Abstract

A two-dimensional (2D) Fourier transform algorithm for the image reconstruction of synthetic-aperture imaging ladar (SAIL) collected data is suggested. This algorithm consists of quadratic phase compensation in azimuth direction and 2D fast Fourier transform. Based on this algorithm and the parallel 2D Fourier transform capability of spherical lens, an optical principle scheme that processes the SAIL data is proposed. The basic principle, design equations, and necessary analysis are presented. To verify this principle scheme, an experimental optical SAIL processor setup is constructed. The imaging results of SAIL data obtained by our SAIL demonstrator are presented. The optical processor is compact, lightweight, and consumes low power. This optical processor can also provide inherent parallel and speed-of-light computing capability, and thus has potential applications in on-board and satellite-borne SAIL systems.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Bashkansky, R. L. Lucke, E. Funk, L. J. Rickard, and J. Reintjes, “Two-dimensional synthetic aperture imaging in the optical domain,” Opt. Lett. 27, 1983–1985 (2002).
    [CrossRef]
  2. S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, “Synthetic-aperture imaging laser radar: laboratory demonstration and signal processing,” Appl. Opt. 44, 7621–7629 (2005).
    [CrossRef]
  3. L. Liu, “Coherent and incoherent synthetic aperture imaging ladars and laboratory-space experimental demonstrations [invited],” Appl. Opt. 52, 579–599 (2013).
    [CrossRef]
  4. Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
    [CrossRef]
  5. L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
    [CrossRef]
  6. P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
    [CrossRef]
  7. L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
    [CrossRef]
  8. A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
    [CrossRef]
  9. I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, “Image reconstruction only by phase data in phase-shifting digital holography,” Appl. Opt. 45, 975–983 (2006).
    [CrossRef]

2013 (2)

L. Liu, “Coherent and incoherent synthetic aperture imaging ladars and laboratory-space experimental demonstrations [invited],” Appl. Opt. 52, 579–599 (2013).
[CrossRef]

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

2009 (1)

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

2008 (1)

P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
[CrossRef]

2006 (1)

2005 (1)

2002 (1)

1981 (1)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

1966 (1)

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Bashkansky, M.

Beck, S. M.

Bergeron, A.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
[CrossRef]

Bourqui, P.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
[CrossRef]

Buck, J. R.

Buell, W. F.

Chateauneuf, F.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Cutrona, L. J.

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Desnoyers, N.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Dickinson, R. P.

Doucet, M.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Funk, E.

Harnisch, B.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
[CrossRef]

Kozlowski, D. A.

Legros, M.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Leith, E. N.

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Lim, J. S.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Liu, L.

L. Liu, “Coherent and incoherent synthetic aperture imaging ladars and laboratory-space experimental demonstrations [invited],” Appl. Opt. 52, 579–599 (2013).
[CrossRef]

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Luan, Z.

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Lucke, R. L.

Marchese, L.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
[CrossRef]

Marechal, N. J.

Martel, A.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Mercier, L.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Mills, G. A.

Oppenheim, A. V.

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

Porcello, L. J.

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Reintjes, J.

Rickard, L. J.

Savard, M.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Suess, M.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Sun, J.

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Turbide, S.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Turgeon, S.

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Vivian, W. E.

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Wang, L.

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Wright, T. J.

Xu, N.

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Yamaguchi, I.

Yamamoto, K.

Yan, A.

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Yokota, M.

Zhou, Y.

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Acta Opt. Sin. (1)

Y. Zhou, N. Xu, Z. Luan, A. Yan, L. Wang, J. Sun, and L. Liu, “2D imaging experiment of a 2D target in a laboratory-scale synthetic aperture imaging ladar,” Acta Opt. Sin. 29, 2030–2032 (2009).
[CrossRef]

Appl. Opt. (3)

Opt. Lett. (1)

Proc. IEEE (2)

A. V. Oppenheim and J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69, 529–541 (1981).
[CrossRef]

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the application of coherent optical processing techniques to synthetic-aperture radar,” Proc. IEEE 54, 1026–1032 (1966).
[CrossRef]

Proc. SPIE (2)

P. Bourqui, B. Harnisch, L. Marchese, and A. Bergeron, “Optical SAR processor for space application,” Proc. SPIE 6958, 69580J (2008).
[CrossRef]

L. Marchese, M. Doucet, P. Bourqui, B. Harnisch, M. Suess, M. Legros, N. Desnoyers, S. Turbide, S. Turgeon, L. Mercier, M. Savard, A. Martel, F. Chateauneuf, and A. Bergeron, “A global review of optronic synthetic aperture radar/ladar processing,” Proc. SPIE 8714, 871416 (2013).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Geometry for strip-mode side-looking SAIL imaging.

Fig. 2.
Fig. 2.

Relation between the Fourier-transform window and the flow of SAIL collected data.

Fig. 3.
Fig. 3.

Principle scheme of the optical SAIL processor.

Fig. 4.
Fig. 4.

Diagram of the LCSLM.

Fig. 5.
Fig. 5.

Pattern of Fourier transform for the 1D LCSLM pixels.

Fig. 6.
Fig. 6.

Experimental configuration of the optical SAIL processor.

Fig. 7.
Fig. 7.

Target pattern, digital imaging results, and experimental results: (a) target pattern, (b) digital imaging result with complex-valued data, (c) digital imaging result with phase-only data, (d) imaging result of 1D outputting mode, and (e) imaging result of 2D outputting mode.

