Abstract

A Static random perturbation weakly scattering media may significantly reduce image quality, in many kinds of applications. An example of such a medium can be a soft tissue such as skin or flesh, through which one may wish to image an object, such as a bone, located behind. In this paper we present experimental results of newly developed deblurring approach for obtaining a better image of objects positioned behind static random perturbation media. This approach for extraction of the high spatial frequencies is based on iterative computation similar to the well-known Gerchberg–Saxton algorithm for phase retrieval. By focusing a camera onto three or more planes positioned between the imaging camera and the perturbation media, we are able to retrieve the phase distribution of those planes and then reconstruct the intensity of the object by numerical free-space propagation of this extracted complex field, to the estimated position of the object.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (2)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

D. Psaltis and I. N. Papadopoulos, “Imaging: the fog clears,” Nature 491, 197–198 (2012).
[CrossRef]

2010 (1)

2009 (1)

E. Gur and Z. Zalevsky, “Image deblurring through static or time-varying random perturbation medium,” J. Electron. Imaging 18, 033016 (2009).
[CrossRef]

2007 (1)

V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, “Absorption spectra and light penetration depth of normal and pathologically altered human skin,” J. Appl. Spectrosc. 74, 430–439 (2007).
[CrossRef]

1998 (1)

1996 (1)

1994 (1)

J. M. Tanner and R. D. Gibbons, “Automatic bone age measurement using computerized image analysis,” J. Pediatr. Endocrinol. Metab. 7, 141–146 (1994).
[CrossRef]

1991 (1)

A. Ishimaru, “Wave propagation and scattering in random media and rough surfaces,” Proc. IEEE 79, 1359–1366(1991).
[CrossRef]

1990 (3)

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[CrossRef]

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

B. C. Wilson and S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

1982 (1)

1978 (1)

1977 (1)

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977).
[CrossRef]

1973 (3)

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D 6, 2200–2216(1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D 6, 2217–2225(1973).
[CrossRef]

1972 (1)

R. Gerchberg, and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Barun, V. V.

V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, “Absorption spectra and light penetration depth of normal and pathologically altered human skin,” J. Appl. Spectrosc. 74, 430–439 (2007).
[CrossRef]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Dorsch, R. G.

Dror, I.

Fienup, J. R.

Freund, I.

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[CrossRef]

Gerchberg, R.

R. Gerchberg, and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gibbons, R. D.

J. M. Tanner and R. D. Gibbons, “Automatic bone age measurement using computerized image analysis,” J. Pediatr. Endocrinol. Metab. 7, 141–146 (1994).
[CrossRef]

Grossman, E.

Gur, A.

Gur, E.

E. Grossman, R. Tzioni, A. Gur, E. Gur, and Z. Zalevsky, “Optical through-turbulence imaging configuration: experimental validation,” Opt. Lett. 35, 453–455 (2010).
[CrossRef]

E. Gur and Z. Zalevsky, “Image deblurring through static or time-varying random perturbation medium,” J. Electron. Imaging 18, 033016 (2009).
[CrossRef]

Ishimaru, A.

A. Ishimaru, “Wave propagation and scattering in random media and rough surfaces,” Proc. IEEE 79, 1359–1366(1991).
[CrossRef]

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977).
[CrossRef]

Ivanov, A. P.

V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, “Absorption spectra and light penetration depth of normal and pathologically altered human skin,” J. Appl. Spectrosc. 74, 430–439 (2007).
[CrossRef]

Jacques, S. L.

B. C. Wilson and S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

Kopeika, N. S.

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Mendlovic, D.

Misell, D. L.

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D 6, 2200–2216(1973).
[CrossRef]

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D 6, 2217–2225(1973).
[CrossRef]

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Papadopoulos, I. N.

D. Psaltis and I. N. Papadopoulos, “Imaging: the fog clears,” Nature 491, 197–198 (2012).
[CrossRef]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Psaltis, D.

D. Psaltis and I. N. Papadopoulos, “Imaging: the fog clears,” Nature 491, 197–198 (2012).
[CrossRef]

Sandrov, A.

Saxton, O.

R. Gerchberg, and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Tanner, J. M.

J. M. Tanner and R. D. Gibbons, “Automatic bone age measurement using computerized image analysis,” J. Pediatr. Endocrinol. Metab. 7, 141–146 (1994).
[CrossRef]

Tzioni, R.

Ulashchik, V. S.

