Abstract

We propose what to our knowledge is a novel optical system that can scan an optical axis simultaneously in the perpendicular and the longitudinal directions (a two-dimensional scanner), which we have named the FOCOIVA (acronym for focal constant and image variable) lens system. We give the equations for first-order analysis and also the equations of motion for the lenses. Examples calculated with these equations are presented, and finally we give the optical designs for the writing system that will be used for a reader of digital documents.

© 2001 Optical Society of America

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References

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  1. H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
    [CrossRef]
  2. F. J. Kahn, “IR-laser-addressed thermo-optic smectic liquid crystal storage displays,” Appl. Phys. Lett. 22, 111–113 (1973).
    [CrossRef]
  3. A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
    [CrossRef]
  4. T. Matsuda, F. Abe, H. Takahashi, “Laser printer scanning system with a parabolic mirror,” Appl. Opt. 17, 878–884 (1978).
    [CrossRef] [PubMed]
  5. S. Minami, K. Minoura, H. Yamamoto, “Scanning optical system of the Canon laser beam printer,” in Design of Optical Systems Incorporating Low Power Lasers (Critical Reviews), D. C. O’Shea, ed., Proc. SPIE741, 118–139 (1987).
    [CrossRef]
  6. M. Hosoya, T. Susuki, S. Vazquez, “The display system and drawing system of the graphical images,” Japanese patenttoku-gan-Hei-10-364405 (22Dec.1998).
  7. D. C. Sinclair, “First order optics,” in Image-Forming Optics, D. C. Sinclair, ed. (U. Rochester Press, Rochester, N.Y., 1971, Chap. 1.
  8. D. C. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985).
  9. W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1991), Chap. 12.

1978 (1)

1975 (1)

A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
[CrossRef]

1973 (1)

F. J. Kahn, “IR-laser-addressed thermo-optic smectic liquid crystal storage displays,” Appl. Phys. Lett. 22, 111–113 (1973).
[CrossRef]

1972 (1)

H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
[CrossRef]

Abe, F.

Fraser, D. B.

H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
[CrossRef]

Hosoya, M.

M. Hosoya, T. Susuki, S. Vazquez, “The display system and drawing system of the graphical images,” Japanese patenttoku-gan-Hei-10-364405 (22Dec.1998).

Ishibashi, T.

A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
[CrossRef]

Kahn, F. J.

F. J. Kahn, “IR-laser-addressed thermo-optic smectic liquid crystal storage displays,” Appl. Phys. Lett. 22, 111–113 (1973).
[CrossRef]

H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
[CrossRef]

Matsuda, T.

Maydan, D.

H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
[CrossRef]

Melchior, H.

H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
[CrossRef]

Minami, S.

S. Minami, K. Minoura, H. Yamamoto, “Scanning optical system of the Canon laser beam printer,” in Design of Optical Systems Incorporating Low Power Lasers (Critical Reviews), D. C. O’Shea, ed., Proc. SPIE741, 118–139 (1987).
[CrossRef]

Minoura, K.

S. Minami, K. Minoura, H. Yamamoto, “Scanning optical system of the Canon laser beam printer,” in Design of Optical Systems Incorporating Low Power Lasers (Critical Reviews), D. C. O’Shea, ed., Proc. SPIE741, 118–139 (1987).
[CrossRef]

Morioka, T.

A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
[CrossRef]

O’Shea, D. C.

D. C. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985).

Sasaki, A.

A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
[CrossRef]

Sinclair, D. C.

D. C. Sinclair, “First order optics,” in Image-Forming Optics, D. C. Sinclair, ed. (U. Rochester Press, Rochester, N.Y., 1971, Chap. 1.

Susuki, T.

M. Hosoya, T. Susuki, S. Vazquez, “The display system and drawing system of the graphical images,” Japanese patenttoku-gan-Hei-10-364405 (22Dec.1998).

Takagi, T.

A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
[CrossRef]

Takahashi, H.

Vazquez, S.

M. Hosoya, T. Susuki, S. Vazquez, “The display system and drawing system of the graphical images,” Japanese patenttoku-gan-Hei-10-364405 (22Dec.1998).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1991), Chap. 12.

Yamamoto, H.

S. Minami, K. Minoura, H. Yamamoto, “Scanning optical system of the Canon laser beam printer,” in Design of Optical Systems Incorporating Low Power Lasers (Critical Reviews), D. C. O’Shea, ed., Proc. SPIE741, 118–139 (1987).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. Melchior, F. J. Kahn, D. Maydan, D. B. Fraser, “Thermally addressed electrically erased high-resolution liquid-crystal light valves,” Appl. Phys. Lett. 21, 392–394 (1972).
[CrossRef]

F. J. Kahn, “IR-laser-addressed thermo-optic smectic liquid crystal storage displays,” Appl. Phys. Lett. 22, 111–113 (1973).
[CrossRef]

IEEE Trans. Electron Dev. (1)

A. Sasaki, T. Morioka, T. Takagi, T. Ishibashi, “Thermally addressed liquid-crystal display for dynamic figures,” IEEE Trans. Electron Dev. 63, 805–806 (1975).
[CrossRef]

Other (5)

S. Minami, K. Minoura, H. Yamamoto, “Scanning optical system of the Canon laser beam printer,” in Design of Optical Systems Incorporating Low Power Lasers (Critical Reviews), D. C. O’Shea, ed., Proc. SPIE741, 118–139 (1987).
[CrossRef]

M. Hosoya, T. Susuki, S. Vazquez, “The display system and drawing system of the graphical images,” Japanese patenttoku-gan-Hei-10-364405 (22Dec.1998).

