Abstract

Light field microscopy has been proposed as a new high-speed volumetric computational imaging method that enables reconstruction of 3-D volumes from captured projections of the 4-D light field. Recently, a detailed physical optics model of the light field microscope has been derived, which led to the development of a deconvolution algorithm that reconstructs 3-D volumes with high spatial resolution. However, the spatial resolution of the reconstructions has been shown to be non-uniform across depth, with some z planes showing high resolution and others, particularly at the center of the imaged volume, showing very low resolution. In this paper, we enhance the performance of the light field microscope using wavefront coding techniques. By including phase masks in the optical path of the microscope we are able to address this non-uniform resolution limitation. We have also found that superior control over the performance of the light field microscope can be achieved by using two phase masks rather than one, placed at the objective’s back focal plane and at the microscope’s native image plane. We present an extended optical model for our wavefront coded light field microscope and develop a performance metric based on Fisher information, which we use to choose adequate phase masks parameters. We validate our approach using both simulated data and experimental resolution measurements of a USAF 1951 resolution target; and demonstrate the utility for biological applications with in vivo volumetric calcium imaging of larval zebrafish brain.

© 2014 Optical Society of America

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References

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    [Crossref]
  2. M. Levoy, Z. Zhang, and I. McDowell, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
    [Crossref] [PubMed]
  3. M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-D deconvolution for the light field microscope,” Opt. Express 21(21), 25418–25439 (2013).
    [Crossref] [PubMed]
  4. L. Grosenick, T. Anderson, and S. J. Smith, “Elastic source selection for in vivo imaging of neuronal ensembles,” in IEEE Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’09) (2009), pp. 1263–1266.
  5. R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2014 (3)

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

S. Quirin, J. Jackson, D. S. Peterka, and R. Yuste, “Simultaneous imaging of neural activity in three dimensions,” Front. Neural Circuits 8, 29 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

P. Favaro, “A split-sensor light field camera for extended depth of field and superresolution,” Proc. SPIE 8436, 843602 (2012).
[Crossref]

2010 (1)

2009 (1)

M. Levoy, Z. Zhang, and I. McDowell, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (2)

Q. Yang, L Liu, and J Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272(1), 56–66 (2007).
[Crossref]

A. Castro, Y. Frauel, and B. Javidi, “Integral imaging with large depth of field using an asymmetric phase mask,” Opt. Express 15(16), 10266–10273 (2007).
[Crossref] [PubMed]

2006 (2)

S. Abrahamsson, S. Usawab, and M. Gustafssona, “A new approach to extended focus for high-speed, high-resolution biological microscopy,” Proc. SPIE 6090, 60900N (2006).
[Crossref]

A. Greengard, Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31(2), 181–183 (2006).
[Crossref] [PubMed]

1995 (1)

E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” App. Opt. 34(11), 1859–1866 (1995).
[Crossref]

Abrahamsson, S.

S. Abrahamsson, S. Usawab, and M. Gustafssona, “A new approach to extended focus for high-speed, high-resolution biological microscopy,” Proc. SPIE 6090, 60900N (2006).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings of ACM SIGGRAPH (2006), 924–934.
[Crossref]

Andalman, A.

Anderson, T.

L. Grosenick, T. Anderson, and S. J. Smith, “Elastic source selection for in vivo imaging of neuronal ensembles,” in IEEE Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’09) (2009), pp. 1263–1266.

Arnison, M. R.

M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.
[Crossref]

Bando, Y.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
[Crossref]

Boyden, E. S.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Broxton, M.

Castro, A.

Cathey, W. T.

E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” App. Opt. 34(11), 1859–1866 (1995).
[Crossref]

Cogswell, C. J.

M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.
[Crossref]

Cohen, N.

Deisseroth, K.

Doblas, A.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

Dowski, E. R.

E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” App. Opt. 34(11), 1859–1866 (1995).
[Crossref]

Durand, F.

A. Levin, S. W. Hasinoff, P. Green, F. Durand, and W. T. Freeman, “4D frequency analysis of computational cameras for depth of field extension,” in Proceedings of ACM SIGGRAPH (2009), 97.

Favaro, P.

P. Favaro, “A split-sensor light field camera for extended depth of field and superresolution,” Proc. SPIE 8436, 843602 (2012).
[Crossref]

Feng, H.

Fleischer, J.

C. H. Lu, S. Muenzel, and J. Fleischer, “High-resolution light-field microscopy,” in Computational Optical Sensing and Imaging, Microscopy and Tomography I (2013), CTh3B.

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings of ACM SIGGRAPH (2006), 924–934.
[Crossref]

Frauel, Y.

