Abstract

This paper describes an all-holographic straight-line scanner consisting only of a holographic disk and a holographic lens. Scanning beam aberration correction was extensively analyzed using diffraction theory. A new technique for simultaneously optimizing the phase transfer functions of these two holograms is proposed, and a method to construct these two holograms using holographic recording is discussed. This technique led to a compact, high resolution holographic line scanner with a 1/e2 scanning beam spot size of 100–120 μm for a scanning width of 252 mm. The radius of the disk at the center of illumination is only 28 mm.

© 1991 Optical Society of America

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References

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  1. C. J. Kramer, “Holographic Laser Scanner for Nonimpact Printing,” Laser Focus 17, 70–82 (1981).
  2. M. V. Antipin, N. G. Kiselev, “Laser Beam Deflector Utilizing Transmission Holograms,” Tech. Kino I Telev. 6, 43–45 (1979), in Russian.
  3. Y. Ono, N. Nishida, “Holographic Disk Scanners for Bow-Free Scanning,” Appl. Opt. 22, 2132–2136 (1983).
    [CrossRef] [PubMed]
  4. S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “Straight-Line Scanning Analysis of an All Holographic Scanner,” Appl. Opt. 28, 5317–5325 (1989).
    [CrossRef] [PubMed]
  5. Y. Ishii, K. Murata, “Optimum Holographic Disk Scanners With Bow-Locus Corrections,” Proc. Soc. Photo-Opt. Instrum. Eng. 673, 426–433 (1986).
  6. H. P. Herzig, R. Dandliker, “Holographic Optical Scanning Elements With Minimum Aberrations,” Appl. Opt. 27, 4739–4746 (1988).
    [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).
  8. K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded With Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208–217 (1983).
    [CrossRef]
  9. F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).
  10. S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).
  11. R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133–140 (1982).
    [CrossRef]
  12. D. P. Feder, “Automatic Optical Design,” Appl. Opt. 2, 1209–1226 (1963).
    [CrossRef]
  13. S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

1989 (1)

1988 (1)

1987 (1)

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).

1986 (2)

F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).

Y. Ishii, K. Murata, “Optimum Holographic Disk Scanners With Bow-Locus Corrections,” Proc. Soc. Photo-Opt. Instrum. Eng. 673, 426–433 (1986).

1983 (2)

1982 (1)

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

1981 (1)

C. J. Kramer, “Holographic Laser Scanner for Nonimpact Printing,” Laser Focus 17, 70–82 (1981).

1979 (1)

M. V. Antipin, N. G. Kiselev, “Laser Beam Deflector Utilizing Transmission Holograms,” Tech. Kino I Telev. 6, 43–45 (1979), in Russian.

1963 (1)

Antipin, M. V.

M. V. Antipin, N. G. Kiselev, “Laser Beam Deflector Utilizing Transmission Holograms,” Tech. Kino I Telev. 6, 43–45 (1979), in Russian.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Dandliker, R.

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

Feder, D. P.

Fienup, J. R.

K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded With Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208–217 (1983).
[CrossRef]

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

Hasegawa, S.

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “Straight-Line Scanning Analysis of an All Holographic Scanner,” Appl. Opt. 28, 5317–5325 (1989).
[CrossRef] [PubMed]

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).

F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).

S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

Herzig, H. P.

Ikeda, H.

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “Straight-Line Scanning Analysis of an All Holographic Scanner,” Appl. Opt. 28, 5317–5325 (1989).
[CrossRef] [PubMed]

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).

F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).

S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

Inagaki, T.

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “Straight-Line Scanning Analysis of an All Holographic Scanner,” Appl. Opt. 28, 5317–5325 (1989).
[CrossRef] [PubMed]

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).

F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).

S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

Ishii, Y.

Y. Ishii, K. Murata, “Optimum Holographic Disk Scanners With Bow-Locus Corrections,” Proc. Soc. Photo-Opt. Instrum. Eng. 673, 426–433 (1986).

Kato, M.

S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

Kiselev, N. G.

M. V. Antipin, N. G. Kiselev, “Laser Beam Deflector Utilizing Transmission Holograms,” Tech. Kino I Telev. 6, 43–45 (1979), in Russian.

Kramer, C. J.

C. J. Kramer, “Holographic Laser Scanner for Nonimpact Printing,” Laser Focus 17, 70–82 (1981).

Murata, K.

Y. Ishii, K. Murata, “Optimum Holographic Disk Scanners With Bow-Locus Corrections,” Proc. Soc. Photo-Opt. Instrum. Eng. 673, 426–433 (1986).

Nishida, N.

Ono, Y.

Winick, K. A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Yamagishi, F.

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “Straight-Line Scanning Analysis of an All Holographic Scanner,” Appl. Opt. 28, 5317–5325 (1989).
[CrossRef] [PubMed]

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).

F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).

