Abstract

The digital holography has immense potential related to many applications of science and engineering. It has many advantages compared to conventional holography i.e. characterization of online dynamic phenomena and imaging in small scale microscopic systems. However, its primary limitation is the size of sensors and number of sensors compared to the conventional holographic plate. The critical issue of digital holography is the numerical reconstruction procedure. The present study proposes a new reconstruction algorithm known as ‘Within Depth Intensity Averaging (WDIA)’. The effectiveness of the WDIA algorithm is demonstrated using both experiment and simulation for single particle, 2D and 3D distribution of particles. The 3D distribution of particles is experimentally simulated by using gelatin film on the glass slide. The particle images from digital holography compare well with that of microscopic images demonstrating the success of the proposed algorithm compared to the existing reconstruction procedure. The depth error significantly reduces (maximum 100%) and particles of any size can be characterized by the WDIA reconstruction algorithm contrary to the existing reconstruction algorithm available in literature. The effect of particle number density, particle size and sample volume depth on reconstruction effectiveness using the WDIA algorithm has been investigated and compared with the literature demonstrating its superiority in performance.

© 2010 OSA

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References

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  1. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
    [CrossRef] [PubMed]
  2. L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).
  3. B. Miller, K. A. Sallam, K. C. Lin, and C. Carter, “Digital holographic spray analyzer”, in Proceedings of FEDSM2006,2006ASME Joint U.S.-European Fluids Engineering Summer Meeting, Miami, FL, July 17–20, pp. 1–6.
  4. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
    [CrossRef] [PubMed]
  5. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
    [CrossRef] [PubMed]
  6. S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
    [CrossRef]
  7. T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901–233904 (2007).
    [CrossRef] [PubMed]
  8. Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
    [CrossRef]
  9. G. Pan, and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics”, in Proceedings of 4th Internatinal Symposium on Particle Image Velocimetry, Germany, Sep. 2001, PIV’01 Paper 1008.
  10. G. Pan, and H. Meng, “Digital holographic PIV for 3D flow measurement”, in Proceedings of IMECE’02 2002 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, Nov. 17–22 (2002), IMECE2002–33173.
  11. G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
    [CrossRef] [PubMed]
  12. S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
    [CrossRef] [PubMed]
  13. M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
    [CrossRef] [PubMed]
  14. T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (WILEY-VCH Verlag GmbH & Co. KGaA, 2005).
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  16. Gonzalez and Woods, Digital Image Processing (Pearson Education, India, 2007).

2007 (1)

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901–233904 (2007).
[CrossRef] [PubMed]

2006 (2)

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
[CrossRef]

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

2004 (2)

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
[CrossRef] [PubMed]

2003 (1)

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[CrossRef] [PubMed]

2002 (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
[CrossRef] [PubMed]

2001 (2)

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[CrossRef] [PubMed]

2000 (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[CrossRef]

Allano, D.

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
[CrossRef] [PubMed]

Asundi, A. K.

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).

Coëtmellec, S.

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
[CrossRef] [PubMed]

De Nicola, S.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

Ferraro, P.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

Finizio, A.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

Fink, H. W.

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901–233904 (2007).
[CrossRef] [PubMed]

Garcia-Sucerquia, J.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

Grilli, S.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

Jericho, M. H.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[CrossRef] [PubMed]

Jericho, S. K.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

Klages, P.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

Kompenhans, J.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
[CrossRef]

Kreuzer, H. J.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[CrossRef] [PubMed]

Latychevskaia, T.

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901–233904 (2007).
[CrossRef] [PubMed]

Lebrun, D.

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
[CrossRef] [PubMed]

Malek, M.

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
[CrossRef] [PubMed]

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[CrossRef] [PubMed]

Meng, H.

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[CrossRef] [PubMed]

Meucci, R.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

Miao, J.

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).

Murata, S.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[CrossRef]

Pan, G.

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[CrossRef] [PubMed]

Peng, X.

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).

Pierattini, G.

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

Schröder, A.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
[CrossRef]

Shen, G.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
[CrossRef]

Xu, L.

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).

Xu, W.

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[CrossRef] [PubMed]

Yasuda, N.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[CrossRef]

Zhang, Y.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
[CrossRef]

Appl. Opt. (3)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41(25), 5367–5375 (2002).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[CrossRef] [PubMed]

Opt. Eng. (1)

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45(7), 075801–075810 (2006).
[CrossRef]

Opt. Express (2)

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci, “Whole optical wavefields reconstruction by digital holography,” Opt. Express 9(6), 294–302 (2001).
[CrossRef] [PubMed]

M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field,” Opt. Express 12(10), 2270–2279 (2004).
[CrossRef] [PubMed]

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[CrossRef]

Opt. Mem. Neural Networks (1)

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “In-line digital microscopic holography: principles and applications in micro-metrology,” Opt. Mem. Neural Networks 13(4), 163–177 (2004).

