Abstract

A detailed theoretical treatment based on Gaussian beam theory is provided for optical scanning holography [ J. Opt. Soc. Am. A 2, 512 ( 1985)]. Topics addressed include the derivation of the impulse response for the optical scanning holographic system, methods of achieving off-axis holographic recordings, reconstructed image resolution, magnification, and distortion. Also presented is experimental verification of the technique based on measurements of the hologram of a simple transmissive slit object.

© 1992 Optical Society of America

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References

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  1. R. K. Mueller, “Acoustic holography,” Proc. IEEE 59, 1319–1334 (1971).
    [CrossRef]
  2. N. H. Farhat, W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE Lett. 59, 1383–1384 (1971).
    [CrossRef]
  3. R. W. Larson, J. S. Zelenka, E. L. Johansen, “A microwave hologram radar system,”IEEE Trans. Aerosp. Electron. Syst. AES-8, 202–217 (1972).
    [CrossRef]
  4. A. Macovski, “Considerations of television holography,” Opt. Acta 18, 31–39 (1971).
    [CrossRef]
  5. T. -C. Poon, A. Korpel, “Optical transfer function of an acousto-optic heterodyne image processor,” Opt. Lett. 4, 317–319 (1979).
    [CrossRef] [PubMed]
  6. T. -C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985).
    [CrossRef]
  7. T. -C. Poon, “Optical heterodyne scanning holography,” in Optical Society of America 1989 Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper Thdd 6.
  8. G. Cochran, “New method of making fresnel transforms with incoherent light,”J. Opt. Soc. Am. 56, 1513–1517 (1966).
    [CrossRef]
  9. T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
    [CrossRef]
  10. Product information sheet for EBSLM model X3636 provided by Hamamatsu Photonics K.K., Japan, and Hamamatsu Corp., Bridgewater, N.J. (1989).
  11. L. H. Lin, “A method of hologram information reduction by spatial frequency sampling,” Appl. Opt. 7, 545–548 (1968).
    [CrossRef] [PubMed]
  12. L. H. Enloe, W. C. Jakes, C. B. Rubinstein, “Hologram heterodyne scanners,” Bell Syst. Tech. J. 47, 1875–1878 (1968).
  13. A. W. Lohmann, “Incoherent optical processing of complex data,” Appl. Opt. 16, 261–263 (1977).
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  14. W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Appl. Opt. 17, 2454–2466 (1978).
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  15. A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1151 (1978).
    [CrossRef] [PubMed]
  16. T. -C. Poon, “Method of two-dimensional bipolar incoherent image processing by acousto-optic two-pupil synthesis,” Opt. Lett. 10, 197–199 (1985).
    [CrossRef] [PubMed]
  17. T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
    [CrossRef]
  18. T. -C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
    [CrossRef]
  19. F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).
  20. P. P. Banerjee, T. -C. Poon, Principles of Applied Optics (Aksen, Boston, Mass., 1991).
  21. B. D. Duncan, “Investigation of real-time optical scanning holography,” Ph.D. dissertation (Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va., 1991).
  22. B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).
  23. B. Y. Kim, J. N. Blake, H. E. Engan, H. J. Shaw, “All-fiber acoustic-optic frequency shifter,” Opt. Lett. 11, 389–391 (1986).
    [CrossRef] [PubMed]
  24. D. A. Jackson, R. G. Priest, A. Dandridge, A. B. Tveten, “Elimination of drift in a single-mode optical fiber interferometer using a piezoelectrically stretched coiled fiber,” Appl. Opt. 19, 2926–2929 (1980).
    [CrossRef] [PubMed]
  25. B. J. Thompson, “Holographic methods for particle size and velocity measurement–recent advances,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 308–326 (1989).
    [CrossRef]

1990 (2)

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

T. -C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

1988 (1)

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

1986 (1)

1985 (2)

1980 (1)

1979 (1)

1978 (2)

1977 (1)

1972 (1)

R. W. Larson, J. S. Zelenka, E. L. Johansen, “A microwave hologram radar system,”IEEE Trans. Aerosp. Electron. Syst. AES-8, 202–217 (1972).
[CrossRef]

1971 (3)

A. Macovski, “Considerations of television holography,” Opt. Acta 18, 31–39 (1971).
[CrossRef]

R. K. Mueller, “Acoustic holography,” Proc. IEEE 59, 1319–1334 (1971).
[CrossRef]

N. H. Farhat, W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE Lett. 59, 1383–1384 (1971).
[CrossRef]

1968 (2)

L. H. Lin, “A method of hologram information reduction by spatial frequency sampling,” Appl. Opt. 7, 545–548 (1968).
[CrossRef] [PubMed]

L. H. Enloe, W. C. Jakes, C. B. Rubinstein, “Hologram heterodyne scanners,” Bell Syst. Tech. J. 47, 1875–1878 (1968).

1966 (1)

Banerjee, P. P.

P. P. Banerjee, T. -C. Poon, Principles of Applied Optics (Aksen, Boston, Mass., 1991).

Blake, J. N.

Cochran, G.

Dandridge, A.

Duncan, B. D.

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

B. D. Duncan, “Investigation of real-time optical scanning holography,” Ph.D. dissertation (Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va., 1991).

B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).

Engan, H. E.

Enloe, L. H.

L. H. Enloe, W. C. Jakes, C. B. Rubinstein, “Hologram heterodyne scanners,” Bell Syst. Tech. J. 47, 1875–1878 (1968).

Farhat, N. H.

N. H. Farhat, W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE Lett. 59, 1383–1384 (1971).
[CrossRef]

Guard, W. R.

N. H. Farhat, W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE Lett. 59, 1383–1384 (1971).
[CrossRef]

Indebetouw, G.

T. -C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

Jackson, D. A.

Jakes, W. C.

L. H. Enloe, W. C. Jakes, C. B. Rubinstein, “Hologram heterodyne scanners,” Bell Syst. Tech. J. 47, 1875–1878 (1968).

Johansen, E. L.

R. W. Larson, J. S. Zelenka, E. L. Johansen, “A microwave hologram radar system,”IEEE Trans. Aerosp. Electron. Syst. AES-8, 202–217 (1972).
[CrossRef]

Kim, B. Y.

Korpel, A.

Larson, R. W.

R. W. Larson, J. S. Zelenka, E. L. Johansen, “A microwave hologram radar system,”IEEE Trans. Aerosp. Electron. Syst. AES-8, 202–217 (1972).
[CrossRef]

Lin, L. H.

Lohmann, A. W.

Macovski, A.

A. Macovski, “Considerations of television holography,” Opt. Acta 18, 31–39 (1971).
[CrossRef]

Mueller, R. K.

R. K. Mueller, “Acoustic holography,” Proc. IEEE 59, 1319–1334 (1971).
[CrossRef]

Park, J.

T. -C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

Poon, T. -C.

T. -C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

T. -C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985).
[CrossRef]

T. -C. Poon, “Method of two-dimensional bipolar incoherent image processing by acousto-optic two-pupil synthesis,” Opt. Lett. 10, 197–199 (1985).
[CrossRef] [PubMed]

T. -C. Poon, A. Korpel, “Optical transfer function of an acousto-optic heterodyne image processor,” Opt. Lett. 4, 317–319 (1979).
[CrossRef] [PubMed]

T. -C. Poon, “Optical heterodyne scanning holography,” in Optical Society of America 1989 Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper Thdd 6.

P. P. Banerjee, T. -C. Poon, Principles of Applied Optics (Aksen, Boston, Mass., 1991).

Poon, T.-C.

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).

Priest, R. G.

Rhodes, W. T.

Rubinstein, C. B.

L. H. Enloe, W. C. Jakes, C. B. Rubinstein, “Hologram heterodyne scanners,” Bell Syst. Tech. J. 47, 1875–1878 (1968).

Shaw, H. J.

Shinoda, K.

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).

Stoner, W.

Suzuki, Y.

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).

Thompson, B. J.

B. J. Thompson, “Holographic methods for particle size and velocity measurement–recent advances,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 308–326 (1989).
[CrossRef]

Tveten, A. B.

Wu, M.

B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).

Wu, M. H.

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).

Zelenka, J. S.

R. W. Larson, J. S. Zelenka, E. L. Johansen, “A microwave hologram radar system,”IEEE Trans. Aerosp. Electron. Syst. AES-8, 202–217 (1972).
[CrossRef]

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

L. H. Enloe, W. C. Jakes, C. B. Rubinstein, “Hologram heterodyne scanners,” Bell Syst. Tech. J. 47, 1875–1878 (1968).

IEEE Trans. Aerosp. Electron. Syst. (1)

R. W. Larson, J. S. Zelenka, E. L. Johansen, “A microwave hologram radar system,”IEEE Trans. Aerosp. Electron. Syst. AES-8, 202–217 (1972).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Jpn. Appl. Phys. (1)

T. -C. Poon, B. D. Duncan, M. H. Wu, K. Shinoda, Y. Suzuki, “Real-time optical holography using a spatial light modulator,” Jpn. Appl. Phys. 29, L1840–L1842 (1990).
[CrossRef]

Opt. Acta (1)

A. Macovski, “Considerations of television holography,” Opt. Acta 18, 31–39 (1971).
[CrossRef]

Opt. Commun. (1)

T.-C. Poon, J. Park, G. Indebetouw, “Optical realization of textural edge extraction,” Opt. Commun. 65, 1–6 (1988).
[CrossRef]

Opt. Eng. (1)

T. -C. Poon, J. Park, G. Indebetouw, “Real-time tunable incoherent spatial filtering: two-pupil processing technique,” Opt. Eng. 29, 1507–1510 (1990).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

R. K. Mueller, “Acoustic holography,” Proc. IEEE 59, 1319–1334 (1971).
[CrossRef]

Proc. IEEE Lett. (1)

N. H. Farhat, W. R. Guard, “Millimeter wave holographic imaging of concealed weapons,” Proc. IEEE Lett. 59, 1383–1384 (1971).
[CrossRef]

Other (7)

Product information sheet for EBSLM model X3636 provided by Hamamatsu Photonics K.K., Japan, and Hamamatsu Corp., Bridgewater, N.J. (1989).

T. -C. Poon, “Optical heterodyne scanning holography,” in Optical Society of America 1989 Annual Meeting, Vol. 18 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper Thdd 6.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).

P. P. Banerjee, T. -C. Poon, Principles of Applied Optics (Aksen, Boston, Mass., 1991).

B. D. Duncan, “Investigation of real-time optical scanning holography,” Ph.D. dissertation (Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va., 1991).

B. D. Duncan, T.-C. Poon, M. Wu, K. Shinoda, Y. Suzuki, “Real-time reconstruction of scanned optical holograms using an electron beam addressed spatial light modulator,” J. Mod. Opt. (to be published).

B. J. Thompson, “Holographic methods for particle size and velocity measurement–recent advances,” in Holographic Optics II: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1136, 308–326 (1989).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Optical heterodyne scanning system The pupil functions U1 and V1 are offset in temporal frequency.

Fig. 2
Fig. 2

Optical scanning holography system (with notation consistent with that of Ref. 6). RF, radio frequency; AOM, acousto-optic modulator; BPF, bandpass filtering; BS, beam splitter; PIN, photodiode.

Fig. 3
Fig. 3

Simulated and experimentally measured hologram cross section of a 50-μm slit.

Fig. 4
Fig. 4

Overlay of input and reconstructed point objects.

Fig. 5
Fig. 5

(a) Resolution, Δx and Δz, as a function of ωu and the depth parameter z, with scale factor M = 1. (b) Longitudinal resolution Δz as a function of ωu and the depth parameter z, with scale factor M = 5. (c) Longitudinal resolution Δz as a function of ωu and the depth parameter z, with scale factor M = 0.2.

Equations (39)

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v ( x , y ; z , y ) = [ V 2 ( x 2 - x , y 2 - y ; z ) + U 2 ( x 2 - x , y 2 - y ; z ) exp ( - j 2 π f c t ) ] × Γ 2 ( x 2 , y 2 ) 2 d x 2 d y 2 ,
v ˜ ( x , y ; z , t ) = Re [ U 2 ( x 2 - x , y 2 - y ; z ) × V 2 * ( x 2 - x , y 2 - y ; z ) × Γ 2 ( x 2 , y 2 ) 2 d x 2 d y 2 exp ( - j 2 π f c t ) ] ,
v ˜ ( x , y ; z , t ) = Re [ V ˜ ( x , y ; z ) exp ( - j 2 π f c t ) ] ,
V ˜ ( x , y ; z ) = U 2 ( x 2 - x , y 2 - y ; z ) × V 2 * ( x 2 - x , y 2 - y ; z ) Γ 2 ( x 2 , y 2 ) 2 d x 2 d y 2 = ( U 2 V 2 * ) Γ 2 2 ,
V ˜ δ ( x , y ; z ) = U 2 ( - x , - y ; z ) V 2 * ( - x , - y ; z ) .
V ˜ δ ( x , y ; z ) = exp ( j π 2 ) λ z exp { - j π λ z [ ( x - d z f 2 ) 2 + y 2 ] } ,
v ( x , y ; z , t ) = V D C + Re [ V ˜ δ ( x , y ; z ) exp ( - j 2 π f c t ) ] .
v ( x , y ; z ) = V D C + Re [ V ˜ δ ( x , y ; z ) exp ( - j 2 π f c v x x ) ] ,
v ( x , y ; z ) = C 1 + C 2 cos { π λ z [ ( x - x 0 ) 2 + y 2 ] - ϕ } ,
C 1 = V D C , C 2 = A λ z , x 0 = z d f 2 - λ z f c v x , ϕ = ϕ u v + π 2 + π λ z ( f c v x ) 2 [ 1 - 2 ( z d f 2 ) ( v x f c ) ]
v ( x , y ; z ) = V D C + Re [ V ˜ ( x , y ; z ) exp ( - j 2 π f 0 v x x ) ] ,
V ˜ ( x , y ; z ) = V ˜ δ ( x , y ; z ) * Γ 2 ( x , y ) 2 ,
v ( x , y ) = V D C + Re [ V ˜ ( x , y ) exp ( - j 2 π f 0 v x x ) ] ,
V ˜ ( x , y ) = z 0 z 0 + δ z V ˜ δ ( x , y ; z ) * Γ 2 ( x , y ; z ) 2 d z
V 1 ( x , y ) = 1 π ω v 2 exp [ - ( x 2 + y 2 ) ω v 2 ] ,
exp [ - ( x 2 + y 2 ) ( M c u ω 0 ) 2 ] = F { U 1 }
= U 1 ( x , y ) × exp ( - j 2 π f x x - j 2 π f y y ) d x d y ,
U 1 ( x , y ) = 1 π ω u 2 exp { - [ ( x - d ) 2 + y 2 ] ω u 2 } ,
- - Ψ 1 d x d y = 1 ,
V ˜ δ ( x , y ; z ) = 1 G exp ( - K ) exp { - π 2 G [ ( x + j H π ) 2 + y 2 ] } ,
G = [ η ( λ f 2 ω v ) 2 + η ( π ω u z f 2 ) 2 + j π λ ( 1 - 2 η ) z ] , H = η d ( λ f 2 ω v 2 + j π f 2 ) , K = d 2 η ω v 2 ,             η = ω v 2 ω u 2 + ω v 2 .
rect ( x a , y b ) = { 1 - a 2 x a 2             - b 2 y b 2 0 elsewhere .
v ( x , y ; z 0 ) = V D C + 1 2 V ˜ δ ( x , y ; z 0 ) + 1 2 V ˜ δ * ( x , y ; z 0 ) ,
I r = V ˜ δ ( x , y ; z 0 ) * h ( x , y ; z 0 ) 2 ,
h z ( x , y ; z 0 ) = 1 j λ z 0 exp [ j π λ z 0 ( x 2 + y 2 ) ] .
I r = | 1 4 π G exp [ - ( x 2 + y 2 ) 4 G ] | 2 ,
4 G = [ η π 2 ( λ f 2 ω v ) 2 + η ( ω u z f 2 ) 2 - j 2 λ z π ( η - 1 ) ] .
I r exp [ - ( x 2 + y 2 ) ω u 2 ] .
Γ 2 2 = δ ( x , y ; z - z 0 ) + δ ( x - x 0 , y , z - z 0 ) + δ [ x , y ; z - ( z 0 + Δ z 0 ) ] ,
l 1 = λ 1 λ 2 1 M 2 z 0
I r 1 exp [ - ( x 2 + y 2 ) ω r 1 2 ] ,
ω r 1 2 = 1 2 [ ( ω u M ) 2 ( + z 0 2 f 2 2 ) ]
l 3 = λ 1 λ 2 1 M 2 ( z 0 + Δ z 0 ) , ω r 3 2 = 1 2 { ( ω u M ) 2 [ + ( z 0 + Δ z 0 ) 2 f 2 2 ] } .
M long = l 3 - l 1 Δ z 0 = λ 1 λ 2 1 M 2 ,
M lat = l 2 x x 0 = 1 M .
M long = λ 1 λ 2 M lat 2 .
Δ z = λ 2 λ 1 M ω u 2 { ( + z 2 f 2 ) 1 / 2 + [ + ( z + Δ z ) 2 f 2 2 ] 1 / 2 } ,
Δ z = 2 λ 2 λ 1 M ω u ( + z 2 f 2 2 ) 1 / 2 1 - λ 2 λ 1 M ω u 2 ( + z 2 f 2 2 ) 1 / 2 ( z f 2 2 + z 2 ) .
Δ x = 2 ω u ( + z 2 f 2 2 ) 1 / 2 .

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