Abstract

We present an active optical synthetic aperture-imaging system. A phase-step digital holographic setup is used as a wavefront sensor in the far field. The overlap of the holograms enables the estimation and compensation of their relative positions and phase with a speckle cross-correlation algorithm. Experimental results on a short-range synthetic aperture setup at 633 nm are presented that are based on 128 × 128 holograms. The synthesis is executed in one direction by means of rotation of the object. Test images show a significant gain of resolution in the synthesis direction. Processing errors are estimated through experiment. Random processing errors of a synthetic pupil composed of 33 merged holograms are negligible, but biases induced by unknown optical aberrations of the reference wave induce defocusing and astigmatism.

© 2002 Optical Society of America

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References

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2001

2000

1999

1998

1995

1989

1984

1983

H. Saito, S. Nakadate, T. Yatagai, “Computer-aided electronic speckle pattern interferometry,” Appl. Opt. 23, 237–243 (1983).

1981

1980

1947

A. Marechal, Revue d’Optique, Theor. Instr. 26, 257–277 (1947).

Aruga, Tadashi

Bevilacqua, F.

Binet, R.

R. Binet, J. Colineau, J-C Lehureau, Rev. Electr. Electron. 2, 31–38 (2001).
[CrossRef]

Capron, B. A.

Colella, B. D.

Colineau, J.

R. Binet, J. Colineau, J-C Lehureau, Rev. Electr. Electron. 2, 31–38 (2001).
[CrossRef]

Collot, L.

Cuche, E.

Cutrona, L. J.

L. J. Cutrona, “Synthetic Aperture Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1970), Chap. 23.

Depeursinge, C.

Eichel, P. H.

Ennos, A. E.

A. E. Ennos, “Speckle Interferometry” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Topics in Applied Physics, Vol. 9 (Springer-Verlag, Berlin), Chap. 6, p. 240.

Fienup, J. R.

J. R. Fienup, “Synthetic-aperture radar autofocus by maximizing sharpness,” Opt. Lett. 25, 4, 221–223 (2000).
[CrossRef]

Franze, B.

Ghiglia, D. C.

Goodman, J. W.

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

Green, T. J.

Gross, M.

Haible, P.

Hariharan, P.

Harney, R. C.

Jakowatz, C. V.

Joenathan, C.

LeClerc, F.

Lehureau, J-C

R. Binet, J. Colineau, J-C Lehureau, Rev. Electr. Electron. 2, 31–38 (2001).
[CrossRef]

Marcus, S.

Marechal, A.

A. Marechal, Revue d’Optique, Theor. Instr. 26, 257–277 (1947).

Nakadate, S.

H. Saito, S. Nakadate, T. Yatagai, “Computer-aided electronic speckle pattern interferometry,” Appl. Opt. 23, 237–243 (1983).

H. Saito, S. Nakadate, T. Yatagai, “Electronic speckle pattern interferometry using digital image processing techniques,” Appl. Opt. 19, 1879–1883 (1980).
[CrossRef] [PubMed]

Oliver, C.

C. Oliver, Shaun Quegan, “Principles of SAR Image Formation,” in Understanding Synthetic Aperture Radar Images, ed. (Artech House Publishers, London, 1998), Chap. 2.

Oreb, B.

Quegan, Shaun

C. Oliver, Shaun Quegan, “Principles of SAR Image Formation,” in Understanding Synthetic Aperture Radar Images, ed. (Artech House Publishers, London, 1998), Chap. 2.

Saito, H.

H. Saito, S. Nakadate, T. Yatagai, “Computer-aided electronic speckle pattern interferometry,” Appl. Opt. 23, 237–243 (1983).

H. Saito, S. Nakadate, T. Yatagai, “Electronic speckle pattern interferometry using digital image processing techniques,” Appl. Opt. 19, 1879–1883 (1980).
[CrossRef] [PubMed]

Shapiro, J. H.

Sharon, B.

Tiziani, H. J.

Yatagai, T.

H. Saito, S. Nakadate, T. Yatagai, “Computer-aided electronic speckle pattern interferometry,” Appl. Opt. 23, 237–243 (1983).

