Abstract

Diffraction imaging in the far-field can detect 3D morphological features of an object for its coherent nature. We describe methods for accurate calculation and analysis of diffraction images of scatterers of single and double spheres by an imaging unit based on microscope objective at non-conjugate positions. A quantitative study of the calculated diffraction imaging in spectral domain has been performed to assess the resolving power of diffraction imaging. It has been shown numerically that with coherent illumination of 532 nm in wavelength the imaging unit can resolve single spheres of 2 μm or larger in diameters and double spheres separated by less than 300 nm between their centers.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2016 (2)

2015 (1)

2014 (3)

2012 (1)

2011 (3)

2009 (2)

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. 34(19), 2985–2987 (2009).
[Crossref] [PubMed]

2003 (3)

J. Neukammer, C. Gohlke, A. Höpe, T. Wessel, and H. Rinneberg, “Angular distribution of light scattered by single biological cells and oriented particle agglomerates,” Appl. Opt. 42(31), 6388–6397 (2003).
[Crossref] [PubMed]

M. M. Hanczyc, S. M. Fujikawa, and J. W. Szostak, “Experimental models of primitive cellular compartments: encapsulation, growth, and division,” Science 302(5645), 618–622 (2003).
[Crossref] [PubMed]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

2002 (1)

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

1998 (1)

1980 (1)

M. Portnoff, ““Time-frequency representation of digital signals and systems based on short-time Fourier analysis,” IEEE T. Acous,” Speech Signal Proces. 28(1), 55–69 (1980).
[Crossref]

1975 (1)

M. Bessis and N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Backman, V.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Badizadegan, K.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Bertrand, F. E.

Bessis, M.

M. Bessis and N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Boone, C. W.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Bottiger, J. R.

Brock, R. S.

K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express 2(6), 1717–1726 (2011).
[Crossref] [PubMed]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

Castellone, R.

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

Chang, R. K.

Chernyshev, A. V.

Chernyshova, E. S.

Dasari, R. R.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Ding, J.

J. Zhang, Y. Feng, W. Jiang, J. Q. Lu, Y. Sa, J. Ding, and X. H. Hu, “Realistic optical cell modeling and diffraction imaging simulation for study of optical and morphological parameters of nucleus,” Opt. Express 24(1), 366–377 (2016).
[Crossref] [PubMed]

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

Dong, K.

Ekpenyong, A. E.

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

Farwell, M. A.

Feld, M. S.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Feng, Y.

Fujikawa, S. M.

M. M. Hanczyc, S. M. Fujikawa, and J. W. Szostak, “Experimental models of primitive cellular compartments: encapsulation, growth, and division,” Science 302(5645), 618–622 (2003).
[Crossref] [PubMed]

Gilev, K. V.

Gohlke, C.

Goodwin, P. M.

Gupta, M.

Hanczyc, M. M.

M. M. Hanczyc, S. M. Fujikawa, and J. W. Szostak, “Experimental models of primitive cellular compartments: encapsulation, growth, and division,” Science 302(5645), 618–622 (2003).
[Crossref] [PubMed]

Hill, S. C.

Hillis, D. B.

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
[Crossref]

Holler, S.

Höpe, A.

Hu, X. H.

J. Zhang, Y. Feng, W. Jiang, J. Q. Lu, Y. Sa, J. Ding, and X. H. Hu, “Realistic optical cell modeling and diffraction imaging simulation for study of optical and morphological parameters of nucleus,” Opt. Express 24(1), 366–377 (2016).
[Crossref] [PubMed]

H. Wang, Y. Feng, Y. Sa, Y. Ma, J. Q. Lu, X. H. Hu, and X. H. Hu, “Acquisition of cross-polarized diffraction images and study of blurring effect by one time-delay-integration camera,” Appl. Opt. 54(16), 5223–5228 (2015).
[Crossref] [PubMed]

H. Wang, Y. Feng, Y. Sa, Y. Ma, J. Q. Lu, X. H. Hu, and X. H. Hu, “Acquisition of cross-polarized diffraction images and study of blurring effect by one time-delay-integration camera,” Appl. Opt. 54(16), 5223–5228 (2015).
[Crossref] [PubMed]

R. Pan, Y. Feng, Y. Sa, J. Q. Lu, K. M. Jacobs, and X. H. Hu, “Analysis of diffraction imaging in non-conjugate configurations,” Opt. Express 22(25), 31568–31574 (2014).
[Crossref] [PubMed]

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

S. Yu, J. Zhang, M. S. Moran, J. Q. Lu, Y. Feng, and X. H. Hu, “A novel method of diffraction imaging flow cytometry for sizing microspheres,” Opt. Express 20(20), 22245–22251 (2012).
[Crossref] [PubMed]

K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express 2(6), 1717–1726 (2011).
[Crossref] [PubMed]

K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. 34(19), 2985–2987 (2009).
[Crossref] [PubMed]

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

Jacobs, K. M.