Phys. Rev. Lett. (1)

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901–233904 (2007).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001).
[CrossRef] [PubMed]

Other (6)

T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (WILEY-VCH Verlag GmbH & Co. KGaA, 2005).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gonzalez and Woods, Digital Image Processing (Pearson Education, India, 2007).

B. Miller, K. A. Sallam, K. C. Lin, and C. Carter, “Digital holographic spray analyzer”, in Proceedings of FEDSM2006,2006ASME Joint U.S.-European Fluids Engineering Summer Meeting, Miami, FL, July 17–20, pp. 1–6.

G. Pan, and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics”, in Proceedings of 4th Internatinal Symposium on Particle Image Velocimetry, Germany, Sep. 2001, PIV’01 Paper 1008.

G. Pan, and H. Meng, “Digital holographic PIV for 3D flow measurement”, in Proceedings of IMECE’02 2002 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, Nov. 17–22 (2002), IMECE2002–33173.

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Figures (15)

Fig. 1
Fig. 1

Schematic of recording and reconstruction of particle field: (a) hologram generation of 3D particle field using plane wave illumination, and (b) plane-wise 3D numerical reconstruction of particle field from digital hologram of (a).

Fig. 2
Fig. 2

Morphological determination procedure of particle size and location: (a) Set A is the object in which all points/pixels of an element Y are to be determined. The initial point p of this element is known (shown as different hatching) from other element of Y indicating that they have not been found by the algorithm; (b) It shows the structuring element, B which convolves over p to determine the points of Y, connected with p; (c) The results of first iterative step involving dilation and intersection after which the points of Y connected with p are found out; (d) The results after second iterative step; (e) The results of final iteration i.e. after determination of all the points of element Y.

Fig. 3
Fig. 3

The normalized intensity distribution along axial direction about the focal plane at different recording distances (zo/zc = 0.25, 1, 1.2 and 7) for single particle of size dp = 1 pixel. The lines and symbols correspond to the present data & that of Zhang et al. [8] respectively. The distance between the two successive planes during reconstruction is δz = dp .

Fig. 4
Fig. 4

The importance of dual peak removal: (a) the cartesian coordinate system with a bright particle (size, dp = 3 pixels) in dark background, whose hologram is reconstructed along z-direction; (b) the normalized intensity distribution about the focal plane for each pixel element of the particle, showing dual peaks for some pixel elements; (c) the normalized averaged intensity compared to the intensity distribution of the core pixel element.

Fig. 5
Fig. 5

The normalized intensity distribution along axial direction about the focal plane for core pixel element of particle ((a), (c), (e) and (g)) and the corresponding averaged intensity ((b), (d), (f) and (h)) for particle of size, dp = 2, 4, 6, and 8 pixels respectively as a function of recording distances (zo/zc = 0.65, 0.80, 1, 1.5 and 2). This figure demonstrates that by averaging the intensity over all elements of the particle single peak during reconstruction is obtained for particles of different sizes and at different recording distances.

Fig. 6
Fig. 6

Procedure explaining the depth error reduction: (a) The normalized intensity distribution about the focal plane, averaged over all elements of a particle of size dp = 3 pixels, along axial direction for the recording distance, zo/zc = 0.95. The depth error is equal to 1.25*dp ; (b) The intensity distribution for individual pixel elements of the same particle. The normalized intensity peak of elements 2, 4, 5, 6, and 8 lies outside 4*dp of focus and that of 1, 3, 7 and 9 pixel elements lies inside (here we call these elements as ‘within depth’ elements); (c) The intensity distribution of ‘within depth’ elements of particle. (d) The intensity distribution averaged over ‘within depth’ elements (pixel elements 1, 3, 7, & 9) of particle. The depth error is equal to 0.25*dp showing 80% reduction in comparison to 1.25*dp depth error value in (a) i.e. without any correction

Fig. 7
Fig. 7

The improvement in reconstruction effectiveness because of the correction of ‘outside-depth’ pixel elements influence for particle size, (a) dp = 2 pixels and (b) dp = 3 pixels. Here, total 200 number of particles are distributed over a 2D plane of size 512 × 512 pixels and the recording distance, zo/ zc is equal to 0.95. There is significant improvement in reconstruction effectiveness when axial intensity is averaged over only ‘within depth’ elements of each particle.

Fig. 8
Fig. 8

The comparison of presence of false particles from the ‘Present approach’ with that of Zhang et al [8] at different recording distances: (a) zo/zc = 0.65, (b) zo/zc = 0.75, and (c) zo/zc = 1.35. Here, 310 particles (100 particles of size 1 pixel, 100 particles of size 2 pixels and 110 particles of size 3 pixels) are randomly distributed in the object plane of size 512 x 512 pixels. The distance between two successive planes during reconstruction, δz = 3 pixels.

Fig. 9
Fig. 9

The comparison of the proposed holographic reconstruction algorithm with that of microscopic images: (a) The microscopic image of copper particles of size 20 to 30 μm distributed over a glass plate, (b) The experimental hologram of particle field in (a), (c) The reconstructed particle field using hologram of (b).

