The pinhole optics approximation is useful as a “black box” but diverges from the real case as the lenses grow in complexity. In designing photographic objectives, the aberrations and distortions are minimized by, in short, manipulating the path of the incoming rays. As mentioned before, the aperture is the only place that all rays must pass through. As one looks at the ray paths away from the aperture (that is, forwards or backwards within the lens assembly), rays emanating from different field points take different paths. The image of the aperture as seen from the front of the lens is called theentrance pupil and it is possible that it changes position and size as the observer moves through the field. In fact, lens designers have been known to purposefully distort the entrance pupil as a function of field position in wide angle lenses to attempt to decrease light fall-off. As the field decreases in width and height this movement is decreased but still existent, so thatthere is absolutely no guarantee that a given lens has an equivalent “pinhole” system. In other words, if an exact ray trace is performed for a given lens and points in space are connected by straight lines to their respective images the lines will not intersect at exactly one point, and, most importantly, the Z coordinate of the intersection region will be a function of the Z coordinates of the points.
For a given sensor size, the effect will be amplified as the focal length of the lens decreases and barrel distortion begins to appear (remember this type of distortion can be seen as a local change in magnification which can be viewed as a local change in the location of the pinhole). In other words, a lens that generates measurably perfect images may have an “equivalent pinhole” (within some tolerance) for a givenZ coordinate, but the location of this pinhole will move withZ.3
Figures 6.3-3and 6.3-4 show the measured location of the equivalent pinhole as a function of Z for the Ian Camera and the Emilio Camera, respectively. The measurement is done by taking a dewarping set in air, connecting the field points (dewarping target dots) to their images with straight lines, and finding the average intersection4in space of these lines for each dewarping plane.
3This is essentially because the pinhole optics model ignores the fact that real lenses have distinct entrance and exit pupil planes.
4Since the rays are not guaranteed to all intersect with each other, the “intersection” point is in fact the average
Figure 6.3-1: The region of intersection for the “pinhole equivalent” rays emanating from the central row of dots in the dewarping target at the reference plane for the Ian Camera’s blue aperture. The rays resemble those of a point source through a lens with spherical aberration because of the barrel distortion. Note that the pattern is asymmetrical because the sensor is not on-axis with the lens.
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Equivalent pinhole rays at the focal plane, Ian Camera blue aperture
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A sample of these ray bundles is shown in figure 6.3-1 for the Ian Camera and figure 6.3-2 for the Emilio Camera. The barrel distortion propagates itself as a change in theZ coordinate of the intersection of the rays of a single dewarping plane (directly analogous to spherical aberration of the rays from a point source), which is clearly visible in the Ian Camera ray plot (the focal length of the lenses in the Ian Camera is 28 mm). The Emilio Camera, on the other hand, has a much more rectilinear image, both because the lens is longer focal length and because the sensor-lens offset is not as large as in the Ian Camera. Thus its rays seem to intersect much more neatly at a single point for a single plane.
of the midpoints of the shortest segment connecting any two rays.
Figure 6.3-2: The region of intersection for the “pinhole equivalent” rays emanating from the central row of dots in the dewarping target at the reference plane for the Emilio Camera’s blue aperture. The smaller sensor-lens shift and longer focal length contribute to a much “cleaner” intersection bundle.
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Equivalent pinhole rays at the focal plane, Emilio Camera blue aperture
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Figure 6.3-3: Measured location of the equivalent pinhole for each aperture of the Ian Camera.
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Measured equivalent aperture Z location, Ian Camera
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Figure 6.3-4: Measured location of the equivalent pinhole for each aperture of the Emilio Camera. The slight variation in Xis due to misalignment of theZtraverse with the optical axis.
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Measured equivalent aperture Y location, Emilio Camera
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Measured equivalent aperture Z location, Emilio Camera
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Part II
Details of the Instrument
Chapter 7
History of Defocusing Cameras
7.1 Defocusing Camera “Concepts” and “Generations”
Several concepts were explored to some depth during the development of DDPIV. Of these, only two were considered for hardware implementation. “Concept 1” refers to single-lens, multiple-aperture cameras such as the one in Willert and Gharib [1992]. “Concept 5” was formulated in April of 1998 and is the model introduced in chapter4; it is the arrangement used for all modern defocusing cameras.
Within Concept 5, there are three generations: “first-generation” cameras had straight, sim- ple lenses and alignment stages, “second-generation” cameras had tilted lenses and for the most part relied in some way or another on sensor alignment, and “third-generation” cameras feature photographic objectives and no sensor alignment.
To date, 10 cameras have been built under the Concept 5 model. Two of these were built by Viosense, eight were built at Caltech; five were for use by the Gharib group, two for use the Hornung group, and one went to Dr. Ian Bartol of Old Dominion University. Of these, 1 is first-generation, 7 are second-generation, and two are third-generation. Of the original, one-lens design only two were built with the intention of use for measurement—Concept 1 was quickly abandoned for Concept 5.