Abstract

Fresnel type lenses of high precision and excellent surface quality have been made in thin sheet plastic materials. The prismatic elements are very fine—about 0.003″ to 0.005″—and are not visible to the average unaided eye. A high degree of correction for spherical aberration has been achieved. Molded from high precision molds, lenses have been made in diameters of two to fifteen inches and focal lengths of 212 to 2212 inches. Relative apertures in excess of f/1.0 have been made. These lenses have found many applications as light collecting elements where weight and space are limited. Such applications include uses for large condensers, large field lenses in finders, camera viewing screens, and translucent screens for projection.

© 1951 Optical Society of America

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References

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  1. Oeuvres Complètes d’Augustín Fresnel (Complete Works of Augustin Fresnel) (Paris, 1870), Vol. III, Footnote, pp. 75–76.
  2. Oeuvres Complètes d’Augustin Fresnel (Complete Works of Augustin Fresnel) (Paris, 1870), Vol. III, Plate I.
  3. E. L. Gaylord, U.S.P.760,191.
  4. Frederico G. Lundi, U.S.P.1,237,352.
  5. A. V. H. Morey, Ind. Eng. Chem. 19, 1106–1109 (1927); J. G. Davidson and H. G. McClure, Ind. Eng. Chem. 25, 645–652 (1933); Ostromislenski, U.S.P.1,683,401; Buckholz, U.S.P.1,810,126; Bull, U.S.P.1,970,358; Hill, U.S.P.1,980,483.
    [CrossRef]
  6. C. W. Frederick, U.S.P.1,572,236, February9, 1926.
  7. Bull, U.S.P.1,970,358.
  8. R. R. Law and R. G. Maloff, J. Opt. Soc. Am. 38, 6, 496–502 (1948).
  9. Private Communication.
  10. The authors are indebted to Paul Stevens of the Hawk-Eye Lens Design Department, who calculated the values of spherical aberration shown graphically in Fig. 5.
  11. American Standards Association, Z38.4.20-1948, American Standard Methods of Designating and Measuring Apertures and Related Quantities Pertaining to Photographic Lenses.
  12. R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd Edition, pp. 77–78.
  13. D. L. MacAdam, J. Opt. Soc. Am. 40, 589–595 (1950).
    [CrossRef]

1950 (1)

1948 (1)

R. R. Law and R. G. Maloff, J. Opt. Soc. Am. 38, 6, 496–502 (1948).

1927 (1)

A. V. H. Morey, Ind. Eng. Chem. 19, 1106–1109 (1927); J. G. Davidson and H. G. McClure, Ind. Eng. Chem. 25, 645–652 (1933); Ostromislenski, U.S.P.1,683,401; Buckholz, U.S.P.1,810,126; Bull, U.S.P.1,970,358; Hill, U.S.P.1,980,483.
[CrossRef]

Bull,

Bull, U.S.P.1,970,358.

Frederick, C. W.

C. W. Frederick, U.S.P.1,572,236, February9, 1926.

Gaylord, E. L.

E. L. Gaylord, U.S.P.760,191.

Law, R. R.

R. R. Law and R. G. Maloff, J. Opt. Soc. Am. 38, 6, 496–502 (1948).

Lundi, Frederico G.

Frederico G. Lundi, U.S.P.1,237,352.

MacAdam, D. L.

Maloff, R. G.

R. R. Law and R. G. Maloff, J. Opt. Soc. Am. 38, 6, 496–502 (1948).

Morey, A. V. H.

A. V. H. Morey, Ind. Eng. Chem. 19, 1106–1109 (1927); J. G. Davidson and H. G. McClure, Ind. Eng. Chem. 25, 645–652 (1933); Ostromislenski, U.S.P.1,683,401; Buckholz, U.S.P.1,810,126; Bull, U.S.P.1,970,358; Hill, U.S.P.1,980,483.
[CrossRef]

Wood, R. W.

R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd Edition, pp. 77–78.

Ind. Eng. Chem. (1)

A. V. H. Morey, Ind. Eng. Chem. 19, 1106–1109 (1927); J. G. Davidson and H. G. McClure, Ind. Eng. Chem. 25, 645–652 (1933); Ostromislenski, U.S.P.1,683,401; Buckholz, U.S.P.1,810,126; Bull, U.S.P.1,970,358; Hill, U.S.P.1,980,483.
[CrossRef]

J. Opt. Soc. Am. (2)

D. L. MacAdam, J. Opt. Soc. Am. 40, 589–595 (1950).
[CrossRef]

R. R. Law and R. G. Maloff, J. Opt. Soc. Am. 38, 6, 496–502 (1948).

Other (10)

Private Communication.

