Abstract

We present a method for fast geometrical inspection of micro deep drawing parts. It is based on single-shot two-wavelength contouring digital holographic microscopy (DHM). Within the capturing process, spatial multiplexing is utilized in order to record the two required holograms in a single-shot. For fast evaluation, determining the locations where the object is in focus and stitching all focus object’s areas together is achieved digitally without the need for any external intervention using an autofocus algorithm. Thus, the limited depth of focus of the microscope objective is improved. The autofocus algorithm is based on minimizing the total variation (TV) of phase difference residuals of the two-wavelength measurements. In contrast to standard DHM, an object side telecentric microscope objective is used for overcoming the image scaling distortions caused by a conventional microscope objective. The method is used to reconstruct the 3D geometrical shape of a cold drawing micro cup. Experimental results verify the improvement of DHM’s depth of focus.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Speckle noise reduction in single-shot holographic two-wavelength contouring,” Proc. SPIE 10233, 102330R (2017).
[Crossref]

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Spatial multiplexing digital holography for speckle noise reduction in single-shot holographic two-wavelength contouring,” Opt. Eng. 56, 124101 (2017).
[Crossref]

2016 (1)

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

2015 (4)

S. T. Thurman and A. Bratcher, “Multiplexed synthetic-aperture digital holography,” Appl. Opt. 54, 559–568 (2015).
[Crossref]

M. Agour, K. El-Farahaty, E. Seisa, E. Omar, and T. Sokkar, “Single-shot digital holography for fast measuring optical properties of fibers,” Appl. Opt. 54, E188–E195 (2015).
[Crossref] [PubMed]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54, 024110 (2015).
[Crossref]

M. Agour, “Optimal strategies for wave fields sensing by means of multiple planes phase retrieval,” J. Opt. 17, 085604 (2015).
[Crossref]

2014 (1)

2012 (3)

2011 (1)

2010 (2)

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[Crossref] [PubMed]

M. Agour, P. Huke, C. v. Kopylow, and C. Falldorf, “Shape measurement by means of phase retrieval using a spatial light modulator,” AIP Conf. Proc. 1236, 265–270 (2010).
[Crossref]

2009 (1)

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

2007 (2)

2006 (2)

2005 (2)

2004 (3)

2003 (3)

2002 (1)

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 4737 (2002).

2001 (1)

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

2000 (1)

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring,” Opt. Eng. 39, 79–86 (2000).
[Crossref]

1994 (1)

1991 (1)

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

1989 (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9, 19–25 (1989).
[Crossref]

1982 (1)

1977 (1)

C. Wykes, “De-correlation effects in speckle-pattern interferometry. 1. wavelength change dependent de-correlation with application to contouring and surface roughness measurement,” Opt. Acta: Int. J. Opt. 24, 517–532 (1977).
[Crossref]

1974 (1)

N. George and A. Jain, “Space and wavelength dependence of speckle intensity,” Appl. physics 4, 201–212 (1974).
[Crossref]

1965 (1)

K. Haines and B. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Agour, M.

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Speckle noise reduction in single-shot holographic two-wavelength contouring,” Proc. SPIE 10233, 102330R (2017).
[Crossref]

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Spatial multiplexing digital holography for speckle noise reduction in single-shot holographic two-wavelength contouring,” Opt. Eng. 56, 124101 (2017).
[Crossref]

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

M. Agour, K. El-Farahaty, E. Seisa, E. Omar, and T. Sokkar, “Single-shot digital holography for fast measuring optical properties of fibers,” Appl. Opt. 54, E188–E195 (2015).
[Crossref] [PubMed]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54, 024110 (2015).
[Crossref]

M. Agour, “Optimal strategies for wave fields sensing by means of multiple planes phase retrieval,” J. Opt. 17, 085604 (2015).
[Crossref]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval for optical inspection of technical components,” J. Opt. 14, 065701 (2012).
[Crossref]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[Crossref] [PubMed]

M. Agour, P. Huke, C. v. Kopylow, and C. Falldorf, “Shape measurement by means of phase retrieval using a spatial light modulator,” AIP Conf. Proc. 1236, 265–270 (2010).
[Crossref]

Bally, G. v.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

D. Carl, B. Kemper, G. Wernicke, and G. v. Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536–6544 (2004).
[Crossref]

Benkouider, A.

Bergmann, R. B.