S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Laser Focus (1)

C. J. Kramer, “Holographic Laser Scanner for Nonimpact Printing,” Laser Focus 17, 70–82 (1981).

Opt. Eng. (1)

R. C. Fairchild, J. R. Fienup, “Computer-Originated Aspheric Holographic Optical Elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

Y. Ishii, K. Murata, “Optimum Holographic Disk Scanners With Bow-Locus Corrections,” Proc. Soc. Photo-Opt. Instrum. Eng. 673, 426–433 (1986).

F. Yamagishi, S. Hasegawa, H. Ikeda, T. Inagaki, “Lensless Holographic Line Scanner,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 126–132 (1986).

S. Hasegawa, F. Yamagishi, H. Ikeda, T. Inagaki, “High Resolution Holographic Line Scanner for Use in Diode Laser Printers,” Proc. Soc. Photo-Opt. Instrum. Eng. 747, 8–16 (1987).

Tech. Kino I Telev. (1)

M. V. Antipin, N. G. Kiselev, “Laser Beam Deflector Utilizing Transmission Holograms,” Tech. Kino I Telev. 6, 43–45 (1979), in Russian.

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975).

S. Hasegawa, M. Kato, F. Yamagishi, H. Ikeda, T. Inagaki, “Holographic Lens(3)—Wavelength Shift Compensation,” in Extended Abstracts, Thirty-Second Spring Meeting, Japanese Society of Applied Physics (1985), paper 31p-p-7, in Japanese.

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Figures (13)

Fig. 1
Fig. 1

All-holographic straight-line scanner.

Fig. 2
Fig. 2

Laser beam behavior for different construction and reconstruction wavelengths of the holographic zone plate disk: (a) construction with wavelength λ1 and (b) reconstruction wavelength λ2 is longer than λ1. The reconstructed wave is a plane wave.

Fig. 3
Fig. 3

Laser beam behavior using a divergent spherical reconstructed wave with wavelength λ2. The disk is a holographic zone plate with different construction and reconstruction wavelengths.

Fig. 4
Fig. 4

Parameters for a straight-line scanning holographic disk using a divergent spherical wave as the reference wave. The reconstructed wave is a convergent spherical wave and differs from the reference wave; x-y-z coordinates are defined in the hologram plane, and the z = 0 plane is on the surface of the holographic disk. Reference wave G is a divergent spherical wave; F2 is the distance between the disk and point light source A of the object wave. Point D is the projection of point light source A onto the disk, y2 is the distance between point D and the center of the disk, and R is the distance between the center of the disk and the principal axis of the reconstructed wave on the disk.

Fig. 5
Fig. 5

Coordinates for a holographic disk and holographic lens.

Fig. 6
Fig. 6

Scanning beam diffraction intensity distribution using a holographic disk and aspheric holographic lens.

Fig. 7
Fig. 7

Aspheric holographic disk and aspheric lens design.

Fig. 8
Fig. 8

Scanning beam diffraction intensity distribution using an aspheric holographic disk and aspheric lens: S = 2.40, R = 40 mm.

Fig. 9
Fig. 9

Scanning beam compensation using a holographic disk and lens. The dashed line represents rays of the designed wavelength and the solid line represents other wavelengths.

Fig. 10
Fig. 10

Scanning beam wave aberration for laser diode wavelength deviation. The solid line corresponds to the disk and lens and the dot–dash line to a disk only: d = 10 mm. The disk parameters in Sec. III are used and the F/No. in both cases is 75.

Fig. 11
Fig. 11

Holographic disk recording system geometry. The unaberrated focal point P1 of an object wave was designed using backward skew ray tracing. After P1 is aberration corrected, a point light source is placed at P1.

Fig. 12
Fig. 12

Holographic lens recording system geometry. Focal point Q1 through the plano–concave lens and Q2 through the plano–convex lens are designed using backward ray tracing. The focal points are between the surface of the hologram and the auxiliary optics, and hence, convergent spherical waves toward points Q1 and Q2 are incident on the auxiliary optics for holographic recording.

Fig. 13
Fig. 13

Scanning beam diffraction intensity distribution of holographic recording design. The distance between a laser diode aperture and the holographic lens is 17.00 mm.

Equations (36)

