Optical diffraction tomography can be performed with low phototoxicity and photobleaching to analyze 3D cells and tissues. It is desired to develop high throughput and powerful data processing capabilities. We propose high bandwidth holographic microscopy (HBHM). Based on the analyticity of complex amplitudes, the unified holographic multiplexing transfer function is established. A high bandwidth scattering field is achieved via the k-space optical origami of two 2D wavefronts from one interferogram. Scanning illumination modulates the high-horizontal and axial k-space to endow synthetic-aperture from 2D high space-bandwidth product (SBP) scattering fields. The bright-field counterpart SBP of a single scattering field from HBHM is 14.6 megapixels, while the number of pixels is only 13.7 megapixels. It achieves an eight-fold SBP enhancement under the same number of pixels and diffraction limit. The HBHM paves the way toward the performance of high throughput, large-scale, and non-invasive histopathology, cell biology, and industrial inspection.

Rapid and accurate estimation of the viability of biological cells is important for assessing the impact of drugs and physical or chemical stimulants. To comprehend the underlying pathophysiology and clinical situations, microscopic analyses of biopsied and resected tissues are essential.1,2 Most of the microscopic specimens are translucent to visible light. The visualization of cells can be increased by transforming substrates into colorful or fluorescent products using exogenous labels like hematoxylin and eosin (H&E) or immunohistochemical labeling. The tedious labeling procedure and toxicity of the stains may have an impact on the long-term investigation of the normal physiological activities of cells.3 The explorations of three-dimensional (3D) label-free subcellular structures and their abnormal states facilitate insight into multiple pathological mechanisms, which are expected to achieve the early diagnosis and effective therapy of diseases. Therefore, non-invasive and high-throughput 3D imaging is of great significance for attaining precise and quantitative analysis of subcellular features.

The refractive index (RI) distribution correlates strongly with cellular properties, such as dry mass, proteins, lipids, and chemical concentrations. It translates into the optical thickness by taking light as a ruler, reflecting in the phase of the scattering field. Hence, accurate detection of the wavefront in spatial and temporal space is essential for the interaction between waves and samples. One must go beyond typical optical imaging and solve an inverse problem from measurement in the real domain to wavefront in the complex domain. Digital holographic microscopy (DHM), as an interferometric microscopy, provides a method for quantitative phase imaging (QPI) in weakly scattered samples with mathematical integrity.4–12 It has been used in stain-free observations of biological cells,13–16 ultra-thin incoherent imaging systems,17 and phase profiling of chemical processes.18 With the development of computing capability, the learning-based method recently enabled QPI to have the capacity for disease prediction and diagnosis.19–22 The amount of light scattering by a biological sample depends on its optical thickness and RI inhomogeneity. However, the throughput of reconstruction is limited by the number of pixels and the camera’s bandwidth.23,24 The number of pixels in a commercially available image sensor is much lower than the space-bandwidth product (SBP) of the optical microscope. The trend of label-free imaging toward existing techniques is the high throughput regarding high SBP reconstruction without sacrificing the collection efficiency and calculating burden.

The 3D Fourier space of the sample relates to multiple 2D scattering fields by the Fourier diffraction theorem. The SBP of the 2D scattering field determines the spatial scale of the corresponding 3D reconstruction. The illumination wavelength and numerical aperture (NA) are concerned with the resolving power in microscopy.25 Oblique beam illumination downshifts the high spatial frequency of the object into the coherent transfer function (CTF), containing sub-resolution information without sacrificing the imaging field of view (FOV),13,26–31 which has been used in lens-based32–34 or lens-free systems.35,36 To obtain the 3D distribution of cells and tissues, one must go beyond the typical quantities measured in phase imaging by integrating microscopy, holography, and light scattering theory.37 By mapping the 3D frequency from multiple two-dimensional (2D) scattering fields based on Fourier diffraction theory, the 3D k-space can be extended simultaneously to achieve optical diffraction tomography (ODT).13,38–46 Illumination scanning or object rotations access different 3D spatial frequencies through the relative angular changes between the sample and the illumination beams. However, ODT is generally implemented with holographic microscopy, and the maximum achievable imaging bandwidth of the 2D scattering field for ODT is still limited in the interferometric setup despite the advances in optical and electronic devices. The 3D analysis of large-scale samples may be impeded despite the growth of horizontal and vertical frequencies.