Fig. 10
Fig. 10

The histogram showing the depth error by (a) including all the pixel elements during average intensity calculation and (b) the average intensity calculation carried out by including only the ‘within-depth’ pixels of particles. The left hand side of figure corresponds to the experiment and the right hand side corresponds to the simulated data at similar condition as the experiment. The experiment uses copper particles of size dp = 20 to 30 μm distributed over glass plate at recording distance, zo/zc = 0.80. There is appreciable reduction in rms depth error (zrms ) of both experiment and simulation. The distance between two successive planes during reconstruction, δz = 3 pixels.

Fig. 11
Fig. 11

Comparison of extracted particles percentage between the ‘Present Study’ with that of Malek et al [13] as a function of particle density for different depth of sample volume (L).

Fig. 12
Fig. 12

The comparison of reconstruction effectiveness between the ‘Present Study’ and that of Pan and Meng [11]. Both the studies have sample volume depth of 10 mm and the hologram/sample size is equal to 3.48 x 3.48 mm2. The density of particles for present study is 6 and 18 (1/mm3) in comparison to 18 (1/mm3) for Pan and Meng [11].

Fig. 13
Fig. 13

The comparison between microscopic and holographic particle field images: (a) The schematic showing particle field distribution on two opposite surfaces of glass slide of thickness 1.2 mm; (b) The hologram of particle field in (a); (c & d) The bright field microscopic images of the particle field in plane-1 and plane-2 respectively; (e & f) The holographic reconstructed images of particle field in plane-1 and plane-2 corresponding to 21 & 81 plane in the reconstruction volume respectively; (g & h) The particle field images after implementation of proposed WDIA algorithm on the particle field of (e) & (f) respectively.

Fig. 14
Fig. 14

The comparison between microscopic and holographic particle field images: (a) The schematic showing copper particle distribution on a glass slide (plane-1) and cover slip (plane-2) with gelatin film sandwiched in between; (b) The hologram of particle field in field (a); (c & d) The bright field microscopic images of particle field in plane-1 and plane-2 respectively; (e & f) The holographic reconstructed images of particle field in plane-1 and plane-2 corresponding to 51 and 71 plane in the reconstruction volume respectively; (g & h) The particle field images after implementation of proposed WDIA algorithm on particle field of (e) & (f) respectively.

Fig. 15
Fig. 15

Comparison between microscopic and holographic particle field images: (a) The schematic showing the particle distribution in plane-1 (cover slip), plane-2 (one side of the glass slide with gelatin film sandwiched in between, plane-3 (other side of the glass slide with gelatin film layer above it); (b) The hologram of particle field in (a); (c, d & (e) The bright field microscopic image of particle field in plane-1, plane-2 and plane-3 respectively; (f, g & (h) The holographic reconstructed images of particle field in plane-1, plane-2 & plane-3 corresponding to 70, 91, and 151 plane in the reconstruction volume respectively; (i, j, & k) The particle field images after implementing the proposed WDIA algorithm on particle field of (f), (g), & (h) respectively.

Tables (3)

Tables Icon

Table 1 Percentage reduction in depth error due to the removal of off-focal plane intensity peaks as a function of recording distance (zo/zc ) for particle of size, dp = 2 and 3 pixels. Total number of particles (No ) is equal to 200.

Tables Icon

Table 2 Percentage reduction in depth error due to the removal of off-focal plane intensity peaks as function of recording distance (zo/zc ) for experimentally generated hologram and numerically simulated hologram with same parameters as that of the experiment.

Tables Icon

Table 3 Comparison of normalized rms depth error (zrms/dp ) from present study with that of literature (Murata and Yasuda [6], Pan and Meng [11]) as a function of sample volume depth (L) and particle density (Ns ) for sample/hologram size of 3.48 x 3.48 mm2. The pixel size is equal to 6.8 μm.

Equations (8)

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

E o ( ξ , η ) = exp ( i k z o ) i λ z o + + t ( x o , y o ) exp { i k 2 z o [ ( ξ x o ) 2 + ( η y o ) 2 ] } d x o d y o
I H ( ξ , η ) = | E r + E o ( ξ , η ) | 2 = A r 2 + | E o ( ξ , η ) | 2 + A r E o ( ξ , η ) + A r E o ( ξ , η )
E i ( x i , y i ) = exp ( i k z r ) i λ z r + + I H ( ξ , η ) exp { i k 2 z r [ ( x i ξ ) 2 + ( y i η ) 2 ) ] } d ξ d η
I r ( x i , y i ) = | E i ( x i , y i ) | 2
I n , p ( z ) = I a v g , p ( z ) I min , p I max , p I min , p
I n , p i x ( z ) = I p i x ( z ) I min , p i x I max , p i x I min , p i x
X k = ( X k 1 B ) A k = 1 , 2 , 3 , .........
z c = Δ ξ 2 × N λ

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