Abstract

Recently, the use of magnetic-resonance-guided navigation to improve the safety and effectiveness of surgical procedures has shown great promise. The purpose of the present study was to develop and demonstrate an imaging strategy that allows surgeons to continue operating without delays caused by imaging. The phase-scrambling Fourier-imaging technique has two prominent characteristics: localized image reconstruction and holographic image reconstruction. The combination of these characteristics allows images to be observed even during the data-acquisition period, because the acquired signal is converted into a hologram and the image is reconstructed instantly in the coherent optical image-processing system. Experimental studies have shown that the phase-scrambling Fourier-imaging technique enables the motion of objects to be imaged more quickly than the standard fast imaging. The proposed running reconstruction strategy can be easily implemented in the well-established magnetic-resonance imaging equipment that is currently in use.

© 2002 Optical Society of America

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References

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  1. P. Mansfield, “Multi-planar image formation using NMR spin echos,” J. Phys. C 10, L55–L58 (1977).
    [Crossref]
  2. R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
    [Crossref] [PubMed]
  3. K. Kose, T. Inoue, “A real-time NMR image reconstruction system using echo-planar imaging and a digital processor,” Meas. Sci. Technol. 3, 1161–1165 (1992).
    [Crossref]
  4. T. Haishi, K. Kose, “Real-time image reconstruction and display system for MRI using a high-speed personal computer,” J. Magn. Reson. 134, 138–141 (1998).
    [Crossref] [PubMed]
  5. A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
    [Crossref] [PubMed]
  6. A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).
  7. A. A. Maudsley, “Dynamic range improvement in NMR imaging using phase scrambling,” J. Magn. Reson. 76, 287–305 (1988).
  8. V. J. Wedeen, Y. S. Chao, J. L. Ackerman, “Dynamic range compression in MRI by means of a nonlinear gradient pulse,” Magn. Reson. Med. 6, 287–295 (1988).
    [Crossref] [PubMed]
  9. R. Turner, “Optical reconstruction of NMR images,” J. Phys. E:Sci. Instrum. 18, 875–878 (1985).
    [Crossref]
  10. Y. Yamada, S. Ito, T. Tanaka, “Holographic reconstruction of NMR images in Fresnel transform technique,” Electron. Commun. Jpn. Part 2 Electron. 73, 855–861 (1990).
    [Crossref]
  11. S. Ito, O. Sato, Y. Yamada, Y. Kamimura, “On-line holographic reconstruction of NMR images by means of a liquid crystal spatial light modulator,” in Proceedings of the IEEE International Conference on Image Processing—96, Lausanne, Switzerland, III, 531–534 (IEEE Inc., Belgium, 1996).
  12. S. Ito, Y. Yamada, Y. Kamimura, “Real-time holographic reconstruction of NMR Images in Fresnel Transform Imaging Technique,” in Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 2.2.1-e, 467 (Soetekouw a/v productions, The Netherlands, 1997), pp. 467–469.
  13. Y. Yamada, S. Ito, Y. Kamimura, “Holographic image reconstruction system in NMR Fresnel transform techniqueusing liquid crystal spatial light modulator,” in Proceedings of the 15th Annual Meeting of European Society for Magnetic Resonance in Medicine and Biology, Geneva, Switzerland, 351, 144 (Elsevier, The Netherlands, 1998).
  14. Y. Yamada, K. Tanaka, Z. Abe, “NMR Fresnel transform imaging technique using a quadratic nonlinear field gradient,” Rev. Sci. Instrum. 63, 5348–5358 (1992).
    [Crossref]
  15. G. W. Stroke, An Introduction to COHERENT OPTICS and HOLOGRAPHY (Academic Press, New York, London, 1969).
  16. D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
    [Crossref] [PubMed]

1998 (1)

T. Haishi, K. Kose, “Real-time image reconstruction and display system for MRI using a high-speed personal computer,” J. Magn. Reson. 134, 138–141 (1998).
[Crossref] [PubMed]

1996 (1)

A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
[Crossref] [PubMed]

1992 (3)