The authors are indebted to Paul Stevens of the Hawk-Eye Lens Design Department, who calculated the values of spherical aberration shown graphically in Fig. 5.

American Standards Association, Z38.4.20-1948, American Standard Methods of Designating and Measuring Apertures and Related Quantities Pertaining to Photographic Lenses.

R. W. Wood, Physical Optics (The Macmillan Company, New York, 1934), 3rd Edition, pp. 77–78.

Oeuvres Complètes d’Augustín Fresnel (Complete Works of Augustin Fresnel) (Paris, 1870), Vol. III, Footnote, pp. 75–76.

Oeuvres Complètes d’Augustin Fresnel (Complete Works of Augustin Fresnel) (Paris, 1870), Vol. III, Plate I.

E. L. Gaylord, U.S.P.760,191.

Frederico G. Lundi, U.S.P.1,237,352.

C. W. Frederick, U.S.P.1,572,236, February9, 1926.

Bull, U.S.P.1,970,358.

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of a mechanical arrangement for engraving a mold for a plastic Fresnel lens.

Fig. 2(a)
Fig. 2(a)

Diagram showing a ray parallel to the axis of a Fresnel lens, incident on the smooth side of the lens, and passing through one prismatic element.

Fig. 2(b)
Fig. 2(b)

Diagram showing a ray parallel to the axis of a Fresnel lens, incident on the molded side of the lens, and passing through one prismatic element.

Fig. 3
Fig. 3

Concentric zonal elements of a spherical surface aligned with their edges lying in a plane to form a flat Fresnel lens.

Fig. 4
Fig. 4

Plots of prism angle vs. zone angle referred to the principal focus. (Curves are numbered the same as the corresponding equations given in the text.)

Fig. 5
Fig. 5

Longitudinal spherical aberration of a Fresnel lens compared to a simple plano-convex lens.

Fig. 6
Fig. 6

Photomicrographs of radial sections of a Fresnel lens surface. Width of the grooves is 0.005″. Sections a, b, c, and d were cut at progressively greater distances from the center of the lens.

Fig. 7
Fig. 7

Ray diagram illustrating the difference in the sizes of the entrance windows of a flat Fresnel lens and of an ideal lens having the same aperture ratio and paraxial focal length, f.

Fig. 8
Fig. 8

Schematic ray diagrams, incident light coming from the principal focus of a Fresnel lens, such as in a searchlight. (a) Light incident on the smooth side of the lens. (b) Light incident as in (a) but with a different groove angle. (c) Light incident on the molded prismatic surface. (d) Light incident as in (c) but with a less favorable groove angle.

Fig. 9
Fig. 9

Schematic ray diagrams; light from a distant source on the axis of a Fresnel lens, incident on the prismatic side of the lens. (a), (b), and (c) illustrate different groove angles.

Fig. 10
Fig. 10

Schematic ray diagrams; light from a distant source on the lens axis, incident on the smooth side of a Fresnel lens. (a), (b), and (c) show the effect of different groove angles.

Fig. 11
Fig. 11

Ray diagram illustrating a narrow parallel pencil of light traversing a prism.

Fig. 12
Fig. 12

Ray diagram of a narrow pencil of light traversing a single prismatic element of a Fresnel lens.

Fig. 13
Fig. 13

Plot of cos θ cos ϕ cos ϕ vs. θ for a flat Fresnel lens. This represents the maximum luminance when the prism magnification is greater than unity.

Equations (13)

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tan ϕ = h / D ,
f p = D / ( n - 1 ) .
tan θ = h / f p .
tan ϕ = tan θ / ( n - 1 ) .
tan ϕ = sin θ / ( n - cos θ ) .
tan ϕ = sin θ / ( n - cos θ ) ,
sin ϕ = tan θ / ( n - 1 ) ,
D 0 = D cos θ ,
f p = f m cos θ .
R.A. = f m / D .
M p = - d i / d i = cos i cos r / cos i cos r = a / b .
L = L 0 b / h .
L = L 0 ( cos θ cos ϕ / cos ϕ ) .