Quantitative Phase Imaging & Optical Diffraction Tomography

Quantitative phase imaging

Quantitativ phase imaging of single cells. a) The schematic drawing of the cross-section along the optical axis illustrates the phase delay ∆Φ of light passing through a cell (wavefronts drawn as red lines). The phase delay is caused by the RI of the cell, which is larger than that of the surrounding medium n m . The images in (b) and (c) show phase and intensity images of a representative HL60/S4 cell.
Quantitative phase imaging of a single cell. a) The schematic drawing of the cross-section along the optical axis illustrates the phase delay ∆Φ of light passing through a cell (wavefronts drawn as red lines). The phase delay is caused by the RI of the cell, which is larger than that of the surrounding medium. The images in (b) and (c) show phase and intensity images of an HL60/S4 cell. Figure reproduced from [1].

Quantitative phase imaging (QPI) is a marker-free technique for quantifying the optical thickness of cells. We are interested in optical properties that can be derived from the optical thickness, including refractive index (RI) or mass density of cells. QPI is commonly performed using digital holographic microscopy (DHM) [2]. In addition, we employ commercial QPI hardware (Phasics, S.A., France) that is based on quadriwave lateral-shearing interferometry [3]. We apply these techniques, for example, to find average RI values for single cells or cell populations and we are employing QPI to study various biological processes.

Optical diffraction tomography

3D Refractive Index of an HL60 cell
Refractive index reconstruction of an HL60/S4 cell. The 3D visualization shows the iso-surfaces at 1.339 (violet), 1.357 (yellow), 1.363 (orange) and 1.380 (red). Figure reproduced from [1].

Optical diffraction tomography (ODT) is a 3D imaging technique that is used to obtain the quantitative RI distribution within cells. ODT employs QPI techniques to record 2D phase images of a cell from multiple angles which are then used for the tomographic 3D reconstruction. The tomographic approach is crucial for 3D RI imaging, because it allows to deduce the RI from the  optical thickness that is measured with QPI.

In practice, we employ optical and microfluidic devices (see Optical Trapping) to rotate single cells while acquiring QPI data. To obtain the 3D refractive index from these data, we use a backpropagation algorithm that is based on the Rytov approximation [4, 5]. Our approach to ODT allows to image single cells in suspension, but requires elaborate pre-processing steps. Thus, we are constantly developing state of the art image registration and tomographic reconstruction algorithms [6, 1]. If you are interested in our QPI and ODT techniques, please check out our QPI & ODT libraries.

  1. P. Müller, “Optical Diffraction Tomography for Single Cells,” PhD Thesis, 2016.
    [BibTeX] [Abstract] [Download PDF]

    Analyzing the structure of a single cell based on its refractive index (RI) distribution is a common and valued approach, because it does not require any artificial markers. The RI is an inherent structural marker that can be quantified in three dimensions with optical diffraction tomography (ODT), an inverse scattering technique. This work reviews the theory of ODT and its implementation with an emphasis on single-cell analysis, identifying the Rytov approximation as the most efficient descriptor for light propagation. The accuracy of the reconstruction method is verified with in silico data and imaging artifacts associated with the inverse scattering approach are addressed. Furthermore, an experimental ODT setup is presented that consists of a bright-field microscope, a phase-imaging camera, and an optical trap combined with a microfluidic chip. A novel image analysis pipeline is proposed that addresses image corrections and frame alignment of the recorded data prior to the RI reconstruction. In addition, for a rotational axis that is tilted with respect to the image plane, an improved reconstruction algorithm is introduced and applied to single, suspended cells in vitro, achieving sub-cellular resolution.

    @PHDTHESIS{MuellerThesis,
    author = {Paul M{\"{u}}ller},
    title = {{Optical Diffraction Tomography for Single Cells}},
    school = {TU Dresden},
    year = {2016},
    file = {:http\://www.qucosa.de/fileadmin/data/qucosa/documents/20226/Mueller_ODT_SingleCells_Diss_2016_print.pdf:URL},
    owner = {paul},
    timestamp = {2016.08.03},
    url = {http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-202261},
    abstract = {Analyzing the structure of a single cell based on its refractive index (RI) distribution is a common and valued approach, because it does not require any artificial markers. The RI is an inherent structural marker that can be quantified in three dimensions with optical diffraction tomography (ODT), an inverse scattering technique. This work reviews the theory of ODT and its implementation with an emphasis on single-cell analysis, identifying the Rytov approximation as the most efficient descriptor for light propagation. The accuracy of the reconstruction method is verified with in silico data and imaging artifacts associated with the inverse scattering approach are addressed. Furthermore, an experimental ODT setup is presented that consists of a bright-field microscope, a phase-imaging camera, and an optical trap combined with a microfluidic chip.
    A novel image analysis pipeline is proposed that addresses image corrections and frame alignment of the recorded data prior to the RI reconstruction.
    In addition, for a rotational axis that is tilted with respect to the image plane, an improved reconstruction algorithm is introduced and applied to single, suspended cells in vitro, achieving sub-cellular resolution.}
    }

