Abstract

A new technique has been found that uses in-phase and quadrature phase (I∕Q) demodulation to optimize the images produced with an amplitude-modulated laser imaging system. An I∕Q demodulator was used to collect the I∕Q components of the received modulation envelope. It was discovered that by adjusting the local oscillator phase and the modulation frequency, the backscatter and target signals can be analyzed separately via the I∕Q components. This new approach enhances image contrast beyond what was achieved with a previous design thatprocessed only the composite magnitude information.

© 2007 Optical Society of America

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References

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  1. M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
    [CrossRef]
  2. J. S. Jaffe, "Performance bounds on synchronous laser line scan systems," Opt. Express 13, 738-748 (2006).
    [CrossRef]
  3. F. R. Dalgleish, F. M. Caimi, C. H. Mazel, and J. M. Glynn, "Extended range underwater optical imaging architecture," in IEEE Oceans 2006 (IEEE, 2006).
    [CrossRef]
  4. J. J. Shirron and T. E. Giddings, "A model for the simulation of a pulsed laser line scan system," in IEEE Oceans 2006 (IEEE, 2006).
    [CrossRef]
  5. L. Mullen, V. M. Contarino, and P. R. Herczfeld, "Hybrid lidar-radar ocean experiment," IEEE Trans. Microwave Theory Tech. 44, 2703-2710 (1996).
  6. L. Morvan, N. Lai, D. Dolfi, J. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, "Building blocks for a two-frequency laser lidar-radar: a preliminary study," Appl. Opt. 41, 5702-5712 (2002).
    [CrossRef] [PubMed]
  7. D. Kao, T. Kane, and L. Mullen, "Development of an amplitude-modulated Nd:YAG pulsed laser with modulation frequency tunability up to 60 GHz by dual seed injection," Opt. Lett. 29, 1203-1205 (2004).
    [CrossRef] [PubMed]
  8. L. Mullen, A. Laux, B. Concannon, E. Zege, I. Katsev, and A. Prikhach, "Amplitude-modulated laser imager," Appl. Opt. 43, 3874-3892 (2004).
    [CrossRef] [PubMed]
  9. A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
    [CrossRef]

2006

2004

2002

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

L. Morvan, N. Lai, D. Dolfi, J. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, "Building blocks for a two-frequency laser lidar-radar: a preliminary study," Appl. Opt. 41, 5702-5712 (2002).
[CrossRef] [PubMed]

1996

L. Mullen, V. M. Contarino, and P. R. Herczfeld, "Hybrid lidar-radar ocean experiment," IEEE Trans. Microwave Theory Tech. 44, 2703-2710 (1996).

1995

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Billmers, R.

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Bretenaker, F.

Brunel, M.

Caimi, F. M.

F. R. Dalgleish, F. M. Caimi, C. H. Mazel, and J. M. Glynn, "Extended range underwater optical imaging architecture," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

Cindrich, I.

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Concannon, B.

L. Mullen, A. Laux, B. Concannon, E. Zege, I. Katsev, and A. Prikhach, "Amplitude-modulated laser imager," Appl. Opt. 43, 3874-3892 (2004).
[CrossRef] [PubMed]

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Contarino, V.

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Contarino, V. M.

L. Mullen, V. M. Contarino, and P. R. Herczfeld, "Hybrid lidar-radar ocean experiment," IEEE Trans. Microwave Theory Tech. 44, 2703-2710 (1996).

Dalgleish, F. R.

F. R. Dalgleish, F. M. Caimi, C. H. Mazel, and J. M. Glynn, "Extended range underwater optical imaging architecture," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

Davis, J.

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Dolfi, D.

Dubey, A. C.

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Giddings, T. E.

J. J. Shirron and T. E. Giddings, "A model for the simulation of a pulsed laser line scan system," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

Glynn, J. M.

F. R. Dalgleish, F. M. Caimi, C. H. Mazel, and J. M. Glynn, "Extended range underwater optical imaging architecture," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

Herczfeld, P. R.

