Abstract

Correlation of two-dimensional digitally recorded holograms is introduced as a novel approach for object recognition without the need for quantitative assessment of the retrieved complex field, based on the fact that a hologram contains the three-dimensional information of the object. Actual objects with different three-dimensional features such as depth and surface roughness are assessed through processing of the correlation of their two-dimensional holograms. Correlation peak values are extracted as a metric to evaluate correlation of three-dimensional objects. The effect of hologram windowing size on correlation of three-dimensional objects is investigated, and improvements in computation time and dynamic range are assessed. Critical figures of merit used for assessment of correlation of images are applied to the correlation of holograms for object recognition.

© 2019 Optical Society of America

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References

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  1. U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2010).
  2. L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
    [Crossref]
  3. L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Holographic volume displacement calculations via multiwavelength digital holography,” Appl. Opt. 53, 1597–1603 (2014).
    [Crossref]
  4. U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
    [Crossref]
  5. W. Zhou, T.-C. Poon, U. Abeywickrema, and P. P. Banerjee, “Multi-wavelength digital holography using acousto-optics,” in Imaging and Applied Optics (2018), paper DW3F.4.
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    [Crossref]
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    [Crossref]
  10. M. S. Alam and M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
    [Crossref]
  11. K. Fujiwara, M. Kano, and S. Hasebe, “Development of correlation-based pattern recognition algorithm and adaptive soft-sensor design,” Control Eng. Pract. 20, 371–378 (2012).
    [Crossref]
  12. D. Abookasis and J. Rosen, “Computer generated correlation holograms,” in 23rd IEEE Convention of Electrical and Electronic Engineers in Israel (2004), pp. 258–261.
  13. J. Rosen and G. Brooker, “Fresnel incoherent correlation holography (FINCH): a review of research,” Adv. Opt. Technol. 1, 151–169 (2012).
    [Crossref]
  14. T. Kim and T.-C. Poon, “Three-dimensional matching by use of phase only holographic information and the Wigner distribution,” J. Opt. Soc. Am. A 17, 2520–2528 (2000).
    [Crossref]
  15. U. Abeywickrema, R. Gnawali, and P. P. Banerjee, “Identification of 3D objects using correlation of holograms,” Proc. SPIE 10752, 1075219 (2018).
    [Crossref]
  16. G. Nehmetallah, J. Khoury, M. A. Alam, and P. P. Banerjee, “Photorefractive two-beam coupling joint transform correlator: modeling and performance evaluation,” Appl. Opt. 55, 4011–4023 (2016).
    [Crossref]
  17. P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
    [Crossref]
  18. H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
    [Crossref]
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  20. H. Zhou, R. Hou, B. Bordbar, and P. P. Banerjee, “Effect of hologram size on 3D reconstruction using multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging 2019 (OSA, 2019), paper W4B.2.
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    [Crossref]
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    [Crossref]

2019 (2)

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

2018 (1)

U. Abeywickrema, R. Gnawali, and P. P. Banerjee, “Identification of 3D objects using correlation of holograms,” Proc. SPIE 10752, 1075219 (2018).
[Crossref]

2017 (1)

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

2016 (1)

2014 (2)

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Holographic volume displacement calculations via multiwavelength digital holography,” Appl. Opt. 53, 1597–1603 (2014).
[Crossref]

2012 (2)

K. Fujiwara, M. Kano, and S. Hasebe, “Development of correlation-based pattern recognition algorithm and adaptive soft-sensor design,” Control Eng. Pract. 20, 371–378 (2012).
[Crossref]

J. Rosen and G. Brooker, “Fresnel incoherent correlation holography (FINCH): a review of research,” Adv. Opt. Technol. 1, 151–169 (2012).
[Crossref]

2007 (1)

2000 (1)

1996 (1)

1995 (1)

1994 (1)

M. S. Alam and M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[Crossref]

1986 (1)

1974 (1)

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Abeywickrema, U.

