Abstract

Reflection phase imaging provides label-free, high-resolution characterization of biological samples, typically using interferometric-based techniques. Here, we investigate reflection phase microscopy from intensity-only measurements under diverse illumination. We evaluate the forward and inverse scattering model based on the first Born approximation for imaging scattering objects above a glass slide. Under this design, the measured field combines linear forward-scattering and height-dependent nonlinear back-scattering from the object that complicates object phase recovery. Using only the forward-scattering, we derive a linear inverse scattering model and evaluate this model’s validity range in simulation and experiment using a standard reflection microscope modified with a programmable light source. Our method provides enhanced contrast of thin, weakly scattering samples that complement transmission techniques. This model provides a promising development for creating simplified intensity-based reflection quantitative phase imaging systems easily adoptable for biological research.

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

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2019 (11)

M. E. Kandel, C. Hu, G. N. Kouzehgarani, E. Min, K. M. Sullivan, H. Kong, J. M. Li, D. N. Robson, M. U. Gillette, and C. Best-Popescu, “Epi-illumination gradient light interference microscopy for imaging opaque structures,” Nat. Commun. 10(1), 4691 (2019).
[Crossref]

B. Simon, L. Vonna, and O. Haeberlé, “A versatile transmission/reflection tomographic diffractive microscopy approach,” J. Opt. Soc. Am. A 36(11), C18–C27 (2019).
[Crossref]

P. Ledwig and F. E. Robles, “Epi-mode tomographic quantitative phase imaging in thick scattering samples,” Biomed. Opt. Express 10(7), 3605–3621 (2019).
[Crossref]

A. Matlock and L. Tian, “High-throughput, volumetric quantitative phase imaging with multiplexed intensity diffraction tomography,” Biomed. Opt. Express 10(12), 6432 (2019).
[Crossref]

K. D. Unger, P. C. Chaumet, G. Maire, A. Sentenac, and K. Belkebir, “Versatile inversion tool for phaseless optical diffraction: tomography,” J. Opt. Soc. Am. A 36(11), C1–C8 (2019).
[Crossref]

S. Khadir, P. C. Chaumet, G. Baffou, and A. Sentenac, “Quantitative model of the image of a radiating dipole through a microscope,” J. Opt. Soc. Am. A 36(4), 478–484 (2019).
[Crossref]

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3d refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211–1219 (2019).
[Crossref]

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

Y. Xue, S. Cheng, Y. Li, and L. Tian, “Reliable deep-learning-based phase imaging with uncertainty quantification,” Optica 6(5), 618 (2019).
[Crossref]

2018 (9)

H.-Y. Liu, D. Liu, H. Mansour, P. T. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: Sparsity-driven image reconstruction under multiple scattering,” IEEE Trans. Comput. Imaging 4(1), 73–86 (2018).
[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

Y. Sun, Z. Xia, and U. S. Kamilov, “Efficient and accurate inversion of multiple scattering with deep learning,” Opt. Express 26(11), 14678–14688 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

J. M. Soto, J. A. Rodrigo, and T. Alieva, “Optical diffraction tomography with fully and partially coherent illumination in high numerical aperture label-free microscopy,” Appl. Opt. 57(1), A205–A214 (2018).
[Crossref]

R. Ling, W. Tahir, H. Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130–2141 (2018).
[Crossref]

P. Ledwig, M. Sghayyer, J. Kurtzberg, and F. E. Robles, “Dual-wavelength oblique back-illumination microscopy for the non-invasive imaging and quantification of blood in collection and storage bags,” Biomed. Opt. Express 9(6), 2743–2754 (2018).
[Crossref]

Y. Choi, P. Hosseini, J. W. Kang, S. Kang, T. D. Yang, M. G. Hyeon, B.-M. Kim, P. T. So, and Z. Yaqoob, “Reflection phase microscopy using spatio-temporal coherence of light,” Optica 5(11), 1468–1473 (2018).
[Crossref]

2017 (4)

2016 (8)

