Abstract

Diffraction from a point light source (a laser diode) was studied. The diffraction images were found to be magnified without using a lens and to move corresponding to the displacement of the slit aperture. A digital encoder using this diffraction is proposed to obtain very high resolution without a lens.

© 1988 Optical Society of America

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References

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  1. C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
    [Crossref]
  2. S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
    [Crossref]
  3. S. Kataoka, Y. Shibata, K. Takahasi, H. Yamazaki, Sensor Handbook (Baifukan, Tokyo, 1986), pp. 430–435.
  4. S. Moriyama, T. Harada, “A Precision Displacement Measurement Using a Diffraction Grating,” J.J.S.P.E., 49, No. 6, 94 (1983).
  5. H. Kubota, Wave Optics (Iwanami Shoten, Tokyo, 1971), p. 244 Eq. (18-16). (1971).
  6. H. Machida, J. Nitta, A. Seko, H. Kobayashi, “High-Efficiency Fiber Grating for Producing Multiple Beams of Uniform Intensiy,” Appl. Opt. 23, 330 (1984).
    [Crossref] [PubMed]
  7. M. C. Hutley, Diffraction Gratings (Academic, New York, 1982), p. 293.

1984 (1)

1983 (1)

S. Moriyama, T. Harada, “A Precision Displacement Measurement Using a Diffraction Grating,” J.J.S.P.E., 49, No. 6, 94 (1983).

1982 (1)

S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
[Crossref]

1981 (1)

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Gottsmann, H.

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Harada, T.

S. Moriyama, T. Harada, “A Precision Displacement Measurement Using a Diffraction Grating,” J.J.S.P.E., 49, No. 6, 94 (1983).

Hayashi, H.

S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
[Crossref]

Hijikata, T.

S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
[Crossref]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982), p. 293.

Kataoka, S.

S. Kataoka, Y. Shibata, K. Takahasi, H. Yamazaki, Sensor Handbook (Baifukan, Tokyo, 1986), pp. 430–435.

Kobayashi, H.

Kubota, H.

H. Kubota, Wave Optics (Iwanami Shoten, Tokyo, 1971), p. 244 Eq. (18-16). (1971).

Machida, H.

Marschall, P.

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Moriyama, S.

S. Moriyama, T. Harada, “A Precision Displacement Measurement Using a Diffraction Grating,” J.J.S.P.E., 49, No. 6, 94 (1983).

Nitta, J.

Petermann, K.

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Pfister, W.

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Seko, A.

Shibata, Y.

S. Kataoka, Y. Shibata, K. Takahasi, H. Yamazaki, Sensor Handbook (Baifukan, Tokyo, 1986), pp. 430–435.

Takahasi, K.

S. Kataoka, Y. Shibata, K. Takahasi, H. Yamazaki, Sensor Handbook (Baifukan, Tokyo, 1986), pp. 430–435.

Vollmer, H-P.

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Wolk, C.

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

Yamamoto, S.

S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
[Crossref]

Yamazaki, H.

S. Kataoka, Y. Shibata, K. Takahasi, H. Yamazaki, Sensor Handbook (Baifukan, Tokyo, 1986), pp. 430–435.

Yano, S.

S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Yamamoto, H. Hayashi, S. Yano, T. Hijikata, “Visible GaAlAs V-Channeled Substrate Inner Stripe Laser with Stabilized Mode Using p-GaAs Substrate,” Appl. Phys. Lett. 40, 372 (1982).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Wolk, H. Gottsmann, P. Marschall, K. Petermann, W. Pfister, H-P. Vollmer, “Criteria for Designing V-Groove Lasers,” IEEE J. Quantum Electron. QE-17, 756 (1981).
[Crossref]

J.J.S.P.E. (1)

S. Moriyama, T. Harada, “A Precision Displacement Measurement Using a Diffraction Grating,” J.J.S.P.E., 49, No. 6, 94 (1983).

Other (3)

H. Kubota, Wave Optics (Iwanami Shoten, Tokyo, 1971), p. 244 Eq. (18-16). (1971).

S. Kataoka, Y. Shibata, K. Takahasi, H. Yamazaki, Sensor Handbook (Baifukan, Tokyo, 1986), pp. 430–435.

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982), p. 293.

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Figures (8)

Fig. 1
Fig. 1

Diffraction from a point light source.

Fig. 2
Fig. 2

Light intensity vs ϕ0 (first phase difference) at x = 0 on a screen.

Fig. 3
Fig. 3

(a) Diffraction images when ϕ0 = (k/5)π. (b) Diffraction images when ϕ0 = (k/7)π.

Fig. 4
Fig. 4

Diagram of the experimental system.

Fig. 5
Fig. 5

Diffraction images and intensity distribution detected on the cursor line.

Fig. 6
Fig. 6

Theoretical intensity distribution.

Fig. 7
Fig. 7

Concept of a rotary encoder by using point source diffraction.

Fig. 8
Fig. 8

Diffraction grating formed by a fiber array.

Tables (1)

Tables Icon

Table I Displacement and Magnification Ratios of the Diffraction Image

Equations (14)

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U ( p ) = U 0 i λ f cos θ · exp ( i k β ) · d ξ ,
1 f = 1 b 0 + 1 b .
β = ( Q T - b 0 ) + ( T P - T 0 P ) = 1 2 f · [ ( ξ - x ) 2 - x 2 ] ,
x = b 0 b 0 + b · x .
U ( p ) = U 0 i λ f · exp ( - i k · x 2 / 2 f ) · exp [ i k · ( ξ - x ) 2 / 2 f ] d ξ .
K = U 0 i λ f ɛ 0 ξ 0 , ξ = n ξ 0 , ϕ 0 = π ξ 0 2 λ f , x = m ξ 0
u ( p ) = K · exp ( - i ϕ m ) · Σ exp ( i ϕ n ) .
ϕ 0 = an odd number : k an odd number : h × π .
ϕ 0 = ( a certain irreducible fraction ) × π = 1 / 5 , 2 / 5 , 3 / 5 , 4 / 5 × π [ Fig .3 ( a ) ] = 1 / 7 , 2 / 7 , 3 / 7 , 4 / 7 × π [ Fig .3 ( b ) ] .
M = 1 + b b 0 .
P = k = h π · ϕ 0 = h · ξ 0 2 λ · ( 1 b 0 + 1 b ) ( P = 1 , 2 , 3 , 4 , , k ) .
b 0 = α · M M - 1 · 1 P , b = α · M P ·
α = h · ξ 0 2 λ ,             ( h / P is an irreducible fraction ) .
ξ 0 = M P · ξ 0 = λ ξ 0 · b h .

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