Abstract

New compound eye systems for nonunity magnification projection are shown. As all the beams of light on the optical axes of erect or inverted real image systems intersect perpendicular to the object and image planes in these systems, it becomes possible to get rid of any local variation in magnification, which deteriorates the image quality of earlier compound eye systems.

© 1990 Optical Society of America

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References

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  1. J. D. Rees, D. Kay, W. L. Lama, “Gradient Index Lens Array Having Reducing Properties,” U.S. Patent4,331,380 (25May1982).
  2. M. Nishikawa, “Non-Unity Magnification Projection Systems,” Japanese Patent Laid-Open Publication45420 (14Mar.1984).
  3. M. Nishikawa, “Non-Unity Magnification Projection Systems Using Lens Arrays,” Japanese Patent Laid-Open Publication198422 (10Nov.1984).
  4. J. D. Rees, W. L. Lama, “Reduction/Enlargement Gradient-Index Lens Arrays,” Appl. Opt. 23, 1715–1724 (1984).
    [CrossRef] [PubMed]
  5. J. F. Goldenberg, J. J. Miceli, D. T. Moore, “Photocopy Reduction Arrays: Design and Analysis,” Appl. Opt. 24, 4288–4296 (1985).
    [CrossRef] [PubMed]
  6. K. Araki, “Optical Projection System,” U.S. Patent4,750,022 (7June1988).

1985 (1)

1984 (1)

Araki, K.

K. Araki, “Optical Projection System,” U.S. Patent4,750,022 (7June1988).

Goldenberg, J. F.

Kay, D.

J. D. Rees, D. Kay, W. L. Lama, “Gradient Index Lens Array Having Reducing Properties,” U.S. Patent4,331,380 (25May1982).

Lama, W. L.

J. D. Rees, W. L. Lama, “Reduction/Enlargement Gradient-Index Lens Arrays,” Appl. Opt. 23, 1715–1724 (1984).
[CrossRef] [PubMed]

J. D. Rees, D. Kay, W. L. Lama, “Gradient Index Lens Array Having Reducing Properties,” U.S. Patent4,331,380 (25May1982).

Miceli, J. J.

Moore, D. T.

Nishikawa, M.

M. Nishikawa, “Non-Unity Magnification Projection Systems,” Japanese Patent Laid-Open Publication45420 (14Mar.1984).

M. Nishikawa, “Non-Unity Magnification Projection Systems Using Lens Arrays,” Japanese Patent Laid-Open Publication198422 (10Nov.1984).

Rees, J. D.

J. D. Rees, W. L. Lama, “Reduction/Enlargement Gradient-Index Lens Arrays,” Appl. Opt. 23, 1715–1724 (1984).
[CrossRef] [PubMed]

J. D. Rees, D. Kay, W. L. Lama, “Gradient Index Lens Array Having Reducing Properties,” U.S. Patent4,331,380 (25May1982).

Appl. Opt. (2)

Other (4)

K. Araki, “Optical Projection System,” U.S. Patent4,750,022 (7June1988).

J. D. Rees, D. Kay, W. L. Lama, “Gradient Index Lens Array Having Reducing Properties,” U.S. Patent4,331,380 (25May1982).

M. Nishikawa, “Non-Unity Magnification Projection Systems,” Japanese Patent Laid-Open Publication45420 (14Mar.1984).

M. Nishikawa, “Non-Unity Magnification Projection Systems Using Lens Arrays,” Japanese Patent Laid-Open Publication198422 (10Nov.1984).

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Figures (19)

Fig. 1
Fig. 1

Compound eye system of erect unity (one to one) magnification: (1) object plane; (2) image plane; (3) compound eye system; and IS is an image system.

Fig. 2
Fig. 2

Example of an earlier compound eye system for nonunity magnification projection. All the notations are the same as in Fig. 1.

Fig. 3
Fig. 3

Second example of an earlier compound eye system for nonunity magnification projection. All the notations are the same as in Fig. 1.

Fig. 4
Fig. 4

Third example of an earlier compound eye system for nonunity magnification projection. All the notations are the same as in Fig. 1.

Fig. 5
Fig. 5

Types of degraded images caused by overlapping mismatch: (A) pattern on the object plane; A1, B1, C1, D1, and E1 correspond to the fields of view of the respective image systems; (B)–(F) A2, B2, C2, D2, and E2 indicate the projected pattern on the image plane corresponding to A1, B1, C1, D1, and E1; (B) matching of images on the image plane at unity magnification; (C) mismatching of images at reduced magnification; (D) mismatching caused by local variation in magnification; (E) mismatching caused by image rotation; (F) matching of images at reduced magnification.

Fig. 6
Fig. 6

Explanation of local variation in magnification: (1) object plane of the whole system; (2) image plane of the whole system; (1′) local object plane for magnification m; (2′) local image plane for magnification m; α, field angle of an erect real image system; , tilt angle of a local object plane or a local image plane with respect to the object and image planes; X, coordinate of intersection of the optical axis of an image system with the object plane of the whole system; A, local coordinate of the object with respect to the intersection of the optical axis of an image system; m, projection magnification of the whole system; m1, local projection magnification on the image plane, which is gradually varied around m in the field of view, in the case where the image system IS is tilted with respect to the object and image planes.

