Abstract

The performance of long distance imaging systems is typically degraded by phase errors imparted by atmospheric turbulence. In this paper we apply coherent imaging methods to determine, and remove, these phase errors by digitally processing coherent recordings of the image data. In this manner we are able to remove the effects of atmospheric turbulence without needing a conventional adaptive optical system. Digital holographic detection is used to record the coherent, complex-valued, optical field for a series of atmospheric and object realizations. Correction of atmospheric phase errors is then based on maximizing an image sharpness metric to determine the aberrations present and correct the underlying image. Experimental results that demonstrate image recovery in the presence of turbulence are presented. Results obtained with severe turbulence that gives rise to anisoplanatism are also presented.

© 2009 Optical Society of America

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References

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  1. J. W. Goodman, D. W. Jackson, M. Lehmann, and J. Knotts, "Experiments in Long-Distance Holographic Imagery," Appl. Opt. 8, 1581-1586 (1969).
    [CrossRef] [PubMed]
  2. J. W. Goodman and R.W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  3. R. A. Muller and A. Buffington, "Real-time correction of atmospherically degraded telescope images through image sharpening," J. Opt. Soc. Am. 64, 1200-1210 (1974).
    [CrossRef]
  4. R. G. Paxman and J. C. Marron, "Aberration Correction of Speckled Imagery With an Image Sharpness Criterion," In Proc. of the SPIE Conference on Statistical Optics, 976, San Diego, CA, August (1988).
  5. J. R. Fienup and J. J. Miller, "Aberration Correction by Maximizing Generalized Image Sharpness Metrics," J. Opt. Soc. Am. A 20, 609-620 (2003).
    [CrossRef]
  6. TheU.S.  Department of Commerce Table Mountain Field Site and Radio Quiet Zone. http://www.its.bldrdoc.gov/table_mountain/.
  7. M. C. Roggeman and B. Welsh, Imaging Through Turbulence (CRC, New York, N.Y. 1996).
  8. R. R. Beland, "Propagation through atmospheric optical turbulence," in The Infrared and Electro-Optical Handbook, Vol. 2: Atmospheric Propagation of Radiation, F. G. Smith, ed. (SPIE Optical Engineering Press: Bellingham, Wash., 1993), pp. 157-232.
  9. J. Marron and G. M. Morris, "Image-plane speckle from rotating, rough objects," J. Opt. Soc. Am. A 2, 1395-1402 (1985).
    [CrossRef]
  10. J. C. Dainty, "Stellar speckle interferometry," in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. Springer-Verlag, Berlin, (1983), pp. 256-320.
  11. G. April and H. H. Arsenault, "Nonstationary image-plane speckle statistics," J. Opt. Soc. Am. A 1, 738-741 (1984).
    [CrossRef]
  12. M. Tur, K. C. Chin, and J. W. Goodman, "When is speckle noise multiplicative?," Appl. Opt. 21, 1157-1159 (1982).
    [CrossRef] [PubMed]
  13. R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207- 211 (1976).
    [CrossRef]

2003 (1)

1985 (1)

1984 (1)

1982 (1)

1976 (1)

1974 (1)

1969 (1)

1967 (1)

J. W. Goodman and R.W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

April, G.

Arsenault, H. H.

Buffington, A.

Chin, K. C.

Fienup, J. R.

Goodman, J. W.

Jackson, D. W.

Knotts, J.

Lawrence, R.W.

J. W. Goodman and R.W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Lehmann, M.

Marron, J.

Miller, J. J.

Morris, G. M.

Muller, R. A.

Noll, R. J.

Tur, M.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. W. Goodman and R.W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Other (5)

TheU.S.  Department of Commerce Table Mountain Field Site and Radio Quiet Zone. http://www.its.bldrdoc.gov/table_mountain/.

M. C. Roggeman and B. Welsh, Imaging Through Turbulence (CRC, New York, N.Y. 1996).

R. R. Beland, "Propagation through atmospheric optical turbulence," in The Infrared and Electro-Optical Handbook, Vol. 2: Atmospheric Propagation of Radiation, F. G. Smith, ed. (SPIE Optical Engineering Press: Bellingham, Wash., 1993), pp. 157-232.

R. G. Paxman and J. C. Marron, "Aberration Correction of Speckled Imagery With an Image Sharpness Criterion," In Proc. of the SPIE Conference on Statistical Optics, 976, San Diego, CA, August (1988).