In this work, we propose a high bandwidth holographic microscopy (HBHM) that exploits 2D synthetic-aperture phase imaging and 3D RI volumetric reconstruction. To achieve high SBP scattering field reconstruction, two complex waves are optically folded in each measurement by inspiring artificial origami. The forward imaging model of HBHM is established to depict the multiplexing transfer function under modulated illuminations and holographic multiplexing precisely and elegantly. Scanning illumination modulates the high-horizontal and axial spatial frequencies, endowing 2D synthetic-aperture QPI (SA-QPI) and 3D RI tomography. An eight-fold SBP enhancement can be achieved under the same number of pixels and diffraction limit. The throughput restriction of interferometric-based diffraction tomography can be circumvented. The HBHM maximizes the available bandwidth of a single exposure. As a result, the HBHM realizes large-scale 3D tomography. Different tumor types and a variety of precursor pathologies can be visualized label-free.

The optical configuration is depicted in Fig. 1(a). The light source is an Nd:YAG continuous wave (CW) laser at a wavelength of 532 nm. Fiber-coupled-out (FCO) mode splits the laser into two beams. The dual-axis Galvano scanning mirror (GSM, GVS212, Thorlabs) periodically scans the k-space of illumination. The lens (L) and condenser lens (CL) are combined into a modulated illumination 4f system. The CL is used with the same parameters as the microscopic objective (MO). The diffracted wave from the microscope is divided into two channels, which are reflected by two mirrors (M). As shown in Fig. 1(b), channels 1 and 2 produce lateral displacements in the camera plane by adjusting two M. It created two linear and perpendicular off-axis interference fringe patterns with the reference wave. The polarizer (P) is placed in front of the camera. Two channels are simultaneously recorded by using a single camera, resulting in double high-bandwidth CTFs in one measurement. Modulated illumination is built into the HBHM to reconstruct the high-frequency of the optical field. The angle of illumination is controlled by the GSM, which corresponds to the Fourier transform (FT) of the focused pattern in the Fourier plane of the condenser lens (CL), as shown in Fig. 1(c). The higher spatial frequency in the opposite direction of the oblique illumination is downshifted in the passband of the diffraction-limited imaging system. An expanded passband of the Fourier spectrum can be obtained by synthesizing the object’s aperture from several directions. We established the framework of digital adaptive optics for the background phase aberration corrections by manipulating spatial-angular measurements in postprocessing without additional wavefront sensors or spatial light modulators, as shown in Fig. 1(d). Different angular components can be manipulated in postprocessing for aberration corrections in 2D SA and 3D RI reconstruction.47 Two expanded 3D CTFs with high bandwidth can be obtained by synthesizing the object’s aperture from several directions, as shown in Fig. 1(e). To address the resolution of HBHM, we measured the 3D point spread function by using the experimental parameters with an ideal 3D coherent transfer function and non-negative RI constraint, which is shown in Fig. 1(f).

FIG. 1.

Schematic of hardware implementation and working flow of HBHM. (a) The optical setup of the HBHM system. CW: Continuous wave. L: Lens. BS: Beam splitter; GSM: Dual-axis Galvano scanning mirror; CL: Condenser lens; MO: Microscopic objective; TL: Tube lens; M: Mirrors; P: Polarizer. (b) Optical process of optical origami and multiplexing. (c) The Fourier spectrum of illumination with different incident angles and the aperture of the diffraction-limited imaging system with a cutoff frequency kobj. (d) Illustrations of postprocessing, different angular components can be manipulated in postprocessing for numerical focusing and phase aberration corrections for 2D SA and 3D RI reconstruction, FP: Fourier plane. (e) The whole field reconstruction by using HBHM. (f) The 3D point spread function uses the experimental parameters with an ideal 3D coherent transfer function, in which the full-width at half-maximum (FWHM) is calculated.

FIG. 1.

Schematic of hardware implementation and working flow of HBHM. (a) The optical setup of the HBHM system. CW: Continuous wave. L: Lens. BS: Beam splitter; GSM: Dual-axis Galvano scanning mirror; CL: Condenser lens; MO: Microscopic objective; TL: Tube lens; M: Mirrors; P: Polarizer. (b) Optical process of optical origami and multiplexing. (c) The Fourier spectrum of illumination with different incident angles and the aperture of the diffraction-limited imaging system with a cutoff frequency kobj. (d) Illustrations of postprocessing, different angular components can be manipulated in postprocessing for numerical focusing and phase aberration corrections for 2D SA and 3D RI reconstruction, FP: Fourier plane. (e) The whole field reconstruction by using HBHM. (f) The 3D point spread function uses the experimental parameters with an ideal 3D coherent transfer function, in which the full-width at half-maximum (FWHM) is calculated.