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

R. Pan, Y. Feng, Y. Sa, J. Q. Lu, K. M. Jacobs, and X. H. Hu, “Analysis of diffraction imaging in non-conjugate configurations,” Opt. Express 22(25), 31568–31574 (2014).
[Crossref] [PubMed]

K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express 2(6), 1717–1726 (2011).
[Crossref] [PubMed]

K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. 34(19), 2985–2987 (2009).
[Crossref] [PubMed]

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

Janowska-Wieczorek, A.

Jiang, W.

J. Zhang, Y. Feng, W. Jiang, J. Q. Lu, Y. Sa, J. Ding, and X. H. Hu, “Realistic optical cell modeling and diffraction imaging simulation for study of optical and morphological parameters of nucleus,” Opt. Express 24(1), 366–377 (2016).
[Crossref] [PubMed]

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

Kirkwood, S. E.

Li, Z.

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

Lu, J. Q.

J. Zhang, Y. Feng, W. Jiang, J. Q. Lu, Y. Sa, J. Ding, and X. H. Hu, “Realistic optical cell modeling and diffraction imaging simulation for study of optical and morphological parameters of nucleus,” Opt. Express 24(1), 366–377 (2016).
[Crossref] [PubMed]

H. Wang, Y. Feng, Y. Sa, Y. Ma, J. Q. Lu, X. H. Hu, and X. H. Hu, “Acquisition of cross-polarized diffraction images and study of blurring effect by one time-delay-integration camera,” Appl. Opt. 54(16), 5223–5228 (2015).
[Crossref] [PubMed]

R. Pan, Y. Feng, Y. Sa, J. Q. Lu, K. M. Jacobs, and X. H. Hu, “Analysis of diffraction imaging in non-conjugate configurations,” Opt. Express 22(25), 31568–31574 (2014).
[Crossref] [PubMed]

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

S. Yu, J. Zhang, M. S. Moran, J. Q. Lu, Y. Feng, and X. H. Hu, “A novel method of diffraction imaging flow cytometry for sizing microspheres,” Opt. Express 20(20), 22245–22251 (2012).
[Crossref] [PubMed]

K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express 2(6), 1717–1726 (2011).
[Crossref] [PubMed]

K. M. Jacobs, J. Q. Lu, and X. H. Hu, “Development of a diffraction imaging flow cytometer,” Opt. Lett. 34(19), 2985–2987 (2009).
[Crossref] [PubMed]

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

Ma, Y.

Maltsev, V. P.

Marquez-Curtis, L.

Mohandas, N.

M. Bessis and N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Moran, M. S.

Neukammer, J.

Pan, R.

Pan, Y.

Portnoff, M.

M. Portnoff, ““Time-frequency representation of digital signals and systems based on short-time Fourier analysis,” IEEE T. Acous,” Speech Signal Proces. 28(1), 55–69 (1980).
[Crossref]

Qiu, Y.

Rinneberg, H.

Rozmus, W.

Sa, Y.

Strokotov, D. I.

Su, X.

Szostak, J. W.

M. M. Hanczyc, S. M. Fujikawa, and J. W. Szostak, “Experimental models of primitive cellular compartments: encapsulation, growth, and division,” Science 302(5645), 618–622 (2003).
[Crossref] [PubMed]

Tsui, Y. Y.

Wang, H.

Wax, A.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Werner, J. H.

Wessel, T.

Yang, C.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Yang, L. V.

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

K. Dong, Y. Feng, K. M. Jacobs, J. Q. Lu, R. S. Brock, L. V. Yang, F. E. Bertrand, M. A. Farwell, and X. H. Hu, “Label-free classification of cultured cells through diffraction imaging,” Biomed. Opt. Express 2(6), 1717–1726 (2011).
[Crossref] [PubMed]

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

Yang, P.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48(24), 4165–4172 (2003).
[Crossref] [PubMed]

Yu, S.

