We present a method for measuring the transverse electric field profile of a beam of light which allows for direct phase retrieval. The measured values correspond, within a normalization constant, to the real and imaginary parts of the electric field in a plane normal to the direction of propagation. This technique represents a self-referencing method for probing the wavefront characteristics of light.

© 2012 OSA

1. J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature474(7350), 188–191 (2011). [CrossRef] [PubMed]
2. J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A7(9), 1598–1608 (1990). [CrossRef]
3. R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, and L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature353(6340), 144–146 (1991). [CrossRef]
4. A. Zhang, C. H. Rao, Y. D. Zhang, and W. H. Jiang, “Novel detecting methods of Shack-Hartmann wavefront sensor at low light levels,” J. Phys.: Conf. Ser.48, 190–195 (2006). [CrossRef]
5. G. Sirat and D. Psaltis, “Conoscopic holography,” Opt. Lett.10(1), 4–6 (1985). [CrossRef] [PubMed]
6. K. Buse and M. Luennemann, “3D imaging: wave front sensing utilizing a birefringent crystal,” Phys. Rev. Lett.85(16), 3385–3387 (2000). [CrossRef] [PubMed]
7. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).
8. F. Zernike, “How I Discovered Phase Contrast,” in Nobel Lectures, Physics (Elsevier, 1964), pp. 239–246.
9. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral interferometry,” Opt. Lett.30(15), 1953–1955 (2005). [CrossRef] [PubMed]
10. R. Juanola-Parramon, N. Gonzalez, and G. Molina-Terriza, “Characterization of optical beams with spiral phase interferometry,” Opt. Express16(7), 4471–4478 (2008). [CrossRef] [PubMed]
11. G. L. Abbas, V. W. S. Chan, and T. K. Yee, “Local-oscillator excess-noise suppression for homodyne and heterodyne detection,” Opt. Lett.8(8), 419–421 (1983). [CrossRef] [PubMed]
12. J. Goodman, Introduction to Fourier Optics (Roberts & Co Publishers, 2005).
13. K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996). [CrossRef] [PubMed]

J. Opt. Soc. Am. A

• J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A7(9), 1598–1608 (1990). [CrossRef]

J. Phys.: Conf. Ser.

• A. Zhang, C. H. Rao, Y. D. Zhang, and W. H. Jiang, “Novel detecting methods of Shack-Hartmann wavefront sensor at low light levels,” J. Phys.: Conf. Ser.48, 190–195 (2006). [CrossRef]

Nature

• R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, and L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature353(6340), 144–146 (1991). [CrossRef]
• J. S. Lundeen, B. Sutherland, A. Patel, C. Stewart, and C. Bamber, “Direct measurement of the quantum wavefunction,” Nature474(7350), 188–191 (2011). [CrossRef] [PubMed]

Opt. Express

• R. Juanola-Parramon, N. Gonzalez, and G. Molina-Terriza, “Characterization of optical beams with spiral phase interferometry,” Opt. Express16(7), 4471–4478 (2008). [CrossRef] [PubMed]

Opt. Lett.

• G. L. Abbas, V. W. S. Chan, and T. K. Yee, “Local-oscillator excess-noise suppression for homodyne and heterodyne detection,” Opt. Lett.8(8), 419–421 (1983). [CrossRef] [PubMed]
• S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral interferometry,” Opt. Lett.30(15), 1953–1955 (2005). [CrossRef] [PubMed]
• G. Sirat and D. Psaltis, “Conoscopic holography,” Opt. Lett.10(1), 4–6 (1985). [CrossRef] [PubMed]

Optik (Stuttg.)

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

Phys. Rev. Lett.

• K. Buse and M. Luennemann, “3D imaging: wave front sensing utilizing a birefringent crystal,” Phys. Rev. Lett.85(16), 3385–3387 (2000). [CrossRef] [PubMed]
• K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996). [CrossRef] [PubMed]

Other

• J. Goodman, Introduction to Fourier Optics (Roberts & Co Publishers, 2005).
• F. Zernike, “How I Discovered Phase Contrast,” in Nobel Lectures, Physics (Elsevier, 1964), pp. 239–246.

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