K. Kose, T. Inoue, “A real-time NMR image reconstruction system using echo-planar imaging and a digital processor,” Meas. Sci. Technol. 3, 1161–1165 (1992).
[Crossref]

Y. Yamada, K. Tanaka, Z. Abe, “NMR Fresnel transform imaging technique using a quadratic nonlinear field gradient,” Rev. Sci. Instrum. 63, 5348–5358 (1992).
[Crossref]

D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
[Crossref] [PubMed]

1990 (1)

Y. Yamada, S. Ito, T. Tanaka, “Holographic reconstruction of NMR images in Fresnel transform technique,” Electron. Commun. Jpn. Part 2 Electron. 73, 855–861 (1990).
[Crossref]

1989 (1)

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

1988 (2)

A. A. Maudsley, “Dynamic range improvement in NMR imaging using phase scrambling,” J. Magn. Reson. 76, 287–305 (1988).

V. J. Wedeen, Y. S. Chao, J. L. Ackerman, “Dynamic range compression in MRI by means of a nonlinear gradient pulse,” Magn. Reson. Med. 6, 287–295 (1988).
[Crossref] [PubMed]

1986 (1)

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

1985 (1)

R. Turner, “Optical reconstruction of NMR images,” J. Phys. E:Sci. Instrum. 18, 875–878 (1985).
[Crossref]

1977 (1)

P. Mansfield, “Multi-planar image formation using NMR spin echos,” J. Phys. C 10, L55–L58 (1977).
[Crossref]

Abe, Z.

Y. Yamada, K. Tanaka, Z. Abe, “NMR Fresnel transform imaging technique using a quadratic nonlinear field gradient,” Rev. Sci. Instrum. 63, 5348–5358 (1992).
[Crossref]

Ackerman, J. L.

V. J. Wedeen, Y. S. Chao, J. L. Ackerman, “Dynamic range compression in MRI by means of a nonlinear gradient pulse,” Magn. Reson. Med. 6, 287–295 (1988).
[Crossref] [PubMed]

Ailion, D. C.

D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
[Crossref] [PubMed]

Berchem, T. A.

A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
[Crossref] [PubMed]

Case, T. A.

D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
[Crossref] [PubMed]

Chao, Y. S.

V. J. Wedeen, Y. S. Chao, J. L. Ackerman, “Dynamic range compression in MRI by means of a nonlinear gradient pulse,” Magn. Reson. Med. 6, 287–295 (1988).
[Crossref] [PubMed]

Christman, R. A.

D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
[Crossref] [PubMed]

Ehsani, A. R.

A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
[Crossref] [PubMed]

Farzaneh, F.

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

Frahm, J.

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

Ganesan, K.

D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
[Crossref] [PubMed]

Gmitro, A. F.

A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
[Crossref] [PubMed]

Haishi, T.

T. Haishi, K. Kose, “Real-time image reconstruction and display system for MRI using a high-speed personal computer,” J. Magn. Reson. 134, 138–141 (1998).
[Crossref] [PubMed]

Hanicke, W.

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

Hasse, A.

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

Inoue, T.

K. Kose, T. Inoue, “A real-time NMR image reconstruction system using echo-planar imaging and a digital processor,” Meas. Sci. Technol. 3, 1161–1165 (1992).
[Crossref]

Ito, S.

Y. Yamada, S. Ito, T. Tanaka, “Holographic reconstruction of NMR images in Fresnel transform technique,” Electron. Commun. Jpn. Part 2 Electron. 73, 855–861 (1990).
[Crossref]

S. Ito, O. Sato, Y. Yamada, Y. Kamimura, “On-line holographic reconstruction of NMR images by means of a liquid crystal spatial light modulator,” in Proceedings of the IEEE International Conference on Image Processing—96, Lausanne, Switzerland, III, 531–534 (IEEE Inc., Belgium, 1996).

S. Ito, Y. Yamada, Y. Kamimura, “Real-time holographic reconstruction of NMR Images in Fresnel Transform Imaging Technique,” in Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 2.2.1-e, 467 (Soetekouw a/v productions, The Netherlands, 1997), pp. 467–469.