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

U. Abeywickrema, R. Gnawali, and P. P. Banerjee, “Identification of 3D objects using correlation of holograms,” Proc. SPIE 10752, 1075219 (2018).
[Crossref]

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

W. Zhou, T.-C. Poon, U. Abeywickrema, and P. P. Banerjee, “Multi-wavelength digital holography using acousto-optics,” in Imaging and Applied Optics (2018), paper DW3F.4.

Abookasis, D.

D. Abookasis and J. Rosen, “Computer generated correlation holograms,” in 23rd IEEE Convention of Electrical and Electronic Engineers in Israel (2004), pp. 258–261.

Alam, M.

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

Alam, M. A.

Alam, M. S.

M. S. Alam and M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[Crossref]

Asakura, T.

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Aylo, R.

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).

Banerjee, P.

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

Banerjee, P. P.

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

U. Abeywickrema, R. Gnawali, and P. P. Banerjee, “Identification of 3D objects using correlation of holograms,” Proc. SPIE 10752, 1075219 (2018).
[Crossref]

G. Nehmetallah, J. Khoury, M. A. Alam, and P. P. Banerjee, “Photorefractive two-beam coupling joint transform correlator: modeling and performance evaluation,” Appl. Opt. 55, 4011–4023 (2016).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Holographic volume displacement calculations via multiwavelength digital holography,” Appl. Opt. 53, 1597–1603 (2014).
[Crossref]

H. Zhou, R. Hou, B. Bordbar, and P. P. Banerjee, “Effect of hologram size on 3D reconstruction using multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging 2019 (OSA, 2019), paper W4B.2.

W. Zhou, T.-C. Poon, U. Abeywickrema, and P. P. Banerjee, “Multi-wavelength digital holography using acousto-optics,” in Imaging and Applied Optics (2018), paper DW3F.4.

Bordbar, B.

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

H. Zhou, R. Hou, B. Bordbar, and P. P. Banerjee, “Effect of hologram size on 3D reconstruction using multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging 2019 (OSA, 2019), paper W4B.2.

Brooker, G.

J. Rosen and G. Brooker, “Fresnel incoherent correlation holography (FINCH): a review of research,” Adv. Opt. Technol. 1, 151–169 (2012).
[Crossref]

Cao, L.

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

Casasent, D.

Castro, A.

Chang, W. T.

Frauel, Y.

Fujii, H.

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Fujiwara, K.

K. Fujiwara, M. Kano, and S. Hasebe, “Development of correlation-based pattern recognition algorithm and adaptive soft-sensor design,” Control Eng. Pract. 20, 371–378 (2012).
[Crossref]

Gnawali, R.

U. Abeywickrema, R. Gnawali, and P. P. Banerjee, “Identification of 3D objects using correlation of holograms,” Proc. SPIE 10752, 1075219 (2018).
[Crossref]

Hasebe, S.

K. Fujiwara, M. Kano, and S. Hasebe, “Development of correlation-based pattern recognition algorithm and adaptive soft-sensor design,” Control Eng. Pract. 20, 371–378 (2012).
[Crossref]

Hennelly, B.

Hou, R.

H. Zhou, R. Hou, B. Bordbar, and P. P. Banerjee, “Effect of hologram size on 3D reconstruction using multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging 2019 (OSA, 2019), paper W4B.2.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

Javidi, B.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2010).

Kano, M.

K. Fujiwara, M. Kano, and S. Hasebe, “Development of correlation-based pattern recognition algorithm and adaptive soft-sensor design,” Control Eng. Pract. 20, 371–378 (2012).
[Crossref]

Karim, M. A.

M. S. Alam and M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[Crossref]

Khoury, J.

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

G. Nehmetallah, J. Khoury, M. A. Alam, and P. P. Banerjee, “Photorefractive two-beam coupling joint transform correlator: modeling and performance evaluation,” Appl. Opt. 55, 4011–4023 (2016).
[Crossref]

Kim, T.

Kota, A.

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

Kumar, B. V. K. V.

Lakhtakia, A.

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

Mahalanobis, A.

Maycock, J.

McDonald, B. J.

Naughton, J. T.

Nehmetallah, G.

