Abstract

Light field microscopy (LFM) uses a microlens array (MLA) near the sensor plane of a microscope to achieve single-shot 3D imaging of a sample without any moving parts. Unfortunately, the 3D capability of LFM comes with a significant loss of lateral resolution at the focal plane. Placing the MLA near the pupil plane of the microscope, instead of the image plane, can mitigate the artifacts and provide an efficient forward model, at the expense of field-of-view (FOV). Here, we demonstrate improved resolution across a large volume with Fourier DiffuserScope, which uses a diffuser in the pupil plane to encode 3D information, then computationally reconstructs the volume by solving a sparsity-constrained inverse problem. Our diffuser consists of randomly placed microlenses with varying focal lengths; the random positions provide a larger FOV compared to a conventional MLA, and the diverse focal lengths improve the axial depth range. To predict system performance based on diffuser parameters, we, for the first time, establish a theoretical framework and design guidelines, which are verified by numerical simulations, and then build an experimental system that achieves < 3 µm lateral and 4 µm axial resolution over a 1000 × 1000 × 280 µm3 volume. Our diffuser design outperforms the MLA used in LFM, providing more uniform resolution over a larger volume, both laterally and axially.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (3)

2019 (4)

2018 (4)

2017 (2)

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
[Crossref]

J. K. Adams, V. Boominathan, B. W. Avants, D. G. Vercosa, F. Ye, R. G. Baraniuk, J. T. Robinson, and A. Veeraraghavan, “Single-frame 3D fluorescence microscopy with ultraminiature lensless FlatScope,” Sci. Adv. 3(12), e1701548 (2017).
[Crossref]

2016 (3)

R. Berlich, A. Bräuer, and S. Stallinga, “Single shot three-dimensional imaging using an engineered point spread function,” Opt. Express 24(6), 5946–5960 (2016).
[Crossref]

E. A. Pnevmatikakis, D. Soudry, Y. Gao, T. A. Machado, J. Merel, D. Pfau, T. Reardon, Y. Mu, C. Lacefield, W. Yang, M. Ahrens, R. Bruno, T. M. Jessell, D. S. Peterka, R. Yuste, and L. Paninski, “Simultaneous denoising, deconvolution, and demixing of calcium imaging data,” Neuron 89(2), 285–299 (2016).
[Crossref]

A. Llavador, J. Sola-Pikabea, G. Saavedra, B. Javidi, and M. Martínez-Corral, “Resolution improvements in integral microscopy with Fourier plane recording,” Opt. Express 24(18), 20792–20798 (2016).
[Crossref]

2015 (2)

X. Lin, J. Wu, G. Zheng, and Q. Dai, “Camera array based light field microscopy,” Biomed. Opt. Express 6(9), 3179–3189 (2015).
[Crossref]

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. Moerner, “Precise three-dimensional scan-free multiple-particle tracking over large axial ranges with tetrapod point spread functions,” Nano Lett. 15(6), 4194–4199 (2015).
[Crossref]

2014 (2)

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]

N. Cohen, S. Yang, A. Andalman, M. Broxton, L. Grosenick, K. Deisseroth, M. Horowitz, and M. Levoy, “Enhancing the performance of the light field microscope using wavefront coding,” Opt. Express 22(20), 24817–24839 (2014).
[Crossref]

2013 (2)

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]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2013).
[Crossref]

2010 (3)

C. Maurer, S. Khan, S. Fassl, S. Bernet, and M. Ritsch-Marte, “Depth of field multiplexing in microscopy,” Opt. Express 18(3), 3023–3034 (2010).
[Crossref]

Y. Luo, S. B. Oh, and G. Barbastathis, “Wavelength-coded multifocal microscopy,” Opt. Lett. 35(5), 781–783 (2010).
[Crossref]

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations Trends Mach. learning 3(1), 1–122 (2010).
[Crossref]

2009 (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref]

2008 (3)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33(2), 156–158 (2008).
[Crossref]

2006 (4)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

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

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14(25), 12096–12108 (2006).
[Crossref]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

2005 (1)

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

2004 (2)

J.-S. Jang and B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. 29(11), 1230–1232 (2004).
[Crossref]

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans.on Nanobioscience 3(4), 237–242 (2004).
[Crossref]

2003 (2)

1999 (1)

1997 (1)

1994 (1)

H. P. Kao and A. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67(3), 1291–1300 (1994).
[Crossref]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60(1-4), 259–268 (1992).
[Crossref]

1978 (1)

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” The Astronomical J. 79, 745 (1974).
[Crossref]

1972 (1)

1968 (1)

R. Dicke, “Scatter-hole cameras for x-rays and gamma rays,” The Astrophysical J. 153, L101 (1968).
[Crossref]

1908 (1)

G. Lippmann, “Épreuves réversibles donnant la sensation du relief,” J. Phys. Theor. Appl. 7(1), 821–825 (1908).
[Crossref]

Abrahamsson, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2013).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Adams, J.