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Spatial multiplexing digital holography for speckle noise reduction in single-shot holographic two-wavelength contouring,” Opt. Eng. 56, 124101 (2017).
[Crossref]

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Speckle noise reduction in single-shot holographic two-wavelength contouring,” Proc. SPIE 10233, 102330R (2017).
[Crossref]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54, 024110 (2015).
[Crossref]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval for optical inspection of technical components,” J. Opt. 14, 065701 (2012).
[Crossref]

C. Falldorf, S. H. von Luepke, C. von Kopylow, and R. B. Bergmann, “Reduction of speckle noise in multiwavelength contouring,” Appl. Opt. 51, 8211–8215 (2012).
[Crossref] [PubMed]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[Crossref] [PubMed]

C. v. Kopylow and R. B. Bergmann, “Optical metrology,” in Micro Metal Forming, F. Vollertsen, ed. (Springer, 2013), pp. 392–404.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Transactions on Image Process. 16, 698–709 (2007).
[Crossref]

Bratcher, A.

Callens, N.

Carl, D.

Chang, W.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Charrière, F.

Coëtmellec, S.

Colomb, T.

Coppola, G.

Cuche, E.

Deiwick, M.

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Deleré, H.

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Depeursinge, C.

Dirksen, D.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Distante, C.

Droste, H.

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Dubois, F.

Egli, M.

El-Bakary, M. A.

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

El-Farahaty, K.

El-Farahaty, K. A.

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

Emery, Y.

Falldorf, C.

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Speckle noise reduction in single-shot holographic two-wavelength contouring,” Proc. SPIE 10233, 102330R (2017).
[Crossref]

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Spatial multiplexing digital holography for speckle noise reduction in single-shot holographic two-wavelength contouring,” Opt. Eng. 56, 124101 (2017).
[Crossref]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54, 024110 (2015).
[Crossref]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval for optical inspection of technical components,” J. Opt. 14, 065701 (2012).
[Crossref]

C. Falldorf, S. H. von Luepke, C. von Kopylow, and R. B. Bergmann, “Reduction of speckle noise in multiwavelength contouring,” Appl. Opt. 51, 8211–8215 (2012).
[Crossref] [PubMed]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[Crossref] [PubMed]

M. Agour, P. Huke, C. v. Kopylow, and C. Falldorf, “Shape measurement by means of phase retrieval using a spatial light modulator,” AIP Conf. Proc. 1236, 265–270 (2010).
[Crossref]

U. Schanars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (SpringerBerlin / Heidelberg, 2015).

N. Wang, C. v. Kopylow, and C. Falldorf, “Rapid shape measurement of micro deep drawing parts by means of digital holographic contouring,” in Proceedings of the 36th International MATADOR Conference, S. Hinduja and L. Li, eds. (Springer London, London, 2010), pp. 45–48.

Ferraro, P.

Finizio, A.

Flotte, T.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Franco-Obregón, A.

George, N.

N. George and A. Jain, “Space and wavelength dependence of speckle intensity,” Appl. physics 4, 201–212 (1974).
[Crossref]

Georgiev, G. K.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

Gillespie, J.

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9, 19–25 (1989).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).

Gregory, K.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Grilli, S.

Haines, K.

K. Haines and B. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Hamza, A. A.

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

Häusler, G.

Hee, M.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Hildebrand, B.

K. Haines and B. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Huang, D.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Huke, P.

M. Agour, P. Huke, C. v. Kopylow, and C. Falldorf, “Shape measurement by means of phase retrieval using a spatial light modulator,” AIP Conf. Proc. 1236, 265–270 (2010).
[Crossref]

Ida, T.

Ina, H.

Ivanova, L.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

Jain, A.

N. George and A. Jain, “Space and wavelength dependence of speckle intensity,” Appl. physics 4, 201–212 (1974).
[Crossref]

Javidi, B.

Jin, H.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A: Pure Appl. Opt. 6, 396 (2004).
[Crossref]

Jüptner, W.

U. Schnars and W. Jüptner, “Direct recording of holograms by a ccd target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref] [PubMed]

U. Schanars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (SpringerBerlin / Heidelberg, 2015).

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” (1998).

Kemper, B.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

D. Carl, B. Kemper, G. Wernicke, and G. v. Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536–6544 (2004).
[Crossref]

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Ketelhut, I. B. S.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

King, R. A.

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9, 19–25 (1989).
[Crossref]

Klattenhoff, R.

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Speckle noise reduction in single-shot holographic two-wavelength contouring,” Proc. SPIE 10233, 102330R (2017).
[Crossref]

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Spatial multiplexing digital holography for speckle noise reduction in single-shot holographic two-wavelength contouring,” Opt. Eng. 56, 124101 (2017).
[Crossref]

Kobayashi, S.

Kopylow, C. v.

