Common-path diffraction optical tomography for investigation of three-dimensional structures and dynamics of biological cells

We present an optical holographic micro-tomographic technique for imaging both the three-dimensional structures and dynamics of biological cells. Optical light field images of a sample, illuminated by a plane wave with various illumination angles, are measured in a commonpath interferometry, and thus both the three-dimensional refractive index tomogram and two-dimensional dynamics of live biological cells are measured with extremely high sensitivity. The applicability of the technique is demonstrated through quantitative and measurements of morphological, chemical, and mechanical parameters at the individual cell level. ©2014 Optical Society of America OCIS codes: (180.3170) Interference microscopy; (180.6900) Three-dimensional microscopy; (170.1530) Cell analysis. References and links 1. G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill Professional, 2011). 2. K. Lee, K. Kim, J. Jung, J. H. Heo, S. Cho, S. Lee, G. Chang, Y. J. Jo, H. Park, and Y. K. 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Introduction
In the last decade, there have been significant advances in quantitative phase imaging (QPI) techniques, which have potential for diverse applications in various research fields [1][2][3].Due to its non-invasiveness and quantitative and label-free imaging capability, QPI has played important roles in several emerging biophysical studies including the pathophysiology of human red blood cells (RBCs) [4][5][6][7][8][9], the live cell imaging [10], the investigation of bacteria [11] and neuron cells [12], the measurements of angle resolved light scattering from individual cells [13][14][15][16], and the measurements of cellular growth and division [17,18].
QPI techniques based on a common-path interferometry design have recently achieved extremely high phase-sensitivity [19][20][21][22][23][24]; sensitivity of optical path lengths of about a few milliradian can be realized, enabling quantification of subtle cell membrane motions [25,26].One the other hand, tomographic QPI techniques have been employed to measure the 3D tomograms of individual biological samples [27][28][29][30][31][32][33][34][35][36][37].Tomographic QPI techniques, typically based on a Mach-Zehnder interferometer, measure multiple 2D optical fields with various illumination angles to reconstruct the 3D tomogram of a sample based on appropriate algorithms.These two technical advances have significantly extended the applications of the QPI including measurement of the 3D structures of living cells and the dynamic fluctuation in cell membranes [5][6][7]38].None of the existing techniques, however, precisely measure both 3D tomograms and 2D dynamics of live individual biological cells using a single optical setup.Current commonpath QPI techniques can measure the 2D dynamic phase images of a sample with high stability.However, the measured phase images are translated into physical thickness information assuming the refractive index (RI) of the sample, because the RI of the sample should be independently measured.Existing QPI tomography methods typically employ Mach-Zehnder interferometry and suffer from phase noise, which impedes stable measurement of a sample with high stability.One of the unexplored applications of QPI is to simultaneously measure the local RI of individual cells and the dynamic membrane fluctuation of the cells at the single cell level.This can offer the possibility of investigating the subtle alterations associated with pathophysiology of several diseases at the single cell level [39].Although there is strong motivation for single cell profiling, achieving a full-field common-path tomographic phase imaging technique has been regarded as technically challenging.To fully profile individual cells, morphological, chemical, and mechanical parameters should be quantified at the individual cell level, which requires measuring both the 3-D RI tomogram and dynamic fluctuations at the individual cell level.For this purpose, optical instruments should provide 3-D RI tomography capability while providing commonpath interferometry for highly stable dynamic phase measurement.
Here, a novel common-path quantitative phase tomography, referred to as common-path diffraction optical tomography (cDOT), is presented to measure both the 3D RI tomogram and 2D dynamic phase images of a sample.The angle of the beam impinging onto a sample is scanned over a wide range for tomographic measurements, and the beam diffracted from the sample is de-scanned to ensure common-path interferometry.This non-invasive and label-free technique simultaneously characterizes the 3D structures and 2D dynamics of individual cells.We demonstrate the capability of cDOT by measuring morphological, chemical, and mechanical parameters of healthy human red blood cells (RBCs) at the single cell level.In addition, we also show the tomographic image of a hepatocyte cell as a model eukaryotic cell.