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Δ Φ θ ( X , Y ) = Φ out θ ( X , Y ) Φ out θ ( X , Y ) ,
Φ out ( θ ) ( X , Y ) = k 2 [ X x ( θ ) ] 2 + [ Y y ( θ ) + R ] 2 + L 2 .
A 1 = k 2 2 ( 1 a 0 ( 1 S 2 ) R 2 + F 1 2 R 2 + F 1 2 S { ( y 2 cos θ R ) 2 + F 2 2 [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 + F 2 2 ] 3 / 2 1 R 2 + F 1 2 } + 1 L ( 1 S 2 ) [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 ] + F 2 2 [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 + F 2 2 ] 3 / 2 × [ ( y 2 cos θ R ) 2 + ( 1 S 2 ) ( y 2 sin θ ) 2 + F 2 2 ] ) ,
A 2 = k 2 2 ( 1 a 0 [ ( 1 S 2 ) R 2 + F 1 2 R 2 + F 1 2 ] 3 / 2 S { ( y 2 sin θ ) 2 + F 2 2 [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 + F 2 2 ] 3 / 2 F 1 2 ( R 2 + F 1 2 ) 3 / 2 } + 1 L ( 1 S 2 ) [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 ] + F 2 2 [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 + F 2 2 ] 3 / 2 × [ ( 1 S 2 ) ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 + F 2 2 ] ) ,
A 12 = k 1 ( y 2 cos θ R ) y 2 sin θ [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 + F 2 2 ] 3 / 2 × { 1 S ( 1 S 2 ) [ ( y 2 cos θ R ) 2 + ( y 2 sin θ ) 2 ] + F 2 2 L } .
F 1 = F 2 , y 2 = 2 R .
a 0 = S ( 1 S 2 ) R 2 + F 2 2 .
L = S ( 1 S 2 ) R 2 + F 2 2 .
F 2 = ( S 2 1 ) y 2 ( y 2 R cos θ c ) ,
a 0 = L = S R ( S 2 1 ) ( 3 2 cos θ c ) .
a 0 = L = S R S 2 1 .
E 2 = η k = N N W k A [ Φ out k ( X , Y ) Φ out ( k ) ( X , Y ) ] 2 d X d Y = η k = N N W k A [ Φ in ( X , Y ) + Φ H k ( X , Y ) Φ out ( k ) ( X , Y ) ] 2 d X d Y ,
E 2 Φ in ( X , Y ) = 0 .
Φ in opt ( X , Y ) = k = N N W k Ψ k ( X , Y ) k = N N W k , ( X , Y ) A , Ψ k ( X , Y ) Φ out ( k ) ( X , Y ) Φ H k ( X , Y ) .
Φ H , L ( x , y ) = Φ in opt ( x , y ) Φ L ( x , y ) ,
E 2 Φ in ( X , Y ) = 0 ,
E 2 Φ H ( X , Y ) = 0 .
Φ H ( X , Y ) = Φ H ( 0 ) ( X , Y ) + Φ H ( A ) ( X , Y ) .
Φ H ( 0 ) ( X , Y ) = k 1 [ X 2 + ( Y + R ) 2 + F 1 2 X 2 + ( Y + R y 2 ) 2 + F 2 2 ] ,
Φ H ( A ) ( X , Y ) = k 1 i j C i j X i Y j = k 1 [ C 20 X 2 + C 40 X 4 + C 60 X 6 + C 80 X 8 + C 02 Y 2 + C 04 Y 4 + C 06 Y 6 + C 08 Y 8 + C 22 X 2 Y 2 + C 44 X 4 Y 4 ] .
θ d L = tan 1 [ λ 2 f ( R ) ( d cos θ d L + cos θ i ) ] ,
Φ out = Φ in + Φ H = ( Φ in opt + Φ H ) + ( Φ L Φ L ) .
Φ R ( X , Y ) = k 1 l in .
Φ o ( X , Y ) = k 1 [ l in + T ( X 2 + ( Y + R ) 2 + F 1 2 X 2 + ( Y + R y 2 ) 2 + F 2 2 + i j C i j X i Y j ) ] ,
sin θ i = T R R 2 + F 1 2 ,
a 0 = T ( 1 T 2 ) R 2 + F 2 2 .
l in ( x , y ) = 1 2 π 1 S L Φ in opt ( x , y ) x , m in ( x , y ) = 1 2 π 1 S L Φ in opt ( x , y ) y , n in ( x , y ) = 1 l in ( x , y ) 2 m in ( x , y ) 2 ,
Φ d L = sin 1 ( 1 S L sin θ d L ) ,
l r ( r ) = 1 2 π 1 S L Φ L ( r ) r .
Φ H ( X , Y ) = k 1 R obj ( X , Y ) Φ R ( X , Y ) ,
Φ H , L ( x , y ) = k 1 L [ R L , obj ( x , y ) R L , ref ( x , y ) ] ,
Δ Φ k ( X , Y ) = Φ L ( x , y ) + Φ H , L ( x , y ) + Φ H k ( X , Y ) Φ L G ( x , y ) Φ out k ( 0 ) ( X , Y ) ,
Φ out θ ( X , Y ) = k 2 X 2 + ( Y + a 0 tan θ i ) 2 + a 0 2 + k 1 { X 2 + ( Y + R ) 2 + F 1 2 X 2 + ( Y + R ) 2 + y 2 2 2 y 2 [ X sin θ + ( Y + R ) cos θ ] + F 2 2 } ,
sin θ i = S R R 2 + F 1 2 ,
x ( θ ) = L S y 2 sin θ ( 1 S 2 ) ( R 2 + y 2 2 2 y 2 R cos θ ) + F 2 2 ,
y ( θ ) = L S ( y 2 cos θ R ) ( 1 S 2 ) ( R 2 + y 2 2 2 y 2 R cos θ ) + F 2 2 + R .

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