Optical: systems and elements – Single channel simultaneously to or from plural channels – By surface composed of lenticular elements
Reexamination Certificate
2000-04-12
2002-04-09
Mack, Ricky (Department: 2873)
Optical: systems and elements
Single channel simultaneously to or from plural channels
By surface composed of lenticular elements
Reexamination Certificate
active
06369949
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to optical devices wherein the image seen by a viewer depends on the viewer's angle of regard with respect to the plane of a windowpane-shaped device. More particularly, the invention relates to a lenticular sheet with periodic optical elements formed such that the viewer perceives a series of images which change depending on the viewer's angle of regard of the windowpane-shaped device.
DESCRIPTION OF THE RELATED ART
Existing optical systems can present a sequence of two or more images which appear as the viewer changes their angle of regard over a range of less than 90°, typically about 45°. The viewer's angle of regard is the angle between a normal to a plane and a viewer's eye. These systems use a device consisting of a regular array of plano-convex cylindrical lens elements with a periodicity that depends on a viewing distance for which the device is designed. For example, at normal viewing distances for reading of 18 inches, the periodicity of the cylindrical elements is preferably 100 elements to the inch or more. Optical system designs of up to 250 elements per inch can be achieved using such systems. Each lens element brings a slice of an underlying printed image into focus. The underlying printed image is composed by a computer program from a desired image sequence, the optics used and viewing geometry. Without the array of lenses, the printed image appears to be a set of stripes that run orthogonally to the axes of the lenses with a multi-image stripe periodicity equal to the lens periodicity but divided into image-specific stripes by the number of images in the set. For example, if the set has eight images and the lenses are at 100 per inch, a periodicity of eight stripes in 0.01 inches are used, one stripe for each image. The viewer sees the intersection of a focused stripe due to the lens and the printed stripe. Technically, two configurations exist, one in which the cylindrical axes are vertical, and one in which the axes are horizontal. In the vertical case, the images are selected to appear at differing depths since the right and left eyes of the viewer have differing angles of regard. The device can be stationary, and, typically, eight images that appear to be at differing depths are superimposed. In the horizontal case, the viewer's angle of regard must be changed. As the device is rotated through a series of angles of regard, a sequence of images is seen. Various effects are possible depending on the design of the stripes. One image can gradually transform into another, termed “morphing”. A sequence of images of various stages of an action scene can give a motion-like effect, termed “motion”. If the images are unrelated, the viewer will see the unrelated sequence appear, termed “flip”. One image can be a magnification of the preceding image and the effect is similar to looking through a zoom lens, termed “zoom”.
Existing lens array are fabricated by first designing a cutting tool with a desired lens shape, then using this tool to cut the shape of an array of flat lenses into a flat plate or cylinder. This pattern is then transferred to a plastic sheet using conventional methods. The striped image array can be produced by a thermal or piezoelectric ink jet printer that is readily capable of producing 1200 picture elements per inch and laminated to the flat side of the array. When the thickness of the lens array sheet is small enough, the pattern can be reverse printed using a printing press. Reverse printing using a transfer printing press is an option for array resolutions of greater than 60 elements per inch. Another option for directly printing a reverse image on the array is screen printing which is an option for array resolutions of greater than 10 elements per inch up to about 60 elements per inch. The lamination technique is broadly applicable. The printing medium may be plastic or paper. Since the printed array has the same frequency as the lens array, the print that contains the multiple image information must be linearly registered to the lens. The device operation is designed into the image dissection and the lens array. The lens array is typically fabricated from a plastic. Many different materials can be used, for example acrylics, polystyrenes, polycarbonates, polyesters or equivalent materials. The thickness of the finished sheet is related to the periodicity of the lens elements, which effects the lens cross section. The thickness of the array depends on the index of refraction of the plastic material.
T
∝
Dn
2
(
n
-
1
)
[
1
]
Where:
T is the thickness of the sheet,
D is the width of a lens element (in consistent units with T),
n is the index of refraction of the material.
The above formula assumes that the lens cross section is substantially circular. Other cross sections have been proposed. For example, U.S. Pat. No. 5,642,226 suggests a parabolic cross-section. The proportionality relation still holds for the parabolic cross-section, but the constant that must be introduced to make the equation an equality is different.
The criteria for a satisfactory lens design include the ability for the lens to sharply focus on the image plane. In order to provide an unequivocal differentiation from one selection to the next, the uncertainty of the focus at each selected angle of the array must be small enough. For a sequence of eight images, the uncertainty should be about 6% of the width of the lens or less. The range of foci along the dimension orthogonal to the lens axis determines the range of angles available for the image effects. At an angle of regard larger than about 30°, each lens focuses on a slice that is under the orthogonal projection of the next lens element on the image plane. However, the selection quality can nonetheless be judged over the ±30° range. Within the range of angles used in the design, the foci should stay within such orthogonal projection. The range of useful angles is established using the angle at which the foci cross a line that represents the edge of the projection.
For example, in existing designs using acrylic lens material, the line is typically crossed at about 30°, yielding a better than 45° viewing range for images. Each image becomes stable with a rotation of about 6°. If the range were very small, the viewer would be challenged to maintain the orientation over an angle much less than 6° or the design would be required to reduce the repertoire of images to fewer than eight. It can be useful to think of this in reverse. That is, determine the angles of regard that correspond to desired selection points. The viewer can easily and unnoticeably vary an angle of regard by a few degrees. Consequently, the set of angles of regard are not required to form a linear series.
Two cross sections have been used in industry, circular and parabolic. The circular cross section has only a single parameter, the radius, which is typically greater than D/2. The choice of a radius determines the constant of proportionality that makes formula [1] into an equality. The reason the radius is greater than D/2 is that adjacent lenses meet at an angle that must be fabricated. Were the radius exactly D/2, the angle would be an impractical 0°. For simplicity of discussion, all dimensions are normalized by dividing by D/2.
After normalization, the viewer's eye is typically 3000 units or more away. From the point of view of an individual element, the change in angles of regard across the element can be neglected. This is not true from the point of view of the array, and the stripe design accounts for this difference. The circular cross section in these normalized units is defined by x
2
+y
2
>1. To analyze the focusing power, a normal to the surface is used to apply Snell's refraction law. The angle of the normal to the circular surface is arctan(y/x).
To apply the solutions disclosed in U.S. Pat. No. 5,642,226, a parabolic cross section is defined by the less familiar: y=k(1−x
2
), which is presente
Dougherty & Clements LLP
Mack Ricky
O'Neill Gary
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