Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

In-line holographic microscopy with model-based analysis

Abstract

An in-line holographic microscope is an optical microscope outfitted with a coherent light source, such as a laser. Light scattered by the specimen interferes with the transmitted beam, and the intensity of that interference pattern constitutes a hologram. Unlike a conventional photograph, a hologram contains information about the phase of the scattered light that is useful for measuring the composition and 3D arrangement of microscopic objects in the specimen. This Primer presents an overview of experimental methods and discusses three recent analysis techniques: fitting scattering models to the hologram; using machine learning to localize and classify the specimen; and a hybrid approach that uses machine learning to initialize fits. The combination of holographic microscopy and model-based analysis is well suited to applications where precise, quantitative results are needed with high acquisition speed. Such applications include studying properties of heterogeneous colloidal dispersions, measuring colloidal interactions, monitoring stresses in soft materials, detecting molecular binding and aggregation, and following the motion of microorganisms in three dimensions. We discuss the reproducibility and current limitations of each method. Finally, we anticipate directions for future development and provide an outlook on the integration between experiment and computational analysis, an emerging paradigm for microscopy.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Hologram formation and analysis.
Fig. 2: Detailed set-up of an in-line holographic microscope.
Fig. 3: Data normalization for hologram analysis.
Fig. 4: Approaches to quantitative analysis of holograms.
Fig. 5: Motion and tracking.
Fig. 6: Property estimation and characterization.

References

  1. Sheng, J., Malkiel, E. & Katz, J. Digital holographic microscope for measuring three-dimensional particle distributions and motions. Appl. Opt. 45, 3893–3901 (2006).

    ADS  Google Scholar 

  2. Gabor, D. A new microscopic principle. Nature 161, 777–778 (1948).

    ADS  Google Scholar 

  3. Gabor, D. & Bragg, W. L. Microscopy by reconstructed wave-fronts. P. Roy. Soc. Lond. A Mat. 197, 454–487 (1949). Together with Gabor (1948), this paper demonstrates that it is possible to optically reconstruct a 3D representation of a specimen from its recorded hologram, a finding that launched the field of holographic microscopy.

    ADS  MATH  Google Scholar 

  4. Xu, W., Jericho, M. H., Meinertzhagen, I. A. & Kreuzer, H. J. Digital in-line holography for biological applications. Proc. Natl Acad. Sci. USA 98, 11301–11305 (2001).

    ADS  Google Scholar 

  5. Xu, W., Jericho, M. H., Kreuzer, H. J. & Meinertzhagen, I. A. Tracking particles in four dimensions with in-line holographic microscopy. Opt. Lett. 28, 164–166 (2003).

    ADS  Google Scholar 

  6. Berg, M. J. Tutorial: Aerosol characterization with digital in-line holography. J. Aerosol Sci. 165, 106023 (2022).

    ADS  Google Scholar 

  7. Kim, M. K. Principles and techniques of digital holographic microscopy. SPIE Rev. 1, 018005 (2010).

    Google Scholar 

  8. Jericho, S. K., Garcia-Sucerquia, J., Xu, W., Jericho, M. H. & Kreuzer, H. J. Submersible digital in-line holographic microscope. Rev. Sci. Instrum. 77, 043706 (2006).

    ADS  Google Scholar 

  9. Garcia-Sucerquia, J. et al. Digital in-line holographic microscopy. Appl. Opt. 45, 836–850 (2006).

    ADS  Google Scholar 

  10. Bishara, W., Zhu, H. & Ozcan, A. Holographic opto-fluidic microscopy. Opt. Express 18, 27499–27510 (2010).

    ADS  Google Scholar 

  11. Marquet, P. et al. Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy. Opt. Lett. 30, 468–470 (2005).

    ADS  Google Scholar 

  12. Mölder, A. et al. Non-invasive, label-free cell counting and quantitative analysis of adherent cells using digital holography. J. Microsc. 232, 240–247 (2008).

    MathSciNet  Google Scholar 

  13. Kemper, B. & Bally, G. V. Digital holographic microscopy for live cell applications and technical inspection. Appl. Opt. 47, A52–A61 (2008).