V. Boominathan, J. Adams, J. Robinson, and A. Veeraraghavan, “PhlatCam: Designed phase-mask based thin lensless camera,” IEEE Transactions on Pattern Analysis and Machine Intelligence (2020).

Adams, J. K.

J. K. Adams, V. Boominathan, B. W. Avants, D. G. Vercosa, F. Ye, R. G. Baraniuk, J. T. Robinson, and A. Veeraraghavan, “Single-frame 3D fluorescence microscopy with ultraminiature lensless FlatScope,” Sci. Adv. 3(12), e1701548 (2017).
[Crossref]

Agard, D. A.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10(1), 60–63 (2013).
[Crossref]

Ahrens, M.

E. A. Pnevmatikakis, D. Soudry, Y. Gao, T. A. Machado, J. Merel, D. Pfau, T. Reardon, Y. Mu, C. Lacefield, W. Yang, M. Ahrens, R. Bruno, T. M. Jessell, D. S. Peterka, R. Yuste, and L. Paninski, “Simultaneous denoising, deconvolution, and demixing of calcium imaging data,” Neuron 89(2), 285–299 (2016).
[Crossref]

Alexander, E.

Q. Guo, Z. Shi, Y.-W. Huang, E. Alexander, C.-W. Qiu, F. Capasso, and T. Zickler, “Compact single-shot metalens depth sensors inspired by eyes of jumping spiders,” Proc. Natl. Acad. Sci. 116(46), 22959–22965 (2019).
[Crossref]

Altshuller, Y.

Andalman, A.

Antipa, N.

K. Monakhova, J. Yurtsever, G. Kuo, N. Antipa, K. Yanny, and L. Waller, “Learned reconstructions for practical mask-based lensless imaging,” Opt. Express 27(20), 28075–28090 (2019).
[Crossref]

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5(1), 1–9 (2018).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-shot diffuser-encoded light field imaging,” in 2016 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2016), pp. 1–11.

F. L. Liu, V. Madhavan, N. Antipa, G. Kuo, S. Kato, and L. Waller, “Single-shot 3D fluorescence microscopy with Fourier DiffuserCam,” in Novel Techniques in Microscopy, (Optical Society of America, 2019), pp. NS2B–3.

K. Yanny, N. Antipa, R. Ng, and L. Waller, “Miniature 3D fluorescence microscope using random microlenses,” in Optics and the Brain, (Optical Society of America, 2019), pp. BT3A–4.

G. Kuo, N. Antipa, R. Ng, and L. Waller, “3d fluorescence microscopy with diffusercam,” in Computational Optical Sensing and Imaging, (Optical Society of America, 2018), pp. CM3E–3.

Arai, J.

Asif, M. S.

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “Flatcam: Replacing lenses with masks and computation,” in 2015 IEEE international conference on computer vision workshop (ICCVW), (IEEE, 2015), pp. 663–666.

Avants, B. W.

J. K. Adams, V. Boominathan, B. W. Avants, D. G. Vercosa, F. Ye, R. G. Baraniuk, J. T. Robinson, and A. Veeraraghavan, “Single-frame 3D fluorescence microscopy with ultraminiature lensless FlatScope,” Sci. Adv. 3(12), e1701548 (2017).
[Crossref]

Ayremlou, A.

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “Flatcam: Replacing lenses with masks and computation,” in 2015 IEEE international conference on computer vision workshop (ICCVW), (IEEE, 2015), pp. 663–666.

Backer, A. S.

Y. Shechtman, L. E. Weiss, A. S. Backer, S. J. Sahl, and W. Moerner, “Precise three-dimensional scan-free multiple-particle tracking over large axial ranges with tetrapod point spread functions,” Nano Lett. 15(6), 4194–4199 (2015).
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Supplementary Material (1)

NameDescription
» Visualization 1       A live adult C. elegans organism that is pan-neuronally expressing a GCaMP fluorescent indicator. The raw video is recorded at 25 fps.

