Abstract

Low-coherence interferometric microscopy (LCIM) enables to image through scattering media by filtration of ballistic light from diffuse light. The filtration mechanism is called coherence gating. We show that coherence-controlled holographic microscope (CCHM), which belongs to LCIM, enables to image through scattering media not only with ballistic light but also with diffuse light. The theoretical model was created which derives the point spread function of CCHM for imaging through diffuse media both with ballistic and diffuse light. The results of the theoretical model were compared to the experimental results. In the experiment the resolution chart covered by a ground glass was imaged. The experimental results are in the good agreement with the theoretical results. It was shown both by experiments and the theoretical model, that with ballistic and diffuse light we can obtain images with diffraction limited resolution.

© 2014 Optical Society of America

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2013 (2)

2012 (1)

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

2010 (5)

M. Lošt’ák, P. Kolman, Z. Dostál, R. Chmelík, “Diffuse light imaging with a coherence controlled holographic microscope,” Proc. SPIE 7746, 77461N (2010).
[CrossRef]

T. Slabý, M. Antoš, Z. Dostál, P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Proc. SPIE 7746, 77461R (2010).
[CrossRef]

N. L. Patel, “Relative capacities of time-gated versus continuous-wave imaging to localize tissue embedded vessels with increasing depth,” J. Biomed. Opt. 15(1) 016015 (2010).
[CrossRef]

Y. Cotte, M. F. Toy, N. Pavillon, C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields.,” Opt. Express 18, 19462–19478 (2010).
[CrossRef] [PubMed]

P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express 18, 21990–22003 (2010).
[CrossRef] [PubMed]

2006 (3)

S. Tamano, Y. Hayasaki, N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt. 45, 953–959 (2006).
[CrossRef] [PubMed]

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

R. Chmelík, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. 53, 2673–2689 (2006).
[CrossRef]

2000 (1)

1997 (3)

1996 (1)

1994 (3)

1993 (1)

1992 (1)

1991 (1)

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

1988 (1)

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

1987 (1)

1973 (1)

1972 (1)

1970 (1)

1965 (1)

H. Kogelnik, “Holographic image projection through inhomogeneous media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).
[CrossRef]

1962 (1)

Antoš, M.

Babacan, S. D.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

Bednarz, M.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 2002).

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Chang, B. J.

Chang, W.

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

Chen, C.

Chen, H.

Chen, Y.

Chmelík, R.

T. Slabý, P. Kolman, Z. Dostál, M. Antoš, M. Lošt’ák, R. Chmelík, “Off-axis setup taking full advantage of incoherent illumination in coherence-controlled holographic microscope,” Opt. Express 21, 14747–14762 (2013).
[CrossRef] [PubMed]

T. Slabý, M. Antoš, Z. Dostál, P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Proc. SPIE 7746, 77461R (2010).
[CrossRef]

M. Lošt’ák, P. Kolman, Z. Dostál, R. Chmelík, “Diffuse light imaging with a coherence controlled holographic microscope,” Proc. SPIE 7746, 77461N (2010).
[CrossRef]

P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express 18, 21990–22003 (2010).
[CrossRef] [PubMed]

R. Chmelík, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. 53, 2673–2689 (2006).
[CrossRef]

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Y. Cotte, M. F. Toy, N. Pavillon, C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields.,” Opt. Express 18, 19462–19478 (2010).
[CrossRef] [PubMed]

Crane, R. B.

Debeir, O

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Decaestecker, C.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Y. Cotte, M. F. Toy, N. Pavillon, C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields.,” Opt. Express 18, 19462–19478 (2010).
[CrossRef] [PubMed]

Dilworth, D.

Do, M. N.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

Dorn, P.

Dostál, Z.

T. Slabý, P. Kolman, Z. Dostál, M. Antoš, M. Lošt’ák, R. Chmelík, “Off-axis setup taking full advantage of incoherent illumination in coherence-controlled holographic microscope,” Opt. Express 21, 14747–14762 (2013).
[CrossRef] [PubMed]

T. Slabý, M. Antoš, Z. Dostál, P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Proc. SPIE 7746, 77461R (2010).
[CrossRef]

M. Lošt’ák, P. Kolman, Z. Dostál, R. Chmelík, “Diffuse light imaging with a coherence controlled holographic microscope,” Proc. SPIE 7746, 77461N (2010).
[CrossRef]

Dubois, F.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Flotte, T.

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

Fujimoto, J.

Genack, A.

Golding, I.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

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

Gregory, K.

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

Haskell, R. C.

Hayasaki, Y.

Hee, M.

J. Izatt, M. Hee, G. Owen, E. Swanson, J. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

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

Huang, D.

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

Indebetouw, G.

Izatt, J.

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Kempe, M.

Kiss, R.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Klysubun, P.

Knüttel, A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 16(8) 2226–2235 (1994)
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Holographic image projection through inhomogeneous media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).
[CrossRef]

Kolman, P.