O. Avci, R. Adato, A. Y. Ozkumur, and M. S. Ünlü, “Physical modeling of interference enhanced imaging and characterization of single nanoparticles,” Opt. Express 24(6), 6094–6114 (2016).
[Crossref]

T. Kim, R. Zhou, L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

R. Horstmeyer, J. Chung, X. Ou, G. Zheng, and C. Yang, “Diffraction tomography with fourier ptychography,” Optica 3(8), 827–835 (2016).
[Crossref]

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2014 (5)

2013 (2)

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2012 (3)

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2011 (2)

2010 (5)

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Figures (5)

Fig. 1.
Fig. 1. (a) Reflection intensity phase microscope design with illumination grid and imaging geometry. A scannable LED in a conjugate plane to the objective’s back focal plane enables programmable oblique illumination up to 0.25NA. (b) Normalized reflection images, Fourier coverage, and model transfer functions for illuminations at 0.17, 0, and 0.2NA. The phase transfer function show asymmetric behavior at oblique illumination and cancellation for on-axis illumination. (c) The average real refractive index (RI) contrast reconstructions from transmission Intensity Diffraction Tomography [50] (Red) and our reflection system (Blue). Transmission better recovers large nuclear structures while reflection captures thin membrane features.
Fig. 2.
Fig. 2. (a) Illumination and expected scattering behavior under transmission and reflection geometries. (b) Comparison of on-axis brightfield and differential phase contrast (DPC) images of Henrietta Lacks (HeLa) cells in reflection and transmission. DPC images were generated from the difference of the images taken with the shown illuminations (Green - Red). The additional forward-scattering in reflection enhances thin cellular feature contrast.
Fig. 3.
Fig. 3. (a) 3D Cuboid distribution above partially reflective surface from DDA simulations. (b) Cuboid intensity contrast ($\Delta n_{\mathrm {re}}=0.01$, $h=210nm$, $\lambda =530nm$) with red ovals highlighting evaluated contrast region. (c) Linear reflection model (Orange) and DDA simulation (blue) intensity contrast under 0.2NA illumination for objects with heights $0.12-1\mu m$ and increasing RI contrast for $\lambda =530nm$. The linear model adequately predicts the contrast at weak object permittivities but overestimates larger RI object contrast. (d) Intensity contrast at fixed real RI ($\Delta n_{\mathrm {re}} = 0.01,0.2$ for d$_1$, $_2$ respectively) with increasing height across multiple wavelengths. The nonlinear term’s period follows $\lambda /2$ until high RI contrast objects are evaluated. (e) Intensity contrast highlighting linear trends for increasing RI contrast at fixed object heights.
Fig. 4.
Fig. 4. (a) Linear model reconstructions of cuboid average permittivity contrast. The color scales are adjusted based on the ground truth object’s properties to show correctly recovered cuboids in red. Weak permittivity (left) objects are more accurately recovered compared to strong permittivity (right) structures. (b) Cuboid reconstruction error at $\lambda =530nm$ across different object heights at fixed permittivity contrast values. Nonlinear error is always present from backscattering, and increasingly tall objects quickly become underestimated from the enhanced sensitivity of our model. (c) Cuboid reconstruction error at $\lambda =530nm$ across different permittivity contrasts for fixed object heights. The error is linear with permittivity contrast following Eq. (5). (d) Cuboid reconstruction error for a $\Delta n_{\mathrm {re}}=0.01$ object across multiple heights at different wavelengths ($\lambda = 450, 530, 650nm$). We observe nonlinear error also shifts with period following Fig. 3(d).
Fig. 5.
Fig. 5. (a) Full FOV complex RI contrast reconstructions for reflection and transmission (HeLa cells); (b) Outset regions show (1) cell boundaries and filopodia, and (2) cell nuclei reconstructions; (c) Cross-sections compare reflection and transmission average RI contrast reconstructions and overlays of transmission and reflection reconstructions. Outset 1 show better membrane structure contrast in reflection than transmission with agreement on the recovered average RI contrast values. Outset 2 shows reflection underestimates the RI contrast of tall nuclear features as expected from simulation.