Close modal
To achieve high SBP scattering field reconstruction, a high bandwidth multiplexing tomographic framework is established. Inspired by traditional origami, double reflectors enable optical origami in holographic recording outside of the camera’s FOV by modulating the self-coherence of diffraction waves from the microscope, as shown in Figs. 1(a) and 1(b). It forms two CTFs in the k-space, and their arrangement direction is perpendicular to the direction of kR/kR. The radius of CTF is defined by NA and the wavelength. The generalized reference beam can be expressed as Rr=R0ei2πkRr. The multiplexed hologram is23,48
Imr=Rr+S1mr+S2mr2,
(1)
where r = r1r + r2r, which represents the horizontal and vertical coordinates, and m is the mth angle of illumination. S1mr and S2mr are the complex-amplitudes of samples 1 and 2, respectively, which are FOV 1 and FOV 2 in HBHM. For a plane incident wave, the sample fields are Ŝ1mk=Ŝ1kkmP1mk and Ŝ2mk=Ŝ2kkmP2mk, where Ŝ1k and Ŝ2k are the FT of samples 1 and 2, respectively, and Ŝ1mk and Ŝ2mk are the Fourier spaces of samples 1 and 2 under the mth angle of illumination, respectively. kkx,ky is the transverse wave vector. km is the wave vector of the incident plane wave. P1mk and P2mk are the 2D pupil functions of the imaging system under a specific incident angle. The interferogram is normalized by the intensity of the reference wave Rr. The normalized multiplexed hologram is
Imnr=ei2πkRr+s1mr+s2mrei2πkRr2,
(2)
where Imnr is the normalized interferogram by the intensity of reference wave, s1mr=S1mr/R0, s2mr=S2mr/R0, where S1mr and S2mr are the complex-amplitude of samples 1 and 2, respectively. We assume a complex-function to describe the multiplexing complex-waves Emnr=ei2πkRr+s1mr+s2mrei2πkRr. It can be transformed to RelnEmnr=lnImnr/2, where Re. denotes the real part of complex values. The high SBP wavefronts can be transferred and encoded for sideband distribution by introducing holographic multiplexing. The two chief ray directions of object waves are assumed to be placed on the x-z plane. The angle between the chief ray direction of the reference wave and the x-z plane is θ. By changing the angle θ of the reference wave in Fig. 1(b), the negative domain in lnEmnr of the reference wave vector k=kR/kR is vanished in the Fourier space. The asymmetric Fourier space indicates the analyticity in the upper half-plane. Causality and analyticity are interchangeable.50–52 In the pixelated matrix, the imaginary part of lnEmnr is calculated by the directional Hilbert transform,53,
ImlnEmnr=iF1FRelnEmnrsgnkk,
(3)
where “sgn” is the signum function, Im. denotes the imaginary part of complex values, F is the 2D FT. k = k1k + k2k represents the coordinates in the spatial frequency domain and k=kR/kR. The multiplexing complex-waves are expressed as
S1mr+S2mr=R0explnImnr2+F1FlnImnr2sgnkk+i2πkRrR0ei2πkRr,
(4)
which shows that multiplexing complex-waves can be fully recovered from the interferogram based on the analyticity of lnEmnr. By using the variable sparse splitting framework in reconstructed complex-waves,49 the phase background aberration can be separated from S1mr and S2mr. Both waves in the Fourier space are distributed in the half-plane of the reference wave vector k=kR/kR. The multiplexing complex-waves carried by two FOVs can be retrieved with the maximum bandwidth Bo = 0.5Bc, where Bo and Bc are the bandwidths of CTF and the camera, respectively. A high bandwidth scattering field is obtained via the optical origami of two 2D FOVs from one interferogram. By comparing the conventional ODT with the interferometric-based bandwidth Bo = 0.25Bc, an eight-fold increase in the Fourier space area in both complex-waves can be promoted. Therefore, the SBP is increased by eight-fold with the same number of pixels and the same diffraction limit. Tilt focal plane calibration is performed in both reconstructions (see supplementary material).

The object wave is described by S1mr=Arexpiϕr, where Ar and ϕr represent the amplitude and phase components of the object wavefront, respectively. For the 2D k-space, the higher spatial frequency in the opposite direction of the oblique illumination is downshifted in the passband of the diffraction-limited imaging system. Three complex-amplitudes whose k-space around the origin is enough for the reconstruction.43,54 The complex-amplitude of samples 1 S1r can be reconstructed by an aberration-free synthetic aperture (see supplementary material).

