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    Young-Hoo/ Biomch-L colleagues ...

    Young-Hoo has identified a "problem" which recurs quite frequently--not
    only in sports/biomedical environments, but also in industrial and
    military environments. Here are some thoughts ...

    The refraction "problem" associated with underwater photography can be
    "solved" in two ways: a) physically, and b) analytically. However, a
    combination of the two methods will generally provide the best results.

    Refraction, per se, is not a problem--without it we would be reduced to
    pinhole cameras. Refraction is in fact the very foundation of all
    lenses. The only difference between the optics of the underwater "problem"
    and an "in-air" problem is the air/water or glass/water interface.
    However, the result is the same--rays bend as they do at a glass/air

    So what's the problem? The real problem is that the lenses we want to
    use underwater were originally designed for a glass/air interface at the
    outermost element. When the lens is used underwater rays are bent far
    more than they would be in an air environment. The result is ...
    optical distortion, the lens aberration. In order to use the lens
    underwater we generally introduce another "element" to keep the water
    from reaching the lens. This element may be a flat glass plate (a
    plano-plano lens), or a dome (a concave-convex lens), or some other
    combination. But the fact remains, that outer shield becomes another
    element of the lens. If you (as they say) "judiciously" select and place
    that outer element you can (theoretically) eliminate the refraction
    "problem". I'll not go into the details here, but those with an interest
    in the topic might want to obtain copies of the following ...

    Walton, J.S. "Underwater Tracking in Three-Dimensions Using the Direct
    Linear Transformation and a Video-Based Motion Analysis System."
    Proceedings of the 32nd International Technical Symposium on Optical and
    Optoelectronic Applied Science and Engineering. Volume 980: "Underwater
    Imaging". San Diego, CA, August 1988.


    Reinhardt, A. and Walton, J.S. "The Recovery and Utilization of
    Space-Suit Range-of-Motion Data," Proceedings of the 18th Intersociety
    Conference on Environmental Systems. SAE Paper 881091. San Francisco, CA
    July 1988.

    Reinhardt, A. "Results and Applications of a Space Suit Range-of-Motion
    Study. NASA Technical Memorandum 102204. Ames Research Center, Moffett
    Field, CA. July 1989.

    (These two reports describe how the DLT was used with four underwater
    cameras to measure the range-of-motion of space-suits in the underwater
    test facility at the Marshall Space Flight Center, Huntsville, AL.)

    Very briefly, if you place the center of curvature of a dome at the front
    node of the original lens, all rays will appear to pass directly though
    the dome at right-angles to the surface of the dome. In this case, the
    rays are not bent, regardless of whether the outer surface of the dome is
    in air or water. (All of this is an oversimplification to get the basic
    idea across.) Thus all of the required assumptions of the DLT are met.
    I've used it, and it works well.

    Now the refinements. It is difficult to place the center of curvature of
    a dome over the front node of the original lens. It is possible to get
    quite close (see the first paper described above), but the result is a
    crude first estimate at best. After the dome has been added and
    adjusted, what you have is a compound lens (with one extra element) with
    some extra optical distortion and probably some decentering distortion
    (because the center of curvature of the dome is not precisely aligned
    with the axis of the original lens.) So to improve matters, simply use
    the standard mathematical models for optical and decentering distortion
    to "clean-up" the data. I think you will find the results can be

    One last note. I've seen some papers advocating the use of "periscopes"
    in the last few years. These will allow you to get further back from the
    subject and thus use longer lenses, but periscopes do NOT deal with the
    refraction at the air/water interface. Furthermore, they severely limit
    the field-width. Rays associated with longer lenses will cross the
    air/water interface with LESS distortion of the rays because they strike
    the surface of the water less obliquely, but at the margins of the image
    the distortion may be significant. This can cause problems if you plan to
    use any form of automatic tracking based on the DLT.

    Hope all this helps.

    Jim Walton
    Chairman, SPIE Working Group on
    High-Speed Photography/Videography and Photonics
    Industrial Liason, 22nd International Congress of High-Speed
    Photography & Photonics, Santa Fe, NM 1996.

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    On Fri, 15 Sep 1995, Young-Hoo Kwon wrote:

    > Dear Colleagues on Biomch-L:
    > I am currently writing a paper on the role of the light refraction at the
    > water/air interface on the accuracy of the space reconstruction in the
    > underwater motion analysis using 2-D and 3-D DLT. I've read some papers
    > dealing with 3-D underwater motion analysis of the Olympic swimmers using the
    > DLT, underwater panning videography, shape of the face of the waterproof
    > camera housing, etc. Although people seem to already use the DLT in the
    > underwater motion analysis quite a bit, I haven't found any paper dealing
    > with the nature of the refraction and the potential problems due to the
    > refraction.
    > As you know, the DLT is based on the so-called 'collinearity condition' which
    > requires the camera node, object and image to form a straight line. But this
    > rule is violated in the underwater motion analysis due to the refraction.
    > Some investigators have reported studies using the DLT but without telling
    > the magnitude of the calibration error. Some investigators tried to connect
    > the above-water space and the below-water space using a technique which seems
    > to have potential problems.
    > Are there any in-depth studies reported on the nature and role of the
    > refraction in the underwater motion analysis which are out of my reach? If
    > any, they will be most valuable for my paper. I also invite your comments on
    > this matter.
    > Looking forward to hearing from you,
    > Young-Hoo Kwon, Ph.D.
    > Senior Researcher
    > Korea Sport Science Institute
    > 223-19 Gongneung-Dong
    > Seoul, 139-242
    > KOREA
    > Phone: +82-2-9709-555
    > Fax: +82-2-9709-502
    > Internet: