Abstract

We describe a characterization method based on diffraction for obtaining the phase response of spatial light modulators (SLMs), which in general exhibit both amplitude and phase modulation. Compared with the conventional interferometer-based approach, the method is characterized by a simple setup that enables in situ measurements, allows for substantial mechanical vibration, and permits the use of a light source with a fairly low temporal coherence. The phase determination is possible even for a SLM with a full amplitude modulation depth, i.e., even if there are nulls in the amplitude transmission characteristic of the SLM. The method successfully determines phase modulation values in the full 2π rad range with high accuracy. The experimental work includes comparisons with interferometer measurements as well as a SLM characterization with a light-emitting diode (LED).

© 2006 Optical Society of America

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  1. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
    [CrossRef]
  2. D. C. Dayton, S. L. Browne, S. P. Sandven, J. D. Gonglewski, and A. V. Kudryashov, "Theory and laboratory demonstrations on the use of a nematic liquid-crystal phase modulator for controlled turbulence generation and adaptive optics," Appl. Opt. 37, 5579-5589 (1998).
    [CrossRef]
  3. M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
    [CrossRef]
  4. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]
  5. G. Yang, B. Dong, B. Gu, J. Zhuang, and O. K. Ersoy, "Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison," Appl. Opt. 33, 209-218 (1994).
    [CrossRef] [PubMed]
  6. B. Löfving, "Measurement of the spatial phase modulation of a ferroelectric liquid-crystal modulator," Appl. Opt. 35, 3097-3103 (1996).
    [CrossRef] [PubMed]
  7. Z. Zhang, G. Lu, and F. T. S. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
    [CrossRef]
  8. J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
    [CrossRef]
  9. J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
    [CrossRef]
  10. P. Delaye and G. Roosen, "Simple technique for the determination of the complex transmittance of spatial light modulator," Optik 110, 95-98 (1999).
  11. J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996).
  12. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).
    [CrossRef]
  13. HOLOEYE Photonics AG, http://www.holoeye.com/.

1999

P. Delaye and G. Roosen, "Simple technique for the determination of the complex transmittance of spatial light modulator," Optik 110, 95-98 (1999).

M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
[CrossRef]

1998

1996

B. Löfving, "Measurement of the spatial phase modulation of a ferroelectric liquid-crystal modulator," Appl. Opt. 35, 3097-3103 (1996).
[CrossRef] [PubMed]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
[CrossRef]

1994

1982

Browne, S. L.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Dayton, D. C.

Delaye, P.

P. Delaye and G. Roosen, "Simple technique for the determination of the complex transmittance of spatial light modulator," Optik 110, 95-98 (1999).

Dong, B.

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Erbach, P. S.

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
[CrossRef]

Ersoy, O. K.

Fienup, J. R.

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Gonglewski, J. D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996).

Gregory, D. A.

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
[CrossRef]

Gu, B.

Haist, T.

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Holtz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Kudryashov, A. V.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Löfving, B.

Lu, G.

Z. Zhang, G. Lu, and F. T. S. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

McClain, J. L.

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
[CrossRef]

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Reicherter, M.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Roosen, G.

P. Delaye and G. Roosen, "Simple technique for the determination of the complex transmittance of spatial light modulator," Optik 110, 95-98 (1999).

Sandven, S. P.

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Tiziani, H.

Wagemann, E.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Yang, G.

Yu, F. T. S.

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
[CrossRef]

Z. Zhang, G. Lu, and F. T. S. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

Zhang, Z.

Z. Zhang, G. Lu, and F. T. S. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

Zhuang, J.

Appl. Opt.

Opt. Eng.

Z. Zhang, G. Lu, and F. T. S. Yu, "Simple method for measuring phase modulation in liquid crystal television," Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Spatial light modulator phase depth determination from optical diffraction information," Opt. Eng. 35, 951-954 (1996).
[CrossRef]

Opt. Lett.

Optik

P. Delaye and G. Roosen, "Simple technique for the determination of the complex transmittance of spatial light modulator," Optik 110, 95-98 (1999).

Proc. IEEE

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holtz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, "Optical phased array technology," Proc. IEEE 84, 268-298 (1996).
[CrossRef]

Proc. SPIE

J. L. McClain, P. S. Erbach, D. A. Gregory, and F. T. S. Yu, "Diffractive method for measurement of coupled amplitude and phase modulation in spatial light modulators," in Optical Pattern Recognition VII, D. P. Casasent and T.-H. Chao, eds., Proc. SPIE 2752, 153-161 (1996).
[CrossRef]

SIAM J. Optim.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9, 112-147 (1998).
[CrossRef]

Other

HOLOEYE Photonics AG, http://www.holoeye.com/.

J. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1996).

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Figures (17)

Fig. 1
Fig. 1

Example of one period of a grating consisting of three levels with different pixel settings. Note that the staircase shape of the grating is only a way to illustrate the difference in phase between the levels; in reality the values of A 1 , A 2 , A 3 , φ 1 , φ 2 , and φ 3 , are unknown at the beginning of the characterization.

Fig. 2
Fig. 2

Assumed (a) amplitude and (b) phase modulation used to simulate the performance of the diffraction-based characterization method. In (a), the range of possible noisy values, with a noise amplitude of n a = 0.10 , is indicated with gray, and one specific example is also plotted (the irregular curve).

Fig. 3
Fig. 3

Results from the original optimization; shown are the multiple solutions for Δ φ 1 (pluses) and Δ φ 2 (squares) for each value of L 1 and the chosen boundaries (dashed lines) defining the range used to find the actual value of Δ φ 2 .

Fig. 4
Fig. 4

Final postoptimized phase modulation response of Δ φ 1 (circles). Also shown are those phase pairs ( Δ φ 1 , Δ φ 2 ) in Fig. 3 having a Δ φ 2 value between the two boundaries (pluses and squares), the averaged values of Δ φ 2 (dashed line), and the correct phase modulation (solid lines).

Fig. 5
Fig. 5

Multiple solutions for Δ φ 1 (pluses) and Δ φ 2 (squares) and the boundaries for identifying the correct solution for Δ φ 2 (dashed lines) from the original optimization in the presence of noise with a noise amplitude n a = 0.10 .

Fig. 6
Fig. 6

Results from a complete optimization in the presence of noise with n a = 0.10 . Those phase pairs ( Δ φ 1 , Δ φ 2 ) in Fig. 3 that were used for the determination of Δ φ 2 are marked as pluses ( Δ φ 1 ) and squares ( Δ φ 2 ) ; also indicated are the average value of Δ φ 2 (dashed line), the postoptimized Δ φ 1 values (circles), and the ideal phase modulation (solid lines).

Fig. 7
Fig. 7

Simulated standard deviation of the obtained phase modulation values from the correct ones, in the presence of noise. Shown are the simulation results and corresponding fitted lines for the cases where only values corresponding to an amplitude modulation above 0.1 (circles and dashed line, respectively) and 0.2 (squares and dotted line, respectively) were used. The standard deviation within each value of n a is also indicated.

Fig. 8
Fig. 8

(Color online) Michelson interferometer setup. The beam is expanded by two lenses ( L 1 and L 2 ) before a desired polarization state is generated by a polarizer ( P 1 ) and a quarter-wave plate (QWP). The beam is divided by a nonpolarizing beam splitter cube (BS). The SLM is placed in the measurement arm, while the reference arm only holds a flat mirror (M). The outgoing light from the SLM and the mirror is made linearly polarized with a polarizer ( P 2 ) before the interference pattern is captured by a CCD camera.

Fig. 9
Fig. 9

Picture captured by the CCD camera during the interferometer measurements. The upper and lower halves of the picture show the fringe pattern for the pixel settings L = 0 and L > 0 , respectively. The somewhat curved fringes are caused by the slightly spherical backplane of the SLM.

Fig. 10
Fig. 10

(Color online) Setup used both in the amplitude characterization and in the diffraction-based phase characterization. It differs from the setup in Fig. 8 in that the flat mirror is removed and that a lens ( L 3 ) is used to transform the output from the device to its far-field intensity distribution, which is then magnified with a second lens ( L 4 ) onto a plane where a moveable detector (D) is positioned in either the zeroth or first diffraction order.

Fig. 11
Fig. 11

Measured normalized amplitude modulation as a function of pixel setting for the three different modulation characteristics of the SLM, corresponding to the three different input polarization states on the SLM.

Fig. 12
Fig. 12

Retrieved phase modulation values from the two stages of the characterization method, for input polarization state 1.

Fig. 13
Fig. 13

Resulting phase modulation for input polarization state 1.

Fig. 14
Fig. 14

Resulting phase modulation for input polarization state 2.

Fig. 15
Fig. 15

Resulting phase modulation for input polarization state 3.

Fig. 16
Fig. 16

(Color online) LED-based setup used both in the amplitude characterization and in the diffraction-based phase characterization. A lens ( L 1 ) is used to collect the light emitted from the surface-mounted LED. The polarization state is controlled by a polarizer ( P 1 ) and a quarter-wave plate (QWP). A microscope objective ( L 2 ) is used to demagnify the LED 10 times, and an aperture (A) further reduces the effective emitting area of the LED. A third lens ( L 3 ) images the aperture plane via the beam splitter (BS) and the SLM. The outgoing light is made linearly polarized with a polarizer ( P 2 ) before the far field is magnified with a microscope objective ( L 4 ) . The central diffraction orders are detected with a CCD camera.

Fig. 17
Fig. 17

Obtained phase modulation characteristics for input polarization state 1. Note that the results from the diffraction-based methods (circles, pluses, and squares) were obtained with an LED ( λ 530   nm ) as a light source, while the interferometer measurements (dotted curve) were achieved with a laser ( λ = 543.5   nm ) .

Tables (2)

Tables Icon

Table 1 Parameters of the 19 Different Grating Geometries Used (pixels)

Tables Icon

Table 2 Standard Deviation of the Obtained Phase Modulation from the Reference Phase Modulation a

Equations (209)

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2 π
2 π
L 1
L 2
L 3
A 1
A 2
A 3
φ 1
φ 2
φ 3
Δ φ 1 = φ 1 φ 3
Δ φ 2 = φ 2 φ 3
a 1
a 2
a 1
a 2
I M
a 1
a 2
L 1
L 2
L 3
Δ φ 1
Δ φ 2
E + 1 = 0 d A ( x ) exp [ i φ ( x ) ] exp ( i 2 π x d ) d x = A 1  exp ( i φ 1 ) 0 a 1 exp ( i 2 π x d ) d x + A 2  exp ( i φ 2 ) a 1 a 2 exp ( i 2 π x d ) d x + A 3  exp ( i φ 3 ) a 2 d exp ( i 2 π x d ) d x = T [ C 1 A r , 1 exp ( i Δ φ 1 ) + C 2 A r , 2 exp ( i Δ φ 2 ) + C 3 ] ,
T = d i 2 π A 3   exp ( i φ 3 ) ;
k = 2 π / λ
C 1 = exp ( i 2 π a 1 / d ) 1 ,
C 2 = exp ( i 2 π a 2 / d ) exp ( i 2 π a 1 / d ) ,
C 3 = 1 exp ( i 2 π a 2 / d ) ,
A r , 1 = A 1 / A 3 , A r , 2 = A 2 / A 3 ,
I T = | E + 1 | 2 = | T [ C 1 A r , 1   exp ( i Δ φ 1 ) + C 2 A r , 2 × exp ( i Δ φ 2 ) + C 3 ] | 2 .
Δ φ 1
Δ φ 2
a 1
a 2
C 1
C 2
C 3
I M ( 1 )
I M ( 2 )
, I M ( N )
I T
I M
f ( Δ φ 1 , Δ φ 2 ) = n = 1 N [ I M ( n ) n = 1 N I M ( n ) I T ( n ) ( Δ φ 1 , Δ φ 2 ) n = 1 N I T ( n ) ( Δ φ 1 , Δ φ 2 ) ] 2 ,
Δ φ 1
Δ φ 2
I T
I M
I T
f ( Δ φ 1 , Δ φ 2 )
( Δ φ 1 , Δ φ 2 )
( Δ φ 1 , Δ φ 2 )
19 × 19
( Δ φ 1 , Δ φ 2 )
L 1
L 2
Δ φ 1
Δ φ 2
L 1
L 1 = [ 0 , 1 , , 255 ]
L 1
L 1
L 1 = [ 0 , 10 , , 250 ]
L 2
L 2
L 1
L 1
L 3 = 0
L 2
( Δ φ 1 , Δ φ 2 )
L 1
Δ φ 2
L 1
Δ φ 2
L 1
Δ φ 2
L 1
Δ φ 2
f ( Δ φ 1 , Δ φ 2 )
Δ φ 2
Δ φ 1
L 1 = [ 0 , 10 , , 250 ]
Δ φ 2
Δ φ 1
Δ φ 1
L 1
L 1
L 1
Δ φ 1
Δ φ 2
Δ φ 1
Δ φ 1
Δ φ 1
Δ φ 1
I T
L 1
L 2
I M ( n )
Δ φ 1 ( L 1 )
Δ φ 2
Δ φ 2
Δ φ 2
Δ φ 2
Δ φ 2
( Δ φ 1 , Δ φ 2 )
Δ φ 2
Δ φ 2
L 1
( L 1 = 130
L 1 = 170
L 1 = 240
( Δ φ 1 , Δ φ 2 )
L 1
L 2
L 3
φ ( L 1 ) = m 2 π + φ ( L 2 )   rad
φ ( L 1 ) = m 2 π + φ ( L 3 )   rad
I M , ideal ( n )
I M ( n ) = I M , ideal ( n ) ( 1 + N 1 ) .
A M = ( A ideal ) 2 ( 1 + N 2 ) .
N 1
N 2
[ n a , n a ]
n a
n a = 0.10
Δ φ 2
Δ φ 2
L 1 > 220
n a
n a
L 1
Δ φ 2
1024 × 768
L = [ 0 , 1 , , 255 ]
543.5   nm
L = 0
L = [ 0 , 10 , …   , 250 ]
L = 0
L = [ 0 , 10 , , 250 ]
L 1
L 2
L 3
L 2 = 150
L 3 = 0
L 1 = [ 0 , 10 , , 250 ]
L 1
L 2
L 3
( Δ φ 1 , Δ φ 2 )
Δ φ 2
Δ φ 2
L 2
L 3
Δ φ 2
L 2
L 2
25 μ m
528 ± 9   nm
30   nm
( 530
543.5   nm
P 1
L 1
5 %
A 1
A 2
A 3
φ 1
φ 2
φ 3
n a = 0.10
Δ φ 1
Δ φ 2
L 1
Δ φ 2
Δ φ 1
( Δ φ 1 , Δ φ 2 )
Δ φ 2
Δ φ 2
Δ φ 1
Δ φ 2
Δ φ 2
n a = 0.10
n a = 0.10
( Δ φ 1 , Δ φ 2 )
Δ φ 2
( Δ φ 1 )
( Δ φ 2 )
Δ φ 2
Δ φ 1
n a
( L 1
L 2
( P 1 )
( P 2 )
L = 0
L > 0
( L 3 )
( L 4 )
( L 1 )
( P 1 )
( L 2 )
( L 3 )
( P 2 )
( L 4 )
( λ 530   nm )
( λ = 543.5   nm )

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