    Google Scholar 

  14. Park, Y., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nat. Photonics 12, 578–589 (2018).

    ADS  Google Scholar 

  15. Barty, A., Nugent, K. A., Roberts, A. & Paganin, D. Quantitative phase tomography. Opt. Comm. 175, 329–336 (2000).

    ADS  Google Scholar 

  16. Popescu, G. Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill Education, 2011).

  17. Popescu, G. et al. Imaging red blood cell dynamics by quantitative phase microscopy. Blood Cell Mol. Dis. 41, 10–16 (2008).

    Google Scholar 

  18. Marquet, P., Depeursinge, C. & Magistretti, P. J. Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders. Neurophotonics 1, 020901 (2014).

    Google Scholar 

  19. Mie, G. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen [German]. Ann. Phys. 330, 377–445 (1908).

    MATH  Google Scholar 

  20. Ovryn, B. & Izen, S. H. Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope. JOSA 17, 1202–1213 (2000). The authors fit a generative model based on Lorenz–Mie theory to a recorded hologram to determine the properties of a microscopic particle.

    Google Scholar 

  21. Lee, S.-H. et al. Characterizing and tracking single colloidal particles with video holographic microscopy. Opt. Express 15, 18275–18282 (2007). This paper presents a straightforward generative model for hologram formation from a simple sphere, which has become the basis for many later studies on various systems.

    ADS  Google Scholar 

  22. Wang, A., Rogers, W. B. & Manoharan, V. N. Effects of contact-line pinning on the adsorption of nonspherical colloids at liquid interfaces. Phys. Rev. Lett. 119, 108004 (2017).

    ADS  Google Scholar 

  23. Wang, A. et al. Using the discrete dipole approximation and holographic microscopy to measure rotational dynamics of non-spherical colloidal particles. J. Quant. Spectrosc. Radiat. Transf. 146, 499–509 (2014).

    ADS  Google Scholar 

  24. Fung, J. et al. Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy. Opt. Express 19, 8051 (2011).

    ADS  Google Scholar 

  25. Yurkin, M. A. & Hoekstra, A. G. The discrete dipole approximation: an overview and recent developments. J. Quant. Spectrosc. Radiat. Transf. 106, 558–589 (2007).

    ADS  Google Scholar 

  26. Yurkin, M. A. & Hoekstra, A. G. The discrete-dipole-approximation code ADDA: capabilities and known limitations. J. Quant. Spectrosc. Radiat. Transf. 112, 2234–2247 (2011).

    ADS  Google Scholar 

  27. Pu, Y. & Meng, H. Intrinsic aberrations due to Mie scattering in particle holography. J. Opt. Soc. Am. A 20, 1920 (2003).

    ADS  Google Scholar 

  28. Dulin, D., Barland, S., Hachair, X. & Pedaci, F. Efficient illumination for microsecond tracking microscopy. PLoS ONE 9, e107335 (2014).

    ADS  Google Scholar 

  29. Giuliano, C. B., Zhang, R. & Wilson, L. G. Digital inline holographic microscopy (DIHM) of weakly-scattering subjects. J. Vis. Exp. 84, e50488 (2014).

    Google Scholar 

  30. Kanka, M., Riesenberg, R., Petruck, P. & Graulig, C. High resolution (NA = 0.8) in lensless in-line holographic microscopy with glass sample carriers. Opt. Lett. 36, 3651–3653 (2011).

    ADS  Google Scholar 

  31. Garcia-Sucerquia, J. Noise reduction in digital lensless holographic microscopy by engineering the light from a light-emitting diode. Appl. Opt. 52, A232–A239 (2013).

    ADS  Google Scholar 

  32. Hell, S., Reiner, G., Cremer, C. & Stelzer, E. H. K. Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index. J. Microsc. 169, 391–405 (1993).

    Google Scholar 

  33. Wu, Y. & Ozcan, A. Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring. Methods 136, 4–16 (2018).

    Google Scholar 

  34. Deng, N.-N. et al. Simple and cheap microfluidic devices for the preparation of monodisperse emulsions. Lab. Chip 11, 3963–3969 (2011).

    Google Scholar 

  35. Kaz, D. M., McGorty, R., Mani, M., Brenner, M. P. & Manoharan, V. N. Physical ageing of the contact line on colloidal particles at liquid interfaces. Nat. Mater. 11, 138–142 (2012). This application of a generative modelling approach demonstrates the usefulness of the method: the fast, precise measurements enabled by the approach reveal a previously indiscernible phenomenon.

