Abstract

The most commonly used configurations in digital holography—namely Fourier holograms, Fresnel holograms, and image-plane holograms—are analyzed with respect to Seidel’s wave aberration theory. This analysis is performed by taking into account the phase terms involved in the recording and reconstruction processes. The combined phase term from both processes is compared with the Gaussian-reference sphere, from which the wave aberration terms can be obtained. In conjunction with the analysis, for each of the aberration terms, conditions can be set to eliminate them. Wave aberrations are plotted to show how strongly different setups are affected.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
    [CrossRef]
  2. R. W. Meier, “Magnification and third-order aberrations in holography,” J. Opt. Soc. Am. 55, 987–992 (1965).
  3. E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. A 57, 51–55 (1967).
  4. C. S. Vikram and M. L. Billet, “Aberration limited resolution in fraunhofer holography with collimated beams,” Opt. Laser Technol. 21, 173–184 (1989).
    [CrossRef]
  5. J. N. Latta, “Fifth-order hologram aberrations,” Appl. Opt. 10, 666–667 (1971).
    [CrossRef]
  6. P. R. Hobson and J. Watson, “The principles and practice of holographic recording of plankton,” J. Opt. A 4, S23–S49 (2002).
    [CrossRef]
  7. W. Zhou, Y. Yu, and A. Asundi, “Study on aberration suppressing methods in digital micro-holography,” Opt. Lasers Eng. 47, 264–270 (2009).
    [CrossRef]
  8. T. Colomb, J. Kühn, F. Charrière, and C. Depeursinge, “Total aberrations compensation in digital holographic microscopy,” Opt. Express 14, 4300–4306 (2006).
    [CrossRef]
  9. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 23, 3177–3190 (2006).
    [CrossRef]
  10. L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
    [CrossRef]
  11. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45, 851–863 (2006).
    [CrossRef]
  12. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  14. H. Gross, ed., Handbook of Optical Systems: Aberration Theory and Correction of Optical Systems (Wiley-VCH, 2007), Chap. Aberrations.
  15. W. Osten, ed., Optical Inspection of Microsystems (Taylor and Francis, 2006).
  16. D. Claus, “Resolution improvement methods applied to digital holography,” Ph.D. thesis (University of Warwick, 2010).

2009

W. Zhou, Y. Yu, and A. Asundi, “Study on aberration suppressing methods in digital micro-holography,” Opt. Lasers Eng. 47, 264–270 (2009).
[CrossRef]

2007

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

2006

2002

P. R. Hobson and J. Watson, “The principles and practice of holographic recording of plankton,” J. Opt. A 4, S23–S49 (2002).
[CrossRef]

1989

C. S. Vikram and M. L. Billet, “Aberration limited resolution in fraunhofer holography with collimated beams,” Opt. Laser Technol. 21, 173–184 (1989).
[CrossRef]

1971

1967

E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. A 57, 51–55 (1967).

1965

Alfieri, D.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Aspert, N.

Asundi, A.

W. Zhou, Y. Yu, and A. Asundi, “Study on aberration suppressing methods in digital micro-holography,” Opt. Lasers Eng. 47, 264–270 (2009).
[CrossRef]

Billet, M. L.

C. S. Vikram and M. L. Billet, “Aberration limited resolution in fraunhofer holography with collimated beams,” Opt. Laser Technol. 21, 173–184 (1989).
[CrossRef]

Bourquin, S.

Champagne, E. B.

E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. A 57, 51–55 (1967).

Charrière, F.

Claus, D.

D. Claus, “Resolution improvement methods applied to digital holography,” Ph.D. thesis (University of Warwick, 2010).

Colomb, T.

Cuche, E.

De Petrocellis, L.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Depeursinge, C.

Ferraro, P.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Finizio, A.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grilli, S.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Haist, T.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Hobson, P. R.

P. R. Hobson and J. Watson, “The principles and practice of holographic recording of plankton,” J. Opt. A 4, S23–S49 (2002).
[CrossRef]

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Kühn, J.

Latta, J. N.

Marian, A.

Marquet, P.

Meier, R. W.

Miccio, L.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Montfort, F.

Nicola, S. D.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Reicherter, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Seifert, L.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Vikram, C. S.

C. S. Vikram and M. L. Billet, “Aberration limited resolution in fraunhofer holography with collimated beams,” Opt. Laser Technol. 21, 173–184 (1989).
[CrossRef]

Watson, J.

P. R. Hobson and J. Watson, “The principles and practice of holographic recording of plankton,” J. Opt. A 4, S23–S49 (2002).
[CrossRef]

Wu, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Yu, Y.

W. Zhou, Y. Yu, and A. Asundi, “Study on aberration suppressing methods in digital micro-holography,” Opt. Lasers Eng. 47, 264–270 (2009).
[CrossRef]

Zhou, W.