T. Slabý, P. Kolman, Z. Dostál, M. Antoš, M. Lošt’ák, R. Chmelík, “Off-axis setup taking full advantage of incoherent illumination in coherence-controlled holographic microscope,” Opt. Express 21, 14747–14762 (2013).
[CrossRef] [PubMed]

T. Slabý, M. Antoš, Z. Dostál, P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Proc. SPIE 7746, 77461R (2010).
[CrossRef]

M. Lošt’ák, P. Kolman, Z. Dostál, R. Chmelík, “Diffuse light imaging with a coherence controlled holographic microscope,” Proc. SPIE 7746, 77461N (2010).
[CrossRef]

P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express 18, 21990–22003 (2010).
[CrossRef] [PubMed]

Kuei, C.

Kurtz, C. N.

Legros, J.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Leith, E.

Leith, E. N.

Lin, C.

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

Lopez, J.

Lošt’ák, M.

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Minsky, M.

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

Mir, M.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

Monnom, O.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Nishida, N.

Owen, G.

Patel, N. L.

N. L. Patel, “Relative capacities of time-gated versus continuous-wave imaging to localize tissue embedded vessels with increasing depth,” J. Biomed. Opt. 15(1) 016015 (2010).
[CrossRef]

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Y. Cotte, M. F. Toy, N. Pavillon, C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields.,” Opt. Express 18, 19462–19478 (2010).
[CrossRef] [PubMed]

Popescu, G.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Puliafito, C.

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

Rudd, J.

Rudolph, W.

Schmitt, J. M.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 16(8) 2226–2235 (1994)
[CrossRef]

Schotland, J. C.

Schuman, J.

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

Slabý, T.

Stinson, W.

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

Sun, P.

Svaasand, L. O.

Swanson, E.

J. Izatt, M. Hee, G. Owen, E. Swanson, J. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

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

Tamano, S.

Toy, F.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Toy, M. F.

Tromberg, B. J.

Tsay, T. T.

Tuchin, V.

V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE Press, 2007).
[CrossRef]

Upatnieks, J.

Valdmanis, J.

Van Ham, P.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Vossler, G.

Welsch, E.

Wilson, T.

T. Wilson, Confocal Microscopy (Academic Press, 1990).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 2002).

Yadlowsky, M.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 16(8) 2226–2235 (1994)
[CrossRef]

Yourassowsky, C.

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Holographic image projection through inhomogeneous media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).
[CrossRef]

J. Biomed. Opt. (2)

N. L. Patel, “Relative capacities of time-gated versus continuous-wave imaging to localize tissue embedded vessels with increasing depth,” J. Biomed. Opt. 15(1) 016015 (2010).
[CrossRef]

F. Dubois, C. Yourassowsky, O. Monnom, J. Legros, O Debeir, P. Van Ham, R. Kiss, C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11, 054032 (2006).
[CrossRef] [PubMed]

J. Mod. Opt. (2)

R. Chmelík, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. 53, 2673–2689 (2006).
[CrossRef]

W. Rudolph, M. Kempe, “Trends in optical biomedical imaging,” J. Mod. Opt. 441617–1642 (1997).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (5)

Nature Photon. (1)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, C. Depeursinge, “Marker-free phase nanoscopy,” Nature Photon. 7, 113–117 (2013).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

PLOS ONE (1)

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLOS ONE 7, e39816 (2012).
[CrossRef] [PubMed]

Proc. SPIE (2)

M. Lošt’ák, P. Kolman, Z. Dostál, R. Chmelík, “Diffuse light imaging with a coherence controlled holographic microscope,” Proc. SPIE 7746, 77461N (2010).
[CrossRef]

T. Slabý, M. Antoš, Z. Dostál, P. Kolman, R. Chmelík, “Coherence-controlled holographic microscope,” Proc. SPIE 7746, 77461R (2010).
[CrossRef]

Scanning (1)

M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

Science (1)

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

Other (5)

M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 2002).

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

W. H. Press, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

T. Wilson, Confocal Microscopy (Academic Press, 1990).

V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE Press, 2007).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Optical setup of CCHM. Incoherent light source (S), relay lens (L), beam splitters (BS), mirrors (M), condensers (C), object plane (Sp), reference plane (R), microscope objectives (O), tube lenses (TL), diffraction grating (DG), output lens (OL), output plane (OP), detector (D). Figure adapted, with permission, from [27].

Fig. 2
Fig. 2

Simplified drawings for explanation of principle of imaging in CCHM through diffuse medium by ballistic and diffuse light. IS1, IS2...imaginary sources in object planes of the condensers C1, C2. Sp, R...object planes of microscope objectives O1, O2. D...diffuser. AO, AR...images of point A in the output plane OP. AB...ballistic image of point A. AD...diffuse image of point A. Dotted line...scattered light, continuous line...unscattered light. a) Imaging without diffuser. b) Imaging with diffuser by ballistic light, mutual shift Δxi = 0. c) Imaging with diffuser by diffuse light, reference arm is shifted by nonzero Δxi.

