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    Positive Focal Length Fresnel Lens Used as a Collector

    Positive Focal Length Fresnel Lens Used as a Collimator

    Negative Focal Length Fresnel Lens Used as a Diverger

    HIGH QUALITY FRESNEL LENSES IN AVARIETY OF SIZES & FOCAL LENGTHS

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    The Fresnel Lens

    Centuries ago, it was recognized that the contour of therefracting surface of a conventional lens defines its focusingproperties. The bulk of material between the refracting sur-faces has no effect (other than increasing absorption losses)on the optical properties of the lens. In a Fresnel (pointfocus) lens the bulk of material has been reduced by theextraction of a set of coaxial annular cylinders of material, asshown in Figure 1. (Positive focal length Fresnel lenses are

    almost universally plano-convex.) The contour of the curvedsurface is thus approximated by right circular cylindricalportions, which do not contribute to the lens optical proper-ties, intersected by conical portions called grooves. Nearthe center of the lens, these inclined surfaces or groovesare nearly parallel to the plane face; toward the outer edge,the inclined surfaces become extremely steep, especially forlenses of low fnumber. The inclined surface of each grooveis the corresponding portion of the original aspheric surface,translated toward the plano surface of the lens; the angle ofeach groove is modified slightly from that of the originalaspheric profile to compensate for this translation.

    The earliest stepped-surface lens was suggested in 1748

    by Count Buffon, who proposed to grind out material fromthe plano side of the lens until he was left with thin sectionsof material following the original spherical surface of thelens, as shown schematically in Figure 2a). Buffons workwas followed by that of Condorcet and Sir D. Brewster, bothof whom designed built-up lenses made of stepped annuli.The aspheric Fresnel lens was invented in 1822 by Augustin

    Jean Fresnel (17881827), a French mathematician andphysicist also credited with resolving the dispute betweenthe classical corpuscular and wave theories of light throughhis careful experiments on diffraction. Fresnels original lenswas used in a lighthouse on the river Gironde; the maininnovation embodied in Fresnels design was that the center

    of curvature of each ring receded along the axis according toits distance from the center, so as practically to eliminatespherical aberration. Fresnels original design, including thespherical-surfaced central section, is shown schematically inFigure 2b). The early Fresnel lenses were cut and polished inglass an expensive process, and one limited to a few largegrooves. Figure 3 shows a Fresnel lens, constructed in thisway, which is used in the lighthouse at St Augustine, Florida,USA. The large aperture and low absorption of Fresnellenses were especially important for use with the weaklamps found in lighthouses before the invention of high-brightness light sources in the 1900s. The illustrated system

    is catadioptric: the glass rings above and below the Fresnellens band in the center of the light are totally-internally-reflecting prisms, which serve to collect an additional frac-tion of the light from the source. The use of catadioptric sys-tems in lighthouses was also due to Fresnel.

    Until the 1950s, quality Fresnel lenses were made fromglass by the same grinding and polishing techniques used in1822. Cheap Fresnel lenses were made by pressing hot glassinto metal molds; because of the high surface tension ofglass, Fresnel lenses made in this way lacked the necessarydetail, and were poor indeed.

    In the last forty years or so, the advent of optical-qualityplastics, compression and injection molding techniques,

    Figure 1 Construction of a Fresnel lens from its corresponding asphere. Each groove of the Fresnel lens is asmall piece of the aspheric surface, translated toward the plano side of the lens. The tilt of each suface must be modified slightly from that of theoriginal portion of aspheric surface, in order tocompensate for the translation.

