C. J. R. Sheppard, K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik 107, 79–87 (1997).

T. C. Wedberg, J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).

[CrossRef]

T. E. Gureyev, A. Roberts, K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995).

[CrossRef]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wavefield reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

C. J. R. Sheppard, T. J. Connolly, M. Gu, “Scattering by a one-dimensional rough surface, and surface profile reconstruction confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993).

[CrossRef]
[PubMed]

F. Gori, M. Santarsiero, G. Guattari, “Coherence and the spatial distribution of intensity,” J. Opt. Soc. Am. A 10, 673–679 (1993).

[CrossRef]

P. J. Shaw, D. A. Agard, Y. Hiraoka, J. W. Sedat, “Tilted view reconstruction in optical microscopy,” Biophys. J. 55, 101–110 (1989).

[CrossRef]
[PubMed]

M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phases,” J. Opt. Soc. Am. A 72, 1199–1209 (1982).

[CrossRef]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).

[CrossRef]
[PubMed]

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension: underlying theory,” Optik 61, 247–262 (1982).

I. M. Bruck, L. G. Sodin, “On the ambiguity of the image restoration problem,” Opt. Commun. 30, 304–308 (1979).

[CrossRef]

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

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).

[CrossRef]

A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1962).

[CrossRef]

P. J. Shaw, D. A. Agard, Y. Hiraoka, J. W. Sedat, “Tilted view reconstruction in optical microscopy,” Biophys. J. 55, 101–110 (1989).

[CrossRef]
[PubMed]

H. P. Baltes, “Introduction,” in Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 1–10.

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension: underlying theory,” Optik 61, 247–262 (1982).

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wavefield reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

I. M. Bruck, L. G. Sodin, “On the ambiguity of the image restoration problem,” Opt. Commun. 30, 304–308 (1979).

[CrossRef]

C. J. Cogswell, K. G. Larkin, H. U. Klemm, “Fluorescence microtomography: multiangle image acquisition and 3D digital reconstruction,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, eds., Proc. SPIE2655, 109–115 (1996).

[CrossRef]

C. J. R. Sheppard, T. J. Connolly, M. Gu, “Scattering by a one-dimensional rough surface, and surface profile reconstruction confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993).

[CrossRef]
[PubMed]

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).

[CrossRef]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).

[CrossRef]
[PubMed]

M. H. Maleki, A. J. Devaney, “Phase retrieval in inverse scattering,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 398–408 (1992).

[CrossRef]

M. H. Maleki, A. J. Devaney, “Holographic techniques for inverse scattering and tomographic imaging,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2176, 184–194 (1994).

[CrossRef]

H. A. Ferweda, “The phase reconstruction problem for wave amplitudes and coherence functions,” in Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 13–38.

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

C. J. R. Sheppard, T. J. Connolly, M. Gu, “Scattering by a one-dimensional rough surface, and surface profile reconstruction confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993).

[CrossRef]
[PubMed]

P. J. Shaw, D. A. Agard, Y. Hiraoka, J. W. Sedat, “Tilted view reconstruction in optical microscopy,” Biophys. J. 55, 101–110 (1989).

[CrossRef]
[PubMed]

M. Kaveh, M. Soumekh, “Computer-assisted diffraction tomography,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), pp. 369–413.

C. J. Cogswell, K. G. Larkin, H. U. Klemm, “Fluorescence microtomography: multiangle image acquisition and 3D digital reconstruction,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, eds., Proc. SPIE2655, 109–115 (1996).

[CrossRef]

C. J. R. Sheppard, K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik 107, 79–87 (1997).

C. J. Cogswell, K. G. Larkin, H. U. Klemm, “Fluorescence microtomography: multiangle image acquisition and 3D digital reconstruction,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, eds., Proc. SPIE2655, 109–115 (1996).

[CrossRef]

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).

[CrossRef]

M. H. Maleki, A. J. Devaney, “Holographic techniques for inverse scattering and tomographic imaging,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2176, 184–194 (1994).

[CrossRef]

M. H. Maleki, A. J. Devaney, “Phase retrieval in inverse scattering,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 398–408 (1992).

[CrossRef]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wavefield reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wavefield reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

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

P. J. Shaw, D. A. Agard, Y. Hiraoka, J. W. Sedat, “Tilted view reconstruction in optical microscopy,” Biophys. J. 55, 101–110 (1989).