D. C. Sinclair, “First order optics,” in Image-Forming Optics, D. C. Sinclair, ed. (U. Rochester Press, Rochester, N.Y., 1971, Chap. 1.

D. C. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985).

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1991), Chap. 12.

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Figures (26)

Fig. 1
Fig. 1

Layout of the writing system for the RDD, lateral view.

Fig. 2
Fig. 2

Top view of the writing system for the RDD.

Fig. 3
Fig. 3

Layout of the FOCOIVA lens system.

Fig. 4
Fig. 4

Image position versus the position of lens L2 and its power φ2.

Fig. 5
Fig. 5

Image position versus the position of lens L2; φ2 = 0.014 mm-1.

Fig. 6
Fig. 6

Position of lens L3 relative to that of L2.

Fig. 7
Fig. 7

Motions of lenses for Case 1.

Fig. 8
Fig. 8

Image position versus the position of lens L2 and power for the interval [1.7 × 10-15, 0.0228].

Fig. 9
Fig. 9

Image position versus the position of lens L2 and power for the interval [-0.0184, 0.0149].

Fig. 10
Fig. 10

Image position relative to the position of lens L2, φ2 = 0.005 mm-1, Case 2.

Fig. 11
Fig. 11

Position of lens L3 relative to that of L2, Case 2.

Fig. 12
Fig. 12

Motions of lenses for Case 2.

Fig. 13
Fig. 13

Lenses for the glass version of the RDD.

Fig. 14
Fig. 14

Lenses and ray trace in lateral scanning for the glass version.

Fig. 15
Fig. 15

Wave-front aberrations for the glass version; image position, 300 mm.

Fig. 16
Fig. 16

Wave-front aberrations for the glass version; image position, 450 mm.

Fig. 17
Fig. 17

Wave-front aberrations for the glass version; image position, 599.3 mm.

Fig. 18
Fig. 18

Spot size for total lateral scanning in six longitudinal positions, glass version.

Fig. 19
Fig. 19

Spot shape for 49 positions on the total scan area.

Fig. 20
Fig. 20

Motions of lenses for the WS, glass version.

Fig. 21
Fig. 21

Lenses for the plastic version.

Fig. 22
Fig. 22

Lenses and ray trace in lateral scanning for the plastic version.

Fig. 23
Fig. 23

Wave-front aberrations for the plastic version; image position, 202.2 mm.

Fig. 24
Fig. 24

Wave-front aberrations for the plastic version; image position, 323.4 mm.

Fig. 25
Fig. 25

Wave-front aberrations for the plastic version; image position, 446.4 mm.

Fig. 26
Fig. 26

Lens motions for the WS, plastic version.

Tables (3)

Tables Icon

Table 1 Data for Cases 1 and 2 of the Lens System

Tables Icon

Table 2 Construction Parameters for the Glass Version of the RDD Writing Systema

Tables Icon

Table 3 Construction Parameters for the Plastic Version of the RDD Writing Systema

Equations (41)

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abcd=1-φ40110d311-φ30110d21×1-φ20110d111φ101,
a=1-d1φ21-d3φ41-d2φ3-d2φ4-d11-d3φ4φ3+φ4,
b=-1-d1φ2φ1+φ21-d3φ41-d2φ3-d2φ4-1-d1φ11-d3φ4φ3+φ4,
c=1-d1φ21-d2φ3d3+d2+d11-d3φ3,
d=1-d1φ11-d3φ3-1-d1φ2φ1+φ2×1-d2φ3d3+d2
φ=-b;
φ=1-d1φ2φ1+φ21-d3φ41-d2φ3-d2φ4+1-d1φ11-d3φ4φ3+φ4.
u4h4=abcd0h0,
u4=bh0,
h4=dh0,
d4=-h4/u4.
d4=1/φ1-d1φ11-d3φ3-1-d1φ2φ1+φ21-d2φ3d3+d2.
D=d1+d2+d3.
ū4h¯4=abcdααd0,
mα=ū4/α,
mα=1-d1φ21-d3φ41-d2φ3-d2φ4-d11-d3φ4φ3+φ4-φd0.
h¯5=α/φ.
d1i=0,d2i=D,d3i=0.
-φ3φ41-d1φ2φ1+φ2d32+1+D-d1φ41-d1φ2φ1+φ2-1-d1φ1φ4φ3d3+1-d1φ2φ1+φ21-D-d1φ3+φ4+1-d1φ1φ3+φ4-φ=0.
φ=φ1+φ2+φ3+φ4-Dφ1+φ2φ3+φ4,
d4i=1/φ1-Dφ1+φ2,
mαi=1-Dφ3+φ4-φd0,
φ4=φ1+φ21-Dφ1+φ2,
C1=1-mαi-φd0D,
C2=1-φd4iD,
φ1=C2-φ2,
φ3=C1-φ4,
φ4=C21-DC2,
mαi=1-φD1-C2D-φd0.
d1i=0,d2i=0,d3i=D.
φ=φ1+φ2+φ3+φ4-Dφ4φ1+φ2+φ3,
d4i=1/φ1-Dφ1+φ2+φ3,
mαi=1-Dφ4-φd0.
φ3φ41-d1φ2φ1+φ2d22+1+D-d1φ4×1-d1φ2φ1+φ2-1-d1φ1φ4φ3d2×1-d1φ2φ1+φ21-D-d1φ4+1-d1φ1φ3+φ4-D-d1φ3φ4-φ=0.
φ4=φ1+φ21+Dφ1+φ2,
φ4=1-mαi-φd0D.
φ4=C1.
φ1=C11-C1D-φ2,
φ3=C21-C1D-C11-C1D.
d0=30 mm,D=60 mm,d4i=200 mm.
w02-w02f2+2zw02f-w02z2+π2w04w0216λ2=0,

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