L. Mullen, V. M. Contarino, and P. R. Herczfeld, "Hybrid lidar-radar ocean experiment," IEEE Trans. Microwave Theory Tech. 44, 2703-2710 (1996).

Huignard, J.

Jaffe, J. S.

Kane, T.

Kao, D.

Katsev, I.

Lai, N.

Laux, A.

L. Mullen, A. Laux, B. Concannon, E. Zege, I. Katsev, and A. Prikhach, "Amplitude-modulated laser imager," Appl. Opt. 43, 3874-3892 (2004).
[CrossRef] [PubMed]

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Le Floch, A.

Mazel, C. H.

F. R. Dalgleish, F. M. Caimi, C. H. Mazel, and J. M. Glynn, "Extended range underwater optical imaging architecture," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

Morvan, L.

Mullen, L.

L. Mullen, A. Laux, B. Concannon, E. Zege, I. Katsev, and A. Prikhach, "Amplitude-modulated laser imager," Appl. Opt. 43, 3874-3892 (2004).
[CrossRef] [PubMed]

D. Kao, T. Kane, and L. Mullen, "Development of an amplitude-modulated Nd:YAG pulsed laser with modulation frequency tunability up to 60 GHz by dual seed injection," Opt. Lett. 29, 1203-1205 (2004).
[CrossRef] [PubMed]

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

L. Mullen, V. M. Contarino, and P. R. Herczfeld, "Hybrid lidar-radar ocean experiment," IEEE Trans. Microwave Theory Tech. 44, 2703-2710 (1996).

Prentice, J.

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Prikhach, A.

Ralston, J. M.

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Rigano, K. A.

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Shirron, J. J.

J. J. Shirron and T. E. Giddings, "A model for the simulation of a pulsed laser line scan system," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

Strand, M. P.

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Zege, E.

Appl. Opt.

IEEE Trans. Microwave Theory Tech.

L. Mullen, V. M. Contarino, and P. R. Herczfeld, "Hybrid lidar-radar ocean experiment," IEEE Trans. Microwave Theory Tech. 44, 2703-2710 (1996).

J. Mod. Opt.

A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, and V. Contarino, "The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment," J. Mod. Opt. 49, 439-451 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

M. P. Strand, "Underwater electro-optical system for mine identification," in Detection Technologies for Mines and Minelike Targets, A. C. Dubey, I. Cindrich, J. M. Ralston, and K. A. Rigano, eds., Proc. SPIE 2496, 487-497 (1995).
[CrossRef]

Other

F. R. Dalgleish, F. M. Caimi, C. H. Mazel, and J. M. Glynn, "Extended range underwater optical imaging architecture," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

J. J. Shirron and T. E. Giddings, "A model for the simulation of a pulsed laser line scan system," in IEEE Oceans 2006 (IEEE, 2006).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Block diagram of the amplitude modulated laser imaging system using an I∕Q demodulator toprocess the modulated return signal.

Fig. 2
Fig. 2

Diagram of system geometry and signal components for (a) the background-only case (no target) and for (b) the case when a target is illuminated.

Fig. 3
Fig. 3

Model-generated magnitude data and associated bottom-backscatter phase difference φ BOT ( r ) φ BSN ( r ) plotted as a function of modulation frequency. The local maxima of M ¯ ( r ) correspond to destructive interference, while the local minima correlate with destructive interference.

Fig. 4
Fig. 4

(a) Plots of M ¯ ( r ) for both experimental and model (MVS) data for c = 1.6 m 1 and a receiver field of view of 1°. The model-generated i f ,BSN ( r ) , and bottom, i 0 ,BOT ( r ) , data are also plotted. (b) Phase data corresponding to the amplitude date in (a) are plotted as a function of modulation frequency. The dashed lines indicate the frequencies that were used to generate the images in Figs. 5 and 6.

Fig. 5
Fig. 5

Images obtained with the MVS program for I, Q, and M for c = 1.6 m 1 and a receiver field of view of 1°. Also shown are the images for the WF and the dc return signal.

Fig. 6
Fig. 6

Images obtained with experimental data for I, Q, and M for c = 1.6 m 1 and a receiver field of view of 1°. Also shown are the images for the WF and the dc return signal.