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Figures (7)

Fig. 1.
Fig. 1. System overview for Fourier DiffuserScope and Fourier light field microscopy (FLFM). A diffuser or microlens array is placed in the Fourier plane of the objective (relayed by a 4f system) and a sensor is placed one microlens focal length after. From a single 2D sensor measurement, together with a previously calibrated point spread function (PSF) stack, 3D objects can be reconstructed by solving a sparsity-constrained inverse problem. Here, we compare three choices of diffuser/microlens array: FLFM with a uni-focal microlens array (MLA), random uni-focal microlenses (RUM) and our Fourier DiffuserScope with random multi-focal microlenses (RMM). Our RMM design provides a non-periodic PSF with different spots coming into focus at different planes, enabling 3D reconstructions with full FOV and high resolution across a wider depth range. Note that the PSF images (bottom right) are shown with a gamma correction of 0.4 for better visibility.
Fig. 2.
Fig. 2. System performance analysis. To analyze lateral resolution, consider the orange and purple point sources, laterally spaced by $\Delta d$ in object space, with images on the sensor spaced by $\Delta d''$. For axial resolution, consider the orange and green point sources, axially separated by $\Delta \mathbf {z}$ in object space, which map to their images on the sensor spaced by $\Delta h$ . The axial resolution is determined by the minimum resolvable separation on the sensor. $\Delta \mathbf {z}$ pointing to the left has a negative value.
Fig. 3.
Fig. 3. Comparison of simulated and theoretical two-point resolution at different depth planes for the three cases of Fourier microlens designs: Fourier light field microscope’s MLA, RUM and our Fourier DiffuserScope’s RMM. (a) Lateral resolution and (b) axial resolution at different depth planes. The MLA used in Fourier light field microscope (red solid line) and the random uni-focal microlenses (blue solid line) have the best resolution at the native focal plane ($z=0$) but the performance degrades rapidly outside a small range of depth planes ($z=-10$ µm to $z=10$ µm), as predicted by theory (cyan dashed line). The RMM used in our Fourier DiffuserScope (orange solid line) has slightly worse resolution at $z=0$, but achieves good resolution across a much larger depth range ($z=-80$ µm to $z=90$ µm). Within this range, the resolution stays fairly close to the predicted multi-focal resolution (magenta dashed line).
Fig. 4.
Fig. 4. Simulations comparing field-of-view (FOV) for different microlens designs. (a) The FLFM (with MLA) reconstruction suffers from ghosting replicas (green regions in the error map) due to its periodic structure. Both the RUM and the RMM reconstruct the phantom successfully. The error of the random diffusers mainly occurs at sharp edges, which can be fixed by adding total variation regularization. Error = reconstruction $-$ ground truth. (b) Cosine similarity between the on-axis PSF and off-axis PSFs is used to quantify the shift-invariance assumption. The MLA has the highest similarity value (red), but its FOV is limited by the microlens pitch. The similarity of RUM (blue) and RMM (orange) are all above $75 \%$ across the full objective FOV.
Fig. 5.
Fig. 5. Simulated 2D measurements and 3D reconstructions of a sparse spiral object with different microlens designs. The ground truth object is a $200$ µm-long spiral made of spheres. The Fourier light field microscope (MLA) and the RUM only resolve the spheres in the area around the native focal plane (green shaded area), whereas our Fourier DiffuserScope (RMM) extends the depth range to cover almost the entire volume.
Fig. 6.
Fig. 6. Experimental results. (a) Two sample PSFs measured with a point source at $z= 0$ µm and $z= 200$ µm depth planes, as well as the 3D PSF plotted with different depth planes color-coded according to the color bar. (b) Experimentally measured resolution, defined as the minimum separation distance at which two sub-resolution fluorescent beads are resolvable. Across the $280$ µm depth range from $z=-150$ µm to $z=130$ µm, the lateral resolution is $< 3$ µm and the axial resolution is less than or equal to $4$ µm. (c) Raw measurements and 3D reconstructions of a GFP-tagged C. elegans recorded at 25 fps. The depth across a 80 µm range is color-coded according to the color bar. The full video is in Visualization 1.
Fig. 7.
Fig. 7. Optimized design of the relay lens in Zemax OpticStudio. The optimized lens set consisting of off-the-shelf elements is shown in (a) orange box, and in (c) its resulting footprints from different field points mostly overlap. However, if a single achromatic doublet with similar focal length is used as the relay lens shown in (b) orange box, the footprints in (b) contains huge aberration and the shift-invariance assumption does not hold.

Tables (2)

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Table 1. Parameter definitions for the optical system.

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Table 2. Lens prescription table.

Equations (7)

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y = z h z x z = H x .
x ^ = argmin x 0 1 2 y H x 2 2 + τ d i a g ( γ ) x 1 .
R l a t e r a l = 1.22 λ 2 NA eff = 1.22 λ N 2 NA obj .
M = f T L f o b j f a v e f R L .
Δ c = p f a v e 2 1 | z d e f o c u s | = p f a v e 2 f T L 2 | Δ z | f R L 2 f o b j 2 .
R a x i a l = N N 1 1 N A o b j R l a t e r a l = N 2 N 1 1.22 λ 2 N A o b j 2 .
D O F m i c r o l e n s = λ n r NA eff 2 + n r s M NA eff .