J. C. Dainty, "Stellar speckle interferometry," in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. Springer-Verlag, Berlin, (1983), pp. 256-320.

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Figures (8)

Fig. 1.
Fig. 1.

The optical layout of the digital holographic detection system is shown. The reference, or local oscillator, and object illuminator are derived from one laser. The telescope entrance pupil is re-imaged onto the detector array and the return light from the distant object is combined with the local oscillator creating the holographic interference pattern. The intensity of the interference pattern is recorded by the 2D detector array.

Fig. 2.
Fig. 2.

The intensity data recorded by the detector array is shown on the left. The circular boundary of the data corresponds to the pupil of the telescope. An expanded view of a small region of the intensity data is shown on the right. Note the spatial carrier frequency that results from the angular offset of the object and reference beams.

Fig. 3.
Fig. 3.

Illustration of the image formation process. The intensity data recorded by the detector array is shown in A) and the absolute value of the complex-valued Fourier transform is shown in B). Note that to form this image a quadratic phase was applied to the pupil data to remove system defocus. As a result one of the conjugate images exhibits improved focus whereas the other is further defocused. C) contains an extracted image that is distorted by residual instrumentation errors and atmospheric phase errors. The image series in this picture is the sum of 16 atmosphere and object speckle realizations.

Fig. 4.
Fig. 4.

Illustration of sharpness maximization process used for correcting image aberrations. (a) shows the magnitude of the initial complex-valued pupil data. (b) shows an example of the real part of a Zernike polynomial phase function applied to the pupil plane data. (c) shows the magnitude of the initial image, (d) shows the real part of the resultant polynomial phase function that corresponds to maximum image sharpness and (e) shows the magnitude of the final image.

Fig. 5.
Fig. 5.

The output of the scintillometer is shown for the afternoon of March 6, 2008. C2 n values ranging over three decades are typically available during the day. As shown, a drop in C2 n generally occurs an hour before sunset.

Fig. 6.
Fig. 6.

Values of Fried’s parameter, r0, are shown for the afternoon of March 6, 2008. The rise in exhibited generally occurs an hour before sunset.

Fig. 7.
Fig. 7.

Images obtained by processing 16 realizations of data. Each image is obtained by adding the intensities of the 16 realizations. The left column (A, B, and C) are images with the fixed aberrations of the optical system corrected and the right column (D, E and F) include correction of the atmospheric turbulence. Each row has a different turbulence strength. The Cn 2 values for each are the following: (A, D) 6.0E-15 m-2/3, (B, E) 5.51E-14 m-2/3, and (C, F) 5.11E -13 m-2/3.

Fig. 8.
Fig. 8.

Demonstration of correction over image regions in the presence of anisoplanatism. The dashed line in each image indicates the area over which the sharpness metric was evaluated while the aberrations were estimated. Each image results from the same set of data used in Fig. 7(C). The value of C0 2 is 5.11E-13 m-2/3. The corresponding Fried Parameter r 0 is 8.3 mm and the isoplanatic patch is 4.6 mm. For comparison the single set of three bars in the lower right corner (set -2:1) is 10 mm by 10 mm.

Tables (1)

Tables Icon

Table 1. Atmospheric parameters for the images in Fig. 7 are given. C2 n was determined using a scintillometer. Fried’s parameter, r0 , the ratio of the aperture diameter D to r0 and the isoplanatic patch size at the object are also given.

Equations (17)

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I=(F+G)2
=F2+G2+FG*+F*G.
FT(I)=ff*+gg*+fg*+f*g,
FT(I)=ff*+δ(x)+f(xb)+f*(x+b).
I(m,n)=t(x,y)eiϕ(x,y)h(m,n;x,y)dxdy2 .
I(m,n)= t(x,y)2 h(m,n;x,y)2 dxdy .
I(m,n)=V (m,n)Is(m,n).
<Ir(m,n)>=r ! Vr (m,n).
S=Σm,nI2(m,n)
S=Σm,nV2(m,n)Is2(m,n),
<S>=2 Σm,n V2 (m,n) .
σ2=20 Σm,n V4 (m,n)
d=<S′><S>σ′σ ,
S=Σm,nIβ(m,n).
S=(Σm,nIβ(m,n))(Σm,nI(m,n))β .
r0=(0.424k2Cn2L)3/5.
α0=(1.09k2Cn2L83)35,

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