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

G. Nehmetallah, J. Khoury, M. A. Alam, and P. P. Banerjee, “Photorefractive two-beam coupling joint transform correlator: modeling and performance evaluation,” Appl. Opt. 55, 4011–4023 (2016).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Holographic volume displacement calculations via multiwavelength digital holography,” Appl. Opt. 53, 1597–1603 (2014).
[Crossref]

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).

Poon, T.-C.

T. Kim and T.-C. Poon, “Three-dimensional matching by use of phase only holographic information and the Wigner distribution,” J. Opt. Soc. Am. A 17, 2520–2528 (2000).
[Crossref]

W. Zhou, T.-C. Poon, U. Abeywickrema, and P. P. Banerjee, “Multi-wavelength digital holography using acousto-optics,” in Imaging and Applied Optics (2018), paper DW3F.4.

Praharaj, S.

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Holographic volume displacement calculations via multiwavelength digital holography,” Appl. Opt. 53, 1597–1603 (2014).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
[Crossref]

Rosen, J.

J. Rosen and G. Brooker, “Fresnel incoherent correlation holography (FINCH): a review of research,” Adv. Opt. Technol. 1, 151–169 (2012).
[Crossref]

D. Abookasis and J. Rosen, “Computer generated correlation holograms,” in 23rd IEEE Convention of Electrical and Electronic Engineers in Israel (2004), pp. 258–261.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2010).

Sims, S. R. F.

Swiontek, S.

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

Williams, L.

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Holographic volume displacement calculations via multiwavelength digital holography,” Appl. Opt. 53, 1597–1603 (2014).
[Crossref]

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
[Crossref]

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).

Yaroslavsky, L. P.

Zhou, H.

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

H. Zhou, R. Hou, B. Bordbar, and P. P. Banerjee, “Effect of hologram size on 3D reconstruction using multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging 2019 (OSA, 2019), paper W4B.2.

Zhou, W.

W. Zhou, T.-C. Poon, U. Abeywickrema, and P. P. Banerjee, “Multi-wavelength digital holography using acousto-optics,” in Imaging and Applied Optics (2018), paper DW3F.4.

Adv. Opt. Technol. (1)

J. Rosen and G. Brooker, “Fresnel incoherent correlation holography (FINCH): a review of research,” Adv. Opt. Technol. 1, 151–169 (2012).
[Crossref]

Appl. Opt. (5)

Control Eng. Pract. (1)

K. Fujiwara, M. Kano, and S. Hasebe, “Development of correlation-based pattern recognition algorithm and adaptive soft-sensor design,” Control Eng. Pract. 20, 371–378 (2012).
[Crossref]

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

Opt. Commun. (1)

H. Fujii and T. Asakura, “Effect of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[Crossref]

Opt. Eng. (2)

M. S. Alam and M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[Crossref]

U. Abeywickrema, P. Banerjee, A. Kota, S. Swiontek, and A. Lakhtakia, “High-resolution topograms of fingerprints using multiwavelength digital holography,” Opt. Eng. 56, 034117 (2017).
[Crossref]

Proc. SPIE (4)

L. Williams, P. P. Banerjee, G. Nehmetallah, and S. Praharaj, “Volume displacement measurement via multi-wavelength digital holographic surface topography at the microscopic level,” Proc. SPIE 9006, 9006OK (2014).
[Crossref]

U. Abeywickrema, R. Gnawali, and P. P. Banerjee, “Identification of 3D objects using correlation of holograms,” Proc. SPIE 10752, 1075219 (2018).
[Crossref]

P. P. Banerjee, U. Abeywickrema, H. Zhou, B. Bordbar, M. Alam, G. Nehmetallah, J. Khoury, and L. Cao, “Taking correlation from 2D to 3D: optical methods and performance evaluation,” Proc. SPIE 10995, 109950B (2019).
[Crossref]

H. Zhou, U. Abeywickrema, B. Bordbar, L. Cao, and P. P. Banerjee, “Correlation of holograms for surface characterization of diffuse objects,” Proc. SPIE 10943, 1094306 (2019).
[Crossref]

Other (6)

G. Nehmetallah, R. Aylo, and L. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).

H. Zhou, R. Hou, B. Bordbar, and P. P. Banerjee, “Effect of hologram size on 3D reconstruction using multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging 2019 (OSA, 2019), paper W4B.2.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2010).