Yurkin, M. A.

K. V. Gilev, M. A. Yurkin, E. S. Chernyshova, D. I. Strokotov, A. V. Chernyshev, and V. P. Maltsev, “Mature red blood cells: from optical model to inverse light-scattering problem,” Biomed. Opt. Express 7(4), 1305–1310 (2016).
[Crossref] [PubMed]

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2234–2247 (2011).
[Crossref]

Zhang, J.

Zhang, N.

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

Zhang, P.

Appl. Opt. (2)

Biomed. Opt. Express (2)

Biophys. J. (1)

A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82(4), 2256–2264 (2002).
[Crossref] [PubMed]

Blood Cells (1)

M. Bessis and N. Mohandas, “A diffractometric method for the measurement of cellular deformability,” Blood Cells 1, 307–313 (1975).

Cytometry A (1)

Y. Feng, N. Zhang, K. M. Jacobs, W. Jiang, L. V. Yang, Z. Li, J. Zhang, J. Q. Lu, and X. H. Hu, “Polarization imaging and classification of Jurkat T and Ramos B cells using a flow cytometer,” Cytometry A 85(9), 817–826 (2014).
[Crossref] [PubMed]

J. Biophotonics (1)

K. M. Jacobs, L. V. Yang, J. Ding, A. E. Ekpenyong, R. Castellone, J. Q. Lu, and X. H. Hu, “Diffraction imaging of spheres and melanoma cells with a microscope objective,” J. Biophotonics 2(8-9), 521–527 (2009).
[Crossref] [PubMed]

J. Quant. Spectrosc. Radiat. Transf. (1)

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Figures (5)

Fig. 1
Fig. 1

(A) Configuration of the DIFC system for DI measurement and simulations with an incident beam of λ = 532nm propagating along z-axis (into paper): f.c. = flow chamber; (B) measured DIs of single spheres in water with nominal diameter value of d = 2.5μm (left), 7.9μm (center) and two spheres of d = 5.7μm (right) at Δx = 150μm; (C) calculated DI of single sphere in water with d = 2.5μm (left) and 7.9μm (right) as I(y, z), nsr = 1.588, nsi = 3.5x10−4, λ = 532nm, nh = 1.334 and Δx = 150μm, dash lines indicates sampled lines Iθ in Eq. (1).

Fig. 2
Fig. 2

The STFT power spectra |S(f, θ; z)| performed on a line Iθ sampled at θ from a calculated DI (insets with dash lines) for different scatterers versus f and z in unit of pixel distance Δ: (A) a single sphere of d = 3.00μm and θ = 0°; (B) two spheres of connection vector (C) with (010) as direction and |(C)| = d, θ = 90°. DI simulation parameters are given by nsr = 1.588, nsi = 3.5x10−4, λ = 532nm, nh = 1.334, Δx = 150μm, dpl = 20.

Fig. 3
Fig. 3

(A) Calculated DIs of single spheres with different diameter d as marked, bar = 10° in detection angle in water; (B) |S(f, 0°; z)| of calculated DIs in (A) at z of maximum Ms with legends showing d and z (in unit of pixel size Δ) values, fv and fs are indicated by the arrows for the case of d = 5.0μm; (C) fs and Msm obtained from DIs versus d, the solid line is a straight line fitted to fs with Msm > 1. Other parameters are the same as those in Fig. 2.

Fig. 4
Fig. 4

Examples of calculated DIs of two spheres with d = 3.0μm, bar = 10°. The direction and magnitude of (C) are marked in each image. Other parameters are the same as those in Fig. 2.

Fig. 5
Fig. 5

The paired contour plots of fsb, C) and Msmb, C) obtained from calculated DIs of two spheres with d = 3.0μm, 0.075μm ≤ C ≤ 6.0 μm and (C) directions as marked in each image. The white dash lines indicate C = 0.30μm. Other parameters are the same as those in Fig. 2.

Equations (2)

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S(f,θ;z)= 0 Σ' I θ (z')exp{ π (z'z) 2 w 2 }exp{2πifz'}dz' ,
M s (θ,z)= |S( f s, θ;z)| |S(0,θ;z)| |S( f s, θ;z)| |S( f v ,θ;z)| ,

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