Abstract

Although digital holography (DH) has many advantages compared to conventional holography, its resolution is limited due to CCDs or other recording devices. Three factors contribute to this limitation, namely, the pixel averaging effect within the finite detection size of one pixel, a finite CCD aperture size limitation, and the sampling effect due to a finite sampling interval. In this paper, interactions of the three factors on resolution are investigated and presented. The resolution of a DH system can be determined for given parameters of these three factors. The domains dominated by different factors are explained along with their accuracy. As a DH system is space variant, influences of object extent on resolution are also discussed. The resolution performance of in-line and off-axis systems is studied and examples of resolution determination for a practical system are provided.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
    [CrossRef] [PubMed]
  2. U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  3. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  4. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [CrossRef]
  5. L. Xu, X. Y. Peng, A. K. Asundi, and J. M. Miao, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
    [CrossRef]
  6. L. Xu, X. Y. Peng, J. M. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
    [CrossRef]
  7. V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
    [CrossRef]
  8. A. Asundi and V. R. Singh, “Amplitude and phase analysis in digital dynamic holography,” Opt. Lett. 31, 2420–2422 (2006).
    [CrossRef] [PubMed]
  9. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005).
    [CrossRef] [PubMed]
  10. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  11. C. Wagner, S. Seebacher, W. Osten, and W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820(1999).
    [CrossRef]
  12. J. Garcia-Sucerquia, W. B. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
    [CrossRef] [PubMed]
  13. H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
    [CrossRef]
  14. D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
    [CrossRef]
  15. L. Xu, X. Y. Peng, Z. X. Guo, J. M. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express 13, 2444–2452 (2005).
    [CrossRef] [PubMed]
  16. A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250(2004).
    [CrossRef]
  17. P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. 44, 337–343 (2005).
    [CrossRef] [PubMed]
  18. P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744–1761 (2008).
    [CrossRef]
  19. D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
    [CrossRef]
  20. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  21. T. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005), pp. 47–53.

2009 (1)

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

2008 (3)

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
[CrossRef]

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744–1761 (2008).
[CrossRef]

2007 (1)

V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[CrossRef]

2006 (2)

2005 (3)

2004 (1)

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250(2004).
[CrossRef]

2002 (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

2001 (2)

L. Xu, X. Y. Peng, A. K. Asundi, and J. M. Miao, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

L. Xu, X. Y. Peng, J. M. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
[CrossRef]

1999 (2)

1994 (2)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Asundi, A.

Asundi, A. K.

L. Xu, X. Y. Peng, J. M. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
[CrossRef]

L. Xu, X. Y. Peng, A. K. Asundi, and J. M. Miao, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

Bevilacqua, F.

Colomb, T.

Cuche, E.

Depeursinge, C.

Emery, Y.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Garcia-Sucerquia, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gougeon, S.

Guo, Z. X.

Hegde, G.

V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[CrossRef]

Hennelly, B. M.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
[CrossRef]

Javidi, B.

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250(2004).
[CrossRef]

Jericho, M. H.

Jericho, S. K.

Jin, H. Z.

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Juptner, W.

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Kelly, D. P.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
[CrossRef]

Klages, P.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005), pp. 47–53.

Kreuzer, H. J.

Leval, J.

Li, Y.

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Magistretti, P. J.

Marquet, P.

McElhinney, C.

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
[CrossRef]

Miao, J. M.

V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[CrossRef]

L. Xu, X. Y. Peng, Z. X. Guo, J. M. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express 13, 2444–2452 (2005).
[CrossRef] [PubMed]

L. Xu, X. Y. Peng, J. M. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046–5051 (2001).
[CrossRef]

L. Xu, X. Y. Peng, A. K. Asundi, and J. M. Miao, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

Mounier, D.

Naughton, T. J.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
[CrossRef]

Osten, W.

Pandey, N.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

Peng, X. Y.

Picart, P.

Qiu, P. Z.

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Rappaz, B.

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

Schnars, U.

Seebacher, S.

Singh, V. R.

V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[CrossRef]

A. Asundi and V. R. Singh, “Amplitude and phase analysis in digital dynamic holography,” Opt. Lett. 31, 2420–2422 (2006).
[CrossRef] [PubMed]

Stern, A.

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250(2004).
[CrossRef]

Wagner, C.

Wan, H.

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Wang, Z. H.

V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[CrossRef]

Xu, L.