For the 3D k-space, we achieve 3D RI reconstruction by HBHM. The total field under an angle of illumination S1mr can be written as the superposition of the incident field S1mir and the scattering field S1msr, S1mr=S1mir+S1msr. Based on scalar diffraction, the object has a 3D RI given by n1r, which is quantitatively correlated with the scattering potential O1r using the equation: O1r=k02n1r2nm, where r=x,y,z is the 3D spatial vector here. The 3D frequency vector in Fourier space is located on the Ewald sphere with a radius of k0 = nm/λ under the constraint kz=k02k2.38,39 The projection of the 2D pupil function onto the Ewald sphere can be achieved by the generalized aperture PEwaldk=Pkδ(kzk02k2).5 We considered Rytov approximations here.55 The linearized relation between the first-order scattering field S1msr and the 3D object function Or is
Ô1kkm=4πikzŜ1mskPmkδkzk02km2,
(5)
where Ô1k and Ŝ1msk are the FT of Or and S1msr. Each measurement of the scattering field Ŝ1msk provides limited spatial frequency by Eq. (5). Adjusting km to enlarge the accessible k-space, the 3D RI tomogram can be achieved by the Fourier diffraction theorem.38 The multi-layer Born model,56 learning method,57,58 and modified Born series59 can be taken into consideration in the HBHM for the multiple scattering of thick specimens. For S2mr from channel 2 in HBHM, it is processed with the same calculations as S1mr. Then the aberration-free synthetic aperture complex-amplitude S2r can be reconstructed. The corresponding 3D RI from channel 2 can be reconstructed. To combine wide FOV from two channels in HBHM, accurate 2D image alignment between two complex-amplitudes S1r and S2r in the x-y axis was achieved by correlation-based subpixel adjustment.60 A wide-field FOV reconstruction can be achieved when there is an overlapped area between two FOVs from two object waves. For the 3D FOV stitching, the axial alignment between RI n1r and n2r in the x-z slice or y-z slice needs to be processed with the correlation-based subpixel adjustment. If there is no overlapping area between S1mr and S2mr, the reconstructions from HBHM can be considered two separate FOVs. In HBHM, the forward imaging model of the high SBP 2D scattering field is established by holographic multiplexing. Scanning illumination modulates the high-horizontal and axial spatial frequencies, endowing both 2D SA-QPI and 3D RI tomography with multiple 2D high SBP scattering fields. The throughput restriction of interferometric-based diffraction tomography can be circumvented by the proposed framework.

Figures 2(a) and 2(b) show the CTF of conventional DHM and HBHM. The radius of CTF can be adjusted through the 4f system with the same NA. Figures 2(c) and 2(d) show the detections from DHM and HBHM under different angles of illumination, respectively. The top of the detections shows the corresponding illumination spectrum. The blue box represents the equivalent imaging FOV in Fig. 2(d). The magnification in Fig. 2(d) is half that in Fig. 2(c) with the same NA, but the radius of CTF is double. Therefore, the area of each CTF and imaging FOV in Fig. 2(d) is four times larger than that in Fig. 2(c) with the same number of pixels. Considering two object waves multiplexing in HBHM, the area of CTFs and imaging SBP in HBHM are eight-fold enhancements of conventional DHM. Figures 2(e) and 2(f) show the spectrum of detection under θ1 angle of illumination from DHM and HBHM, respectively. The blue area represents the zero-order term, and the left and right terms are the twin images and object terms. The areas of CTFs are stationary under different angles of illumination.

FIG. 2.

(a) CTF of conventional DHM, where M is the magnification. (b) CTF of HBHM, where M1 = M/2. (c) Measurements for different angles of incidence in conventional DHM. (d) Measurements for different angles of incidence in HBHM. (e) The k-space of detection from DHM. (f) The k-space of detection from HBHM. (g) The logarithm of detection from HBHM, whose phase is extracted from the Hilbert transform of the logarithm of detection, is shown in the red line in (d) with θ1. (h) The logarithm of detection from HBHM, whose phase is extracted from the Hilbert transform of the logarithm of detection, and the line is shown at the red line in (d) with θn. (i) Original 3D RI distribution of the object. (j) The 3D RI reconstruction from DH-DT by using (c). (k) The 3D RI reconstruction from HBHM by using (d), and the number of pixels in single detection is the same as (j), but eight-fold SBP enhancement can be achieved by HBHM.

FIG. 2.

(a) CTF of conventional DHM, where M is the magnification. (b) CTF of HBHM, where M1 = M/2. (c) Measurements for different angles of incidence in conventional DHM. (d) Measurements for different angles of incidence in HBHM. (e) The k-space of detection from DHM. (f) The k-space of detection from HBHM. (g) The logarithm of detection from HBHM, whose phase is extracted from the Hilbert transform of the logarithm of detection, is shown in the red line in (d) with θ1. (h) The logarithm of detection from HBHM, whose phase is extracted from the Hilbert transform of the logarithm of detection, and the line is shown at the red line in (d) with θn. (i) Original 3D RI distribution of the object. (j) The 3D RI reconstruction from DH-DT by using (c). (k) The 3D RI reconstruction from HBHM by using (d), and the number of pixels in single detection is the same as (j), but eight-fold SBP enhancement can be achieved by HBHM.