Freeman, W. T.

A. Levin, S. W. Hasinoff, P. Green, F. Durand, and W. T. Freeman, “4D frequency analysis of computational cameras for depth of field extension,” in Proceedings of ACM SIGGRAPH (2009), 97.

Goodman, J.

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

Green, P.

A. Levin, S. W. Hasinoff, P. Green, F. Durand, and W. T. Freeman, “4D frequency analysis of computational cameras for depth of field extension,” in Proceedings of ACM SIGGRAPH (2009), 97.

Greengard, A.

Grosenick, L.

M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-D deconvolution for the light field microscope,” Opt. Express 21(21), 25418–25439 (2013).
[Crossref] [PubMed]

L. Grosenick, T. Anderson, and S. J. Smith, “Elastic source selection for in vivo imaging of neuronal ensembles,” in IEEE Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’09) (2009), pp. 1263–1266.

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 1999).

Gustafssona, M.

S. Abrahamsson, S. Usawab, and M. Gustafssona, “A new approach to extended focus for high-speed, high-resolution biological microscopy,” Proc. SPIE 6090, 60900N (2006).
[Crossref]

Hasinoff, S. W.

A. Levin, S. W. Hasinoff, P. Green, F. Durand, and W. T. Freeman, “4D frequency analysis of computational cameras for depth of field extension,” in Proceedings of ACM SIGGRAPH (2009), 97.

Hoffmann, M.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings of ACM SIGGRAPH (2006), 924–934.
[Crossref]

Jackson, J.

S. Quirin, J. Jackson, D. S. Peterka, and R. Yuste, “Simultaneous imaging of neural activity in three dimensions,” Front. Neural Circuits 8, 29 (2014).
[Crossref] [PubMed]

Javidi, B.

Kato, S.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

King, S. V.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

Levin, A.

A. Levin, S. W. Hasinoff, P. Green, F. Durand, and W. T. Freeman, “4D frequency analysis of computational cameras for depth of field extension,” in Proceedings of ACM SIGGRAPH (2009), 97.

Levoy, M.

M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-D deconvolution for the light field microscope,” Opt. Express 21(21), 25418–25439 (2013).
[Crossref] [PubMed]

M. Levoy, Z. Zhang, and I. McDowell, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings of ACM SIGGRAPH (2006), 924–934.
[Crossref]

Z. Zhengyun and M. Levoy, “Wigner distributions and how they relate to the light field,” in Proc. Int. Conf. Comput. Photography (Apr.2009), pp. 1–10.

Li, Q.

Liu, L

Q. Yang, L Liu, and J Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272(1), 56–66 (2007).
[Crossref]

Lu, C. H.

C. H. Lu, S. Muenzel, and J. Fleischer, “High-resolution light-field microscopy,” in Computational Optical Sensing and Imaging, Microscopy and Tomography I (2013), CTh3B.

Martínez-Corral, M.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

Marwah, K.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

McDowell, I.

M. Levoy, Z. Zhang, and I. McDowell, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

Muenzel, S.

C. H. Lu, S. Muenzel, and J. Fleischer, “High-resolution light-field microscopy,” in Computational Optical Sensing and Imaging, Microscopy and Tomography I (2013), CTh3B.

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings of ACM SIGGRAPH (2006), 924–934.
[Crossref]

Pak, N.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Patwary, N.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

Peterka, D. S.

S. Quirin, J. Jackson, D. S. Peterka, and R. Yuste, “Simultaneous imaging of neural activity in three dimensions,” Front. Neural Circuits 8, 29 (2014).
[Crossref] [PubMed]

Piestun, R.

Prasad, S.

Prevedel, R.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Preza, C.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

Y. Shuai and C. Preza, “Computational optical sectioning microscopy using an engineered PSF with reduced depth variability - Proof of concept,” in Proc. of the 9th IEEE International Symposium on Biomedical Imaging (2012), pp. 1739–1742.

Quirin, S.

S. Quirin, J. Jackson, D. S. Peterka, and R. Yuste, “Simultaneous imaging of neural activity in three dimensions,” Front. Neural Circuits 8, 29 (2014).
[Crossref] [PubMed]

Raskar, R.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

Saavedra, G.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martínez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).
[Crossref]

Schechner, Y.

Schrödel, T.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Sheppard, C. J. R.

M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.
[Crossref]

Shuai, Y.

Y. Shuai and C. Preza, “Computational optical sectioning microscopy using an engineered PSF with reduced depth variability - Proof of concept,” in Proc. of the 9th IEEE International Symposium on Biomedical Imaging (2012), pp. 1739–1742.

