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.
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.
−6.74 −6.72 −6.7 −6.68 −6.66 −6.64 −6.62 −6.6 −6.58 −6.56 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1
Equivalent pinhole rays at the focal plane, Ian Camera blue aperture
Z (mm)
X
(mm)
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.
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.
7.82 7.84 7.86 7.88 7.9 7.92 7.94 7.96 7.98 8 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1
Equivalent pinhole rays at the focal plane, Emilio Camera blue aperture
Z (mm)
X
Figure 6.3-3: Measured location of the equivalent pinhole for each aperture of the Ian Camera. 380 400 420 440 460 480 500 520 540 560 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 Field Z (mm) Aperture X (mm)
Measured equivalent aperture X location, Ian Camera
B R G Aperture 380 400 420 440 460 480 500 520 540 560 −8 −6 −4 −2 0 2 4 Field Z (mm) Aperture Y (mm)
Measured equivalent aperture Y location, Ian Camera
B R G Aperture 380 400 420 440 460 480 500 520 540 560 −7.5 −7 −6.5 −6 −5.5 Field Z (mm) Aperture Z (mm)
Measured equivalent aperture Z location, Ian Camera
B R G Aperture
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.
400 450 500 550 600 650 700 −0.06 −0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 Field Z (mm) Aperture X (mm)
Measured equivalent aperture X location, Emilio Camera
B R G Aperture 400 450 500 550 600 650 700 −10 −5 0 5 Field Z (mm) Aperture Y (mm)
Measured equivalent aperture Y location, Emilio Camera
B R G Aperture 400 450 500 550 600 650 700 7.8 7.9 8 8.1 8.2 8.3 8.4 Field Z (mm) Aperture Z (mm)
Measured equivalent aperture Z location, Emilio Camera
B R G Aperture
Part II
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.
7.2
Introduction
All but one of the cameras built to date feature equilateral triangle aperture layouts. This is done so that the sensitivity between all apertures is equal. This is certainly not a requirement.
Traditionally, the aperture on top is referred to as the “blue” aperture, the one on the starboard side (bottom right if looking at the camera from the back) is the “red” aperture, and the port side (bottom left if looking at the camera from the back) is the “green”. The names have been kept for tradition’s sake, but have been referred to as “1”, “2”, and “3” also.
proved (and cost has gone down). But the choice of lens is perhaps the most influential aspect of final image quality. Initially, for the Silver Camera the lenses were chosen to simply allow for the use of a larger aperture while still “keeping” the pinhole-optics aspect of the setup intact. Because of the offset between the sensor center and the lens axis required for defocusing alignment the image quality was terrible since the center of the lens field was not in use. Subsequent cameras had the lenses tilted so that the lens axis would be closer to the center of the sensors. These had slightly better overall image quality by balancing the aberrations with a tilted focal plane1. Inevitably the next step would be to use photographic objectives which would provide far superior image quality at even larger sensor-lens offsets since, for example, 35-mm-format objectives are designed to cover at least a 24 by 36 mm rectangle (the size of a 35-mm-format negative). The factor limiting offsets at this point became the light fall-off experienced as the radial distance from the lens axis grows2.
The larger field allowed the lenses to be mounted straight-on as in the Silver Camera.
As the image quality increased it became easier to identify one of the most critical problems in building a consistent camera—the heat generated by the sensors. During operation some sensors can get very hot—for example, those based on the KAI-20XX chip can reach temperatures of up to +30°C over ambient. The heat is transferred to the sensor body and to some extent whatever conductor is touching it. The mismatch in thermal expansion of the different materials (for example, aluminum camera body and ceramic CCD package) can cause several pixels of shift in the image. In the older cameras, when dewarping was young and misalignments thought to be fatal, the sensors were mounted on stages, so the heat movement was never noticed because cameras were not often reused without having to adjust the stages somehow and recalibrate. With the Taiwan Camera, which had custom-made lockable stages that could resist several pounds of force (in an attempt to minimize the recalibrations required), the heat movement stuck out like a sore thumb. Tests were then run with every available sensor and camera to try to find out exactly what it was that was moving.
Test showed that every sensor3firmly bolted to an optical table, experienced several pixels of shift as they reached a stable operating temperature. The Kodak ES1.0 units, which were remote-head types, were the slowest to stabilize, taking over 90 minutes until no shift was detectable. Others, like the UNIQ’s, reached a stable position in a few minutes. The problem was not so much the movement but the hysteresis of the movement. After one power cycle, the new “cold” position was not equal to the previous one, and once the sensor was turned on again, the new “hot” position was not the same as the previous one. Sensors that were held only by the circuit board (so the chip was only supported 1Since the f-number is usually high so is the depth of field, so a tilted focal plane does not imply a view-camera
style blur.
2The light fall-off of lenses may not be apparent with most film cameras because of the nonlinear exposure charac-
teristics of film and because the microlenses commonly found on digital sensors add an extra bit of loss as a function of angle of incidence.
by its own pins) exhibited even more unstable movement. The only setup that had no hysteresis was the one in the Revelle camera where the chips were bolted to small custom-made aluminum frames which were then epoxied onto holders bolted to the faceplate. It was then believed that the source of the hysteresis was stresses that would build between the sensor body and whatever it was bolted to would not allow a continuous expansion. Whether the source was the force exerted by the screws or the mismatch in material between the sensor body and the screws is unclear, but when the Ian Camera was built by bolting (and gluing) the chips directly to the faceplate tests concluded that this arrangement had no hysteresis. The movement still exists thus there is a warm-up time for cameras. The voluminous faceplates of the new cameras make the warm up times longer but also stabilizes the system against local and sudden changes in temperature.