Fig. 7
Fig. 7

(a) Plots of M ¯ ( r ) for both experimental and model (MVS) data for c = 2 m 1 and a receiver field of view of 1°. The model-generated i f ,BSN ( r ) , and bottom, i 0 ,BOT ( r ) , data are also plotted. (b) Phase data corresponding to the amplitude date in (a) are plotted as a function of modulation frequency. The dashed lines indicate the frequencies that were used to generate the images in Figs. 8 and 9.

Fig. 8
Fig. 8

Images obtained with the MVS program for I, Q, and M for c = 2 m 1 and a receiver field of view of 1°. Also shown are the images for the WF and the dc return signal.

Fig. 9
Fig. 9

Images obtained with experimental data for I, Q, and M for c = 2 m 1 and a receiver field of view of 1°. Also shown are the images for the WF and the dc return signal.

Tables (1)

Tables Icon

Table 1 List of Experimental Parameters Used as Inputs to the MVS Program

Equations (217)

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10 100   MHz
M = ( I 2 + Q 2 ) 1 / 2
( 10 100   MHz )
532   nm
P i ( t ) = P 0 , i 1 + m f , i   sin ( 2 π f t φ i ) ,
P 0 , i
sin ( 2 π f t φ i )
φ i
m f , i
m f , i = 1 2 ( P max, i P min, i ) 1 2 ( P max, i + P min, i ) = 1 2 ( P max, i P min, i ) P 0 , i = 1.
r = r
r = r
r = r
P BKGD ( r , t ) = P BOT ( r , t ) + P BSN ( r , t ) ,
P BOT ( r , t )
P BSN ( r , t )
P BOT ( r , t ) = P 0,BOT ( r ) { 1 + m f ,BOT   sin [ 2 π f t φ BOT ( r ) ] } ,
P BSN ( r , t ) = P 0,BSN ( r ) { 1 + m f ,BSN   sin [ 2 π f t φ BSN ( r ) ] } .
P 0 ,BOT ( r )
P 0 ,BSN ( r )
m f ,BOT
m f ,BSN
φ BOT ( r )
φ BSN ( r )
r = r
P ( r , t ) = P OBJ ( r , t ) + P B S N * ( r , t ) + P B O T * ( r , t ) ,
P OBJ ( r , t ) = P 0 ,OBJ ( r ) { 1 + m f ,OBJ   sin [ 2 π f t φ OBJ ( r ) ] }
P BSN * ( r , t )
P BSN s h ( r , t )
P BSN * ( r , t ) = P BSN ( r , t ) P BSN s h ( r , t )
P BOT * ( r , t )
P BOT * ( r , t ) = P BOT ( r , t ) P BOT s h ( r , t )
P ( r , t ) = [ P OBJ ( r , t ) P BOT s h ( r , t ) P B S N s h ( r , t ) ] + [ P BOT ( r , t ) + P BSN ( r , t ) ] = P OBJ ( r , t ) + P BKGD ( r , t ) ,
P OBJ ( r , t ) = P 0,OBJ ( r ) { 1 + m f ,OBJ sin [ 2 π f t φ OBJ ( r ) ] }
( f < 100   MHz )
m f ,BOT = m f ,OBJ = m f , i = 1
m f ,BSN < 1
m f ,OBJ