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval for optical inspection of technical components,” J. Opt. 14, 065701 (2012).
[Crossref]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[Crossref] [PubMed]

M. Agour, P. Huke, C. v. Kopylow, and C. Falldorf, “Shape measurement by means of phase retrieval using a spatial light modulator,” AIP Conf. Proc. 1236, 265–270 (2010).
[Crossref]

C. v. Kopylow and R. B. Bergmann, “Optical metrology,” in Micro Metal Forming, F. Vollertsen, ed. (Springer, 2013), pp. 392–404.

N. Wang, C. v. Kopylow, and C. Falldorf, “Rapid shape measurement of micro deep drawing parts by means of digital holographic contouring,” in Proceedings of the 36th International MATADOR Conference, S. Hinduja and L. Li, eds. (Springer London, London, 2010), pp. 45–48.

Kreis, T.

T. Kreis, Handbook of holographic interferometry: optical and digital methods (John Wiley & Sons, 2005).

Kühn, J.

Langehanenberg, P.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

Lebrun, D.

Li, Y.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A: Pure Appl. Opt. 6, 396 (2004).
[Crossref]

Liebling, M.

Lin, C.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Ma, L.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A: Pure Appl. Opt. 6, 396 (2004).
[Crossref]

Magistretti, P. J.

Magro, C.

Malek, M.

Marquet, P.

Memmolo, P.

Montfort, F.

Nicola, S. D.

Omar, E.

Omar, E. Z.

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

Osten, W.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring,” Opt. Eng. 39, 79–86 (2000).
[Crossref]

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” (1998).

Paturzo, M.

Pavlícek, P.

Pierattini, G.

Puliafito, C.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Rappaz, B.

Richard, S.

Schanars, U.

U. Schanars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (SpringerBerlin / Heidelberg, 2015).

Scheld, H.

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Schnars, U.

Schockaert, C.

Schuman, J.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Seebacher, S.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring,” Opt. Eng. 39, 79–86 (2000).
[Crossref]

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” (1998).

Seisa, E.

Sokkar, T.

Sokkar, T. Z. N.

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

Stinson, W.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Swanson, E.

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Takeda, M.

Thurman, S. T.

Toy, M. F.

Unser, M.

Valadao, G.

J. M. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Transactions on Image Process. 16, 698–709 (2007).
[Crossref]

Vollmer, A.

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

von Bally, G.

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

von Kopylow, C.

von Luepke, S. H.

Wagner, C.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring,” Opt. Eng. 39, 79–86 (2000).
[Crossref]

Wang, H.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A: Pure Appl. Opt. 6, 396 (2004).
[Crossref]

Wang, N.

N. Wang, C. v. Kopylow, and C. Falldorf, “Rapid shape measurement of micro deep drawing parts by means of digital holographic contouring,” in Proceedings of the 36th International MATADOR Conference, S. Hinduja and L. Li, eds. (Springer London, London, 2010), pp. 45–48.

Watson, J.

U. Schanars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (SpringerBerlin / Heidelberg, 2015).

Wernicke, G.

Wyant, J. C.

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 4737 (2002).

Wykes, C.

C. Wykes, “De-correlation effects in speckle-pattern interferometry. 1. wavelength change dependent de-correlation with application to contouring and surface roughness measurement,” Opt. Acta: Int. J. Opt. 24, 517–532 (1977).
[Crossref]

Yamaguchi, I.

Yamashita, K.

Yokota, M.

Yourassowsky, C.

AIP Conf. Proc. (1)

M. Agour, P. Huke, C. v. Kopylow, and C. Falldorf, “Shape measurement by means of phase retrieval using a spatial light modulator,” AIP Conf. Proc. 1236, 265–270 (2010).
[Crossref]

Appl. Opt. (9)

P. Pavlíček and G. Häusler, “White-light interferometer with dispersion: an accurate fiber-optic sensor for the measurement of distance,” Appl. Opt. 44, 2978–2983 (2005).
[Crossref]

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval by means of a spatial light modulator in the fourier domain of an imaging system,” Appl. Opt. 49, 1826–1830 (2010).
[Crossref] [PubMed]

U. Schnars and W. Jüptner, “Direct recording of holograms by a ccd target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref] [PubMed]

I. Yamaguchi, T. Ida, M. Yokota, and K. Yamashita, “Surface shape measurement by phase-shifting digital holography with a wavelength shift,” Appl. Opt. 45, 7610–7616 (2006).
[Crossref] [PubMed]

S. T. Thurman and A. Bratcher, “Multiplexed synthetic-aperture digital holography,” Appl. Opt. 54, 559–568 (2015).
[Crossref]

