Abstract

Sections of nonrotational aspheric surfaces can be useful in a variety of optical situations. In several examples, image-forming objectives, as for photographic or electronic camera products, are described in which suitably located asymmetric pairs of refractive surfaces are devised, such that relative rotation about a displaced axis of one with respect to the other can be used to produce a focusing effect that is satisfactory for imaging purposes over reasonable fields of view and for practicable apertures and achromatic corrections. Taylor expansions about assignable reference points in any given surface of a sequence, together with suitable coordinate systems, can be employed to relate performance to shape parameters.

© 1999 Optical Society of America

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References

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  1. W. T. Plummer, “Unusual optics of the Polaroid SX-70 land camera,” Appl. Opt. 21, 196–202 (1982).
    [CrossRef] [PubMed]
  2. W. T. Plummer, “Landscape lens,” U.S. patent3,902,792 (2September1975).
  3. R. C. Owen, W. T. Plummer, “Zone focusing optical system,” U.S. patent4,443,067 (17April1984).
  4. J. G. Baker, W. T. Plummer, “Analytic function optical component,” U.S. patent4,650,292 (17March1987).
  5. I. Kitajima, “Improvements in lenses,” British patent250,268 (29July1926).
  6. H. J. Birchall, “Lenses and their combination and arrangement in various instruments and apparatus,” U.S. patent2,001,952 (21May1935).
  7. R. W. Lewis, “Lens and method of producing it,” U.S. patent2,263,509 (18November1941).
  8. L. W. Alvarez, “Two element variable power lens,” U.S. patent3,305,294 (21February1967).
  9. L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent3,507,565 (21April1970).
  10. J. G. Baker, “Variable power, analytic function, optical component in the form of a pair of laterally adjustable plates having shaped surfaces, and optical systems including such components,” U.S. patent3,583,790 (8June1971).
  11. J. G. Baker, “Optical system utilizing a transversely movable plate for focusing,” U.S. patent4,457,592 (3July1984).
  12. J. G. Baker, “Zoom lens,” U.S. patent4,925,281 (15May1990).
  13. Ref. 4, example 7 and Fig. 12.
  14. C. Londono, J. J. Mader, T. O’Hagan, M. Manning, “Development of prototype plastic optics,” in Replication and Molding of Optical Components, M. J. Reidl, ed., Proc. SPIE896, 99–108 (1988).
    [CrossRef]
  15. W. T. Plummer, J. J. Mader, J. W. Roblee, J. Van Tassell, “Precision engineering at polaroid,” in Proceedings of the Preconference Day Addresses on Precision Engineering in Industry—International State of the Art, Eighth International Precision Engineering Seminar, M. Bonis, Y. Alayli, P. Revel, P. McKeown, J. Corbett, eds. (Université de Technologie de Compiègne, Division Systemes Méchaniques, Centre de Recherches de Royallieu, BP 649-F-60206 Compiègne, France, 1995), pp. 24–29.
  16. W. T. Plummer, “Precision: how to achieve a little more of it, even after assembly,” in Intelligent Automation and Soft Computing, Vol. 1 of Proceedings of the World Automation Congress, M. Jamshidi, C. Nguyen, R. Lumia, J. Yuh, ed. (TSI Press, Albuquerque, N.M., 1994), pp. 193–198 (example 2). This example was reprinted in P. R. Yoder, Mounting Lenses in Optical Instruments, Vol. TT 21 of SPIE Tutorial Text Series, A. R. Weeks, ed. (SPIE Press, Bellingham, Wash., 1995), p. 27.

1982 (1)

Alvarez, L. W.

L. W. Alvarez, “Two element variable power lens,” U.S. patent3,305,294 (21February1967).

L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent3,507,565 (21April1970).

Baker, J. G.

J. G. Baker, “Variable power, analytic function, optical component in the form of a pair of laterally adjustable plates having shaped surfaces, and optical systems including such components,” U.S. patent3,583,790 (8June1971).

