On Lenses and Perspective Types

Discussion in 'Digital Photography' started by David Ruether, Jun 22, 2007.

  1. [This article will soon appear on my web page in the articles
    section at - www.donferrario.com/ruether/articles.html, but
    I include it here since there has been so much recent discussion
    (and misconception...) here on the topic...]

    "On Lenses and Perspective Types"

    There are various types of perspectives. Some are rectangular,
    spherical, reverse spherical, orthographic, cylindrical, and

    The pure rectangular perspective type can be defined as one in
    which straight subject lines remain straight in the image regardless
    of how the lens is turned (but, in common with most other
    perspective types, subject element sizes in the image will not
    remain constant as the lens is turned). An example of a camera
    that makes perfect rectangular perspective images is the pinhole

    The pure spherical perspective type can be described as one in
    which small subject elements remain the same size in the image
    regardless of how the lens is turned on its axis, and all subject
    straight lines off axis of the lens will curve away from the image
    center, progressively more the further they are from the lens axis.
    A lens with moderate spherical perspective (or it may be full, but
    with only a small part of the full perspective area being used to
    make the image) is said to have "barrel distortion", but this may
    not truly be distortion (it may be just unwanted). This is most
    common in many wide angles, some fast normal lenses, and most
    zooms toward the shorter FL ends of their zoom ranges.

    A rectangular perspective lens will show the same magnification
    of a small distant subject element placed in the image center as a
    spherical perspective lens (fisheye) of the same FL will (this is
    also true for the other perspective types), but as one looks away
    from the lens image centers (without rotating the lenses) at a series
    of identical objects placed in planes perpendicular to the axes of
    the lenses, the fisheye will show progressively decreasing off axis
    subject magnification and the rectangular perspective lens shows
    constant magnification of these same subject elements. Therefore,
    there is more included subject area (a greater angle of view) with
    the fisheye compared with a rectangular perspective lens of the
    same FL. Or, a fisheye of longer focal length can have a wider
    angle of view than a rectangular perspective lens with an even
    shorter focal length.

    A reverse spherical perspective type of lens will show straight
    subject lines as straight lines in the image only so long as they
    pass through the optical axis of the lens and image center (of an
    unshifted lens - but this characteristic of showing straight image lines
    of subject lines that cross the image center is true for all perspective
    types). Otherwise, the image centers of off-axis subject straight
    lines will curve inward toward the image center, progressively more
    the further they are from the image center. Image edge magnification
    of subject elements will increase, reducing the angle of view. This
    type of perspective is most often seen in modest amounts (called
    "pincushion distortion") with some telephotos and most zooms
    toward the longer FL ends of their zoom ranges.

    An orthographic perspective type of lens shares many of the
    characteristics of the spherical type, but its off-axis curvature is
    somewhat more mild over most of the image area, and then more
    extreme toward the image edge.

    Panoramic cameras that use a swinging lens shooting through a slit
    (which is generally used as a focal-plane type of shutter) produce
    a cylindrical type of perspective, defined as one that shows straight
    subject lines that are perpendicular to the direction of the lens swing
    as straight in the image, but as curved lines in other axes. These
    can produce very wide but natural-looking landscape and cityscape
    photographs if handled well. In digital, stitching of several images
    shot in a sequence along one axis can approximate this perspective

    Isometric projection has essentially no perspective. The effect
    can be approximated by the use of VERY long telephoto lenses,
    which appear to "smash" everything together into one plane, with
    no differentiations due to distance size relationships (everything
    appears to be in the same scale, regardless of distance). This can
    also be seen in old Japanese paintings and drawings of buildings,
    often viewed from above.

    The various perspective types may cause straight lines of subjects
    running off axis of the image center (of an unshifted lens relative to
    the sensor) to be curved, which causes a shift in image magnification
    away from the center of the image, permitting a greater (or lesser)
    angle of view to be photographed using some lens perspective types.

    In all images, made by all lenses, the focal lengths are rated similarly
    (by the distances of the lens' optical centers from the sensors at
    infinity focus). This number, in millimeters, is used in combination
    with the sensor format diagonal dimension and perspective type to
    get an idea of what the resultant angle of view is. Complicating
    this, though, is that many lenses are not accurately rated for FL,
    may change FL with focus (many zooms and macro lenses do this),
    and/or do not accurately follow their perspective types. Sometimes
    perspective types may be combined in one image, as with the
    "wavy-line" or "moustache" rendering of straight lines (combining
    spherical and reverse-spherical perspectives) toward the image edges
    of some wide angles and zooms.

    For more, see my article, "On Seeing and Perspective", at --
    David Ruether, Jun 22, 2007
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