Xu, W. B.

Zhang, Y. P.

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

Appl. Opt. (5)

J. Mod. Opt. (1)

H. Z. Jin, H. Wan, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55, 2989–3000 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[CrossRef]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (1)

V. R. Singh, J. M. Miao, Z. H. Wang, G. Hegde, and A. Asundi, “Dynamic characterization of MEMS diaphragm using time averaged in-line digital holography,” Opt. Commun. 280, 285–290 (2007).
[CrossRef]

Opt. Eng. (3)

L. Xu, X. Y. Peng, A. K. Asundi, and J. M. Miao, “Hybrid holographic microscope for interferometric measurement of microstructures,” Opt. Eng. 40, 2533–2539 (2001).
[CrossRef]

A. Stern and B. Javidi, “Analysis of practical sampling and reconstruction from Fresnel fields,” Opt. Eng. 43, 239–250(2004).
[CrossRef]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (1)

D. P. Kelly, B. M. Hennelly, C. McElhinney, and T. J. Naughton, “A practical guide to digital holography and generalized sampling,” Proc. SPIE 7072, 707215 (2008).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

T. Kreis, Handbook of Holographic Interferometry, Optical and Digital Methods (Wiley-VCH, 2005), pp. 47–53.

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 (13)

Fig. 1
Fig. 1

Width of the PSF of a DH system with different values of 2 p and λ z D to show the interaction of these two parameters on the reconstructed resolution. The x axis represents 2 p and the y axis represents λ z D . Both axes contain 255 points with values from 1.1625 × 10 6 to 148.8 × 10 6 m of interval 0.58125 × 10 6 m [the width is defined by the distance of the first two zeros of the PSF as in Figs. 6h, 7h].

Fig. 2
Fig. 2

The 4th, 64th, and 128th rows and corresponding derivatives. (a), (c), and (e) are the 4th, 64th, and 128th rows of Fig. 1 and correspond to λ z D equal to 2.906 × 10 6 , 3.7781 × 10 5 , and 7.4981 × 10 5 m respectively; (b), (d), and (f) are the corresponding derivatives with respect to x = 2 p of profiles (a), (c), and (e), respectively. The x axis represents the normalized 2 p by the corresponding λ z D . The fluctuations in (d) and (f) come from insufficient padding in reconstruction. With sufficient padding, the curves can be smooth, but the trend of (d) and (f) can already be seen here.

Fig. 3
Fig. 3

Difference of the width of the PSF and 2 p of all the rows in Fig. 1 (calculation: width 2 p 2 p ).

Fig. 4
Fig. 4

The 4th, 64th, and 128th columns and the corresponding derivatives. (a), (c), and (e) are the 4th, 64th, and 128th columns of Fig. 1 and corresponds to 2 p equal to 2.906 × 10 6 , 3.7781 × 10 5 , and 7.4981 × 10 5 m , respectively; (b), (d), and (f) are the corresponding derivatives with respect to y = λ z D of profiles (a), (c), and (e), respectively. The x axis represents the normalized λ z D by the corresponding 2 p . The fluctuations in (b), (d), and (f) come from insufficient padding in reconstruction. With sufficient padding, the curves can be smooth. But the trend of (b), (d) and (f) can already be seen here.

Fig. 5
Fig. 5

Difference of the width of the PSF and λ z D of all the rows in Fig. 1 (calculation: width λ z D λ z D ).

Fig. 6
Fig. 6

PSF investigation of the DH system as in Eq. (5) in case of 2 p / λ z D 1 .

Fig. 7
Fig. 7

PSF investigation of the DH system as in Eq. (5) in case of 2 p / λ z D < 1 .

Fig. 8
Fig. 8

Spectrums of points along the object with extent L 0 at the CCD plane. (a) Positions of the three points: A is at the center, B and C are the edges. (b), (c), and (d) are the spectrums of point A, B, and C, respectively, at the CCD plane.

Fig. 9
Fig. 9

Resolution investigation in case of 2 p / λ z D 1 with object of finite extent L 0 .

Fig. 10
Fig. 10

Resolution investigation in case of 2 p / λ z D < 1 with object of finite extent L 0 .