Y. Yamada, S. Ito, Y. Kamimura, “Holographic image reconstruction system in NMR Fresnel transform techniqueusing liquid crystal spatial light modulator,” in Proceedings of the 15th Annual Meeting of European Society for Magnetic Resonance in Medicine and Biology, Geneva, Switzerland, 351, 144 (Elsevier, The Netherlands, 1998).

Kamimura, Y.

Y. Yamada, S. Ito, Y. Kamimura, “Holographic image reconstruction system in NMR Fresnel transform techniqueusing liquid crystal spatial light modulator,” in Proceedings of the 15th Annual Meeting of European Society for Magnetic Resonance in Medicine and Biology, Geneva, Switzerland, 351, 144 (Elsevier, The Netherlands, 1998).

S. Ito, O. Sato, Y. Yamada, Y. Kamimura, “On-line holographic reconstruction of NMR images by means of a liquid crystal spatial light modulator,” in Proceedings of the IEEE International Conference on Image Processing—96, Lausanne, Switzerland, III, 531–534 (IEEE Inc., Belgium, 1996).

S. Ito, Y. Yamada, Y. Kamimura, “Real-time holographic reconstruction of NMR Images in Fresnel Transform Imaging Technique,” in Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 2.2.1-e, 467 (Soetekouw a/v productions, The Netherlands, 1997), pp. 467–469.

Kose, K.

T. Haishi, K. Kose, “Real-time image reconstruction and display system for MRI using a high-speed personal computer,” J. Magn. Reson. 134, 138–141 (1998).
[Crossref] [PubMed]

K. Kose, T. Inoue, “A real-time NMR image reconstruction system using echo-planar imaging and a digital processor,” Meas. Sci. Technol. 3, 1161–1165 (1992).
[Crossref]

Liu, Y.

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

Mansfield, P.

P. Mansfield, “Multi-planar image formation using NMR spin echos,” J. Phys. C 10, L55–L58 (1977).
[Crossref]

Matthaei, D.

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

Maudsley, A. A.

A. A. Maudsley, “Dynamic range improvement in NMR imaging using phase scrambling,” J. Magn. Reson. 76, 287–305 (1988).

Merboldt, K. D.

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

Riederer, S. J.

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

Rossman, P. J.

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

Sato, O.

S. Ito, O. Sato, Y. Yamada, Y. Kamimura, “On-line holographic reconstruction of NMR images by means of a liquid crystal spatial light modulator,” in Proceedings of the IEEE International Conference on Image Processing—96, Lausanne, Switzerland, III, 531–534 (IEEE Inc., Belgium, 1996).

Snell, R. J.

A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
[Crossref] [PubMed]

Stroke, G. W.

G. W. Stroke, An Introduction to COHERENT OPTICS and HOLOGRAPHY (Academic Press, New York, London, 1969).

Tanaka, K.

Y. Yamada, K. Tanaka, Z. Abe, “NMR Fresnel transform imaging technique using a quadratic nonlinear field gradient,” Rev. Sci. Instrum. 63, 5348–5358 (1992).
[Crossref]

Tanaka, T.

Y. Yamada, S. Ito, T. Tanaka, “Holographic reconstruction of NMR images in Fresnel transform technique,” Electron. Commun. Jpn. Part 2 Electron. 73, 855–861 (1990).
[Crossref]

Turner, R.

R. Turner, “Optical reconstruction of NMR images,” J. Phys. E:Sci. Instrum. 18, 875–878 (1985).
[Crossref]

Wedeen, V. J.

V. J. Wedeen, Y. S. Chao, J. L. Ackerman, “Dynamic range compression in MRI by means of a nonlinear gradient pulse,” Magn. Reson. Med. 6, 287–295 (1988).
[Crossref] [PubMed]

Wright, R. C.

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

Yamada, Y.