J. G. Baker, “Optical system utilizing a transversely movable plate for focusing,” U.S. patent4,457,592 (3July1984).

J. G. Baker, “Zoom lens,” U.S. patent4,925,281 (15May1990).

J. G. Baker, W. T. Plummer, “Analytic function optical component,” U.S. patent4,650,292 (17March1987).

Birchall, H. J.

H. J. Birchall, “Lenses and their combination and arrangement in various instruments and apparatus,” U.S. patent2,001,952 (21May1935).

Humphrey, W. E.

L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent3,507,565 (21April1970).

Kitajima, I.

I. Kitajima, “Improvements in lenses,” British patent250,268 (29July1926).

Lewis, R. W.

R. W. Lewis, “Lens and method of producing it,” U.S. patent2,263,509 (18November1941).

Londono, C.

C. Londono, J. J. Mader, T. O’Hagan, M. Manning, “Development of prototype plastic optics,” in Replication and Molding of Optical Components, M. J. Reidl, ed., Proc. SPIE896, 99–108 (1988).
[CrossRef]

Mader, J. J.

C. Londono, J. J. Mader, T. O’Hagan, M. Manning, “Development of prototype plastic optics,” in Replication and Molding of Optical Components, M. J. Reidl, ed., Proc. SPIE896, 99–108 (1988).
[CrossRef]

W. T. Plummer, J. J. Mader, J. W. Roblee, J. Van Tassell, “Precision engineering at polaroid,” in Proceedings of the Preconference Day Addresses on Precision Engineering in Industry—International State of the Art, Eighth International Precision Engineering Seminar, M. Bonis, Y. Alayli, P. Revel, P. McKeown, J. Corbett, eds. (Université de Technologie de Compiègne, Division Systemes Méchaniques, Centre de Recherches de Royallieu, BP 649-F-60206 Compiègne, France, 1995), pp. 24–29.

Manning, M.

C. Londono, J. J. Mader, T. O’Hagan, M. Manning, “Development of prototype plastic optics,” in Replication and Molding of Optical Components, M. J. Reidl, ed., Proc. SPIE896, 99–108 (1988).
[CrossRef]

O’Hagan, T.

C. Londono, J. J. Mader, T. O’Hagan, M. Manning, “Development of prototype plastic optics,” in Replication and Molding of Optical Components, M. J. Reidl, ed., Proc. SPIE896, 99–108 (1988).
[CrossRef]

Owen, R. C.

R. C. Owen, W. T. Plummer, “Zone focusing optical system,” U.S. patent4,443,067 (17April1984).

Plummer, W. T.

W. T. Plummer, “Unusual optics of the Polaroid SX-70 land camera,” Appl. Opt. 21, 196–202 (1982).
[CrossRef] [PubMed]

W. T. Plummer, “Precision: how to achieve a little more of it, even after assembly,” in Intelligent Automation and Soft Computing, Vol. 1 of Proceedings of the World Automation Congress, M. Jamshidi, C. Nguyen, R. Lumia, J. Yuh, ed. (TSI Press, Albuquerque, N.M., 1994), pp. 193–198 (example 2). This example was reprinted in P. R. Yoder, Mounting Lenses in Optical Instruments, Vol. TT 21 of SPIE Tutorial Text Series, A. R. Weeks, ed. (SPIE Press, Bellingham, Wash., 1995), p. 27.

R. C. Owen, W. T. Plummer, “Zone focusing optical system,” U.S. patent4,443,067 (17April1984).

J. G. Baker, W. T. Plummer, “Analytic function optical component,” U.S. patent4,650,292 (17March1987).

W. T. Plummer, “Landscape lens,” U.S. patent3,902,792 (2September1975).

W. T. Plummer, J. J. Mader, J. W. Roblee, J. Van Tassell, “Precision engineering at polaroid,” in Proceedings of the Preconference Day Addresses on Precision Engineering in Industry—International State of the Art, Eighth International Precision Engineering Seminar, M. Bonis, Y. Alayli, P. Revel, P. McKeown, J. Corbett, eds. (Université de Technologie de Compiègne, Division Systemes Méchaniques, Centre de Recherches de Royallieu, BP 649-F-60206 Compiègne, France, 1995), pp. 24–29.