Close modal

Figures 2(g) and 2(h) show the logarithm of detections and their Hilbert transform argEmnr under θ1 and θn angles of illumination, respectively. The actual implementation of the Hilbert transform is realized in the Fourier domain by using the fast FT and the directional sign function by using Eq. (3). The full field of Emnr is thus derived. The full field can be easily calculated by Eq. (4). Under a large angle of illumination, it results in changing the cycle of interference fringe but with the same area of CTFs as shown in Figs. 2(b) and 2(f). Figure 2(i) shows the original 3D RI of one object with a background RI of 1.336. Figure 2(j) shows the tomogram from conventional DHM-based diffraction tomography (DH-DT) by using the detections in Fig. 2(c). Figure 2(k) shows the tomogram from conventional HBHM by using the detections in Fig. 2(d). Both of them are reconstructed with 1000 × 1000 pixels2. By comparing with the conventional DH-DT, the FOV of reconstruction is increased by eight-fold with the same number of pixels and the same diffraction limit.

We demonstrated the high bandwidth performance of 2D SA-QPI based on HBHM. The quantitative phase microscopic target (QPMT, Benchmark Technologies Inc.) for quantitative phase microscopy is shown in Fig. 3(a). A USAF 1951 resolution target and an optically focused star with a feature height of 300 nm are both included in the QPMT. Figure 3(b) shows the four multiplexed holograms under four different oblique illumination angles by HBHM with 1200 × 1920 pixels. The camera’s entire area is 7.03 × 11.25 mm2. The same settings as for MO are utilized with the CL (MY20X-804, 20×, NA = 0.42). The pixel size is 5.86 μm.

FIG. 3.

SA-QPI reconstruction for quantitative phase target. (a) The QPMT. (b) The multiplexed hologram under four different oblique illumination angles by HBHM. (c) Four Fourier spectra of (b). (d) The k-space of the HBHM. The red dotted circle and blue one represent the k-space obtained under normal illumination and four oblique illumination angles, respectively. (e) The SA-QPI reconstruction using HBHM. (f) The phase reconstruction by using conventional DHM. (g) The zoom view of (e). (h) The zoom view of (f). (i) Comparison of the resolution by HBHM and conventional DHM from (g) and (h). (j) The phase profiles from the purple line in (e).

FIG. 3.

SA-QPI reconstruction for quantitative phase target. (a) The QPMT. (b) The multiplexed hologram under four different oblique illumination angles by HBHM. (c) Four Fourier spectra of (b). (d) The k-space of the HBHM. The red dotted circle and blue one represent the k-space obtained under normal illumination and four oblique illumination angles, respectively. (e) The SA-QPI reconstruction using HBHM. (f) The phase reconstruction by using conventional DHM. (g) The zoom view of (e). (h) The zoom view of (f). (i) Comparison of the resolution by HBHM and conventional DHM from (g) and (h). (j) The phase profiles from the purple line in (e).

Close modal

Figure 3(c) shows the corresponding k-space of Fig. 3(b). The spatial bandwidth utilization is 66.5%, which is defined as the areas’ ratio of the object and its conjugate Fourier spectra to camera bandwidth.23 The k-space of the HBHM is depicted in Fig. 3(d). Figure 3(e) shows SA-QPI reconstruction by using HBHM. The total imaging area in the camera plane is 152.27 mm2, and the overlapping area between the two channels is 5.91 mm2. It expands the FOV of the imaging system by 1.96 times. The illumination k-space on the top of the scale bar displays the scanning illumination corresponding to Fig. 1(f). An expanded NA of the k-space with a radius of NA + NAscan ≈ 1.7NA is achieved horizontally and vertically. The NAscan is determined by the scanning NA of the illumination beam. Figure 3(f) shows the reconstruction of the phase USAF-1951 target by conventional DHM. Figures 3(g) and 3(h) show the resolution comparison. The finest distinguishable pattern is group 9, element 2 under the conventional DHM. By using HBHM, the finest distinguishable pattern is group 9, element 6, with a linewidth of 548 nm. The corresponding phase profiles are shown in Fig. 3(i). Figure 3(j) shows the reconstructed phase profiles from the purple line in Fig. 3(e). Thanks to the combination of the physical detection of frequencies and the direct complex deconvolution model of high bandwidth multiplexing, HBHM reflects the non-iterative resolution expansion on the premise of retaining the FOV.