  2. M. Schürmann, J. Scholze, P. Müller, C. J. Chan, A. E. Ekpenyong, K. J. Chalut, and J. Guck, “Refractive index measurements of single, spherical cells using digital holographic microscopy,” in Biophysical methods in cell biology, E. K. Paluch, Ed., Academic Press, 2015, vol. 125, pp. 143-159. doi:10.1016/bs.mcb.2014.10.016
    [BibTeX] [Abstract]

    Abstract In this chapter, we introduce digital holographic microscopy (DHM) as a marker-free method to determine the refractive index of single, spherical cells in suspension. The refractive index is a conclusive measure in a biological context. Cell conditions, such as differentiation or infection, are known to yield significant changes in the refractive index. Furthermore, the refractive index of biological tissue determines the way it interacts with light. Besides the biological relevance of this interaction in the retina, a lot of methods used in biology, including microscopy, rely on light-tissue or light-cell interactions. Hence, determining the refractive index of cells using {DHM} is valuable in many biological applications. This chapter covers the main topics that are important for the implementation of DHM: setup, sample preparation, and analysis. First, the optical setup is described in detail including notes and suggestions for the implementation. Following that, a protocol for the sample and measurement preparation is explained. In the analysis section, an algorithm for the determination of quantitative phase maps is described. Subsequently, all intermediate steps for the calculation of the refractive index of suspended cells are presented, exploiting their spherical shape. In the last section, a discussion of possible extensions to the setup, further measurement configurations, and additional analysis methods are given. Throughout this chapter, we describe a simple, robust, and thus easily reproducible implementation of DHM. The different possibilities for extensions show the diverse fields of application for this technique.

    @INCOLLECTION{Schuermann2015,
    author = {Sch{\"{u}}rmann, Mirjam and Scholze, Jana and M{\"{u}}ller, Paul
    and Chan, Chii J and Ekpenyong, Andrew E and Chalut, Kevin J and
    Guck, Jochen},
    title = {{Refractive index measurements of single, spherical cells using digital
    holographic microscopy}},
    booktitle = {Biophysical Methods in Cell Biology},
    publisher = {Academic Press},
    year = {2015},
    editor = {Paluch, Ewa K},
    volume = {125},
    series = {Methods in Cell Biology},
    pages = {143--159},
    abstract = {Abstract In this chapter, we introduce digital holographic microscopy
    (DHM) as a marker-free method to determine the refractive index of
    single, spherical cells in suspension. The refractive index is a
    conclusive measure in a biological context. Cell conditions, such
    as differentiation or infection, are known to yield significant changes
    in the refractive index. Furthermore, the refractive index of biological
    tissue determines the way it interacts with light. Besides the biological
    relevance of this interaction in the retina, a lot of methods used
    in biology, including microscopy, rely on light-tissue or light-cell
    interactions. Hence, determining the refractive index of cells using
    {DHM} is valuable in many biological
    applications. This chapter covers the main topics that are important
    for the implementation of DHM: setup, sample preparation, and analysis.
    First, the optical setup is described in detail including notes and
    suggestions for the implementation. Following that, a protocol for
    the sample and measurement preparation is explained. In the analysis
    section, an algorithm for the determination of quantitative phase
    maps is described. Subsequently, all intermediate steps for the calculation
    of the refractive index of suspended cells are presented, exploiting
    their spherical shape. In the last section, a discussion of possible
    extensions to the setup, further measurement configurations, and
    additional analysis methods are given. Throughout this chapter, we
    describe a simple, robust, and thus easily reproducible implementation
    of DHM. The different possibilities for extensions show the diverse
    fields of application for this technique.},
    doi = {10.1016/bs.mcb.2014.10.016},
    issn = {0091-679X},
    owner = {paul},
    timestamp = {2016.08.03},
    }

  3. S. Mousset, C. Rouyer, G. Marre, N. Blanchot, S. Montant, and B. Wattellier, “Piston measurement by quadriwave lateral shearing interferometry,” Optics Letters, vol. 31, iss. 17, pp. 2634-2636, 2006. doi:10.1364/OL.31.002634
    [BibTeX] [Abstract]

    We present what is to our knowledge a new method for measuring the relative piston between two independent beams separated by a physical gap, typical of petawatt facilities. The feasibility of this measurement, based on quadriwave lateral shearing interferometry, has been demonstrated experimentally: piston has been measured with accuracy and sensitivity better than 50 nm.