Roblee, J. W.

W. T. Plummer, J. J. Mader, J. W. Roblee, J. Van Tassell, “Precision engineering at polaroid,” in Proceedings of the Preconference Day Addresses on Precision Engineering in Industry—International State of the Art, Eighth International Precision Engineering Seminar, M. Bonis, Y. Alayli, P. Revel, P. McKeown, J. Corbett, eds. (Université de Technologie de Compiègne, Division Systemes Méchaniques, Centre de Recherches de Royallieu, BP 649-F-60206 Compiègne, France, 1995), pp. 24–29.

Van Tassell, J.

W. T. Plummer, J. J. Mader, J. W. Roblee, J. Van Tassell, “Precision engineering at polaroid,” in Proceedings of the Preconference Day Addresses on Precision Engineering in Industry—International State of the Art, Eighth International Precision Engineering Seminar, M. Bonis, Y. Alayli, P. Revel, P. McKeown, J. Corbett, eds. (Université de Technologie de Compiègne, Division Systemes Méchaniques, Centre de Recherches de Royallieu, BP 649-F-60206 Compiègne, France, 1995), pp. 24–29.

Appl. Opt. (1)

Other (15)

W. T. Plummer, “Landscape lens,” U.S. patent3,902,792 (2September1975).

R. C. Owen, W. T. Plummer, “Zone focusing optical system,” U.S. patent4,443,067 (17April1984).

J. G. Baker, W. T. Plummer, “Analytic function optical component,” U.S. patent4,650,292 (17March1987).

I. Kitajima, “Improvements in lenses,” British patent250,268 (29July1926).

H. J. Birchall, “Lenses and their combination and arrangement in various instruments and apparatus,” U.S. patent2,001,952 (21May1935).

R. W. Lewis, “Lens and method of producing it,” U.S. patent2,263,509 (18November1941).

L. W. Alvarez, “Two element variable power lens,” U.S. patent3,305,294 (21February1967).

L. W. Alvarez, W. E. Humphrey, “Variable power lens and system,” U.S. patent3,507,565 (21April1970).

J. G. Baker, “Variable power, analytic function, optical component in the form of a pair of laterally adjustable plates having shaped surfaces, and optical systems including such components,” U.S. patent3,583,790 (8June1971).

J. G. Baker, “Optical system utilizing a transversely movable plate for focusing,” U.S. patent4,457,592 (3July1984).

J. G. Baker, “Zoom lens,” U.S. patent4,925,281 (15May1990).

Ref. 4, example 7 and Fig. 12.

C. Londono, J. J. Mader, T. O’Hagan, M. Manning, “Development of prototype plastic optics,” in Replication and Molding of Optical Components, M. J. Reidl, ed., Proc. SPIE896, 99–108 (1988).
[CrossRef]

W. T. Plummer, J. J. Mader, J. W. Roblee, J. Van Tassell, “Precision engineering at polaroid,” in Proceedings of the Preconference Day Addresses on Precision Engineering in Industry—International State of the Art, Eighth International Precision Engineering Seminar, M. Bonis, Y. Alayli, P. Revel, P. McKeown, J. Corbett, eds. (Université de Technologie de Compiègne, Division Systemes Méchaniques, Centre de Recherches de Royallieu, BP 649-F-60206 Compiègne, France, 1995), pp. 24–29.