M. Agour, K. El-Farahaty, E. Seisa, E. Omar, and T. Sokkar, “Single-shot digital holography for fast measuring optical properties of fibers,” Appl. Opt. 54, E188–E195 (2015).
[Crossref] [PubMed]

C. Falldorf, S. H. von Luepke, C. von Kopylow, and R. B. Bergmann, “Reduction of speckle noise in multiwavelength contouring,” Appl. Opt. 51, 8211–8215 (2012).
[Crossref] [PubMed]

D. Carl, B. Kemper, G. Wernicke, and G. v. Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536–6544 (2004).
[Crossref]

P. Ferraro, S. D. Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
[Crossref] [PubMed]

Appl. Phys. B (1)

T. Z. N. Sokkar, K. A. El-Farahaty, M. A. El-Bakary, E. Z. Omar, M. Agour, and A. A. Hamza, “Adaptive spatial carrier frequency method for fast monitoring optical properties of fibres,” Appl. Phys. B 122, 138 (2016).
[Crossref]

Appl. physics (1)

N. George and A. Jain, “Space and wavelength dependence of speckle intensity,” Appl. physics 4, 201–212 (1974).
[Crossref]

Biomed. Opt. Express (1)

IEEE Transactions on Image Process. (1)

J. M. Bioucas-Dias and G. Valadao, “Phase unwrapping via graph cuts,” IEEE Transactions on Image Process. 16, 698–709 (2007).
[Crossref]

J. Biomed. Opt. (1)

P. Langehanenberg, L. Ivanova, I. B. S. Ketelhut, A. Vollmer, D. Dirksen, G. K. Georgiev, G. v. Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[Crossref] [PubMed]

J. Opt. (2)

C. Falldorf, M. Agour, C. v. Kopylow, and R. B. Bergmann, “Phase retrieval for optical inspection of technical components,” J. Opt. 14, 065701 (2012).
[Crossref]

M. Agour, “Optimal strategies for wave fields sensing by means of multiple planes phase retrieval,” J. Opt. 17, 085604 (2015).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. A: Pure Appl. Opt. 6, 396 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta: Int. J. Opt. (1)

C. Wykes, “De-correlation effects in speckle-pattern interferometry. 1. wavelength change dependent de-correlation with application to contouring and surface roughness measurement,” Opt. Acta: Int. J. Opt. 24, 517–532 (1977).
[Crossref]

Opt. Eng. (3)

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Spatial multiplexing digital holography for speckle noise reduction in single-shot holographic two-wavelength contouring,” Opt. Eng. 56, 124101 (2017).
[Crossref]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54, 024110 (2015).
[Crossref]

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring,” Opt. Eng. 39, 79–86 (2000).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (1)

D. Dirksen, H. Droste, B. Kemper, H. Deleré, M. Deiwick, H. Scheld, and G. von Bally, “Lensless fourier holography for digital holographic interferometry on biological samples,” Opt. Lasers Eng. 36, 241–249 (2001).
[Crossref]

Opt. Lett. (3)

Pattern Recognit. Lett. (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9, 19–25 (1989).
[Crossref]

Phys. Lett. (1)

K. Haines and B. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[Crossref]

Proc. SPIE (2)

M. Agour, R. Klattenhoff, C. Falldorf, and R. B. Bergmann, “Speckle noise reduction in single-shot holographic two-wavelength contouring,” Proc. SPIE 10233, 102330R (2017).
[Crossref]

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 4737 (2002).

Science (1)

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, C. Puliafito, and et al., “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref] [PubMed]

Other (6)

C. v. Kopylow and R. B. Bergmann, “Optical metrology,” in Micro Metal Forming, F. Vollertsen, ed. (Springer, 2013), pp. 392–404.

N. Wang, C. v. Kopylow, and C. Falldorf, “Rapid shape measurement of micro deep drawing parts by means of digital holographic contouring,” in Proceedings of the 36th International MATADOR Conference, S. Hinduja and L. Li, eds. (Springer London, London, 2010), pp. 45–48.

U. Schanars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing: Principles, Techniques and Applications (SpringerBerlin / Heidelberg, 2015).

S. Seebacher, W. Osten, and W. Jüptner, “Measuring shape and deformation of small objects using digital holography,” (1998).

T. Kreis, Handbook of holographic interferometry: optical and digital methods (John Wiley & Sons, 2005).

J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).

Supplementary Material (1)

NameDescription
» Visualization 1       Visualization of the proposed autofocus approach.