    @ARTICLE{Mousset2006,
    author = {Mousset, Soazic and Rouyer, Claude and Marre, Gabrielle and Blanchot,
    Nathalie and Montant, S{\'{e}}bastien and Wattellier, Benoit},
    title = {{Piston measurement by quadriwave lateral shearing interferometry}},
    journal = {{Optics Letters}},
    year = {2006},
    volume = {31},
    pages = {2634--2636},
    number = {17},
    abstract = {We present what is to our knowledge a new method for measuring the
    relative piston between two independent beams separated by a physical
    gap, typical of petawatt facilities. The feasibility of this measurement,
    based on quadriwave lateral shearing interferometry, has been demonstrated
    experimentally: piston has been measured with accuracy and sensitivity
    better than 50 nm.},
    doi = {10.1364/OL.31.002634},
    issn = {0146-9592},
    owner = {paul},
    timestamp = {2016.08.03}
    }

  4. P. Müller, M. Schürmann, and J. Guck, “The Theory of Diffraction Tomography,” arXiv 1507.00466 [q-bio.QM], 2015.
    [BibTeX] [Abstract] [Download PDF]

    Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for light with short wavelengths, for example in x-ray tomography. For classical tomography, a commonly used reconstruction method is the filtered back-projection algorithm which yields fast and stable object reconstructions. In the context of single-cell imaging, the back-projection algorithm has been used to investigate the cell structure or to quantify the refractive index distribution within single cells using light from the visible spectrum. Nevertheless, these approaches, commonly summarized as optical projection tomography, do not take into account diffraction. Diffraction tomography with the Rytov approximation resolves this issue. The explicit incorporation of the wave nature of light results in an enhanced reconstruction of the object’s refractive index distribution. Here, we present a full literature review of diffraction tomography. We derive the theory starting from the wave equation and discuss its validity with the focus on applications for refractive index tomography. Furthermore, we derive the back-propagation algorithm, the diffraction-tomographic pendant to the back-projection algorithm, and describe its implementation in three dimensions. Finally, we showcase the application of the back-propagation algorithm to computer-generated scattering data. This review unifies the different notations in literature and gives a detailed description of the back-propagation algorithm, serving as a reliable basis for future work in the field of diffraction tomography.

    @OTHER{Mueller15arxiv,
    author = {M{\"{u}}ller, Paul and Sch{\"{u}}rmann, Mirjam and Guck, Jochen},
    eprint = {1507.00466},
    eprintclass = {q-bio.QM},
    eprinttype = {arxiv},
    journal = {{arXiv 1507.00466 [q-bio.QM]}},
    owner = {paul},
    timestamp = {2016.08.03},
    title = {{The Theory of Diffraction Tomography}},
    version = {2},
    year = {2015},
    url = {https://arxiv.org/pdf/1507.00466},
    abstract = {Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for light with short wavelengths, for example in x-ray tomography. For classical tomography, a commonly used reconstruction method is the filtered back-projection algorithm which yields fast and stable object reconstructions. In the context of single-cell imaging, the back-projection algorithm has been used to investigate the cell structure or to quantify the refractive index distribution within single cells using light from the visible spectrum. Nevertheless, these approaches, commonly summarized as optical projection tomography, do not take into account diffraction. Diffraction tomography with the Rytov approximation resolves this issue. The explicit incorporation of the wave nature of light results in an enhanced reconstruction of the object's refractive index distribution. Here, we present a full literature review of diffraction tomography. We derive the theory starting from the wave equation and discuss its validity with the focus on applications for refractive index tomography. Furthermore, we derive the back-propagation algorithm, the diffraction-tomographic pendant to the back-projection algorithm, and describe its implementation in three dimensions. Finally, we showcase the application of the back-propagation algorithm to computer-generated scattering data. This review unifies the different notations in literature and gives a detailed description of the back-propagation algorithm, serving as a reliable basis for future work in the field of diffraction tomography. }
    }

  5. P. Müller, M. Schürmann, and J. Guck, “ODTbrain: a Python library for full-view, dense diffraction tomography,” BMC Bioinformatics, vol. 16, iss. 1, pp. 1-9, 2015. doi:10.1186/s12859-015-0764-0
    [BibTeX] [Abstract] [Download PDF]

    Analyzing the three-dimensional (3D) refractive index distribution of a single cell makes it possible to describe and characterize its inner structure in a marker-free manner. A dense, full-view tomographic data set is a set of images of a cell acquired for multiple rotational positions, densely distributed from 0 to 360 degrees. The reconstruction is commonly realized by projection tomography, which is based on the inversion of the Radon transform. The reconstruction quality of projection tomography is greatly improved when first order scattering, which becomes relevant when the imaging wavelength is comparable to the characteristic object size, is taken into account. This advanced reconstruction technique is called diffraction tomography. While many implementations of projection tomography are available today, there is no publicly available implementation of diffraction tomography so far.