W. T. Plummer, “Precision: how to achieve a little more of it, even after assembly,” in Intelligent Automation and Soft Computing, Vol. 1 of Proceedings of the World Automation Congress, M. Jamshidi, C. Nguyen, R. Lumia, J. Yuh, ed. (TSI Press, Albuquerque, N.M., 1994), pp. 193–198 (example 2). This example was reprinted in P. R. Yoder, Mounting Lenses in Optical Instruments, Vol. TT 21 of SPIE Tutorial Text Series, A. R. Weeks, ed. (SPIE Press, Bellingham, Wash., 1995), p. 27.

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Figures (13)

Fig. 1
Fig. 1

Early concept of optical focus adjustment by parallel lateral translation of nonrotational aspheric lens shapes. Two such shapes may cancel their optical power when adjacent and centered (lower left), but produce a net dioptric power when they are moved laterally (lower right).

Fig. 2
Fig. 2

Schematic of a nonrotational component shaped to provide focusing along optical axis O A by rotatory motion about a parallel mechanical axis R A .

Fig. 3
Fig. 3

Two components, such as shown in Fig. 1, positioned for focusing by the rotation of one or both.

Fig. 4
Fig. 4

Definition of the relationships between the Cartesian coordinates xyz, the polar coordinates ϕ–r, and the bent coordinates .

Fig. 5
Fig. 5

Approximate equivalence between a pair of nonrotational aspheric components (right) and a functionally similar pair of rotationally symmetric components (left). The local air space that is parallel to the optical axis anywhere on the face of one set of plates is matched by the local air space at the corresponding spot on the other pair.

Fig. 6
Fig. 6

Distribution of 19 field locations evaluated for design optimization in the Polaroid Spectra (Vision) camera and the later ProCam. The optical axis of the basic lens design intersects the format at location 1, and the displaced mechanical pivot is similarly projected onto the spot marked P. The lens axis is decentered slightly toward the top of the film.

Fig. 7
Fig. 7

Layout of the inverted telephoto basic system cited in design studies.

Fig. 8
Fig. 8

Standard evaluation of the inverted telephoto basic system of Fig. 7.

Fig. 9
Fig. 9

Schematic layout of the optical parts in the Spectra camera. The f/10 aperture stop, which opens and closes to function as the photographic shutter, is located between the two closely spaced nonrotational aspheric surfaces.

Fig. 10
Fig. 10

(a) Graphic display of the form of the moving nonrotational aspheric component of the Spectra camera. The mechanical axis is marked by the +. (b) Form of the companion fixed nonrotational aspheric component, viewed inverted as a molding tool.

Fig. 11
Fig. 11

Face view of the area swept by the local clear aperture on the moving nonrotational component. Ten overlapping positions were used to achieve ten zones of focus in this arc of only 2.5 aperture diameters extent.

Fig. 12
Fig. 12

Photograph of the three molded optical components, supported by clear glass spaced above grid paper.

Fig. 13
Fig. 13

Cell-mounted glass assembly that is substituted for the plastic front meniscus to remove lateral chromatic aberration. This section is supplied preset to a focus specification and can be snapped into a camera shutter with the molded nonrotational components, with no further adjustment. This model was sold as the Minolta Instant Pro.

Tables (6)

Tables Icon

Table 1 Basic Optical System for Quintic Focus Studies

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Table 2 Computed Design Coefficients of a Contrarotating Pair—Case A

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Table 3 Computed Design Coefficients of a Single Rotating Plate (surface 11); Adjacent Plate (Surface 12) is Real but Fixed—Case B.6

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Table 4 Computed Design Coefficients of a Single Rotating Plate (Surface 10); Adjacent Fixed Plate is Virtual (on Surface 6)—Case C

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Table 5 Summary of rms Blur Diameter Evaluations in Study

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Table 6 Summary of Spectra Camera Focus Performance, rms Blur Diametera (mm)

Equations (80)

