviations are 3.8 and 2.7 microns respectively.

Other systematic distortions have been detected, such as the ones I call a2 and a3 from the radial symmetric part, but none of the importance of the c5 one.

The computations were carried out with the aerotriangulation program of which I am author: Aerotri, common here in Spain.

Yours sincerely,

Javier A. Mgica