[CrossRef]
[PubMed]

P. J. Shaw, D. A. Agard, Y. Hiraoka, J. W. Sedat, “Tilted view reconstruction in optical microscopy,” Biophys. J. 55, 101–110 (1989).

[CrossRef]
[PubMed]

C. J. R. Sheppard, K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik 107, 79–87 (1997).

C. J. R. Sheppard, T. J. Connolly, M. Gu, “Scattering by a one-dimensional rough surface, and surface profile reconstruction confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993).

[CrossRef]
[PubMed]

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

I. M. Bruck, L. G. Sodin, “On the ambiguity of the image restoration problem,” Opt. Commun. 30, 304–308 (1979).

[CrossRef]

M. Kaveh, M. Soumekh, “Computer-assisted diffraction tomography,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), pp. 369–413.

A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1962).

[CrossRef]

P. J. Shaw, D. A. Agard, Y. Hiraoka, J. W. Sedat, “Tilted view reconstruction in optical microscopy,” Biophys. J. 55, 101–110 (1989).

[CrossRef]
[PubMed]

T. C. Wedberg, J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).

[CrossRef]

T. E. Gureyev, A. Roberts, K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995).

[CrossRef]

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).

[CrossRef]

J. R. Fienup, “Phase retrieval using boundary conditions,” J. Opt. Soc. Am. A 3, 284–288 (1986).

[CrossRef]

M. H. Maleki, A. J. Devaney, A. Schatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).

[CrossRef]

F. Gori, M. Santarsiero, G. Guattari, “Coherence and the spatial distribution of intensity,” J. Opt. Soc. Am. A 10, 673–679 (1993).

[CrossRef]

M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phases,” J. Opt. Soc. Am. A 72, 1199–1209 (1982).

[CrossRef]

A. Walther, “The question of phase retrieval in optics,” Opt. Acta 10, 41–49 (1962).

[CrossRef]

I. M. Bruck, L. G. Sodin, “On the ambiguity of the image restoration problem,” Opt. Commun. 30, 304–308 (1979).

[CrossRef]

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).

[CrossRef]

E. Collett, E. Wolf, “Is complete spatial coherence necessary for the generation of highly directional light beams?” Opt. Lett. 2, 27–29 (1978).

[CrossRef]
[PubMed]

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).

[CrossRef]
[PubMed]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. A. Fiddy, B. J. Brames, J. C. Dainty, “Enforcing irreducibility for phase retrieval in two dimensions,” Opt. Lett. 8, 96–98 (1983).

[CrossRef]
[PubMed]

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension: underlying theory,” Optik 61, 247–262 (1982).

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

C. J. R. Sheppard, K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik 107, 79–87 (1997).

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wavefield reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

C. J. R. Sheppard, T. J. Connolly, M. Gu, “Scattering by a one-dimensional rough surface, and surface profile reconstruction confocal imaging,” Phys. Rev. Lett. 70, 1409–1412 (1993).

[CrossRef]
[PubMed]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).

[CrossRef]
[PubMed]

H. P. Baltes, “Introduction,” in Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 1–10.

H. A. Ferweda, “The phase reconstruction problem for wave amplitudes and coherence functions,” in Inverse Source Problems, H. P. Baltes, ed. (Springer-Verlag, Berlin, 1978), pp. 13–38.

M. H. Maleki, A. J. Devaney, “Phase retrieval in inverse scattering,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 398–408 (1992).

[CrossRef]

M. H. Maleki, A. J. Devaney, “Holographic techniques for inverse scattering and tomographic imaging,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2176, 184–194 (1994).

[CrossRef]

M. Kaveh, M. Soumekh, “Computer-assisted diffraction tomography,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), pp. 369–413.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

C. J. Cogswell, K. G. Larkin, H. U. Klemm, “Fluorescence microtomography: multiangle image acquisition and 3D digital reconstruction,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, eds., Proc. SPIE2655, 109–115 (1996).

[CrossRef]

In practice we have access only to discretely sampled measurements over a finite region of space. It is a straightforward procedure to include these limitations and the computation artifacts that ensue. The main effect, which is due to the finite area, is a blurring in the angular spectrum domain.