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z=cx2+y21+1-1-e2c2x2+y21/2+βx2+y22+γx2+y23+,
z=12 cx2+y2+β+181-e2c3x2+y22+γ+1161-e22c5x2+y23+.
AS¯=di+zi+1-zi=di+12ci+1-cix2+y2+Hi+1-Hix2+y22+Ki+1-Kix2+y23+.
Hi=βi+181-ei2ci3,
Ki=γi+1161-e22ci5
ΔAS¯=AS¯-AS¯=12Δcx2+y2+ΔHx2+y22+ΔKx2+y23+,
Δc=ci+1-ci-ci+1-ci,
ΔH=Hi+1-Hi-Hi+1-Hi,
ΔK=Ki+1-Ki-Ki+1-Ki.
zi=k=0Nj=0N-k Aijkx¯jy¯k,
zi+1z¯i+1=k=0Nj=0N-k Aijkx¯jy¯k+zx2+y2xyz,
AS¯=di+zx2+y2xyz¯,
AS¯=di+  Aijkx¯jy¯k+zx2+y2xyz¯-  Aijkx¯jy¯-rθ¯k,
ΔAS¯=  Aijkx¯jky¯k-1rθ¯+
x¯=r-a,
y¯=rϕ,
x=r cos ϕ-a,
y=r sin ϕ.
x=x¯-y¯22a+x¯+y¯424a+x¯3-,
y=y¯-y¯36a+x¯2+y¯5120a+x¯4+,
x¯=x+12a y2-12a2 xy2+12a3 x2y2-18a3 y4+,
y¯=y+16a2 y3-13a3 xy3+12a4 x2y3-11120a4 y5+.
ΔAS¯=12 Δcx¯2+12 Δcy¯2-Δc 12a+x¯ x¯y¯2+ΔHx¯4+2ΔHx¯2y¯2+ΔH-Δc 124a+x¯2y¯4-ΔH 2a+x¯ x¯3y¯2-2ΔH-Δc 124a+x¯2×x¯y¯4a+x¯+ΔKx¯6+3ΔKx¯4y¯2+3ΔK+5ΔH6a+x¯2x¯2y¯4+ΔK-ΔH6a+x¯2+Δc720a+x¯4y¯6+.
zi=zi+1-zx2+y2x¯y¯z¯=Ai21x¯2y¯+Ai03y¯3+Ai13x¯y¯3+Ai41x¯4y¯+Ai23x¯2y¯3+Ai05y¯5+Ai15x¯y¯5+Ai33x¯3y¯3+Ai61x¯6y¯+Ai43x¯4y¯3+Ai25x¯2y¯5+Ai07y¯7+,
Ai21=Δc 12a+x¯θ¯,
Ai03=Δc 16a+x¯θ¯,
Ai13=-Δc 16a+x¯2θ¯,
Ai41=ΔH 1a+x¯θ¯,
Ai23=ΔH 23a+x¯θ¯,
Ai05=ΔH 15a+x¯θ¯-Δc 1120a+x¯3θ¯,
Ai15=-ΔH 25a+x¯2θ¯+Δc 1120a+x¯4θ¯,
Ai33=-ΔH 23a+x¯2θ¯,
Ai61=ΔK 1a+x¯θ¯,
Ai43=ΔK 1a+x¯θ¯,
Ai25=ΔK 35a+x¯θ¯+ΔH 16a+x¯3θ¯,
Ai07=ΔK 17a+x¯θ¯-ΔH 142a+x¯3θ¯+Δc 15040a+x¯5θ¯.
zi=zi+1-zx2+y2rϕ=k=0Nj=0N-k Aijkr-ajrkϕk
zi=zi+1-zx2+y2rϕ=lkj Bijklr-ajrkϕl