Smith, S. J.

L. Grosenick, T. Anderson, and S. J. Smith, “Elastic source selection for in vivo imaging of neuronal ensembles,” in IEEE Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’09) (2009), pp. 1263–1266.

Sun, J

Q. Yang, L Liu, and J Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272(1), 56–66 (2007).
[Crossref]

Török, P.

M. R. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.
[Crossref]

Usawab, S.

S. Abrahamsson, S. Usawab, and M. Gustafssona, “A new approach to extended focus for high-speed, high-resolution biological microscopy,” Proc. SPIE 6090, 60900N (2006).
[Crossref]

Vaziri, A.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Wetzstein, G.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
[Crossref]

Yang, Q.

Q. Yang, L Liu, and J Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272(1), 56–66 (2007).
[Crossref]

Yang, S.

Yoon, Y. G.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

Yuste, R.

S. Quirin, J. Jackson, D. S. Peterka, and R. Yuste, “Simultaneous imaging of neural activity in three dimensions,” Front. Neural Circuits 8, 29 (2014).
[Crossref] [PubMed]

Zhang, Z.

M. Levoy, Z. Zhang, and I. McDowell, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

Zhao, H.

Zhengyun, Z.

Z. Zhengyun and M. Levoy, “Wigner distributions and how they relate to the light field,” in Proc. Int. Conf. Comput. Photography (Apr.2009), pp. 1–10.

Zimmer, M.

R. Prevedel, Y. G. Yoon, M. Hoffmann, N. Pak, G. Wetzstein, S. Kato, T. Schrödel, R. Raskar, M. Zimmer, E. S. Boyden, and A. Vaziri, “Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy,” Nat. Methods 11(7), 727–730 (2014).
[Crossref] [PubMed]

ACM Trans. Graph. (1)

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

App. Opt. (1)

E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” App. Opt. 34(11), 1859–1866 (1995).
[Crossref]

Front. Neural Circuits (1)

S. Quirin, J. Jackson, D. S. Peterka, and R. Yuste, “Simultaneous imaging of neural activity in three dimensions,” Front. Neural Circuits 8, 29 (2014).
[Crossref] [PubMed]

J. Microsc. (1)

M. Levoy, Z. Zhang, and I. McDowell, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

Nat. Methods (1)

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Figures (10)

Fig. 1
Fig. 1

US Air Force (USAF) 1951 resolution test target translated to depths below the native object plane (z = 0 μm) and imaged using a light field microscope with a 20× 0.5NA water-dipping objective. (a) Images taken with a conventional widefield microscope as the target is translated to the z-heights denoted below each image. (b) Light field deconvolution using the method developed in [3] while the microscope was defocused to the same heights as in (a). The resolution is poor at the native plane (red frame in leftmost column), peaks at z = −20 μm and gradually decreases with depth. (c) wavefront coded LFM, which in this example consists of a single cubic phase mask, placed in the back focal plane of the objective. The low-resolution at the native object plane is significantly improved (green frame in leftmost column), and the resolution at z = −100 μm is also slightly improved compared with (b) (rightmost column, red and green frames). This comes at the expense of reduced peak resolution at z = −20 μm.

Fig. 2
Fig. 2

Schematic diagram of the light propagation through our proposed wavefront coded light field microscope. Phase masks (in green) are placed in the back focal plane of the microscope’s objective, where the telecentric stop is placed in a doubly-telecentric microscope configuration, and also in the aperture of each microlens in the microlens array.

Fig. 3
Fig. 3

Wavefront coded light field microscope - image and schematic diagram. The setup is composed of a fluorescence microscope (objective OBJ and tube lens L1), relay optics (L2 and L3) that create a conjugate back focal plane of the objective, a phase mask (PM) that is placed at that conjugate plane on an translation stage, a microlens array (MLA) and a detector (DET), relayed one microlens focal length behind the microlens array using relay optics (L4 and L5).

Fig. 4
Fig. 4

The cubic mask placed at the conjugate back focal plane of the light field microscope objective and its effect on the LFM PSFs for a point on the native object plane. (a) The measured sag of the cubic phase mask. The white circle indicates the size of the back aperture of the 20× 0.5NA objective. (b) With the phase mask, a point source at the native object plane generates a cubic PSF at the native image plane of the LFM (left column, top row) and a complicated diffraction pattern that spans 4 microlenses on the detector (left column, bottom row). Translating the point source by 2 μm in x and y (right column) changes the light field PSF intensity profile significantly. (c) Without the cubic phase mask. By contrast, the light field PSF after a 2 μm translation in x and y still resembles a disk. The greater change in (b) than (c) reflects the higher sensitivity of our wavefront coded LFM to small changes in the specimen at the native object plane, hence its improved spatial resolution at that plane.

