Notes on LEEP ARV-1 Stereoscopic Viewer Optics
Focal Length: 41 mm
Entrance Pupil Diameter: 60 mm
Interaxial Spacing: 64 millimeters. For viewing comfort when shifting from near to distant subjects, it is recommended that the infinity point conjugate spacing of the images in the viewing plane be 62 mm. It is important to note that this image spacing is not determined by the interpupillary distance of any particular person using the viewer, but rather by the requirement that nobody be required to cause their left and right visual axes to diverge, which causes severe eyestrain, and which everybody would have to do to merge an infinite image pair if the spacing exceeded 64 mm. In practice, a slight convergence for infinitely distant subjects is preferable, which accounts (along with a margin for system error) for the 2 mm closer spacing recommended for the stereo pair of images.
Field of View: This is a wiggly parameter. The following remarks pre-suppose that a properly scaled image in the LEEP compressed format is present at the focal plane of the viewer. A 140 degree field is possible if the eyes can move laterally with respect to the viewer — "peer about" through the hole represented by the eye lens perimeter. In a head-mounted display, however, the eyeballs normally are constrained to rotating in azimuth and elevation about their centers. Accordingly the field is limited by the eye lens perimeter (which is also the entrance pupil and the field stop) and by the proximity of the eye to the apex of the eye lens. Most eyes can swivel only about 90 degrees, and it is easy for most people to get close enough to see this much, though eyeglasses may impose an added limit. The significant number is thus the eye lens entrance pupil radius of 30 mm. If the center of rotation of the eyeball is 30 mm away from the center of the entrance pupil , the directly viewed field is then (from the geometry) 90 degrees. (Actually , refraction at the cornea gives a sensibly wider field when looking straight ahead — we call this the "knothole" effect .) The geometry gives us several more numbers: if 1/2" of lateral head motion is allowed each way, the field is 110 degrees; if the eyeball center of rotation is brought to (a possible) 20 mm, the field is 112 degrees; if both motions are allowed, the field is 130 degrees.
Lateral Chromatism: Called also, and more descriptively, "chromatic difference of magnification" this aberration is normally observed as blue and red "fringes" at the extremes of the field of an optical system. In the interest of achieving high magnification and a wide field in the same design, no attempt was made to achromatize individual elements in the LEEP optics. In fact the basic LEEP invention consists mainly in compensating the viewer chromatism by an opposite chromatism in the image viewed. Adequate electronic compensation can be accomplished by making the red image about 1% larger (linearly) than the blue image, with the green in between. LEEP video camera lenses provide a color compensated image when used with a color video camera. The photographic LEEP slides available in the VR demo set were taken with equivalent LEEP camera lenses.
Expansion of Field: In order to make the best possible use of photographic resolution (or video channel bandwidth) most of the image area is devoted to the central field, and the peripheral field is compressed into the edges. The result is an extreme "fisheye-like" image, in which the radial distance from the image center is approximately proportional to the sine of the real, or computer-generated, object-space angle. This distortion is accurately approximated by:
r = f (A - .18A3)
Where: r is the radial distance from the optical axis to any point on the (nominal) focal plane of the viewer, f is the axial focal length of the viewer, and A is the apparent off-axis angle in radians of the image of the same point as seen by a person using the viewer, which is also its angle in object space.
To expand this image, i.e. to restore the orthoscopy of the space (orthospace) the viewer optics must have a large compensating positive radial distortion, so that A is the angle of the collimated beam the optics produce from light emanating from the point in question.