Fig. 7
Fig. 7

Example of a new compound eye system for nonunity magnification. Paths of light L1,L2,L3 … on the optical axes of real image systems IS1,IS2,IS3 … are shown as A1-A2-A3-A4, B1-B2-B3-B4, C1-C2-C3-C4, etc. Points A1,B1,C1 … are on the object plane 1 and are projected to points A4,B4,C4 … on image plane 2. Points A2,B2,C2 … and A3,B3,C3 …, respectively, denote first and second deflecting points. The deflecting means are not shown for the sake of simplicity. All the image systems are erect real ones, and the lengths of optical axes for respective image systems are arranged all the same, so all the image systems can be equivalent.

Fig. 8
Fig. 8

Top plan view of Fig. 7. All the imge systems are arranged so that all the produced lines of the optical axes between two deflecting means intersect at one point 0 in a multilevel manner. Using DL1, and DL2, the projection magnification can be expressed as in Eq. (2).

Fig. 9
Fig. 9

Another example of a new compound eye system for nonunity magnification. All the notations are almost the same as in Fig. 7, but each image system is an inverted real one and a prime was added for the sake of distinction.

Fig. 10
Fig. 10

Top plan view of Fig. 9. All the notations are almost the same as in Fig. 8, but primes were added to distinguish from the case of erect real image systems.

Fig. 11
Fig. 11

Example of a flat plane arrangement. The image systems are erect real ones and are disposed in the same plane, but in this arrangement the total optical length of each image system is different. All the notations are the same as in Fig. 7.

Fig. 12
Fig. 12

Another example of the flat plane arrangement. The image systems are inverted real ones and are disposed in the same plane. All the notations are the same as in Fig. 9.

Fig. 13
Fig. 13

Example of a dense packing arrangement. The image systems are erect real ones and are disposed on several stages between two deflecting means to permit dense packing. All the notations are the same as in Fig. 7.

Fig. 14
Fig. 14

Another example of the dense packing arrangement. Several image systems are inverted real ones and are disposed in two stages between two deflecting means to achieve dense packing. All the notations are the same as in Fig. 9.

Fig. 15
Fig. 15

Example of a multirow arrangement. Erect real image systems are disposed in two rows. All the notations are the same as in Fig. 7.

Fig. 16
Fig. 16

Another example of the multirow arrangement. The inverted real image systems are disposed in two rows. All the notations are the same as in Fig. 9.

Fig. 17
Fig. 17

Example of a new compound eye system using two curved reflectors. Two paraboloidal reflectors are used instead of several mirrors. The first paraboloidal surface includes deflecting points A2,B2,C2 …, and the second paraboloidal surface includes deflecting points A3,B3,C3 …. All the notations are the same as in Fig. 7.

Fig. 18
Fig. 18

Side plan view of Fig. 17. All the notations are the same as those in Fig. 17.

Fig. 19
Fig. 19

Front plan view of Fig. 17. All the notations are the same as those in Fig. 17.

Tables (1)

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Table I Local Variation in Magnification

Equations (13)

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m 1 = m cos ( α + ) / cos ( α - ) .
m = A 4 , B 4 ¯ A 1 , B 1 ¯ = D L 2 D L 1 .
B 1 = ( X , l / 2 , h / 2 ) , B 2 = ( X , l / 2 , - h 1 ) , B 3 = ( m X , - l / 2 , h 2 ) , B 4 = ( m X , - l / 2 , - h / 2 ) .
h 1 + h 2 = - ( 1 - m ) 2 X 2 - l 2 + ( L - h ) 2 2 ( L - h ) ,
L = L 1 + L 2 + z 0 L 1 = [ 1 / m - cos ( g z 0 ) ] n 0 sin ( g z 0 ) , L 2 = - [ m - cos ( g z 0 ) ] n 0 sin ( g z 0 ) ,
n = n 0 ( 1 - g 2 r 2 + h 3 g 4 r 4 + ) 1 / 2 ,
m = A 4 , B 4 ¯ A 1 , B 1 ¯ = D L 2 D L 1 ,
B 1 = ( X , l / 2 + Y , h / 2 ) , B 2 = ( X , l / 2 + Y , - h 1 ) , B 3 = ( m X , - l / 2 + m Y , h 2 ) , B 4 = ( m X , - l / 2 + m Y , - h / 2 ) ,
h 1 + h 2 = - ( 1 - m ) 2 X 2 - { l + ( 1 - m ) Y 2 } + ( L - h ) 2 2 ( L - h ) .
h 1 = - 2 ( 1 - m ) X 2 - 2 ( 1 - m ) Y - 4 l Y - l 2 + ( L - h ) 2 4 ( L - h ) + C ,
h 2 = 2 m ( 1 - m ) X 2 + 2 m ( 1 - m ) Y + 4 m l Y - l 2 + ( L - h ) 2 4 ( L - h ) - C ,
Z = 2 ( 1 - m ) X 2 + 2 ( 1 - m ) Y 2 + 4 l Y + l 2 - ( L - h ) 2 4 ( L - h ) + C ,
Z = 2 ( 1 - m ) X 2 + 2 ( 1 - m ) Y 2 + 4 m l Y - m l 2 + m ( L - h ) 2 4 m ( L - h ) - C ,

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