P B S N s h ( r , t )
( A / W )
i ( r , t ) = P ( r , t ) = i OBJ ( r , t ) + i BKGD ( r , t ) + i SHOT ( r , t ) ,
i SHOT ( r , t )
i 0 ( r , t )
i f ( r , t )
i ( r , t ) = i 0 ( r , t ) + i f ( r , t ) + i SHOT ( r , t ) .
i 0 ( r , t ) = i 0 ,OBJ ( r ) + i 0 ,BKGD ( r ) + i 0,SHOT ( r , t ) = i 0 ,OBJ ( r ) + i 0 ,BOT ( r ) + i 0 ,BSN ( r ) + i 0,SHOT ( r , t ) ,
i f ( r , t ) = i f ,OBJ ( r , t ) + i f ,BKGD ( r , t ) + i f ,SHOT ( r , t ) = i f ,OBJ ( r , t ) + i f ,BOT ( r , t ) + i f ,BSN ( r , t ) + i f ,SHOT ( r , t ) = m f ,OBJ i 0 ,OBJ ( r ) sin [ 2 π f t φ OBJ ( r ) ] + i 0 ,BOT ( r ) sin [ 2 π f t φ BOT ( r ) ] + m f ,BSN i 0 ,BSN ( r ) sin [ 2 π f t φ BSN ( r ) ] + i f ,SHOT ( r , t ) .
i ¯ 0 ( r ) = i 0 ,OBJ ( r ) + i 0 ,BOT ( r ) + i 0 ,BSN ( r ) ,
i 0 ,SHOT ( r , t ) = 0
i f ( r , t )
i LO ( t ) = i LO  sin ( 2 π f t φ LO ) ,
i LO
φ LO
i f ( r , t )
I ( r , t )
I ¯ ( r )
I ¯ ( r ) = G f { i f ,OBJ ( r ) cos [ φ OBJ ( r ) φ LO ] + i f ,BKGD ( r ) cos [ φ BKGD ( r ) φ LO ] } ,
i f ,OBJ ( r ) = m f ,OBJ i 0 ,OBJ ( r )
i f ,BKGD ( r ) = m f ,BKGD i 0 ,BKGD ( r )
G f = I ( r , t ) / i f ( r , t )
i f ( r , t )
Q ( r , t )
I ( r , t )
Q ¯ ( r )
Q ¯ ( r ) = G f { i f ,OBJ ( r ) sin [ φ OBJ ( r ) φ LO ] + i f ,BKGD ( r ) sin [ φ BKGD ( r ) φ LO ] } .
M = ( I 2 + Q 2 ) 1 / 2
M ¯ ( r ) = [ I ¯ 2 ( r ) + Q ¯ 2 ( r ) ] 1 / 2 = G f { i f ,OBJ 2 ( r ) + i f ,BKGD 2 ( r ) + 2 i f ,OBJ ( r ) i f ,BKGD ( r ) × cos [ φ OBJ ( r ) φ BKGD ( r ) ] } 1 / 2 .
φ rf ( r ) φ LO = tan 1 [ Q ¯ ( r ) I ¯ ( r ) ] = tan 1 { i f ,OBJ ( r ) sin [ φ OBJ ( r ) φ LO ] + i f ,BKGD ( r ) sin [ φ BKGD ( r ) φ LO ] i f ,OBJ ( r ) cos [ φ OBJ ( r ) φ LO ] + i f ,BKGD ( r ) cos [ φ BKGD ( r ) φ LO ] } .
r = r
M ¯ ( r ) = G f { i 0 ,BOT 2 ( r ) + i f ,BSN 2 ( r ) + 2 i 0 ,BOT ( r ) i f ,BSN ( r ) cos [ φ BOT ( r ) φ BSN ( r ) ] } 1 / 2 ,
φ BKGD ( r ) φ LO = tan 1 { i 0 ,BOT ( r ) sin [ φ BOT ( r ) φ LO ] + i f ,BSN ( r ) sin [ φ BSN ( r ) φ LO ] i 0 ,BOT ( r ) cos [ φ BOT ( r ) φ LO ] + i f ,BSN ( r ) cos [ φ BSN ( r ) φ LO ] } .
i 0 ,BOT ( r ) i f ,BSN ( r )
M ¯ ( r ) = i 0 ,BOT ( r )
φ BKGD ( r ) = φ BOT ( r )
( m f ,BSN 1 )
M ¯ ( r )
m f ,BOT = 1
i f ,BSN ( r ) i 0 ,BOT ( r )
M ¯ ( r )