    ADS  Google Scholar 

  36. Moyses, H. W., Krishnatreya, B. J. & Grier, D. G. Robustness of Lorenz–Mie microscopy against defects in illumination. Opt. Express 21, 5968 (2013).

    ADS  Google Scholar 

  37. Martin, C., Leahy, B. & Manoharan, V. N. Improving holographic particle characterization by modeling spherical aberration. Opt. Express 29, 18212 (2021).

    ADS  Google Scholar 

  38. Fung, J., Perry, R. W., Dimiduk, T. G. & Manoharan, V. N. Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms. J. Quant. Spectrosc. Radiat. Transf. 113, 2482–2489 (2012).

    ADS  Google Scholar 

  39. Cheong, F. C. et al. Flow visualization and flow cytometry with holographic video microscopy. Opt. Express 17, 13071 (2009).

    ADS  Google Scholar 

  40. Dixon, L., Cheong, F. C. & Grier, D. G. Holographic particle-streak velocimetry. Opt. Express 19, 4393–4398 (2011).

    ADS  Google Scholar 

  41. Edelstein, A. D. et al. Advanced methods of microscope control using μManager software. J. Biol. Methods 1, e10 (2014).

    Google Scholar 

  42. Vercruysse, D. et al. Three-part differential of unlabeled leukocytes with a compact lens-free imaging flow cytometer. Lab Chip 15, 1123–1132 (2015).

    Google Scholar 

  43. Dimiduk, T. G. et al. A simple, inexpensive holographic microscope. in Biomedical Optics and 3-D Imaging, OSA Technical Digest (CD) JMA38 (Optica, 2010).

  44. Fung, J. Measuring the 3D Dynamics of Multiple Colloidal Particles with Digital Holographic Microscopy. PhD Thesis, Harvard Univ. (2013).

  45. Moreno, D., Santoyo, F. M., Guerrero, J. A. & Funes-Gallanzi, M. Particle positioning from charge-coupled device images by the generalized Lorenz–Mie theory and comparison with experiment. Appl. Opt. 39, 5117–5124 (2000).

    ADS  Google Scholar 

  46. Denis, L., Fournier, C., Fournel, T., Ducottet, C. & Jeulin, D. Direct extraction of the mean particle size from a digital hologram. Appl. Opt. 45, 944–952 (2006).

    ADS  Google Scholar 

  47. Guerrero-Viramontes, J. A., Moreno-Hernández, D., Mendoza-Santoyo, F. & Funes-Gallanzi, M. 3D particle positioning from CCD images using the generalized Lorenz–Mie and Huygens–Fresnel theories. Meas. Sci. Technol. 17, 2328–2334 (2006).

    Google Scholar 

  48. Yevick, A., Hannel, M. & Grier, D. G. Machine-learning approach to holographic particle characterization. Opt. Express 22, 26884 (2014). This paper is one of the first applications of machine learning to hologram analysis, and demonstrates the increase in speed of analysis that is possible.

    ADS  Google Scholar 

  49. Hannel, M. D., Abdulali, A., O’Brien, M. & Grier, D. G. Machine-learning techniques for fast and accurate feature localization in holograms of colloidal particles. Opt. Express 26, 15221 (2018).

    ADS  Google Scholar 

  50. Altman, L. E. & Grier, D. G. CATCH: characterizing and tracking colloids holographically using deep neural networks. J. Phys. Chem. B 124, 1602–1610 (2020). This paper demonstrates a fully integrated pipeline for analysis of holograms, with improved automation and precision made possible by combining machine learning with fitting.

    Google Scholar 

  51. Hannel, M., Middleton, C. & Grier, D. G. Holographic characterization of imperfect colloidal spheres. Appl. Phys. Lett. 107, 141905 (2015).

    ADS  Google Scholar 

  52. Duda, R. O. & Hart, P. E. Use of the Hough transformation to detect lines and curves in pictures. Commun. ACM 15, 11–15 (1972).