W. Zhou, T.-C. Poon, U. Abeywickrema, and P. P. Banerjee, “Multi-wavelength digital holography using acousto-optics,” in Imaging and Applied Optics (2018), paper DW3F.4.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

D. Abookasis and J. Rosen, “Computer generated correlation holograms,” in 23rd IEEE Convention of Electrical and Electronic Engineers in Israel (2004), pp. 258–261.

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Figures (7)

Fig. 1.
Fig. 1. Schematic diagram of Michelson interferometer for holographic recording. Laser beam is collimated by a spatial filter, composed of a 10X microscope object lens, a $2.5\,\,{\rm \unicode{x00B5}{\rm m}}$ pinhole, an iris to confine the beam size, and a 50 cm convex lens. M1:M4 are mirrors, while BS1, BS2 are beam splitters.
Fig. 2.
Fig. 2. (a) Picture of 10 washers stacked on each other. The diameter of each washer is 2.0 cm, and its depth/thickness is approximately 1.5 mm. The hole at the center of each washer has a diameter of 0.90 cm. The red circle marked on the object denotes the boundary of the illumination area on the object. (b) Hologram of one washer; (c) hologram of the stack of 10 washers shown in (a).
Fig. 3.
Fig. 3. Averaged correlation peak values plotted versus the depth difference between objects. The depth difference of zero corresponds to average of the autocorrelations of the holograms of one washer, which is set to unity for normalization. The length of the vertical lines indicates the standard deviation obtained for the corresponding correlation peak values.
Fig. 4.
Fig. 4. (a) Hologram of one washer and (b) hologram of stack of 10 washers. Different segments of holograms are shown in different colors. (c) Variation of averaged normalized correlation peak values versus depth difference of washers for different segments with pixel size of $( {512 \times 512} )$ , compared with the averaged normalized correlation peak values using original $( {1024 \times 1024} )$ holograms (black dotted line). While correlation between segments iii are closet to the original hologram correlation results, correlation of segment $v$ shows the maximum dynamic range, implying maximum variation with height difference.
Fig. 5.
Fig. 5. (a) Hologram of one washer; (b) hologram of the stack of 10 washers. Different segments of holograms are shown in different colors. (c) Averaged normalized correlation peak values versus depth difference of washers for different segments with pixel size of $( {512 \times 512} )$ over 10 different digitally recorded holograms. Dashed black line in (c) represents the averaged values of original holograms with grid resolution of $( {1024 \times 1024} )$ .
Fig. 6.
Fig. 6. Variation of (a) DR, (b) PNR2, and (c) PNV with depth difference between the objects. The hologram of one washer (reference object) is correlated with the holograms of multiple washers with increasing depth. Obtained results are averaged over 10 different digitally recorded holograms for each object. Here, $ \langle \cdot \rangle $ represents averaging over 10 different recorded holograms for objects with varying depth in the range of [0, 1.35] cm.
Fig. 7.
Fig. 7. (a) Sandpapers with different grit numbers; (b) examples of digitally recorded holograms with grid resolution of $( {1024 \times 1024} ),$ corresponding to sub-area (g) of sandpapers with different surface roughness.

Tables (3)

Tables Icon

Table 1. Averaged Computational Time and Dynamic Range for Different 2D Window Function Sizes

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Table 2. Averaged Figures of Merit DR, PNR2, and PNV for Different Grit Number Differences with Sandpaper with Grit Number 60 as a Reference

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Table 3. Averaged Figures of Merit DR, PNR2 and PNV for Different Grit Number Differences with Sandpaper with Grit Number 220 as a Reference

Equations (4)

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θ max λ / [ 2 max ( d x , d y ) ] = 514.5 n m 2 × 6.7 n m × 180 π = 2.2 .
D R = P A u t o / P C r o s s
P N R 2 = P C r o s s / E ¯ C r o s s
P N V = P C r o s s / V a r C r o s s

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