Figure 4 shows the SA-QPI of normal intestinal endocrine tumors using HBHM. The CL (UPlanXApo, 20×, NA = 0.8) is used with the same parameters as MO. The pixel size is 5.86 μm. We prepared two consecutive tissue slides. One is conventional H&E staining, and the other is unlabeled. Figure 4(a) shows the full-field SA-QPI reconstruction of label-free tissue using HBHM. The radius of the object’s bandwidth is double that of the conventional DHM, so the area of the object’s CTF and imaging FOV in one channel are four-fold enhancements with the same number of pixels. The total area of the object’s bandwidth and FOV is an eight-fold enhancement of reconstruction. The comparison of FOV is shown in Fig. 4(a). The synthetic NA is close to 1.1. The two channels can combine into one entire FOV in HBHM. Figures 4(b) and 4(c) depict the two regions of interest (ROIs) of Fig. 4(a), respectively. They show the comparisons of the label-free tissue image, H&E staining image, and SA-QPI image. The bright-field image is captured by a microscope with 20× magnification and 0.7 NA. The phase of the label-free tissue is consistent with the in-focus bright-field images of the H&E-stained tissue. Overall tissue anatomy and features are seen in both the H&E-stained and phase images. It provides high-contrast images of weak-scattered samples and a quantitative evaluation of their optical thickness profiles. It is possible to expand the bandwidth and FOV in 3D k-space, promoting applications in large-scale physiology.

FIG. 4.

SA-QPI reconstruction for label-free pathological sample. (a) The reconstructed phase of the normal intestinal endocrine tumor by using SA-QPI in HBHM. The yellow box is the FOV area using conventional DHM. The blue box is the FOV area of the camera. The magnification is 40×. (b) and (c) The ROIs of (a), the bright-field image of the label-free tissue, and its twin H&E staining tissue were considered for comparison.

FIG. 4.

SA-QPI reconstruction for label-free pathological sample. (a) The reconstructed phase of the normal intestinal endocrine tumor by using SA-QPI in HBHM. The yellow box is the FOV area using conventional DHM. The blue box is the FOV area of the camera. The magnification is 40×. (b) and (c) The ROIs of (a), the bright-field image of the label-free tissue, and its twin H&E staining tissue were considered for comparison.

Close modal

We demonstrated the high bandwidth performance of 3D RI tomography based on HBHM. Figure 5 shows the RI tomogram of the Polymethyl Methacrylate (PMMA) microspheres with a diameter of 15 µm, and its RI is n = 1.490 ± 0.005. The beads were sandwiched between coverslips with sunflower seed oil. The RI of sunflower seed oil can be assumed to be uniformly homogeneous, nm = 1.475. The CL (UPlanXApo, 20×, NA = 0.8) is used with the same parameters as MO. The pixel size is 5.86 μm. Rytov approximations with total variation regularization and the non-negative constraint were employed to reconstruct the RI tomogram.39  Figure 5(a) shows the wide FOV RI tomographic reconstruction by using the HBHM. The illumination k-space on the top of the scale bar displays the scanning illumination corresponding to Fig. 1(f). A total of 90 angles are used for 3D tomography. Figures 5(b) and 5(f) show the ROI 1 and ROI 2 of Fig. 5(a), which show the x–y, xz, and yz slices of the RI tomogram, respectively. The reconstructed tomogram shows an RI difference of Δn = 0.015 ± 0.005 between the bead and its surrounding medium. The rendered volumetric RI distribution of the bead cluster is presented in Figs. 5(c) and 5(g). Figures 5(d)5(e) and 5(h)5(i) show the cross-sectional RI distribution in the green line of the xy plane and the xz plane, respectively. The overall morphology and the mean RI value of the beads are in good agreement with the object’s specifications provided by the manufacturer. By combining the physical detection of 3D frequencies with a high bandwidth multiplexing framework, 3D high bandwidth reconstruction can be achieved from multiple 2D high SBP scattering fields. Future directions are to push high-throughput tomography toward overall label-free tissue or cell functionalities.

FIG. 5.

Cross-sectional slices of a reconstructed RI tomogram of PMMA microspheres with a diameter of 15 μm by HBHM. (a) Wide FOV reconstruction from HBHM; the yellow box is the reconstruction by conventional interferometric DHM-based diffraction tomography (DH-DT). The blue box represents the range of the camera’s FOV. Scale bars: 30 μm. The magnification is 40×. (b) Cross-sectional slices of a cluster of PMMA microspheres in the xy, xz, and yz planes of the RI tomograms ROI 1. Scale bars: 15 μm. (c) Rendered RI distribution of (b) as a volume of bead cluster structure. (d) Cross-sectional RI distribution in the green line of the xy plane in (b). (e) Cross-sectional RI distribution in the green line of the xz plane in (b). (f) Cross-sectional slices of a cluster of PMMA microspheres in the xy, xz, and yz planes of the RI tomograms ROI 2. Scale bars: 15 μm. (g) Rendered RI distribution of (f) as a volume of bead cluster structure. (h) Cross-sectional RI distribution in the green line of the xy plane in (f). (i) Cross-sectional RI distribution in the green line of the xz plane in (f).