Common-path diffraction optical tomography
The experimental scheme of cDOT is based on the principles of common-path laserinterferometric microscopy and optical diffraction tomography (Fig. 1).A sample, which is positioned between the condenser lens (CL) and objective lens (OL), is illuminated using a spatially filtered plane-wave laser beam with specific angles of illumination.The angle of the impinging beam is systematically controlled by rotating a two-axis galvanometer mirror (GM1).GM2, which is located at the conjugated plane to the sample and GM1, is synchronized with GM1 such that the angle of the beam reflected from GM2 remains unchanged regardless of the illumination angle.Then, after passing through the sample, the beam can be precisely quantified using a common-path interferometric microscope using the principle of diffraction phase microscopy, the details of which can be found elsewhere [19,20].Finally, a spatially modulated hologram is recorded onto an image sensor from which a full-field optical-field image with both amplitude and phase information is quantitatively retrieved using a phase retrieval algorithm [40].
The synchronized angle-scanning and common-path interferometry are finely tuned to work together, which allows simultaneous measurement of the 3D RI tomography and the dynamic 2D membrane fluctuations of individual biological cells.By changing the angles of the illumination impinging on the sample, cDOT measures multiple 2D optical fields with different illumination angles from which 3D RI tomograms of the sample are reconstructed using optical diffraction tomography [41][42][43].In order to measure the 2D dynamic images of the cell, the illumination angle is fixed at normal to the sample and cDOT can measure high-

Experimental setup
A diode-pumped solid-state (DPSS) laser (λ = 532 nm, 50 mW, Cobolt, Solna, Sweden) was used as an illumination source for an inverted microscope (IX73, Olympus Inc., Center Valley, PA, USA).The laser beam was first spatially filtered by a pinhole with a diameter of 25 μm.The collimated laser beam was steered by a two-axis galvanometric mirror (GM1, GVS012/M, Thorlabs, USA), and then projected onto a sample plane via a 4-f telescopic lens system composed of a lens (L1) and a condenser lens [CL, UPLFLN 60 × , numerical aperture (NA) = 0.9, Olympus, Japan] with a tube lens (f = 200 mm).A sample was prepared and sandwiched between two cover glasses separated by a thin spacer of double side tape.At the sample plane, the illumination angle of the beam can be rapidly scanned by GM1.The diffracted beam from the sample was collected by a high-NA objective lens (OL, UPLSAPO 60 × , oil immersion, NA = 1.42,Olympus, Japan).
To maintain an optical axis for common-path interferometry, the second two-axis galvanometric mirror (GM2, GVS012/M, Thorlabs, USA) was synchronized with GM1.The mirror of GM2 rotates exactly as much as rotated by GM1 but in the opposite direction, such that the beam reflected from GM2 maintains an optical axis regardless of the illumination angle at the sample plane.GM1 and GM2 are placed at the conjugate imaging plane of the sample.Thus, the rotation angle of the GM1 is linearly related with that of GM2.To physically synchronize the galvo mirrors, we first set the rotation angle of GM1 to be the maximum in the k x axis which is determined by the NA of two objective lenses.Then, we set the angle of GM2 so that the beam reflected from GM2 maintains unchanged.After repeating this procedure for both the k x and k y axes, we can synchronize the rotation angle of the galvano mirror.
The optical field of the diffracted beam is quantitatively and precisely measured by a common-path interferometry setup.Here, cDOT employs the principle of diffraction phase Among several orders of diffracted beams, only the 0th and 1st orders of the diffracted beams are used and the others are blocked.The 0th order diffraction beam is spatially filtered by a 4f lens system with a spatial filter to serve as a reference plane wave at the image plane.The 1st order beam is directly projected onto the image plane.At the image plane, the sample and reference beams interfere with a small angle difference defined by the spatial period of the grating and the 4-f lens system, forming spatially-modulated interferograms.The interferograms are recorded by a scientific complementary metal-oxide semiconductor camera (Neo sCMOS, ANDOR Inc., Northern Ireland, UK) with a pixel size of 6.5 μm and × 240 total magnification of the imaging system.