zi=zi+1-zx2+y2rϕ=Δc 12θ¯r-a2ϕ+Δc 16θ¯ r2ϕ3-Δc 16θ¯r-arϕ3+ΔH 1θ¯r-a4ϕ+ΔH 23θ¯r-a2r2ϕ3+ΔH 15θ¯ r4ϕ5-Δc 1120θ¯ r2ϕ5-ΔH 25θ¯r-a×r3ϕ5+Δc 1120θ¯r-arϕ5-ΔH 23θ¯r-a3×rϕ3+ΔK 1θ¯r-a6ϕ+ΔK 1θ¯r-a4r2ϕ3+ΔK 35θ¯r-a2r4ϕ5+ΔH 16θ¯r-a2r2ϕ5+ΔK 17θ¯ r6ϕ7-ΔH 142θ¯ r4ϕ7+Δc 15040θ¯ r2ϕ7+.
zi=Bi201r-a2ϕ+Bi023r2ϕ3+Bi113r-arϕ3+Bi401r-a4ϕ+Bi223r-a2r2ϕ3+Bi045r4ϕ5+Bi025r2ϕ5+Bi135r-ar3ϕ5+Bi115r-arϕ5+Bi313r-a3rϕ3+Bi601r-a6ϕ+Bi423×r-a4r2ϕ3+Bi245r-a2r4ϕ5+Bi225×r-a2r2ϕ5+Bi067r6ϕ7+Bi047r4ϕ7+Bi027r2ϕ7,
Bi201=Δc1/2θ¯,
Bi023=Δc1/6θ¯,
Bi113=-Δc1/6θ¯,
Bi401=ΔH1/θ¯,
Bi223=ΔH2/3θ¯,
Bi045=ΔH1/5θ¯,
Bi025=-Δc1/120θ¯,
Bi135=-ΔH2/5θ¯,
Bi115=Δc1/120θ¯,
Bi313=-ΔH2/3θ¯,
Bi601=ΔK1/θ¯,
Bi423=ΔK1/θ¯,
Bi245=ΔK3/5θ¯,
Bi225=ΔH1/6θ¯,
Bi067=ΔK1/7θ¯,
Bi047=-ΔH1/42θ¯,
Bi027=Δc1/5040θ¯.
zi=zi+1-zx2+y2x¯y¯z¯=Ai21x¯2y¯+Ai03y¯3+Ai31x¯3y¯+Ai13x¯y¯3+Ai41x¯4y¯+Ai23x¯2y¯3+Ai05y¯5+Ai51x¯5y¯+Ai33x¯3y¯3+Ai15x¯y¯5+Ai61x¯6y¯+Ai43x¯4y¯3+Ai25x¯2y¯5+Ai07y¯7+,
Ai21=Δc1/2aθ¯,
Ai03=Δc1/6aθ¯,
Ai31=-Δc1/2a2θ¯,
Ai13=-Δc1/3a2θ¯,
Ai41=Δc 12a2+ΔH1aθ¯,
Ai23=Δc 12a2+23 ΔH1aθ¯,
Ai05=-Δc 1120a2+ΔH 151aθ¯,
Ai51=-Δc 12a3-ΔH 1a1aθ¯,
Ai33=-Δc 23a3-ΔH 43a1aθ¯,
Ai15=Δc 130a3-ΔH 35a1aθ¯,
Ai61=Δc 12a4+ΔH 1a2+ΔK1aθ¯,
Ai43=Δc 56a4+ΔH 2a2+ΔK1aθ¯,
Ai25=-Δc 512a4+ΔH 76a2+ΔK 351aθ¯
Ai07=Δc 15040a4-ΔH 142a2+ΔK 171aθ¯.
zi=zi+1-zx2+y2xyz=Ai21x2y+Ai03y3+Ai31x3y+Ai13xy3+Ai41x4y+Ai23x2y3+Ai05y5+,
Ai21=Δc1/2aθ¯,
Ai03=Δc1/6aθ¯,
Ai31=-Δc1/2a2θ¯,
Ai13=Δc1/6a2θ¯,
Ai41=Δc 12a2+ΔH1aθ¯,
Ai23=-Δc 23a2+23 ΔH1aθ¯,
Ai05=Δc 130a2+15 ΔH1aθ¯.

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