Fig. 5
Fig. 5

Experimental resolution measurements of the standard LFM and our wavefront coded LFM, with a cubic mask placed at the objective back focal plane. (a) Light field deconvolution of experimental data captured with no phase mask. At the native object plane (z = 0 μm) the resolution is low, but at other planes, much higher spatial resolution can be reconstructed. The resolution gradually decreases as we move farther away from the native object plane. (b) Experimental MTF measurements for the standard LFM, based on contrast calculation of different spatial frequencies in the USAF 1951 target. High contrast values MTF are shown as hot (white-yellow), while lower values are cold (blue). Peak resolution of more than 500 lp/mm is achieved at z = 15 μm, but the resolution fluctuates in a region of about 50 μm around the native object plane. (c) The same reconstructed planes, now with the cubic phase mask. The resolution at the native object plane is significantly improved, is similar for z=±50 μm and is also slightly improve at z=±100 μm. (d) The corresponding MTF heat maps show that with the cubic phase mask, the resolution is more uniform around the native object plane, but peak resolution drops to about 350 lp/mm.

Fig. 6
Fig. 6

Volumetric imaging of 2 μm fluorescent beads embedded in agarose, with and without an objective cubic phase mask. (a) Max projections through the volume with no phase mask. (b) Max projections through the volume with the cubic phase mask. (c) Reconstructed bead on the native object plane (red boxes in (a) and (b)) and the corresponding X and Z intensity profiles showing the FWHM for each case. The cubic mask significantly improves both lateral resolution and axial resolution. (d) Reconstructed bead +70 μm off the native object plane (yellow boxes in (a) and (b)). The phase mask improves the lateral resolution slightly but the axial resolution remains the same as the no phase mask case.

Fig. 7
Fig. 7

In vivo volumetric calcium imaging of a larval zebrafish at camera-limited frame rate. (a) The native object plane out of a reconstructed volume at a single point in time using conventional light field deconvolution. The poor spatial resolution makes it hard to distinguish individual fluorescent sources. (b) With the use of a single cubic phase mask at the objective’s back focal plane, the resolution is improved. The insets in (a) and (b) show magnification of the telencephalon, an olfactory and learning center in the forebrain. c,d) XZ maximum projections of the same volumes in (a) and (b) illustrate that no z resolution is traded away to obtain the improvement shown in (b). “Banding” artifacts shown in (c), caused by the low resolution planes (black arrow), are gone in (d).

Fig. 8
Fig. 8

Simulation results of USAF 1951 resolution target at different z planes for several LFM configurations. (a) Standard LFM with no phase masks. (b) An objective cubic phase mask. (c) A combination of cubic phase masks: an objective mask as in (b) and adding a cubic phase mask at each microlens aperture. The resolution around the native object plane is significantly improved compared with (a) and (b), but degrades faster farther away from it. (d) A spiral objective phase mask. The resolution is uniform across a range of 200 μm, but peak performance is reduced compared with (a)–(c). (e) 10% contrast resolution limit across depth for the configurations (a)–(d). At the native object plane, the standard LFM (cyan curve) shows severe aliasing artifacts which result in inaccurate measurement of the resolution. (f) The proposed Fisher information-based performance metric. The metric correlates well with the limiting resolution in (e). Existing differences are due to different the Fisher information metric does not calculate the maximal frequency for a certain contrast threshold, but rather the derivative at a certain fixed step size in the spatial domain.

Fig. 9
Fig. 9

Analysis of the diffraction spot under a single microlens with and without a cubic phase mask at its aperture. In both cases, a cubic phase mask is used in the objective back focal plane. (a) The diffraction spot for a point source at z = 25 μm with no microlens phase mask. (b) the diffraction spot for the same point source position as in (a), with a cubic phase mask at the microlens aperture. (c) Cross-section MTFs of the spots in (a) - in red and in (b) - in blue. The PSF of the microlens with the cubic phase mask shows better frequency response. (c) The diffraction spot for a point source at z = 80 μm with no microlens phase mask. (d) The diffraction spot for the same point source position as in (c), with a cubic phase mask at the microlens aperture. (e) Cross-section MTFs of the spots in (c) - in red and in (d) - in blue. At this depth, the MTF of the microlens with the cubic phase mask is worse compared with not using a microlens phase mask. In this example, adding cubic masks to the microlenses is advantageous only for a certain range of depths of about 80μm around the native object plane.