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

x=αsinφ,y=β,z=αcosφ.
ik(xk,yk:ts,tf)=A(xk,yk)S(xk,ykvyts)×rect(tfTf/2Tf)exp(j2πf˙2Δzkctf)×exp[jπλ(Z/2)(ykvyts)2],
S(x,y)=S(x)S(y)=sinc2(DxxλZ)sinc2(DyyλZ).
Ts=Dyfpvy.
ikex(xk,yk:ts,tf)=rect(tsTs/2Ts)rect(tfTf/2Tf)×ik(xk,yk:ts(P)ts,tf)ts=ts(P)ts,tf=tf.
exp[jφc(ts)]=exp[jvy2λZ/2(tsTs2)2].
Ik(xk,yk:fx,fy:ts(P))=C(xk,yk:fx,fy:ts(P))tri(λZDyvyfy)*sinc(Tsfy)*δ{fyvy2λ(Z/2)[ykvyts(P)+Ts2]}×sinc(Tffx)*sinc(Tffx)*δ(fx2Δzkcf˙),
fy(yk)=vy2λ(Z/2)[ykvyts(P)+Ts2].
Ry=DyvyλZ+1Ts.
fx(zk)=2Δzkcf˙.
Rx=1Ts.
Iplane_one(fx,fy:P)=PIk(fx,fy:xk,yk:ts(P))|fy=0.
|fy,max|=DyfpλZvy.
Iplane_two(fx,fy:P)=PIk(fx,fy:xk,yk:ts(P))||fy|fy,max.
iic(β)=exp(jπλcfcβ2),
ebf(u,v)=1jλcf++fm(α,β)iic(β)×exp[j2π(uλcfε+vλcfη)]dαdβ=1jλcfF{fm(α,β)}*F{iic(β)},
Ibf(u,v)=|ebf(u,v)|2.
fLCSLM(α,β)=rect(αa)rect(βb)++[rect(αDα)*δ(αmTα)][rect(βDβ)*δ(βnTβ)],
mΔtfTf=mTαanΔtsTs=nTβb.
mΔtf=TfamgnΔts=Tsbnh.
tLCSLM(xk,yk:α,β:ts(P))=A(xk,yk)rect(αa)rect(βb)++rect(mTαa/2a)exp(j2πf˙2ΔzkcTfamTα)rect(αDα)*δ(αmTα)×S[xk,ykvyts(P)+TsbvynTβ]rect(nTβb/2b)×exp{jπλZ/2(vyTsb)2[bvyTsykbTsts(P)+nTβ]2}rect(βDβ)*δ(βnTβ).
λcfc=λZ2(bvyTs)2.
fc=λZ2λc(bvyTs)2.
e(xk,yk:u,v:ts(P))=B(xk,yk:u,v)×sinc(bvλcf)*[sinc(Dβvλcf)+tβ(nTβ)δ(vλcfnTβ)]×sinc(auλcf)*[sinc(Dαuλcf)+tα(mTα)δ(uλcfmTα)].
tLCSLM(xk,yk:α,β:ts(P))=A(xk,yk)rect(αa)rect(βb)×S[xk,ykvyts(P)+vyTsbβ]exp(j2πf˙2ΔzkcTfaα)×exp{jπλZ/2(vyTsb)2[bvyTsykbTsts(P)+β]2}.
e(xk,yk:u,v:ts(P))=exp{jπλZ/2[ykvyts(P)]2}×A(xk,yk)1jλcfF{rect(αa)}*δ(uλcf2Δzkf˙cTfa)×F{S[xk,ykvyts(P)+Tsbβ]}*F{rect(βb)}*δ{vλcf1λZ/2vyTsb[ykvyts(P)]},
uk=2λcfTff˙acΔzkvk=λcfvyTsbλZ/2[ykvyts(P)].
Δu=2λcfTff˙cosφacΔα,Δv=λcfvyTsbλZ/2Δβ,
ΔuΔv=Tff˙λZbcosφvyTsacΔαΔβ.
ρSR=Tff˙λZbcosφvyTsac.
f22Δl=λZ2λc(bTs)2.
Δl=2λcf22λZ(Tsb)2.
Ik(xk,yk:fx,fy:ts(P))=++ikex(xk,yk:ts,tf)×exp[jφc(ts)]exp[j2π(fxtf+fyts)]dtfdts=A(xk,yk)exp(jπvy2λ(Z/2){[ykvyts(P)]2(Ts2)2})×λZDyvysinc2(DxxλZ)exp{j2π[ykvyts(P)]fy}×Tsexp(jπTsfy)Tfexp(jπTffs)Tfexp(jπTffs)×tri(λZDyvyfy)*sinc(Tsfy)*δ{fyvy2λ(Z/2)[ykvyts(P)+Ts2]}×sinc(Tffx)*sinc(Tffx)*δ(fx2Δzkcf˙),
e(xk,yk:u,v:ts(P))=1jλcf++tLCSLM(α,β)×exp(jπλcfcβ2)exp[j2π(uαλcf+vβλcf)]dαdβ=A(xk,yk)abDαDβTαTβλcfcexp(jπfcλcf2v2)×sinc(bvλcf)*[sinc(Dβvλcf)+tβ(nTβ)δ(vλcfnTβ)]×sinc(auλcf)*[sinc(Dαuλcf)+tα(mTα)δ(uλcfmTα)],
tα(mTα)=rect(mTαa/2a)exp(j2πf˙2ΔzkcTfamTα)tη(nTβ)=S[xk,ykvyts(P)+TsbnTβ]rect(nTβb/2b)×exp{jπλZ/2(vyTsb)2[bvyTsykbTsts(P)+nTβ]2}.

Metrics