Fig. 3
Fig. 3

Simplified drawing of the object arm for computation of the amplitude in the output plane when imaging a planar object placed in the object plane Sp. In this Fig. the object is a point aperture at coordinate x0 = x0N. D...diffuser, L...thin lens substituting the objective, Ap...aperture diaphragm in the back focal plane of thin lens, OP...output plane.

Fig. 4
Fig. 4

In the left column there are the absolute values of function hobj together with href mutually shifted accordingly to the relevant Δx0, in the right column there is the absolute value of their product |hCCHM| = |hobjhref| normalized to the maximum value of |hCCHM| without diffuser. The row a) shows simulation without diffuser, rows b)–d) and e) respectively represent two different realizations of diffuser. Rows b)–d) represent different mutual shifts Δx0 for the same realization of the diffuser, specifically σ = 0.42λ. In the last row e) there is the result of diffuser realization σ = 0.84λ, it means a stronger diffuser.

Fig. 5
Fig. 5

Results of the PSFs for off-axis points. The first two rows a), b) represent the image with mutual shift Δx0 = 16.0 μm and following two rows c), d) Δx0 = 15.0 μm. Rows a), c) show the absolute values of functions href (red) and hobj (black) mutually shifted according to the relevant Δx0 and rows b) and d) show the absolute value of the microscope PSF |hCCHM| = |hobjhref|. Each column shows the image for different points x0N, consequently: axial point x0N = 0 μm and off-axis points x0N = −10 μm and x0N = −20 μm.

Fig. 6
Fig. 6

Numerical simulation of imaging three infinite equidistant parallel slits. In the upper row there is a computed signal in the gray scale. In the bottom row, there is a plot profile of the upper row. In the left column the spatial frequency of slits is f = 2NAob/λ and the mutual shift Δx0 = 16.0 μm, in the middle column f = NAob/λ, Δx = 16.0 μm and in the right column f = NAob/λ, Δx = 15.0 μm.

Fig. 7
Fig. 7

The experimental results of imaging a resolution chart. The images were performed with objectives 10×/0.25. Interference filter λ = 650nm, 10nm FWHM. a) imaging without diffuser, b) imaging with diffuser - ballistic light, c)–e) imaging with diffuser - diffuse light. The mutual shifts are c) Δx = 44.8 μm d) Δx = 42.7 μm, e) Δx = 47.0 μm. In the second and third column there are magnified details A and B respectively. Orange circles indicate the resolution limit of images in the corresponding row.

Equations (15)

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i ( q t i , K t ) = | u o ( q t i , K t ) + u r ( q t i , K t ) exp ( i 2 π f c x i ) | 2 = = | u o ( q t i , K t ) | 2 + | u r ( q t i , K t ) | 2 + u o ( q t i , K t ) u r * ( q t i , K t ) exp ( i 2 π f c x i ) + + u o * ( q t i , K t ) u r ( q t i , K t ) exp ( i 2 π f c x i ) ,
w ( q t i ) = ( K x 2 + K y 2 ) 1 / 2 < NA ill / λ u o ( q t i , K x , K y ) u r * ( q t i , K x , K y ) d K x d K y ,
w ( x i ) = NA ill / λ NA ill / λ u o ( x i , K x ) u r * ( x i , K x ) d K x .
η obj ( x i , K x ) = C exp ( i 2 π K x x 0 N ) exp ( i π K x 0 N 2 a d ) exp ( i π K x i 2 z ) × × t d ( x d ) I exp [ i π K a d ( 2 x 0 N x d + x d 2 ) ] d x d ,
I = F [ E e ( R p B 2 A ) E e ( R p B 2 A ) ] ,
E e ( x ) = C ( x ) + i S ( x ) = 0 x exp ( i π 2 t 2 ) d t
h CCHM ( x i ) = NA ill / λ NA ill / λ η obj ( x i , K x ) u r * ( x i , K x ) d K x ,
u r ( x i , K x ) = C ref exp ( i 2 π K x x i M ) ,
η obj ( x 0 , K x ) = h obj ( x 0 ) exp ( i 2 π K x x 0 N ) ,
h CCHM ( x 0 ) = h obj ( x 0 ) C ref NA ill / λ NA ill / λ exp [ i 2 π K x ( x 0 N x 0 ) ] d K x h ref ( x 0 ) .
h ref ( x 0 ) = sin [ NA ill ( x 0 x 0 N ) 2 π / λ ] NA ill ( x 0 x 0 N ) 2 π / λ ,
h CCHM ( x 0 ) = h obj ( x 0 ) h ref * ( x 0 ) .
h CCHM ( x 0 ) = | h obj ( x 0 ) | 2 = | h ref ( x 0 ) | 2 .
h CCHM ( x 0 , Δ x 0 ) = h obj ( x 0 ) h ref ( x 0 Δ x 0 ) .
w ( x 0 ) = t ( x 0 ) h CCHM ( x 0 x 0 ) d x 0 .

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