Abstract

In order to deform the wave surface passing through an optical system by the amount ϕ(u,v), it is suggested that a phase Fresnel lens be inserted in the pupil of the optical system. Assuming 0⩽ϕ(u,v)<mλ, the (u,v) that region of the pupil is divided into m zones by Fresnel’s condition

(k-1)λϕ(u,v)<kλ;         kthzone,k=1,2,,m,

where λ is the wavelength. If the phase Fresnel lens be made so that it shifts the wave surface by the amount ϕ(u,v)−(k−1)λ in each kth Fresnel zone, the amount of its deformation in each zone is smaller than λ, but this phase Fresnel lens is quite ϕ(u,v) because of Fresnel’s condition. Some properties of the phase Fresnel lens are discussed. This technique is more applicable to the infrared region.

© 1961 Optical Society of America

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References

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  1. B. Dossier, Rev. opt. 33, 57, 147, 267 (1954) (references before 1954 are described here); P. Croce, Rev. opt. 35, 569, 642 (1956); E. L. O’Neill, I.R.E. Trans. on Inform. Theory IT-2,  56 (1956); A. Maréchal and et al., Optica Acta 5, 256 (1958); J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958); K. Sayanagi, J. Appl. Phys. Japan 27, 623 (1958); H. Saito, J. Appl. Phys. Japan 28, 502 (1959).
    [CrossRef]
  2. J. Tsujiuchi, Rev. opt. 37, 1 (1958); J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958); T. Fujiwara, J. Appl. Phys. Japan 28, 515 (1959).
  3. G. G. Sliusarev, Doklady Akad. Nauk S.S.S.R. 113, 780 (1959); A. I. Tudorovskii, Optika i Spektroskopiya 4, 126 (1959).
  4. H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950). M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).
  5. There is another type of PFL which is made so that it deforms the wave surface by the amount ϕ(u,v)−(k−1)pλ in each k th Fresnel zone defined by the (u,v) region satisfying the condition (k−1)pλ⩽ϕ(u,v)<kpλ, k=1, 2, ⋯, m, where p is some proper integer, assuming 0⩽ϕ(u,v) <mpλ in all (u,v) regions. This type is more easily produced because the width of each Fresnel zone becomes broader; however, the effect of the discontinuities in the wave surface of the different wavelength becomes more serious than that of original PFL.
  6. Taken from the catalog of Nippon Kogaku K. K.

1959 (1)

G. G. Sliusarev, Doklady Akad. Nauk S.S.S.R. 113, 780 (1959); A. I. Tudorovskii, Optika i Spektroskopiya 4, 126 (1959).

1958 (1)

J. Tsujiuchi, Rev. opt. 37, 1 (1958); J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958); T. Fujiwara, J. Appl. Phys. Japan 28, 515 (1959).

1954 (1)

B. Dossier, Rev. opt. 33, 57, 147, 267 (1954) (references before 1954 are described here); P. Croce, Rev. opt. 35, 569, 642 (1956); E. L. O’Neill, I.R.E. Trans. on Inform. Theory IT-2,  56 (1956); A. Maréchal and et al., Optica Acta 5, 256 (1958); J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958); K. Sayanagi, J. Appl. Phys. Japan 27, 623 (1958); H. Saito, J. Appl. Phys. Japan 28, 502 (1959).
[CrossRef]

Dossier, B.

B. Dossier, Rev. opt. 33, 57, 147, 267 (1954) (references before 1954 are described here); P. Croce, Rev. opt. 35, 569, 642 (1956); E. L. O’Neill, I.R.E. Trans. on Inform. Theory IT-2,  56 (1956); A. Maréchal and et al., Optica Acta 5, 256 (1958); J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958); K. Sayanagi, J. Appl. Phys. Japan 27, 623 (1958); H. Saito, J. Appl. Phys. Japan 28, 502 (1959).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950). M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).

Sliusarev, G. G.

G. G. Sliusarev, Doklady Akad. Nauk S.S.S.R. 113, 780 (1959); A. I. Tudorovskii, Optika i Spektroskopiya 4, 126 (1959).

Tsujiuchi, J.

J. Tsujiuchi, Rev. opt. 37, 1 (1958); J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958); T. Fujiwara, J. Appl. Phys. Japan 28, 515 (1959).