Equations (17)

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u 0 ( r , z | ν i ) = A e j 2 π ν i r ( e j 2 π η ( ν i ) z + R ( ν i ) e j 2 π η ( ν i ) z ) ,
u t o t ( r , z | ν i ) = u r ( r , z | ν i ) + 0 O ( r , z ) u 0 ( r , z | ν i ) G ( r r , z z ) d 2 r d z ,
G ( r r , z z ) = j 1 η ( ν ) e j 2 π ( ν ( r r ) η ( ν ) z ) [ e j 2 π η ( ν ) z + R ( ν ) e j 2 π η ( ν ) z ] d 2 ν ,
u s ( r , z | ν i ) = j A k 0 2 4 π h ( r ) 0 1 η ( ν ) e j 2 π ( ν r η ( ν ) z ) [ e j 2 π η + ( ν ) z + R ( ν i ) e j 2 π η ( ν ) z + R ( ν ) e j 2 π η ( ν ) z + R ( ν i ) R ( ν ) e j 2 π η + ( ν ) z ] Δ ϵ ( r , z ) e j 2 π ν r d z d 2 r d 2 ν ,
U s ( ν , z | ν i ) = j A k 0 2 4 π e j 2 π η ( ν ) z η ( ν ) [ F ( ν , r | ν i ) + B ( ν , r | ν i ) ] e j 2 π ν r d 2 r ,
F ( ν , r | ν i ) = Δ ϵ ( r ) h ( r ) s i n c ( π η ( ν ) h ( r ) ) [ R ( ν i ) e j π η ( ν ) h ( r ) + R ( ν ) e j π η ( ν ) h ( r ) ]
B ( ν , r | ν i ) = Δ ϵ ( r ) h ( r ) s i n c ( π η + ( ν ) h ( r ) ) [ e j π η + ( ν ) h ( r ) + R ( ν ) R ( ν i ) e j π η + ( ν ) h ( r ) ]
C = F W H M ( | I N | ) ¯ ,
F ( ν , r | ν i ) = Δ ϵ ( r ) j 2 π η ( ν ) [ R ( ν i ) ( 1 e j 2 π η ( ν ) h ( r ) ) + R ( ν ) ( e j 2 π η ( ν ) h ( r ) 1 ) ]
U s ( v , z | ν i ) = j A k 0 2 4 π e j 2 π η ( ν ) z η ( ν ) R ( ν | ν i ) Φ ^ ( ν ) ,
I l ( r , z | ν i ) = | F 1 { U t o t , l ( ν , z | ν i ) P ( ν ) } | 2 ,
I ^ l N ( ν , z | ν i ) = C [ H r e ( ν , z | ν i ) Φ ^ r e ( ν ) + H i m ( ν , z | ν i ) Φ ^ i m ( ν ) ] ,
H i m , l ( ν , z | ν i ) = P ( ν i ) P ( ν ) D ( ν , z ) R ( ν | ν i ) + P ( ν i ) P ( ν + ) D ( ν + , z ) R ( ν + | ν i ) ,
H r e , l ( ν , z | ν i ) = j { P ( ν i ) P ( ν ) D ( ν , z ) R ( ν | ν i ) P ( ν i ) P ( ν + ) D ( ν + , z ) R ( ν + | ν i ) } .
m i n Φ ^ r e , Φ ^ i m l = 1 L | | I ^ l N ( H i m , l Φ ^ i m + H r e , l Φ ^ r e ) | | 2 2 + τ i m | | Φ ^ i m | | 2 2 + τ r e | | Φ ^ r e | | 2 2 ,
Φ r e ( r ) = F 1 { 1 T [ ( l = 1 L | H i m , l | 2 + τ i m ) ( l = 1 L H r e , l I ^ l N ) ( l = 1 L H r e , l H i m , l ) ( l = 1 L H i m , l I ^ l N ) ] }
Φ i m ( r ) = F 1 { 1 T [ ( l = 1 L | H r e , l | 2 + τ r e ) ( l = 1 L H i m , l I ^ l N ) ( l = 1 L H i m , l H r e , l ) ( l = 1 L H r e , l I ^ l N ) ] }

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