Double-sided grooved Fresnel lens for overhead projector

Abstract: This invention consists of a Fresnel lens (10) having focusing grooves (12,14) on both sides of a single element. The relative frequencies of the grooved surfaces are controlled such that Moire interference patterns between the two grooved surfaces (12,14) are reduced. Specifically, the frequency of the Fresnel elements (12) on one surface of the is at least four times that of the Fresnel elements (14) on the other surface and not a integral multiple thereof.

Description: Field of the Invention The present invention relates generally to overhead projectors, and particularly to condensing lenses for such projectors. Background of the Invention Conventional Fresnel lenses for use as condensers, concentrators, and field lenses usually are of the form of a single element with prismatic, circular grooves on one side and a planar surface on the other. When high transmission is required at a smaller f-number, for example in overhead projectors, two of this type are used together and are sealed together at the periphery. Since these lenses usually lie close to the imaging plane or stage of the projector, Moire Interference patterns can appear on the projected image when the centers of the circular groove structures are not coincident to a certain tolerance. A single element Fresnel lens with identical groove structures on both sides is described in Japanese patent 57-109618. In that patent, two identical dies are replicated from the same groove structure and are very accurately aligned in a fixture using guide posts. The lens is formed by pouring a thermoplastic resin between the dies and subsequently applying heat and pressure. Such a dual-element lens is economically advantageous over the conventional two lens arrangement since only one sheet of lens material is necessary. Unfortunately, the requirement that the center of the grooved surfaces be aligned to a close tolerance increases the expense of a workable dual-element lens, and therefore somewhat offsets its advantages. It is desired to reduce the cost of manufacturing a workable dual-element lens by eliminating or easing the requirement for highly accurate center alignment of the grooved elements on each side of the lens. US-A-4,044,889 relates to a cosmetic container including an integrated flat Fresnel lens structure. A figure of this prior art document illustrates a different groove width on one major surface of the lens to the groove width on the opposite major surface. This document is used to form the preamble of the appended claims. Summary of the Invention According to the present invention, which is defined in claim 1, there is provided a Fresnel lens comprising a single sheet of lens material having grooved Fresnel elements on each major surface, the width of a groove of concern on one major surface being different to the width of the paired groove on the other major surface, the groove width of the Fresnel elements on one major surface of said lens is at least four times the groove width of the Fresnel elements on the other major surface of said lens and not an integral multiple of the groove width of said Fresnel elements on said other major surface, whereby Moire fringes are reduced. The current invention produces a single element, dual-grooved Fresnel lens from non-identical groove structures, using conventional compression molding techniques. The groove angles are designed to maximize light transmission, while the groove frequencies of each surface are carefully controlled to reduce the need for accurate center alignment to eliminate Moire patterns. This invention consists of a high transmission, low f-number single element dual-grooved Fresnel lens. The opposing groove structures are designed for high light transmission, and the groove frequency ratio between the two surfaces is chosen to minimize the production of Moire interference patterns, even if the two stamping dies are not accurately center-aligned during molding of the lens. Specifically, the invention is an improved dual-grooved Fresnel lens wherein a single sheet of lens material includes grooved Fresnel elements on each major surface, and the groove frequency of the Fresnel elements on one major surface of said lens is at least four times the groove frequency of the Fresnel elements on the other major surface of said lens and not an integral multiple of the groove frequency of the Fresnel elements on the other major surface, whereby Moire interference is reduced. In the preferred embodiment of the invention, the groove frequency of said Fresnel elements on one major surface is about 4.74 times the groove frequency of the groove frequency of the Fresnel elements on the other major surface. Brief Description of the Drawings The present invention will be more thoroughly described with respect to the accompanying drawing, wherein like numbers refer to like parts in the several views, and wherein: Figure 1 is a cross-section view of a dual-grooved Fresnel lens according to the present invention. Detailed Description of the Invention Figure 1 shows a dual-grooved Fresnel lens, generally indicated as 10, of the current invention. The term "dual-groove" refers to the fact that the lens 10 is molded from a single sheet of material with circular Fresnel elements 12 and 14 molded into each major surface of the sheet. In conventional dual-grooved lenses, it is important to the elimination or reduction of Moire interference that the centers 16 and 18 of the circular Fresnel elements be aligned to a close tolerance. This alignment is especially critical when the groove frequencies of the two surfaces are identical or nearly so. In practice, however, it is difficult to align two dies in a conventional compression molding operation to maintain the center alignment required to eliminate Moire interference. However, it has been found that by controlling the groove frequency ratio between the two elements, the Moire interference patterns can be reduced to a negligible intensity, even when the centers are not aligned. Specifically, It has been discovered that this occurs when the groove frequency of one grooved surface is at least four times that of the other, and is not an integral multiple thereof. This groove frequency relationship can be satisfied by using either a constant or variable groove width for each surface. Example A specific design example is now given for the dual grooved Fresnel lens 10 for use in an overhead projector. The groove angles of the Fresnel elements 12 and 14 on each surface are described concisely by the following equation, which is derived from the sag equation of a general aspheric surface: where: Y = distance from lens center to groove center α = angle of an individual groove relative to the plane of the lens C = vertex curvature K = conic constant d,e,f,g = aspheric deformation coefficients The dual-grooved Fresnel lens 10 for use in overhead projection has an effective focal length of 182.5 mm and a clear aperture of 350 mm. The groove frequency of each surface is usually in the art between two and eight grooves per millimeter, and the Fresnel lens material is often optical acrylic plastic. In order to minimize the Moire interference patterns, the groove frequency ratio between the Fresnel elements 12 and 14 of the two grooved surfaces should be maintained such that one is at least four times that of the other, and is not an integral multiple thereof. In practice, a groove frequency ratio of about 4.74 has been found to be effective. If each surface has a variable groove width, then this ratio must be maintained for each upper/lower surface groove pair. The groove profile parameters for the surface 12 are: C = 0.00521682 mm⁻¹ K = -1.87385 d = -2.87E-9 e = 2.59E-14 f = -1.53E-19 g = 4.40e-25 The groove profile parameters for the surface 14 are: C = 0.00598319 mm⁻¹ K = -1.344788 d = -4.56E-9 e = 3.47E-14 f - -2.18E-19 g = 8.40E-25 The lens material is optical acrylic plastic, having a refractive index, n d , of 1.491 for yellow light.

Claims: A Fresnel lens (10) consisting of a single sheet of lens material having first and second grooved Fresnel elements (12, 14) respectively formed on first and second major surfaces thereof, the ratio between the widths of pairs of directly opposed grooves on said first and second major surfaces, being not an integral number, said Fresnel lens (10) being characterised in that: said ratio between the widths of said pairs of directly opposed grooves is larger than four, thereby reducing the occurrence of Moire fringes. A Fresnel lens (10) according to claim 1, further characterised in that said ratio between the widths of said pairs of grooves is 4.74 . A Fresnel lens (10) according to claim 1, wherein the width of the grooves of said first and second Fresnel elements (12, 14) varies in dependence on the distance from the centers (16, 18) of said Fresnel elements (12, 14).

Inventors: VANDERWERF DENNIS F C O MINNES, VANDERWERF, DENNIS F. C/O MINNESOTA MINING AND
Applicants: MINNESOTA MINING & MFG, MINNESOTA MINING AND MANUFACTURING COMPANY
Application year: 1989
Main classification: G02B3
IPC codes: G02B3