FIG. 5.

Cross-sectional slices of a reconstructed RI tomogram of PMMA microspheres with a diameter of 15 μm by HBHM. (a) Wide FOV reconstruction from HBHM; the yellow box is the reconstruction by conventional interferometric DHM-based diffraction tomography (DH-DT). The blue box represents the range of the camera’s FOV. Scale bars: 30 μm. The magnification is 40×. (b) Cross-sectional slices of a cluster of PMMA microspheres in the xy, xz, and yz planes of the RI tomograms ROI 1. Scale bars: 15 μm. (c) Rendered RI distribution of (b) as a volume of bead cluster structure. (d) Cross-sectional RI distribution in the green line of the xy plane in (b). (e) Cross-sectional RI distribution in the green line of the xz plane in (b). (f) Cross-sectional slices of a cluster of PMMA microspheres in the xy, xz, and yz planes of the RI tomograms ROI 2. Scale bars: 15 μm. (g) Rendered RI distribution of (f) as a volume of bead cluster structure. (h) Cross-sectional RI distribution in the green line of the xy plane in (f). (i) Cross-sectional RI distribution in the green line of the xz plane in (f).

Close modal

We demonstrated the high bandwidth performance of 3D RI tomography based on HBHM. The magnification of the system is modified to 20× with 0.8 NA. The pixel size is 2.74 μm. Figure 6(a) shows the high-throughput wide-field RI tomogram of normal colonic mucosa by using HBHM with the reconstructed volumes of 860 × 620 × 30 μm3. The whole SBP of a single complex-amplitude reconstruction is 3.66 megapixels from the camera with 3000 × 4572 pixels2. The bandwidth of intensity becomes twice the bandwidth of its corresponding complex-amplitude. Considering the circular CTF of the microscope, the corresponding bright-field intensity counterpart of one complex-amplitude has an SBP of 14.6 megapixels. The number of pixels in the reconstruction exceeds the number of pixels in the camera. Figures 6(b)6(d) show the ROIs of RI reconstruction in Fig. 6(a), which are zoomed to highlight details over a volume of 151 × 151 × 30 μm3. Colonic mucosa structures are well-characterized by the HBHM. The alveoli structures with air spaces are shown by HBHM in the region of the normal colonic mucosa tissue. The multi-layer volumetric structure of three nucleoli in the nucleate cell is revealed in slices of the RI tomogram. The wide-field slice of the vascular tissue of the label-free colonic mucosa is shown in Fig. 6(e). Figures 6(f)6(h) show the ROIs in Fig. 6(e). The blood vessels and tissues are thicker than those in Figs. 6(a)6(d), indicating that richer protein structures exist in this zone. SBP denotes the number of resolvable points in the imaging FOV of optical imaging system. The methods of spatial throughput expansion can be divided into the real-space method and the Fourier-space method. For the conventional roadmap of high-throughput imaging, large-scale image stitching in the real-space method and iterative high-SBP techniques in the Fourier-space method exhibit relatively low SBP per measurement.26 A single image only carries a small part of the object’s information in the spatial domain or spatial frequency domain. The entire imaging process needs to collect multiple images to reconstruct a high SBP image. Data redundancy and multiple measurements are required for the convergence of the phase retrieval,32 especially in the tomographic reconstruction.34 The deterministic complex-amplitude reconstruction can be obtained by the HBHM, becoming a natural advantage for quantitative phase reconstruction and even in RI tomographic reconstruction. The HBHM enables an eight-fold FOV of the reconstruction from DH-DT without sacrificing collection speed or resolution.

FIG. 6.

High-throughput wide-field RI tomogram of label-free normal colonic mucosa by using HBHM. (a) The wide-field slice of label-free normal colonic mucosa. The whole SBP of a single complex-amplitude reconstruction is 3.66 megapixels, and its corresponding bright-field counterpart of the complex-amplitude has an SBP of 14.6 megapixels. (b)–(d) The RI reconstruction of ROI 1, ROI 2, and ROI 3 in (a), which are zoomed to highlight details at different areas in (a) over a volume of 151 × 151 × 30 μm3. Scale bars: 10 μm. (e) The wide-field slice of the vascular tissue of label-free normal colonic mucosa. (f)–(h) The RI reconstruction of ROI 1, ROI 2, and ROI 3 in (e), which are zoomed to highlight details at different areas in (e) over a volume of 151 × 151 × 30 μm3. Scale bars: 10 μm.

FIG. 6.