W. Zhou, Y. Yu, and A. Asundi, “Study on aberration suppressing methods in digital micro-holography,” Opt. Lasers Eng. 47, 264–270 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. D. Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007).
[CrossRef]

Comput. Sci. Eng.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

J. Opt. A

P. R. Hobson and J. Watson, “The principles and practice of holographic recording of plankton,” J. Opt. A 4, S23–S49 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

Opt. Laser Technol.

C. S. Vikram and M. L. Billet, “Aberration limited resolution in fraunhofer holography with collimated beams,” Opt. Laser Technol. 21, 173–184 (1989).
[CrossRef]

Opt. Lasers Eng.

W. Zhou, Y. Yu, and A. Asundi, “Study on aberration suppressing methods in digital micro-holography,” Opt. Lasers Eng. 47, 264–270 (2009).
[CrossRef]

Other

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

H. Gross, ed., Handbook of Optical Systems: Aberration Theory and Correction of Optical Systems (Wiley-VCH, 2007), Chap. Aberrations.

W. Osten, ed., Optical Inspection of Microsystems (Taylor and Francis, 2006).

D. Claus, “Resolution improvement methods applied to digital holography,” Ph.D. thesis (University of Warwick, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Gaussian-reference sphere originating at A and hologram-plane intersection points B and C.

Fig. 2.
Fig. 2.

Radial pupil coordinates ρ and θ.

Fig. 3.
Fig. 3.

Geometric configuration for a Fresnel hologram.

Fig. 4.
Fig. 4.

Geometric configuration of a Fourier hologram.

Fig. 5.
Fig. 5.

Phase-aberrations for Fresnel hologram and Fourier hologram: (a) Coma, (b) astigmatism, (c) field curvature, (d) distortion, and (e) combination of all terms.

Fig. 6.
Fig. 6.

Geometric configuration of an image-plane hologram.

Fig. 7.
Fig. 7.

Phase-aberrations for image-plane hologram with plane and spherical reference wave: (a) Coma, (b) astigmatism, (c) field curvature, and (d) combination of all terms.

Tables (5)

Tables Icon

Table 1. Seidel Aberrations

Tables Icon

Table 2. Fresnel Hologram Seidel Aberrations

Tables Icon

Table 3. Fourier Hologram Seidel Aberrations

Tables Icon

Table 4. Image-Plane Hologram Seidel Aberrations

Tables Icon

Table 5. Image-Plane Hologram: Seidel Aberrations for Plane and Spherical Reference Wave

Equations (27)

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

I(x,y)=|Aobjexp(iφobj)+Arefexp(iφref)|2=Aobj2+Aref2+AobjArefexp[i(φobj+φref)]+AoArexp[i(φobjφref)],
d=π4λ[(xx)2+(yy)2]23,
φreal=φrecφobj+φref,
φobj=k(AB¯AC¯).
φobj=kdobj[1+(xxobj)2dobj2+(yyobj)2dobj21+(xobj2+yobj2)dobj2]
1+a=1+12a18a2+116a3.
φobj=k[12dobj(x22xxobj2yyobj+y2)18dobj3(x4+y4+2x2y24x3xobj4y3yobj4x2yyobj4y2xxobj+6x2xobj2+6y2yobj2+8xxobjyyobj+2x2yobj2+2y2xobj24xxobj34yyobj34xxobjyobj24yyobjxobj2)].
x22xxG2yyG+y2dG=(x22xxrec2yyrec+y2)drec(x22xxobj2yyobj+y2)dobj+(x22xxref2yyref+y2)dref.
1dG=1drec1dobj+1dref,
xG=(xrecdrecxobjdobj+xrefdref)dG,
yG=(yrecdrecyobjdobj+yrefdref)dG.
W(ρ,θ)=2πλ·[18ρ4SISpherical aberration+12ρ3(SIIycosθ+SIIxsinθ)Coma+12ρ2(SIIIxcos2θ+SIIIysin2θ+2SIIIxycosθsinθ)Astigmatism+14ρ2(SIII+SIV)Field curvature+12ρ(SVxcosθ+SVysinθ)]Distortion,
2π8dobj3λ(6x2xobj2)=2πλ12ρ2SIIIxcos2θSIIIx=32xobj2dobj3
dref=drec=±.
1dG=1dobj,
xG=(xrecdrec+xobjdobjxrefdref)dobj,
yG=(yrecdrec+yobjdobjyrefdref)dobj.
dref=dobj=drec.
1dG=1drec=1dobj,
xG=xrec+xobjxref,
yG=yrec+yobjyref.
dobj=[(xx)2+(yy)2]2π4λ3.
φobj=k(M+1M)[12x2+y2d218x4+2x2y2+y4d23],
φG=φrefφobj=x22xxref2yyref+y2drefM+1Mx2+y2d2.
1dG=1drefM+1Md2,xG=dGxrefdref,yG=dGyrefdref.
d2=d1M.
d2=(d2+d1)M1+M=L·M1+M.

Metrics