    @ARTICLE{Mueller15,
    author = {M{\"{u}}ller, Paul and Sch{\"{u}}rmann, Mirjam and Guck, Jochen},
    title = {{ODTbrain: a Python library for full-view, dense diffraction tomography}},
    journal = {{BMC Bioinformatics}},
    year = {2015},
    volume = {16},
    pages = {1--9},
    number = {1},
    abstract = {Analyzing the three-dimensional (3D) refractive index distribution
    of a single cell makes it possible to describe and characterize its
    inner structure in a marker-free manner. A dense, full-view tomographic
    data set is a set of images of a cell acquired for multiple rotational
    positions, densely distributed from 0 to 360 degrees. The reconstruction
    is commonly realized by projection tomography, which is based on
    the inversion of the Radon transform. The reconstruction quality
    of projection tomography is greatly improved when first order scattering,
    which becomes relevant when the imaging wavelength is comparable
    to the characteristic object size, is taken into account. This advanced
    reconstruction technique is called diffraction tomography. While
    many implementations of projection tomography are available today,
    there is no publicly available implementation of diffraction tomography
    so far.},
    doi = {10.1186/s12859-015-0764-0},
    issn = {1471-2105},
    owner = {paul},
    timestamp = {2016.08.03},
    url = {http://bmcbioinformatics.biomedcentral.com/track/pdf/10.1186/s12859-015-0764-0?site=bmcbioinformatics.biomedcentral.com}
    }

  6. P. Müller, M. Schürmann, C. J. Chan, and J. Guck, “Single-cell diffraction tomography with optofluidic rotation about a tilted axis,” in Proceedings of the international society for optics and photonics, 2015, p. 95480U. doi:10.1117/12.2191501
    [BibTeX] [Abstract]

    Optical diffraction tomography (ODT) is a tomographic technique that can be used to measure the three- dimensional (3D) refractive index distribution within living cells without the requirement of any marker. In principle, ODT can be regarded as a generalization of optical projection tomography which is equivalent to com- puterized tomography (CT). Both optical tomographic techniques require projection-phase images of cells mea- sured at multiple angles. However, the reconstruction of the 3D refractive index distribution post-measurement differs for the two techniques. It is known that ODT yields better results than projection tomography, because it takes into account diffraction of the imaging light due to the refractive index structure of the sample. Here, we apply ODT to biological cells in a microfluidic chip which combines optical trapping and microfluidic flow to achieve an optofluidic single-cell rotation. In particular, we address the problem that arises when the trapped cell is not rotating about an axis perpendicular to the imaging plane, but instead about an arbitrarily tilted axis. In this paper we show that the 3D reconstruction can be improved by taking into account such a tilted rotational axis in the reconstruction process.

    @INPROCEEDINGS{Mueller15tilted,
    author = {M{\"{u}}ller, Paul and Sch{\"{u}}rmann, Mirjam and Chan, Chii J and
    Guck, Jochen},
    title = {{Single-cell diffraction tomography with optofluidic rotation about
    a tilted axis}},
    booktitle = {Proceedings of the International Society for Optics and Photonics},
    year = {2015},
    volume = {9548},
    pages = {95480U},
    abstract = {Optical diffraction tomography (ODT) is a tomographic technique that
    can be used to measure the three- dimensional (3D) refractive index
    distribution within living cells without the requirement of any marker.
    In principle, ODT can be regarded as a generalization of optical
    projection tomography which is equivalent to com- puterized tomography
    (CT). Both optical tomographic techniques require projection-phase
    images of cells mea- sured at multiple angles. However, the reconstruction
    of the 3D refractive index distribution post-measurement differs
    for the two techniques. It is known that ODT yields better results
    than projection tomography, because it takes into account diffraction
    of the imaging light due to the refractive index structure of the
    sample. Here, we apply ODT to biological cells in a microfluidic
    chip which combines optical trapping and microfluidic flow to achieve
    an optofluidic single-cell rotation. In particular, we address the
    problem that arises when the trapped cell is not rotating about an
    axis perpendicular to the imaging plane, but instead about an arbitrarily
    tilted axis. In this paper we show that the 3D reconstruction can
    be improved by taking into account such a tilted rotational axis
    in the reconstruction process.},
    doi = {10.1117/12.2191501},
    owner = {paul},
    timestamp = {2016.08.03}
    }