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Figures (10)

Fig. 1
Fig. 1 An image shows micro-cups as an example of metallic cold forming micro-parts. The micro-cups have a size of less than 1 mm in at least two dimensions. This image is captured by Lukas Heinrich, BIAS.
Fig. 2
Fig. 2 Scheme of the digital holographic microscopy (DHM) setup. A long distance microscope objective (LDM) with 10× magnification, a numerical aperture of N.A. = 0.21 and a working distance of 51 mm image the object under test on a CCD camera sensor. Optical fiber splitters and coupler are used for creating the illuminating and reference waves which are combined utilizing a 50:50 beam-splitter in front of the CCD camera. An angle of α = 22° is found to be appropriate for illuminating the micro-cup under test.
Fig. 3
Fig. 3 Scheme showing configuration of object’s illumination and reference waves originating from the laser diodes with wavelength λ1 and λ2 and utilizing optical fiber splitters and couples.
Fig. 4
Fig. 4 Schematic representation of the expected spectrum of a single hologram, where +1, −1, and the dc-term refer to the diffraction orders and fi and fj represents the frequencies in i and j directions. Here, the spectra corresponding to the wavelengths λ1 and λ2 are shown as an example.
Fig. 5
Fig. 5 Scheme representing the implementation of the spatial carrier frequency method which is summarized in steps i) to iv) and utilized to recover the phase information from the captured intensity hologram. ℱ and ℱ−1 refer to the Fourier transform and its inversion, U O λ i is the filtered object wave field corresponding to the λi measurement, i takes 1 or 2 and arg{·} is the argument of a complex number which gives its phase ϕλi.
Fig. 6
Fig. 6 Scheme representing the implementation of the autofocus approach. We start with the two simulated complex amplitudes which are numerically propagated using Eq. (10) starting from z = 0 mm to the subsequent all object layers. Then the two complex amplitudes obtained at each layer are complex conjugate multiplied. Thus, the contouring map across that layer is obtained. Within a window of 80 × 80 pixels, the brown square, the minimum of the error metric LTV is determined within all object layers. By comparing the values of the LTV, its minimum at each pixel within the window is defined which represents where the object is in-focus. Shifting the window to a neighborer area, yellow box, and repeating the process of defining the minimum of the LTV to find other areas where the object is in-focus.
Fig. 7
Fig. 7 Demonstration of the autofocus approach using simulation results. In a) the contouring phase map obtained for the third object layer where z = 150 µm. The yellow highlighted area represents the plane which is shown by the darkest area of the error metric shown in b). c) shows a median filtered version of the error metric. In d) all focus areas found are stitched together to obtain the focus contouring map (see Visualization 1).
Fig. 8
Fig. 8 a) shows the intensity captured hologram which contains object information for the simultaneous illumination using the two wavelengths. The zoomed area shows the interference fringes of the recorded hologram which causes the separation of the recorded information of the two simultaneously captured holograms at the Fourier plane as shown in the hologram’s spectrum b).
Fig. 9
Fig. 9 Reconstructed amplitude images which a) represent a sharp image of the micro-cup under test at one plane for complex amplitude recover from the measurement λ1 and c) across the whole object after the digital extending of the depth of focus of the DHM c) are shown. b) and d) show the corresponding phase difference Δϕ, respectively. Image size is 2200 × 2200 pixels with a pixel pitch of 4.54 µm.
Fig. 10
Fig. 10 3D height map obtained by substituting the phase values obtained from the unwrapped contouring map into Eq. (4). It shows the part of a micro-cup that is observed by the DHM unit. The white spots within the surface refer to areas with phase phase singularities which can not be unwrapped.

Equations (11)

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G λ n ( y ) = exp [ i 2 π Δ x n y ] .
I ( y ) = A ( y ) + n = 1 2 [ U O λ n ( y ) U R λ n * ( y ) G λ n ( y ) ] + n = 1 2 [ U O λ n * ( y ) U R λ n ( y ) G λ n * ( y ) ] .
Δ ϕ = ϕ λ 2 ϕ λ 1 .
Δ ϕ = 2 π Λ z p ( 1 + cos α ) .
Λ = λ 1 λ 2 | λ 2 λ 1 | .
L T V = y R | ϕ R e s | 2 ,
ϕ R e s = Δ ϕ Δ ϕ ˜ .
ϕ R e s = ( ϕ R e s y i ϕ R e s y j ) and | ϕ R e s | 2 = ( ϕ R e s y i ) 2 + ( ϕ R e s y j ) 2 .
ϕ R e s y i | ϕ R e s ( y i + 1 ) ϕ R e s ( y i ) | m o d 2 π .
U 2 = 1 { { U 1 } H z } .
H z ( v ) = exp [ i 2 π Δ z λ 1 1 λ 1 2 | v | 2 ] .

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