High-throughput wide-field RI tomogram of label-free normal colonic mucosa by using HBHM. (a) The wide-field slice of label-free normal colonic mucosa. The whole SBP of a single complex-amplitude reconstruction is 3.66 megapixels, and its corresponding bright-field counterpart of the complex-amplitude has an SBP of 14.6 megapixels. (b)–(d) The RI reconstruction of ROI 1, ROI 2, and ROI 3 in (a), which are zoomed to highlight details at different areas in (a) over a volume of 151 × 151 × 30 μm3. Scale bars: 10 μm. (e) The wide-field slice of the vascular tissue of label-free normal colonic mucosa. (f)–(h) The RI reconstruction of ROI 1, ROI 2, and ROI 3 in (e), which are zoomed to highlight details at different areas in (e) over a volume of 151 × 151 × 30 μm3. Scale bars: 10 μm.

Close modal

In summary, we have presented HBHM, which achieved high-throughput 2D synthetic-aperture phase imaging and 3D RI volumetric reconstruction. The unified holographic multiplexing transfer function is derived based on the complex amplitudes’ analyticity, which connects the 3D object distribution to the multiplexing wave distribution. In the experiment, the multiple complex-waves are optically folded in the camera in each measurement by inspiring with artificial origami. A high bandwidth scattering field is numerically anti-folded from each interferogram. Scanning illumination modulates the high-horizontal and axial spatial frequencies, endowing 2D SA-QPI and 3D RI tomography with multiple 2D high SBP scattering fields. The throughput restriction of interferometric-based diffraction tomography can be circumvented by the proposed framework. The bright-field counterpart SBP of a single scattering field from HBHM is 14.6 megapixels, while the number of pixels is only 13.7 megapixels. The reconstructed volume has an FOV of 860 × 620 × 30 μm3 under a point spread function with 0.42 μm lateral and 1.1 μm axial FWHM. Different tumor types and a variety of precursor lesions and pathologies can be visualized with label-free specimens.

With the increasing computing capability and cell diagnostic needs, non-invasive and high-throughput 3D imaging is of great significance for attaining precise and quantitative analysis with subcellular features. Thanks to the combination of the physical detection of frequencies and high bandwidth multiplexing, HBHM achieves large-scale 3D tomography without any assumptions to be made concerning real-space scanning, iteration, or sparsity. High spatial throughput imaging can be realized by using massive data acquisition, data redundancy, and calculation algorithms, which are very direct and effective. The methods of spatial throughput expansion can be divided into the real-space method and the Fourier-space method. Diffraction tomography can expand the Fourier-space from 2D to 3D. Holographic multiplexing allows us to record multiple object waves with different spatial frequencies in a single hologram, which can reduce the number of image acquisitions in tomographic imaging.61 Real-space scanning methods can shift the imaging samples to reconstruct wide-field imaging.26,62 They exhibit relatively limited SBP per measurement due to data redundancy and multiple measurements. The basic idea of the proposed framework is to increase the effective number of pixels in a single measurement. One stack of exposures is needed for 3D reconstruction in the HBHM, while eight stacks of exposures are needed in the DH-DT for the same throughput. An eight-fold SBP enhancement can be achieved under the same number of pixels and diffraction limit. The final throughput is proportional to the number of pixels acquired, which can further promote the throughput until the upper bound of the microscope.

In the future, more research is needed on imaging fresh tissues and the histological interpretation of RI information. The specificity of fluorescence-assisted techniques can be fused with high throughput holography and RI tomography to provide a wider window and more insights to investigate large-scale biological processes. RI tomograms would be utilized as complementary information, but they do not generate the same data as H&E staining. The generic approach could have far-reaching applications in histopathology and cytometry, possibly in conjunction with newly emerging machine-learning methods for segmentation and cell-type classification. The HBHM paves the way toward the performance of large-scale, non-invasive, and label-free digital pathology with high throughput. It helps to support the development of biological and material science and provides a high-dimension label-free platform for biological manufacturing, material processing, and other fields.

See the supplementary material for a detailed description of tilt calibration, high bandwidth holographic-multiplexing, aberration-free synthetic aperture quantitative phase imaging, Rytov-based tomographic reconstruction, 3D label-free tomography and H&E staining, microsphere mounting, and label-free and H&E staining tissues.

We acknowledge the funding support from the National Natural Science Foundation of China (NSFC) (Grant No. 62235009).

The authors have no conflicts to disclose.

Z.H. and L.C. proposed the framework of this research, developed the theoretical description of the method, and conducted the experiments. Z.H. carried out the computations and data processing. Z.H. and L.C. contributed to the writing of the article.

Zhengzhong Huang: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (lead); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Liangcai Cao: Conceptualization (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (supporting); Methodology (supporting); Project administration (lead); Supervision (lead); Writing – original draft (supporting); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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