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Holographic tomography: techniques and biomedical applications [Invited]

Vinoth Balasubramani, Arkadiusz Kuś, Han-Yen Tu, Chau-Jern Cheng, Maria Baczewska, Wojciech Krauze, and Małgorzata Kujawińska

Open Access Open Access

Abstract

Holographic tomography (HT) is an advanced label-free optical microscopic imaging method used for biological studies. HT uses digital holographic microscopy to record the complex amplitudes of a biological sample as digital holograms and then numerically reconstruct the sample’s refractive index (RI) distribution in three dimensions. The RI values are a key parameter for label-free bio-examination, which correlate with metabolic activities and spatiotemporal distribution of biophysical parameters of cells and their internal organelles, tissues, and small-scale biological objects. This article provides insight on this rapidly growing HT field of research and its applications in biology. We present a review summary of the HT principle and highlight recent technical advancement in HT and its applications.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (19)
Fig. 1.
Fig. 1. Basic modules of holographic tomography: FAT, full-angle tomography; LAT, limited-angle tomography.

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Fig. 2.
Fig. 2. Illustration of a three-dimensional volumetric sample arrangement with spatially distributed refractive values. Reprinted from [54].

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Fig. 3.
Fig. 3. Simplified illustration of holographic tomography image recording, spatial frequency mapping, and 3D image reconstruction of the object used. Reprinted from [54].

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Fig. 4.
Fig. 4. Spatial cutoff frequency coverages of (a) microscopic imaging (single illumination) and (b) tomographic imaging system (multiple illuminations). Reprinted from [54].

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Fig. 5.
Fig. 5. Comparison of coherent transfer functions (CTFs) in three-dimensional space. (a),(b) Single-direction SR approach in which the missing frequency coverage can be seen in the inset images, (c) full-angle SR CTF shows an isotropic frequency coverage. (d),(e) Single-axis ( $x$ and $y$ axis) beam rotation CTF, (f) BRCTF of ${x} {-}{y}$ directions offers laterally extended frequency coverages, but there are still missing frequencies in the axial direction as shown in the inset images. (g) The integrated dual-mode approach offers UFO-like-shaped CTF with benefits of both beam and sample rotation approaches as the sectional images shown in (h) and (i).(j) Shows the extended isotropic frequency coverages in 2D as shown in (k), (l). Reprinted from [57,58].

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Fig. 6.
Fig. 6. Sample rotation HT with rotary holder. (a) Experimental schematic,(b) HT system photo. CL, condenser lens; PD, Petri dish; MO,microscope objective; RH, rotary holder. Reprinted from [77].

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Fig. 7.
Fig. 7. Wave propagation nature of the capillary supported approach. W,plane wave; B1, first boundary of the capillary generatescylindrical wave; S, sample; B2, second boundary of thecapillary creates the aberration in the sample wave; B3, Petridish boundary creates the deformation of the wave field. Reprinted from [87].

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Fig. 8.
Fig. 8. Experimental schematic of the coaxial rotation HT. BS, beamsplitter; CMOS, image sensor. Reprinted from [78].

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Fig. 9.
Fig. 9. Experimental schematic of sample rotation HT. Green representation shows the DHM for the hologram recording, red representation shows the HOT for the sample manipulation, and blue representation shows the fluorescent microscope. Reprinted from [82].

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Fig. 10.
Fig. 10. Mach–Zehnder-based HT with a two-axis galvanometer mirror scanner (GM) and illumination optical system (L2-O1). Reprinted from [98].

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Fig. 11.
Fig. 11. (a) Beam rotation HT using LCoS SLM, reprinted from [63]. The unwanted zero order is blocked by a spatial filter ${F}$ placed in the Fourier plane of the T1-T2 ${4f}$ system and the moving ${+}{1}$ order is transmitted to illuminate the sample. (b) Beam rotation in HT using a DMD, reprinted from [64].

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Fig. 12.
Fig. 12. Single-shot HT with projection multiplexing for a full projection set using a microlens array (MLA) to generate illuminations. Reprinted from [110].

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Fig. 13.
Fig. 13. RI calibration object: (a) model, (b) horizontal and vertical cross sections of the RI measured with beam rotation tomography. Reprinted from [115].

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Fig. 14.
Fig. 14. Comparison of reconstruction results obtained with (a), (b), (g), (h) direct inversion; (c), (d), (i), (j) Gerchberg–Papoulis algorithm with nonnegativity constraint, and (e), (f), (k), (l) Gerchberg–Papoulis algorithm with additional constraint in the form of automatically generated object support. The objects presented are (a)–(f) 3D-printed cell phantom and (g)–(l) keratinocyte cell. The red contour shows the extent of the object support generated with the auxiliary algorithm in the GP-SC method. Reprinted from [119].

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Fig. 15.
Fig. 15. HT measurements and analysis of four cell lines: (a) 3D visualization of cell lines NRK-52E and RAW 264.7, (b) 2D RI cross section of the RI distribution in the best focal plane of live and fixed NRK-52E and RAW 264.7 cells, (c) differences in RI between nucleolus–nucleus and nucleolus–cytoplasm for four representative cell lines. Reprinted from [148].

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Fig. 16.
Fig. 16. HT reconstruction of Candida rugosa (ATCC 200555). (i): RI distribution comparison of center slice results between (a) full-angle sample rotation, (b) beam rotation, and (c) integrated tomography approaches. Scale bar: 3 µm, color bar: RI values. (ii): subcellular tomographic reconstruction. Reprinted from [57].

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Fig. 17.
Fig. 17. Four refractive index images of high and continuous regions of chromosome of DM cells during four stages of mitosis. Reprinted from [150].

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Fig. 18.
Fig. 18. (a) Coronal, (b) sagittal, and (c) axial cross sections of HT reconstructed refractive index contrast of an optically cleared 3 day old zebrafish larva. Reprinted from [160].

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Fig. 19.
Fig. 19. Sliced image comparison of a normal colon tissue (a) bright field and stained with H&E staining and (b) an unstained neighbor tissue imaged with HT. Reprinted from [161].

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Equations (9)

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U t ( r ′ ) = ∫ O ( r ) U o ( r ) G ( r ′ − r ) d r ,
O ( r ) = K 2 [ n s 2 ( r ) − n m 2 ] .
U t ( x ′ , y ′ , z ′ = l ) = ∬ exp ( j ( u x ′ + v y ′ ) ) d u d v × ∭ { ( O ( x , y , z ) U o ( x , y , z ) ) / k 2 − u 2 − v 2 } × exp ⁡ [ − j ( u x + v y ) ] exp [ j k 2 − u 2 − v 2 ( l − z ) ] d x d y d z .
U o ( x , y ; m Δ z ) = U o ( x , y ; ( m − 1 ) Δ z ) × x o ( x , y ; ( m − 1 ) Δ z ) h ( x , y ; Δ z ) ,
F x , y m i c r o s c o p y = 2 n sin ⁡ θ λ a n d F z m i c r o s c o p y = n ( 1 − cos ⁡ θ ) λ .
F x , z S R = 4 n sin ( θ / 2 ) λ a n d F y S R = 2 n sin ⁡ θ λ .
F x , y B R = 4 n sin ⁡ θ λ a n d F z B R = 2 n ( 1 − cos ⁡ θ ) λ .
F x , y I D T = 4 n sin ⁡ θ λ a n d F z I D T = 2 n sin ⁡ θ λ .
F x , y , z i s o t r o p i c = 4 n sin ⁡ θ λ .
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