Fig. 11
Fig. 11

Demonstration of space variant property of the DH system. (a) Amplitude of convolution [ exp ( j π x 0 p x 2 ) rect ( x 2 2 p ) ] * sinc ( 2 D λ z x 2 ) changes as x 0 changes. The y axis represents x 0 changing from 0 to 0.032 and the x z plane represents the profile of amplitude profiles of [ exp ( j π x 0 p x 2 ) rect ( x 2 2 p ) ] * sinc ( 2 D λ z x 2 ) at corresponding x 0 . (b) Profiles when x 0 is 0, 0.0062, 0.0126, 0.0174 in (a).

Fig. 12
Fig. 12

Examples of the violation of Eq. (8): (a) shows the spectra of two differently located point sources at the CCD plane where P2 is under the condition of Eq. (8) and P1 is not; (b) shows the reconstructed images of the points P1 and P2. (c) and (d) are the magnified images of P1, P2 in (b) to show details.

Fig. 13
Fig. 13

Examples of the violation of Eq. (10): (a) shows the spectra of three different located point sources at the CCD plane where P2 is under the condition of Eq. (10) and P1 and P3 violate Eq. (10); (b) shows the reconstructed images of the three points. (c), (d), and (e) are the magnified images of P1, P2, and P3 in (b).

Equations (20)

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

R f ( x 2 ) = Fresnel [ ( { [ f ( x ) * exp ( j π λ z x 2 ) ] × rect ( x 2 D ) } * rect ( x 2 p ) ) × + δ ( x n T ) ] ,
Fresnel ( k ( x ) ) = exp ( j π λ z x 2 2 ) F { k ( x ) × exp ( j π λ z x 2 ) } f = x 2 λ z .
R f ( x 2 ) = exp ( j π λ z x 2 2 ) × [ ( { [ f ( x ) * exp ( j π λ z x 2 ) ] × rect ( x 2 D ) } * rect ( x 2 p ) ) × δ + ( x n T ) × exp ( j π λ z x 2 ) ] f = x 2 λ z ,
R f ( x 2 ) = R 0 f ( x 2 ) * n = δ ( x 2 n λ z T ) ,
R 0 f ( x 2 ) = exp ( j π λ z x 2 2 ) × [ ( { [ f ( x ) * exp ( j π λ z x 2 ) ] × rect ( x 2 D ) } * rect ( x 2 p ) ) × exp ( j π λ z x 2 ) ] f = x 2 λ z .
exp [ j π λ z ( L o 2 ) 2 ] × F { sinc [ 2 p λ z ( x L o 2 ) ] × rect ( x 2 D ) × exp ( j 2 π L o 2 λ z x ) } f x = x 2 λ z .
exp [ j π λ z ( x 0 ) 2 ] × F { sinc [ 2 p λ z ( x x 0 ) ] × rect ( x 2 D ) × exp ( j 2 π x 0 λ z x ) } f x = x 2 λ z .
F { sinc ( 2 p λ z x ) × rect ( x 2 D ) } f x = x 2 λ z ,
exp [ j π λ z ( x 0 ) 2 ] × { [ exp ( j π x 0 p x 2 ) × rect ( x 2 2 p ) ] * sinc ( 2 D λ z x 2 ) * δ ( x 2 x 0 ) } .
D λ z L o 2 λ z 1 2 p .
D λ z L o 2 λ z 6 2 p .
D λ z + L o 2 λ z < 1 2 p .
D λ z + L o 2 λ z < 1 2 × 1 2 p .
L o λ z T .
D x λ z = 1280 × 4.65 × 10 6 2 × 633 × 10 9 × z = 4.701 × 10 3 z
1 2 p = 1 4.65 × 10 6 = 215.05 × 10 3 l / mm .
10.85 μm < R 11.7 μm 11.7 μm < R 12.92 μm R   is unstably worse 0 < | x 0 | 3.83 mm 3.83 mm < | x 0 | 10.637 mm | x 0 | > 10.637 mm ,
D λ z + L o 2 λ z 1 8 T .
R best < R 1.1 × λ z 2 D 1.1 × λ z 2 D < R 1 2 × ( λ z D + 2 p ) R   is unstably worse x o 2 λ z 1 4 p D λ z 1 4 p D λ z < x o 2 λ z 1 2 p D λ z x o 2 λ z > 1 2 p D λ z ,
R best < R 1.1 × p 1.1 × p < R 1 2 × ( λ z D + 2 p ) R   is unstably worse x o 2 λ z D λ z 3 p D λ z 3 p < x o 2 λ z D λ z 1 2 p x o 2 λ z > D λ z 1 2 p ,

Metrics