φ BKGD ( r ) = φ BSN ( r )
( i 0 ,BOT ( r ) i f ,BSN ( r ) )
( i 0 ,BOT 2 ( r ) + i f ,BSN 2 ( r ) )
( 2 i 0 ,BOT ( r ) i f ,BSN ( r ) cos [ φ BOT ( r ) φ BSN ( r ) ] )
φ BOT ( r ) φ BSN ( r )
φ BOT ( r ) φ BSN ( r ) = 2 k π
M ¯ ( r ) = G f [ i 0 ,BOT ( r ) + i f ,BSN ( r ) ] ;
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π
M ¯ ( r ) = G f | i 0 ,BOT ( r ) i f ,BSN ( r ) | ;
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2
M ¯ ( r ) = G f [ i 0 ,BOT 2 ( r ) + i f ,BSN 2 ( r ) ] 1 / 2 .
φ BOT ( r ) φ BSN ( r )
M ¯ ( r )
i f ,OBJ ( r )
i f ,BKGD ( r )
φ OBJ ( r ) φ BKGD ( r )
r = r
I ¯ ( r ) = G f i f ,BKGD ( r ) cos [ φ BKGD ( r ) φ LO ] ,
Q ¯ ( r ) = G f i f ,BKGD ( r ) sin [ φ BKGD ( r ) φ LO ] .
φ LO = φ BKGD ( r )
I ¯ ( r ) = G f i f ,BKGD ( r )
Q ¯ ( r ) = 0
φ LO = φ BKGD ( r )
r = r
I ¯ ( r ) = G f { i f ,OBJ ( r ) cos [ φ OBJ ( r ) φ BKGD ( r ) ] + i f ,BKGD ( r ) cos [ φ BKGD ( r ) φ BKGD ( r ) ] } ,
Q ¯ ( r ) = G f { i f ,OBJ ( r ) sin [ φ OBJ ( r ) φ BKGD ( r ) ] + i f ,BKGD ( r ) sin [ φ BKGD ( r ) φ BKGD ( r ) ] } .
φ LO = φ BKGD ( r )
φ LO = φ BKGD ( r )
φ BKGD ( r ) φ BSN ( r )
φ LO = φ BKGD ( r )
( φ LO = φ BSN ( r ) )
φ LO = φ BSN ( r ) , I ¯ ( r )
Q ¯ ( r )
I ¯ ( r ) = G f { i 0 ,BOT ( r ) cos [ φ BOT ( r ) φ BSN ( r ) ] + m f ,BSN i 0 ,BSN ( r ) } ,
Q ¯ ( r ) = G f i 0 ,BOT ( r ) sin [ φ BOT ( r ) φ BSN ( r ) ] .
I ¯ ( r )
Q ¯ ( r )
r = r
φ LO = φ BSN ( r )
I ¯ ( r ) = G f { i f ,OBJ ( r ) cos [ φ OBJ ( r ) φ BSN ( r ) ] + i 0 ,BOT ( r ) cos [ φ BOT ( r ) φ BSN ( r ) ] + i f ,BSN ( r ) cos ( Δ φ BSN ) } ,
Q ¯ ( r ) = G f { i f ,OBJ ( r ) sin [ φ OBJ ( r ) φ BSN ( r ) ] + i 0 ,BOT ( r ) sin [ φ BOT ( r ) φ BSN ( r ) ] + i f ,BSN ( r ) sin ( Δ φ BSN ) } ,
Δ φ BSN = φ BSN ( r ) φ BSN ( r )
r = r
r = r
Δ φ BSN 0
I ¯ ( r ) = G f { i f ,OBJ ( r ) cos [ φ OBJ ( r ) φ BSN ( r ) ] + i 0 ,BOT ( r ) cos [ φ BOT ( r ) φ BSN ( r ) ] + i f ,BSN ( r ) } ,
Q ¯ ( r ) = G f { i f ,OBJ ( r ) sin [ φ OBJ ( r ) φ BSN ( r ) ] + i 0 ,BOT ( r ) sin [ φ BOT ( r ) φ BSN ( r ) ] } .
( φ LO = φ BSN ( r ) )
φ LO = φ BSN ( r )
φ LO = φ BSN ( r )
φ BOT ( r ) φ BSN ( r ) = 2 k π
( 2 k + 1 ) π
I ¯ ( r ) = G f { ± i f ,OBJ ( r ) cos [ φ OBJ ( r ) φ BOT ( r ) ] ± i 0 ,BOT ( r ) cos ( Δ φ BOT ) + i f ,BSN ( r ) } ,