    Figure 2 Early steppedsurface lenses. In both illustrationsthe black area is material, and the dashed curvesrepresent the original contours of the lenses. a)shows the lens suggested by Count Buffon (1748where material was removed from the plano sideof the lens in order to reduce the thickness. b)shows the original lens of Fresnel (1822), the central ring of which had a spherical surface. InFresnels lens, the center of curvature of each rinwas displaced according to the distance of thatring from the center, so as to eliminate sphericalaberration.

    a) b)

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    and computer-controlled machining have made possiblemanufacture and wide application of Fresnel lenseshigher optical quality than the finest glass Fresnel lenModern computer-controlled machining methods canused to cut the surface of each cone precisely so as to ball paraxial rays into focus at exactly the same point, avoing spherical aberration. Better still, newer methods canused to cut each refracting surface in the correct asphcontour (rather than as a conical approximation to this c

    tour), thus avoiding even the width of the groove (typic0.1 to 1 mm) as a limit to the sharpness of the focus. Ethough each groove or facet brings light precisely to a fothe breaking up of the wavefront by the discontinuous face of a Fresnel lens degrades the visible image quaExcept in certain situations discussed later, Fresnel lensesusually not recommended for imaging applications in visible light region of the spectrum.

    The characteristics of the aspheric correction

    The grinding and polishing techniques used in the manuture of conventional optics lead to spherical surfaces. Spical surfaces produce optics with longitudinal spher

    aberration, which occurs when different annular sectionthe optic bring light rays to a focus at different points althe optical axis. This phenomenon is illustrated for a posifocal length, plano-convex conventional lens in Figure 4all optical illustrations in this brochure, light is takenpropagate from left to right). The lens illustrated is a sectof a sphere with 1" (25 mm) radius of curvature, (36 mm) in diameter; the index of refraction of the mateis 1.5, typical both for optical glasses and for our plasmaterials. The focal length of the illustrated lens is thu(50 mm), and the aperture is /1.3. As is evident fromfigure, the longitudinal spherical aberration is very stroSingle-element spherical lenses are typically restricted

    much smaller apertures (higher numbers) than because longitudinal spherical aberration of the magnitshown in Figure 4 is generally unacceptable. Figure 5 shan aspheric lens of the same focal length and numnote that the surface contour is modified from the spherprofile in such a way as to bring rays passing throughpoints on the lens to a focus at the same position on the ocal axis. A lens made with the aspheric profile illustrateFigure 5, therefore, exhibits no longitudinal spherical abration for rays parallel to the optical axis.

    Since Fresnel lenses are made from the beginning to correct aspheric profile, the notion of correcting for sph

    cal aberration is not meaningful for Fresnel lenses. lenses are more accurately characterized as free fspherical aberration. The combination of the aspheric face (which eliminates longitudinal spherical aberratand the thinness of the lens (which substantially reduboth absorption losses in the material and the changethose losses across the lens profile) allows Fresnel lenwith acceptable performance to be made with very laapertures. In fact, Fresnel lenses typically have far laapertures (smaller numbers) than the /1.3 illustrateFigure 4.

    Figure 6 compares an aspheric plano-convex lens withaspheric Fresnel lens (the Fresnel lens groove structur

    f

    f

    f

    f f

    Figure 3 The light from the St Augustine, Florida (USA) light-house, showing the glass Fresnel optical systemused in the lighthouse. The optical system is about12 feet (3.5 m) tall and 7 feet (2 m) in diameter.

    Figure 4 Illustration of longitudinal spherical aberration.The rays shown were traced through an /1.3spherical-surface lens; the focus is evidentlyspread out over a considerable distance along theoptical axis.

    f

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    highly exaggerated in all the illustrations). The conventionalasphere is characterized by two principal planes; an effec-tive focal length (EFL), , measured from the principal planenearer the plano side; and a back focal length, , measuredfrom the plano side of the lens. In a plano-convex Fresnellens, the separation between the principal planes is inconse-quential, so that is measured from the grooved surface ofthe Fresnel lens.

    Many of the spherical-surface lenses in common use are

    biconvex, often with the same curvature on the two sides.Such lenses exhibit substantial spherical aberration, andother aberrations as well, but are symmetric in their proper-ties. In almost all instances, Fresnel lenses are plano-convex.This fact, along with their aspheric profiles and their low numbers, leads to strongly asymmetric behavior. Figure 7shows a typical Fresnel lens one correct for the case ofgrooves toward a collimated beam, plano side toward thefocus. (This type of Fresnel lens is referred to as groovesout. The terminology arises from the use of a Fresnel lensto focus energy on a detector inside a box