V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, “Absorption spectra and light penetration depth of normal and pathologically altered human skin,” J. Appl. Spectrosc. 74, 430–439 (2007).
[CrossRef]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Volotovskaya, A. V.

V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, “Absorption spectra and light penetration depth of normal and pathologically altered human skin,” J. Appl. Spectrosc. 74, 430–439 (2007).
[CrossRef]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Welch, A. J.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Wilson, B. C.

B. C. Wilson and S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

Zalevsky, Z.

Appl. Opt. (2)

IEEE J. Quantum Electron. (2)

B. C. Wilson and S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

J. Appl. Spectrosc. (1)

V. V. Barun, A. P. Ivanov, A. V. Volotovskaya, and V. S. Ulashchik, “Absorption spectra and light penetration depth of normal and pathologically altered human skin,” J. Appl. Spectrosc. 74, 430–439 (2007).
[CrossRef]

J. Electron. Imaging (1)

E. Gur and Z. Zalevsky, “Image deblurring through static or time-varying random perturbation medium,” J. Electron. Imaging 18, 033016 (2009).
[CrossRef]

J. Pediatr. Endocrinol. Metab. (1)

J. M. Tanner and R. D. Gibbons, “Automatic bone age measurement using computerized image analysis,” J. Pediatr. Endocrinol. Metab. 7, 141–146 (1994).
[CrossRef]

J. Phys. D (3)

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D 6, 2200–2216(1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D 6, 2217–2225(1973).
[CrossRef]

Nature (2)

D. Psaltis and I. N. Papadopoulos, “Imaging: the fog clears,” Nature 491, 197–198 (2012).
[CrossRef]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[CrossRef]

Opt. Lett. (3)

Optik (1)

R. Gerchberg, and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Physica A (1)

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[CrossRef]

Proc. IEEE (2)

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061 (1977).
[CrossRef]

A. Ishimaru, “Wave propagation and scattering in random media and rough surfaces,” Proc. IEEE 79, 1359–1366(1991).
[CrossRef]

Other (1)

“Skin Optics Summary,” http://omlc.ogi.edu/news/jan98/skinoptics.html .

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Figures (7)

Fig. 1.
Fig. 1.

Scheme of Gerchberg–Saxton algorithm (G–S) after being modified by Misell.

Fig. 2.
Fig. 2.

Schematic setup for the Gur–Zalevsky algorithm. An object with a light source. The signal is passing through a diffuser, which is a weakly scattering random pertubation medium. Three or more images are recorded at different planes.

Fig. 3.
Fig. 3.

Schematic flow chart of Gur–Zalevsky algorithm for phase retrieval and image deblurring. N is the number of G–S iterations performed for phase retrieval. n is the number of images used by the algorithm, each image is taken at a different focus plane and n>3. E10En0 are the field distributions at the 1n focal planes. Ei=1n, Ei=1n are the field distributions calculated with G–S algorithm on each iteration. φ0 is the initial phase, random or guessed. φ1φn are the phases calculated with G–S algorithm in each iteration.

Fig. 4.
Fig. 4.

Object, a resolution target of an opaque glass with three slits for light to pass through. From the left-hand side (a) one may see a scheme of the resolution target. From the right-hand side (b) one sees an image of the object behind a tissue.

Fig. 5.
Fig. 5.

Input images, taken from three different focus planes, located 9, 11, and 13 mili-inch from the tissue. Images are after preprocessing of image cropping and Gaussian blurring to reduce high frequency noise.

Fig. 6.
Fig. 6.

(a) Image of the object, taken while the tissue is removed. (b) First image used for the image enhancement algorithm, which is the one where the object is visually the best. It is the reference image. (c) Output image where the object appears better than the first image. It is closer to the reference image.

Fig. 7.
Fig. 7.

(a) Profile of the output image (dark gray line) in comparison to the reference image (light gray line) and the original object’s image (black line), calculated as an average over the y axis (Fig. 6). The two left-hand side peaks represent the two left-hand side slits and have better contrast than the reference line. The right-hand side peak is lower but still clear at the output profile while at the reference profile it is hardly noticed. (b) Spatial correlation between an output image produced at every iteration of the algorithm and the object’s image. The correlation is improved during the 30,000 iteration.

Equations (3)

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

Ei(x,y)=e(2πiλd)iλdEj(x,y)e{πiλd[(xx)2+(yy)2]}dxdy,
q=sensordΩr|f(Ω)|24πdΩ|f(Ω)|2<π(10mm)24π(150mm)21%,
Ei(x,y)=Ii(x,y)eiφ0(x,y),

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