Verification of the angle synchronization in cDOT
In cDOT, GM1 is used to vary the angle of the illumination beam impinging onto a sample.For a common-path interferometry, GM2 is synchronized with GM1 such that the optical axis of the beam passing the sample remains unchanged.To verify the synchronization between GM1 and GM2, representative logarithmic Fourier spectra of the measured optical fields with representative illumination angles are shown in Figs.intensity will be high at the camera plane; otherwise, if it is not synchronized, the beam will not pass through the pinhole and will have low intensity, as shown in Fig. 2(d).
Figure 2(e) shows the maximum intensity of Fourier spectra as a function of the illumination angle controlled by GM1.Over a range of illumination angles from −43° to 43° (inside the medium), high light intensity was observed.Regardless of the illumination angle, the maxima of the Fourier spectra are found at the center of the spectra, indicates that GM1 and GM2 are precisely synchronized with each other.The temporal changes in the intensity with the fixed angle illumination only vary within 0.8%.This demonstrates that over this angle range the two galvanometric mirrors (GM1 & 2) are precisely synchronized with each other such that the common path interferometry works for various illumination angles.This angle range is comparable with the upper limit determined by the NA of the condenser and objective lenses.This shows that the two galvanometric mirrors are synchronized sufficiently to fully utilize the NA of the condenser and objective lenses.

3-D tomographic reconstruction of refractive index
To verify the 3D imaging capability of cDOT, we first measured the 3D RI tomogram of a polystyrene microsphere.Multiple optical fields of a sample illuminated with various angles were recorded in cDOT, from which the 3D RI tomograms of the sample were reconstructed using an optical diffraction tomography algorithm.The detailed optical diffraction tomography algorithm for retrieving the 3D RI map of a sample can be found elsewhere [28,41].In short, the spatial frequencies of diffracted optical fields from a sample at a specific illumination angle are mapped onto a hemispheric surface in the frequency domain called an Ewald sphere.Multiple 2D optical fields with various illumination angles are mapped onto multiple Ewald spheres with corresponding translations in Fourier space, resulting in 3D Fourier spectra.The inverse 3D Fourier transform of the Fourier spectra then provides the 3D RI tomogram of a sample.Due to the weak scattering nature of most biological cells, the first Rytov approximation is applied to simplify the relationship between incident and scattered light fields in the optical diffraction tomography algorithm.Unlike conventional optical diffraction tomography, cDOT considers the rotation of diffracted fields due to the rotation of GM2.The optical field from each illumination is rotated on the surface of the Ewald sphere corresponding to the angle of incident illumination; this can be approximated as the translation of an optical field in a 2-D plane because the rotation angle is less than 1° due to the angular de-magnification at the plane of GM2.Due to the limited accepted angle of the optical system, reconstructed 3-D Fourier spectra have missing information which is so-called the missing cone.This missing cone information was filled using the iterative non-negativity algorithm [29,30,43].
In order to obtain 3D RI tomograms of polystyrene beads, cDOT measures multiple 2D optical-field images of the sample with different angles of illumination; the 3D RI tomogram of the sample is then reconstructed using a diffraction optical tomography algorithm [41].Typically 300 holograms are recorded while the illumination angles draw a spiral trajectory within a range from −35° to 35° in the 2-D sample plane (inside the medium).The total measurement time is less than 0.5 s.The 3D RI tomogram of the polystyrene microsphere with a diameter of 3 μm (79166, Sigma-Aldrich Inc., USA) submersed in immersion oil (n oil = 1.518 at λ = 532 nm) is presented in Fig. 3. Cross-sectional views of the 3D RI tomogram of the bead demonstrate the high resolution capability of cDOT, and both the morphology and the RI values of the beads show good agreement with expected values and previous reports [41,43].and 100 μg/mL streptomycin.The cells were subcultivated for 4 hours before experiments, and then diluted in Dulbecco's phosphate buffered saline (DPBS, n DPBS = 1.337 at λ = 532 nm) before measurements.The same cDOT measurement procedures were performed as previously described.The 3D RI tomograms of a hepatocyte cell in DPBS buffer are presented in Fig. 5.The spherical objects having relatively high RI inside cytoplasm are subcellular organelles.The reconstructed RI tomogram measured by cDOT shows similar quality with that measured by Mach-Zehnder-type quantitative phase tomography [40].
Although the hepatocyte cell is relatively thin, cDOT is capable to resolve the internal structures.