H. Saito, S. Nakadate, T. Yatagai, “Electronic speckle pattern interferometry using digital image processing techniques,” Appl. Opt. 19, 1879–1883 (1980).
[CrossRef] [PubMed]

Yoshikado, S.

Appl. Opt.

Opt. Lett.

Rev. Electr. Electron.

R. Binet, J. Colineau, J-C Lehureau, Rev. Electr. Electron. 2, 31–38 (2001).
[CrossRef]

Theor. Instr.

A. Marechal, Revue d’Optique, Theor. Instr. 26, 257–277 (1947).

Other

A. E. Ennos, “Speckle Interferometry” in Laser Speckle and Related Phenomena, J. C. Dainty, ed., Topics in Applied Physics, Vol. 9 (Springer-Verlag, Berlin), Chap. 6, p. 240.

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

L. J. Cutrona, “Synthetic Aperture Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1970), Chap. 23.

C. Oliver, Shaun Quegan, “Principles of SAR Image Formation,” in Understanding Synthetic Aperture Radar Images, ed. (Artech House Publishers, London, 1998), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

Synthetic aperture principle. The light source can either be static or not.

Fig. 2
Fig. 2

Digital holography setup. BS1, BS2, beam splitters; O1, microscope objective + 50 mm focal length objective; L1, transmitting lens; Pz, piezo actuator translation stage. D is the CCD width. The reference wave comes virtually from a point centered on the object.

Fig. 3
Fig. 3

Speckle far-field rotation dependence with angle of incidence (i) and scattering angle (r).

Fig. 4
Fig. 4

Object orientation: line of sight is axis z. R is the virtual reference point. t is the translation vector of the object. τ is the translation vector of the far field speckle.

Fig. 5
Fig. 5

Images of an United States Air Force scattering test target computed with (a) a single hologram 128 × 128 pixels; (b) a synthetic aperture composed of 33 subpupil holograms merged coherently. The synthetic pupil is 2048 × 128 pixels; (c) is a zoom of the central part. Vertical grating contrast is significantly increased compared with horizontal ones. In (a), (b), and (c), three intensity images, statistically independent, have been averaged to lower the speckle noise.

Fig. 6
Fig. 6

Residual phase-error estimation by double-pass hologram synthesis, with an overlap between the two synthetic pupils: (a) experiment principle, the phase difference of two synthetic pupils where 30% of the overlap is computed; (b) piston phase error per single hologram after global tilt and focus removal.

Tables (1)

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Table 1 Root Mean Square and Peak to Valley Phase Differencea

Equations (11)

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Ekr= Rr+Or · expik-1π22 =|Rr|2+ |Or|2+R*O expik-1π2+RO* exp-ik-1π2,
Ikc, l=Ekr rδ r-cpxex×δ r-lpyey×c 1..nc, l1..nl,
Hc, l=I1c, l-I3c, l-iI2c, l-I4c, l,=4R*rOr rδ r-cpxex×δ r-lpyey,4κR*cpxex, lpyeyOcpxex, lpyey,
Uz0c, l=K · exp-i πpxpyc2+l2λz0×c=1ncl=1nl Hc, l×exp-i πpxpyc2+l2λ1z0-1zR× expi 2πpxpycc+llλz0,
O=expiπr2λzR; R=Rexpiπr2λzRexpiφab,H=4κR*O=4κRexpiφab,PSF=|FTH|2=16κ2 |FT|R|expiφab|
Hc, l=I1c, l-I3c, l-i I2c, l-I4c, lexp[-iφabc, l.
δψ=1+cos icos rδβ.
Ojr=Oir-τ ·expikt · rz+iφp,
R*OiR*Oju= R*rOirR*r+u×Oir+u-τexp× ikt · r+uz+iφpdr
|t  λzD and |r+uD  kt · r+uz1expikt · r+uz1
R*OiR*Oju=expiφp  R*rOirR*r+uOir+u-τdr, =expiφpR*OiR*Oiu-τ, =expiφpFT-1Uz02u-τ,

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