Doklady Akad. Nauk S.S.S.R. (1)

G. G. Sliusarev, Doklady Akad. Nauk S.S.S.R. 113, 780 (1959); A. I. Tudorovskii, Optika i Spektroskopiya 4, 126 (1959).

Rev. opt. (2)

B. Dossier, Rev. opt. 33, 57, 147, 267 (1954) (references before 1954 are described here); P. Croce, Rev. opt. 35, 569, 642 (1956); E. L. O’Neill, I.R.E. Trans. on Inform. Theory IT-2,  56 (1956); A. Maréchal and et al., Optica Acta 5, 256 (1958); J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958); K. Sayanagi, J. Appl. Phys. Japan 27, 623 (1958); H. Saito, J. Appl. Phys. Japan 28, 502 (1959).
[CrossRef]

J. Tsujiuchi, Rev. opt. 37, 1 (1958); J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958); T. Fujiwara, J. Appl. Phys. Japan 28, 515 (1959).

Other (3)

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950). M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959).

There is another type of PFL which is made so that it deforms the wave surface by the amount ϕ(u,v)−(k−1)pλ in each k th Fresnel zone defined by the (u,v) region satisfying the condition (k−1)pλ⩽ϕ(u,v)<kpλ, k=1, 2, ⋯, m, where p is some proper integer, assuming 0⩽ϕ(u,v) <mpλ in all (u,v) regions. This type is more easily produced because the width of each Fresnel zone becomes broader; however, the effect of the discontinuities in the wave surface of the different wavelength becomes more serious than that of original PFL.

Taken from the catalog of Nippon Kogaku K. K.

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Figures (5)

Fig. 1
Fig. 1

Figured plate and wave front. K, propagating direction of light; d(u,v) depth of figuring; ϕ(u,v), amount of deformation of wave surface.

Fig. 2
Fig. 2

Fresnel zone. (a) Figured plate; (b) phase Fresnel Lens.

Fig. 3
Fig. 3

Wave surface of different wavelengths. (a) Phase Fresnel lens; (b) wave surface of fundamental wavelength; (c) wave surface of different wavelength.

Fig. 4
Fig. 4

Examples of the application of PFL., (a) Schmidt camera; (b) triplet.

Fig. 5
Fig. 5

Secondary spectrum of a lens with unit power. Curve (a), Δ(λ) of the thin doublet BSC-F; Curve (b), Δ(λ) of the thin doublet C–SbF; Curve (c), Δ(λ) of the thin doublet BSC-F; and PFL.

Tables (1)

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Table I Indexes of glasses and powers of individual single lens.

Equations (8)

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( k - 1 ) λ ϕ ( u , v ) < k λ ;             k th zone , k = 1 , 2 , , m ,
d ( u , v ) ~ - ϕ ( u , v ) / ( n - 1 ) ,
( k - 1 ) λ ϕ ( u , v ) < k λ ;             k th zone k = 1 , 2 , , m ,
ϕ ( u , v ) - ( k - 1 ) λ ;             k = 1 , 2 , , m ,
( k - 1 ) λ 0 ϕ ( u , v ) < k λ 0 ( k - 1 ) λ ( λ / λ 0 ) ϕ ( u , v ) < k λ .
exp ( 2 π i ϕ / λ ) = l = - A l exp ( 2 π i l θ / λ )
exp ( 2 π i ϕ / λ ) = sin [ π ( λ 0 - λ ) / λ ] π ( λ 0 - λ ) / λ exp { ( 2 π i θ / λ ) - [ π i ( λ 0 - λ ) / λ ] } × { 1 + λ 0 - λ λ 0 exp [ - 2 π i θ / λ ] + λ 0 - λ λ 0 - 2 λ exp [ 2 π i θ / λ ] + } .
φ 1 + φ 2 + φ 3 = 1 x 1 φ 1 + x 2 φ 2 + x 3 φ 3 = 0 y 1 φ 1 + y 2 φ 2 + y 3 φ 3 = 0 , x i = n i ( λ 1 ) - n i ( λ 0 ) n i ( λ 0 ) - 1 ,             y i = n i ( λ 2 ) - n i ( λ 0 ) n i ( λ 0 ) - 1 ,             i = 1 , 2 x 3 = λ 1 - λ 0 λ 0 ,             y 3 = λ 2 - λ 0 λ 0 .