Q ¯ ( r ) = ± G f { i f ,OBJ ( r ) sin [ φ OBJ ( r ) φ BOT ( r ) ] + i 0 ,BOT ( r ) sin ( Δ φ BOT ) } ,
Δ φ BOT = φ BOT ( r ) φ BOT ( r )
( φ OBJ ( r ) φ BOT ( r ) 0 )
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2
I ¯ ( r ) = G f { ± i f ,OBJ ( r ) sin [ φ BOT ( r ) φ OBJ ( r ) ] ± i 0 ,BOT ( r ) sin ( Δ φ BOT ) + m f ,BSN i 0 ,BSN ( r ) } ,
Q ¯ ( r ) = ± G f { i f ,OBJ ( r ) cos [ φ BOT ( r ) φ OBJ ( r ) ] + i 0 ,BOT ( r ) cos ( Δ φ BOT ) } .
φ OBJ ( r ) φ BOT ( r ) 0
φ BKGD ( r ) = φ BSN ( r )
φ LO = φ BSN ( r )
i 0,BOT ( r ) i f ,BSN ( r )
φ BOT ( r ) < φ BKGD ( r ) < φ BSN ( r )
M ¯ ( r )
φ BOT ( r ) φ BSN ( r )
φ BOT ( r )
φ LO = 360 φ BSN ( r )
r = r = 0
20 × 20   cm
40 × 40 = 1600
M = ( I 2 + Q 2 ) 1 / 2
r = r = 0
c = 1.6 m 1
M ¯ ( r )
i f ,BSN ( r )
i 0 ,BOT ( r )
f < 75   MHz
i f ,BSN ( r ) > i 0 ,BOT ( r )
f > 75
( i f ,BSN ( r ) < i 0 ,BOT ( r ) )
f < 75   MHz
f > 75   MHz
f < 75   MHz
( φ BKGD ( r ) φ BSN ( r ) )
75   MHz
( φ = φ BOT ( r ) φ BSN ( r ) = 2 π )
( φ = φ BOT ( r ) φ BSN ( r ) = π )
φ = φ BOT ( r ) φ BSN ( r ) = 3 π / 2 , 5 π / 2
φ LO = φ BSN ( r )
( φ BOT ( r ) φ BSN ( r ) = 2 π )
( φ BOT ( r ) φ BSN ( r ) = π )
M ¯ ( r )
M ¯ ( r )
( φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2 )
φ BOT ( r )
φ LO =360 φ BSN ( r )
Q = 0
( φ OBJ ( r ) = φ BOT ( r ) )
( Δ φ BOT = 0 )
φ BOT ( r ) φ BSN ( r ) = 2 k π
( 2 k + 1 ) π
I ¯ ( r ) > 0
I ¯ ( r ) < 0
I ¯ ( r ) = 0
i f ,BSN ( r ) < i 0 ,BSN ( r )
φ = φ BOT ( r ) φ BSN ( r ) = 3 π / 2
φ = φ BOT ( r ) φ BSN ( r ) = 5 π / 2
φ LO = φ BSN ( r )
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2
I ¯ ( r ) i f ,BSN ( r )
Q ¯ ( r )
i f ,OBJ ( r )
c = 2 m 1
M ¯ ( r )
i 0 ,BOT ( r ) < i f ,BSN ( r )
M ¯ ( r )
f > 80   MHz
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2
I ¯ ( r ) i f ,OBJ ( r )
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2
φ BOT ( r ) φ BSN ( r ) = ( 2 k + 1 ) π / 2
φ LO = φ BSN ( r )
M ( f )
φ BOT ( r ) φ BSN ( r )
M ¯ ( r )
M ¯ ( r )
c = 1.6 m 1
i f ,BSN ( r )
i 0 ,BOT ( r )
c = 1.6 m 1
c = 1.6 m 1
M ¯ ( r )
c = 2 m 1
i f ,BSN ( r )
i 0 ,BOT ( r )
c = 2 m 1
c = 2 m 1

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