Y. Yamada, K. Tanaka, Z. Abe, “NMR Fresnel transform imaging technique using a quadratic nonlinear field gradient,” Rev. Sci. Instrum. 63, 5348–5358 (1992).
[Crossref]

Y. Yamada, S. Ito, T. Tanaka, “Holographic reconstruction of NMR images in Fresnel transform technique,” Electron. Commun. Jpn. Part 2 Electron. 73, 855–861 (1990).
[Crossref]

S. Ito, O. Sato, Y. Yamada, Y. Kamimura, “On-line holographic reconstruction of NMR images by means of a liquid crystal spatial light modulator,” in Proceedings of the IEEE International Conference on Image Processing—96, Lausanne, Switzerland, III, 531–534 (IEEE Inc., Belgium, 1996).

Y. Yamada, S. Ito, Y. Kamimura, “Holographic image reconstruction system in NMR Fresnel transform techniqueusing liquid crystal spatial light modulator,” in Proceedings of the 15th Annual Meeting of European Society for Magnetic Resonance in Medicine and Biology, Geneva, Switzerland, 351, 144 (Elsevier, The Netherlands, 1998).

S. Ito, Y. Yamada, Y. Kamimura, “Real-time holographic reconstruction of NMR Images in Fresnel Transform Imaging Technique,” in Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 2.2.1-e, 467 (Soetekouw a/v productions, The Netherlands, 1997), pp. 467–469.

Electron. Commun. Jpn. Part 2 Electron. (1)

Y. Yamada, S. Ito, T. Tanaka, “Holographic reconstruction of NMR images in Fresnel transform technique,” Electron. Commun. Jpn. Part 2 Electron. 73, 855–861 (1990).
[Crossref]

J. Magn. Reson. (3)

T. Haishi, K. Kose, “Real-time image reconstruction and display system for MRI using a high-speed personal computer,” J. Magn. Reson. 134, 138–141 (1998).
[Crossref] [PubMed]

A. Hasse, J. Frahm, D. Matthaei, W. Hanicke, K. D. Merboldt, “FLASH imaging. Rapid NMR imaging using low flip-angle pulses,” J. Magn. Reson. 67, 258–266 (1986).

A. A. Maudsley, “Dynamic range improvement in NMR imaging using phase scrambling,” J. Magn. Reson. 76, 287–305 (1988).

J. Phys. C (1)

P. Mansfield, “Multi-planar image formation using NMR spin echos,” J. Phys. C 10, L55–L58 (1977).
[Crossref]

J. Phys. E:Sci. Instrum. (1)

R. Turner, “Optical reconstruction of NMR images,” J. Phys. E:Sci. Instrum. 18, 875–878 (1985).
[Crossref]

Magn. Reson. Imaging (1)

D. C. Ailion, K. Ganesan, T. A. Case, R. A. Christman, “Rapid line scan technique for artifact-free images of moving objects,” Magn. Reson. Imaging 10, 747–757 (1992).
[Crossref] [PubMed]

Magn. Reson. Med. (3)

V. J. Wedeen, Y. S. Chao, J. L. Ackerman, “Dynamic range compression in MRI by means of a nonlinear gradient pulse,” Magn. Reson. Med. 6, 287–295 (1988).
[Crossref] [PubMed]

R. C. Wright, S. J. Riederer, F. Farzaneh, P. J. Rossman, Y. Liu, “Real-time MR fluoroscopic data acquisition and image reconstruction,” Magn. Reson. Med. 12, 407–415 (1989).
[Crossref] [PubMed]

A. F. Gmitro, A. R. Ehsani, T. A. Berchem, R. J. Snell, “A real-time reconstruction systems for magnetic resonance imaging,” Magn. Reson. Med. 35, 734–740 (1996).
[Crossref] [PubMed]

Meas. Sci. Technol. (1)

K. Kose, T. Inoue, “A real-time NMR image reconstruction system using echo-planar imaging and a digital processor,” Meas. Sci. Technol. 3, 1161–1165 (1992).
[Crossref]

Rev. Sci. Instrum. (1)

Y. Yamada, K. Tanaka, Z. Abe, “NMR Fresnel transform imaging technique using a quadratic nonlinear field gradient,” Rev. Sci. Instrum. 63, 5348–5358 (1992).
[Crossref]

Other (4)

G. W. Stroke, An Introduction to COHERENT OPTICS and HOLOGRAPHY (Academic Press, New York, London, 1969).

S. Ito, O. Sato, Y. Yamada, Y. Kamimura, “On-line holographic reconstruction of NMR images by means of a liquid crystal spatial light modulator,” in Proceedings of the IEEE International Conference on Image Processing—96, Lausanne, Switzerland, III, 531–534 (IEEE Inc., Belgium, 1996).