Fig. 10
Fig. 10

Backward ray tracing diagrams and corresponding ray-space diagrams for four LFM configurations, assuming paraxial optics. Scale is exaggerated to highlight differences. (a)–(d) Back-traced rays from a detector pixel for no phase masks, microlenses cubic phase masks, objective cubic phase masks and both microlenses and objective masks configurations, respectively. Ray colors distinguish different points inside a pixel’s integration area. The objective and microlenses phase masks spread the rays differently: Ray bundles from each point on the detector are refracted by the microlenses masks so that their intersections with the u plane form a parabolic profile. The objective phase mask on the other hand, introduces different phases to ray bundles that intersect at different positions over the back focal plane, so that their positions on the x plane form a parabolic profile. (e) Ray-space diagram for (a). When no phase masks are used, a thin object on the native object plane (the yellow vertical stripe) is sampled only by pixels under a single microlens (denoted by same-color areas), which collect light over the same area on the x plane. The lack of diversity in position measurement leads to low spatial resolution in the reconstruction. (f) Using only microlenses phase masks the sampling pattern of the x plane does not change. Therefore, the low spatial resolution at the native object cannot be improved. (g) With an objective mask, pixels that sample the object now cover partially overlapping areas on x. The added spatial information leads to higher spatial resolution in the reconstruction. (h) When using objective and microlenses phase masks together, the object is sampled by even more pixels, resulting in further improvement in spatial resolution in the reconstruction.

Equations (20)

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f = Hg ,
U 0 ( x , y , p ) = ι A k n z p 2 π r 2 exp ( ι k n r ) r [ ( x x p ) 2 + ( y y p ) 2 + z p 2 ] 1 / 2 k n = 2 π ( λ / n )
f obj = f t l M .
T obj ( x , y ) = P obj ( x , y ) ( cos θ ) 1 / 2 exp ( ι k 2 f obj ( x 2 + y 2 ) )
P obj ( x , y ) = circ ( ( x 2 + y 2 ) 1 / 2 d obj / 2 ) θ sin 1 ( λ ( x 2 + y 2 ) 1 / 2 n ) .
U 1 ( x , y , p ) = ι exp ( ι k f obj ) λ f obj U 0 ( ξ , η , p ) P obj ( ξ , η ) exp ( ι k f obj ( ξ x + η y ) ) d ξ d η
U 1 + ( x , y , p ) = U 1 ( x , y , p ) exp ( ι ϕ obj ( x , y , Θ obj ) )
U 2 ( x , y , p , Θ obj ) = ι exp ( ι k f t l ) λ f t l U 1 + ( ξ , η , p , Θ obj ) P t l ( ξ , η ) exp ( ι k f t l ( ξ x + η y ) ) d ξ d η
T se ( x , y , Θ μ lens ) = P se ( x , y ) Q se ( x , y , Θ μ lens )
P se ( x , y ) = rect ( x d μ lens , y d μ lens ) * III ( x / p μ lens , y / p μ lens )
Q se ( x , y , Θ μ lens ) = exp ( ι k 2 f μ lens ( x 2 + y 2 ) + ϕ μ lens ( x , y , Θ μ lens ) ) * III ( x / p μ lens , y / p μ lens ) .
U 2 + ( x , y , p , Θ ) = U 2 ( x , y , p , Θ obj ) T se ( x , y , Θ μ lens ) .
U 3 ( x , y , p , Θ ) = exp ( ι k f μ lens ) ι λ f μ lens exp ( ι k 2 f μ lens ( x 2 + y 2 ) ) U 2 + ( ξ , η , p , Θ ) exp ( ι k 2 f μ lens ( ξ 2 + η 2 ) ) exp ( ι k f μ lens ( x ξ + y η ) ) d ξ d η .
h ( x , y , p , Θ ) = | U 3 ( x , y , p , Θ ) | 2 .
( p , Θ ) = [ x p x p ( p , Θ ) x p y p ( p , Θ ) x p z p ( p , Θ ) y p x p ( p , Θ ) y p y p ( p , Θ ) y p z p ( p , Θ ) z p x p ( p , Θ ) z p y p ( p , Θ ) z p z p ( p , Θ ) ]
i j ( p , Θ ) = ( 2 ln h ^ ( x , y , p , Θ ) i j ) h ^ ( x , y , p , Θ ) d x d y
h ^ ( x , y , p , Θ ) = h ( x , y , p , Θ ) h ( x , y , p , Θ ) d x d y .
J ( p , Θ ) = i j ω i j i j ( p , Θ ) .
contrast = ( I max I min ) / ( I max + I min ) ,
ϕ obj ( x , y ) = α ( x 2 + y 2 ) arctan ( y / x )

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