Discussions and conclusions
This paper presents a precise and sensitive optical holographic technique that is well suited for studying biological alterations at the single cell level.By integrating optical diffraction tomography into a common-path interferometer, we demonstrate that cDOT can measure the 3D RI tomography as well as membrane dynamic fluctuations of individual biological cells.3D RI tomograms of individual biological samples are obtained in diffraction-limited resolution.Furthermore, the dynamic membrane fluctuations of the cells were simultaneously measured with sub-10-nm sensitivity.We demonstrate the capability of cDOT by measuring both 3D RI tomograms and the dynamic membrane fluctuation of individual human RBCs.The present method employs a pair of synchronized galvanometer mirrors, which enabled common-path optical diffraction tomography.This approach can also be combined with other modalities in quantitative phase imaging including spectroscopic measurement [47][48][49][50][51], polarization-sensitive phase imaging [52,53], and reflection geometry [54].The primary advantage of cDOT is its ability to analyze single cell profiles of RBCs, and cDOT is expected to find immediate applications in hematology.cDOT can provide not only routine red cell indices (such as cell volume, Hb contents, and Hb concentration) but also other indices such as sphericity, surface area, and membrane fluctuation.The structural, chemical, and mechanical information of RBCs is important for hemodiagnosis, and cDOT can potentially be used to simultaneously measure these parameters at the individual cell level.Although only healthy RBCs were examined to demonstrate the proof of principle, this method is readily applicable to other RBC-related diseases such as malaria, sickle cell disease, and thalassemia [8,16,55,56].Furthermore, we demonstrated that cDOT can also be utilized for other eukaryotic cell type.In order for cDOT to be extended to clinical applications, high-throughput measurement capability is necessary.Currently, the measurement time for probing one cell is nearly 3 sec, but this time is not limited.By employing the principles of flow cytometry and optimizing the measurement instruments, the measurement speed can be significantly enhanced.Furthermore, cDOT can also be applied to other cell types including white blood cells, circulating tumor cells, and endothelial cells for biophysical and medical purposes.

Fig. 1 .
Fig. 1.Experimental setup and principle of cDOT.(a) The cDOT setup is composed of two galvanometric mirrors (GM1, GM2) synchronized with each other and a laser-interferometric microscope in a common-path geometry.A sample is positioned between the condenser and objective lenses.OL: objective lens; CL: condenser lens; GM1-2: galvanometric mirrors; M1-2: mirrors; L1-8: lenses.(b) The angle of an illumination beam impinging onto the sample is scanned by rotating GM1 and is de-scanned by GM2 in a synchronized manner such that the angle of the beam reflected from GM2 remains unchanged.(Inset) The sample is illuminated with a plane wave at different angles of illumination

Fig. 2 .
Fig. 2. (a)-(d) Representative logarithmic Fourier spectra corresponding to specific illumination angles.The dashed circle in (b) represents the cut-off frequency for diffractionlimited optical fields.(e) The maximum intensity value of Fourier spectra as a function of illumination angle.(f) The temporal fluctuations of the intensity at the normal illumination (0°).
2(a) to 2(d).The Fourier spectra were obtained by 2D Fourier transform of the measured optical field images.The maximum intensity of the Fourier spectra corresponds to an unscattered light field, and thus the position that yields the maximum intensity indicates the spatial frequency of the unscattered light field.As can be seen in Fig.2(b), when the angle of the illumination beam is set to 0°, the position of the maximum intensity is located at the exact center, or the DC point in the Fourier spectra.When the illumination angle is changed to −30° or 30° [Figs.2(a)or 2(c)], the maximum intensity is still located at the DC point.This is because GM2 compensates the angle of the beam path to the same degree that the angle is rotated by GM1.When synchronized, the beam will pass the pinhole between two lenses (L7 & 8) and the beam #207328 -$15.00USD Received 27 Feb 2014; revised 11 Apr 2014; accepted 16 Apr 2014; published 22 Apr 2014 (C) 2014 OSA 207328 -$15.00USD Received 27 Feb 2014; revised 11 Apr 2014; accepted 16 Apr 2014; published 22 Apr 2014 (C) 2014 OSA 5 May 2014 | Vol.22, No. 9 | DOI:10.1364/OE.22.010389| OPTICS EXPRESS 10404