S. Ito, Y. Yamada, Y. Kamimura, “Real-time holographic reconstruction of NMR Images in Fresnel Transform Imaging Technique,” in Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, IL, USA, 2.2.1-e, 467 (Soetekouw a/v productions, The Netherlands, 1997), pp. 467–469.

Y. Yamada, S. Ito, Y. Kamimura, “Holographic image reconstruction system in NMR Fresnel transform techniqueusing liquid crystal spatial light modulator,” in Proceedings of the 15th Annual Meeting of European Society for Magnetic Resonance in Medicine and Biology, Geneva, Switzerland, 351, 144 (Elsevier, The Netherlands, 1998).

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Figures (12)

Fig. 1
Fig. 1

Pulse sequence for PSFT. The pulse sequence is repeated with an appropriate repetition time (TR). The quadratic field gradient is applied for a fixed time τ to produce a nonlinear phase scrambling in the x and y directions. The gradient echo signal appearing at the reversal of G x is sampled as the data.

Fig. 2
Fig. 2

In PSFT a localized image can be obtained from a segmented signal by setting the imaging parameter properly: (a) imaging object; (b) k-space signal is restricted in the area, the center of which is located on k n and the width of which is 2k w for the phase encoding direction; (c) image reconstructed from the segmented signal shown in (b); the reconstructed area y w ′ is roughly equal to the segmented signal region in the x′ - y′ coordinate; (d) If the range of motion is small during the t w period as shown in (e); (f) the image of the moving object becomes the sum of all values for Δρ n (x, y) at time t n and the reconstructed image will appear as a diagnonally skewed object.

Fig. 3
Fig. 3

(a) Shows the real-part of the computed echo signal obtained in PSFT consisting of 128 × 128 pixels, with the parameters of γbτ set as 2.45 rad/cm2 to meet the condition of Δy = Δy′. (b) Shows the reconstructed image using the entire signal in k space, (c) is the signal filling the lower-half of the signal space with zero value, and (d) shows the reconstructed image using the signal (c). Almost the entire upper-half of the object is imaged corresponding to the signal space.

Fig. 4
Fig. 4

Received NMR signal is amplified (AMP) and converted to low frequency by means of a phase-sensitive detector (PSD) prior to analog-to-digital conversion (ADC). The real-part of the NMR gradient echo signal is stored in the frame memory of the computer as hologram data and is sent to LC-SLM by the VGA video signal. The reconstruction of the image from the NMR hologram is achieved by taking the optical Fourier transformation of the light passing through the hologram illuminated by coherent laser light. The reconstructed images are obtained as the symmetrical first-order diffraction images at both sides of the zero-order diffraction light on the focal plane.

Fig. 5
Fig. 5

Coil configuration for generating the characteristic field. The long axis of the coil system is aligned along the z direction, i.e., B 0 direction. Rectangular prism coil generates a quadratic nonlinear field gradient having cylindrical contours extending in the z direction when current is supplied in the direction shown by white arrows.

Fig. 6
Fig. 6

In each phase encoding step, the sampled echo signal corresponding to line data in k space is normalized to be shown in a gray-scale hologram and then stored in the frame memory of the computer. After the VGA signal scans the frame memory, the line hologram corresponding to the line data in k space is updated on the LC-SLM. Because the optical computation is performed on the order of ns, the image on the focal plane is updated soon after the hologram is refreshed.

Fig. 7
Fig. 7

Picture of the LC-SLM used in the experiments.

Fig. 8
Fig. 8

(a) Shows the reconstructed images, taken every 0.5 s, while the phantom was being contracted. (b) Shows the phantom used in the experiments. The imaging parameters were set as follows: γbτ = 4.0 rad/cm2, Δx = Δy = 0.16 cm. Although the contraction of the phantom occurred uniformly, shrinking is observed in the image from left to right. (c) Shows the computer-reconstructed image to compare the image quality with optically reconstructed images.

Fig. 9
Fig. 9

Reconstructed images of a phantom moving in the phase-encoding direction from right to left on the image. The phantom used in the experiment is a half-round having a diameter of 37 mm consisting of CuSO4 solution and a three-circular plastic insert. The imaging parameters were set as follows: γbτ = 4.0 rad/cm2, and the spatial resolutions Δx = Δy = 0.12 cm. Because the hologram on the LC-SLM is updated from left to right on the image, the reconstructed image is updated in the same direction in a manner such that the newer images are superimposed onto the older image. A few artifacts are found to be spread over the entire imaging region due to the motion or the effect of localized image reconstruction.

Fig. 10
Fig. 10

Reconstructed images of a phantom rotating in a clockwise direction. The imaging parameters were set as follows: γbτ = 3.2 rad/cm2, Δx = Δy = 0.17 cm. The phase encoding direction is set for the horizontal direction on the image. Although the transitional images, taken every 0.4 s, represent a blurring and degradation caused by motion, no defects or significant artifacts are observed on the transitional images.

Fig. 11
Fig. 11

Reconstructed images of a needle-shaped phantom. The imaging parameters were set as in the rotation experiment. (a) Shows the transient images while the needle-shaped phantom was being translated to another position in a stepwise manner, and (b) shows the transient images while the angle between the needle-shaped phantom and the basement was being varied.

Fig. 12
Fig. 12

Comparison of image quality using a high-SNR MR image. (a) Is the MRI transversal image having a matrix size of 128 × 128 pixels, and (b) is the optical image captured by a CCD camera. The SN ratio appears to be decreased compared to the original image (a), however, the half-tone to which the original image compared, is well represented.

Tables (1)

Tables Icon

Table 1 Specifications of the LC-SLM

Equations (24)

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

vγGxtx, γGyty=exp-jγb0xty+2txr+tx×-ρx, yexp-jγbτ x2+y2exp-jγ Gxtxx+Gytyydxdy,
vkx, ky=exp-jβ0exp-jβ0xkx×-ρx, yexp-jγbτ x2+y2exp-jkxx+kyydxdy,
vx, y=exp-jβ0exp-jβ0xx×expjγbτx2+y2× - ρ x, yexp-jγbτ x-x2+ y-y2dxdy.
Δρnx, y=-1vkx, kyrectky-knkw,
Δρnx, y=-1vkx, ky+knrectkykw.
Δρnx, y=ρ x, yexp-jγbτx2+y2× exp-jkny * sinckwy,= exp-jγbτyn2ρx, yexp-jγbτx2+ y-yn2 * sinckwy,
2πkwyγbτy-yn2y=yw=2π.
ywkw2γbτ,
yn-ywyyn+yw.
ymax=NΔky4γbτ.
ymax=2πΔky=NΔy.
Δky=4γbτπNor Δy=πγbτN.
Δvnkx, ky=vnkx, kyrectky-knkw,
Δρnx, y=exp-jγbτyn2ρnx, yexp-jγbτx2+ y-yn2 * sinckwy,
ρmovx, y=n=0M Δρnx, y.
Hxi, yiopt= Oxi, yi+Rxi, yi2,= Oxi, yi2+ R02+Oxi, yiR0 expjβoptxi+O*xi, yiR0 exp-jβoptxi,
= Oxi, yi2+ R02+2ReOxi, yiR0 expjβoptxi,
Hxi, yioptK+2ReOxi, yiR0 expjβoptxi.
uxi, yi= R0λz2-Ox, y×expj k2zx2+y2×exp-j kzxix+yiydxdy,= R0λz2  Ox, yexpj k2zx2+y2,
vkx, ky=exp-jβ0xkxv kx, ky,
vkx, ky=exp-jβ0-ρx, y×exp-jγbτx2+y2×exp-jkxx+kyydxdy.
HNMR=K+Revkx, ky,
ΔB=bx2+y2,
b=2μ02π2B0r04NI2.

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