    MATH  Google Scholar 

  53. Ballard, D. H. Generalizing the Hough transform to detect arbitrary shapes. Pattern Recogn. 13, 111–122 (1981).

    ADS  MATH  Google Scholar 

  54. Dimiduk, T. G., Perry, R. W., Fung, J. & Manoharan, V. N. Random-subset fitting of digital holograms for fast three-dimensional particle tracking [invited]. Appl. Opt. 53, G177–G183 (2014).

    Google Scholar 

  55. Dimiduk, T. G. & Manoharan, V. N. Bayesian approach to analyzing holograms of colloidal particles. Opt. Express 24, 24045 (2016). This work demonstrates the use of a Bayesian inference framework for hologram analysis, which has lent several advantages over non-linear least-squares fitting routines, including the formal integration of prior information and MCMC calculation of the posterior over parameters.

    ADS  Google Scholar 

  56. Moré, J. J. in Numerical Analysis (ed. Watson, G. A.) 105–116 (Springer, 1978).

  57. Cheong, F. C., Krishnatreya, B. J. & Grier, D. G. Strategies for three-dimensional particle tracking with holographic video microscopy. Opt. Express 18, 13563 (2010).

    ADS  Google Scholar 

  58. Krishnatreya, B. J. et al. Measuring Boltzmann’s constant through holographic video microscopy of a single colloidal sphere. Am. J. Phys. 82, 23–31 (2014).

    ADS  Google Scholar 

  59. Wang, A., McGorty, R., Kaz, D. M. & Manoharan, V. N. Contact-line pinning controls how quickly colloidal particles equilibrate with liquid interfaces. Soft Matter 12, 8958–8967 (2016).

    ADS  Google Scholar 

  60. Wang, A. et al. Before the breach: interactions between colloidal particles and liquid interfaces at nanoscale separations. Phys. Rev. E 100, 042605 (2019).

    ADS  Google Scholar 

  61. Roichman, Y., Sun, B., Stolarski, A. & Grier, D. G. Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability. Phys. Rev. Lett. 101, 128301 (2008).

    ADS  Google Scholar 

  62. Sun, B., Lin, J., Darby, E., Grosberg, A. Y. & Grier, D. G. Brownian vortexes. Phys. Rev. E 80, 010401 (2009).

    ADS  Google Scholar 

  63. O’Brien, M. J. & Grier, D. G. Above and beyond: holographic tracking of axial displacements in holographic optical tweezers. Opt. Express 27, 25375 (2019).

    ADS  Google Scholar 

  64. Xiao, K. & Grier, D. G. Sorting colloidal particles into multiple channels with optical forces: prismatic optical fractionation. Phys. Rev. E 82, 051407 (2010).

    ADS  Google Scholar 

  65. Xiao, K. & Grier, D. G. Multidimensional optical fractionation of colloidal particles with holographic verification. Phys. Rev. Lett. 104, 028302 (2010).

    ADS  Google Scholar 

  66. Winters, A. et al. Quantitative differentiation of protein aggregates from other subvisible particles in viscous mixtures through holographic characterization. J. Pharm. Sci. 109, 2405–2412 (2020).

    Google Scholar 

  67. Wang, C., Shpaisman, H., Hollingsworth, A. D. & Grier, D. G. Celebrating soft matter’s 10th anniversary: monitoring colloidal growth with holographic microscopy. Soft Matter 11, 1062–1066 (2015).

    ADS  Google Scholar 

  68. Shpaisman, H., Jyoti Krishnatreya, B. & Grier, D. G. Holographic microrefractometer. Appl. Phys. Lett. 101, 091102 (2012).

    ADS  Google Scholar 

  69. Cheong, F. C., Duarte, S., Lee, S.-H. & Grier, D. G. Holographic microrheology of polysaccharides from Streptococcus mutans biofilms. Rheol. Acta 48, 109–115 (2009).

    Google Scholar 

  70. Wang, C. et al. Holographic characterization of protein aggregates. J. Pharm. Sci. 105, 1074–1085 (2016).

    Google Scholar 

  71. Fung, J. & Hoang, S. Computational assessment of an effective-sphere model for characterizing colloidal fractal aggregates with holographic microscopy. J. Quant. Spectrosc. Radiat. Transf. 236, 106591 (2019). This work demonstrates the range of validity of the effective-sphere model in hologram analysis, used widely in industrial applications.

    Google Scholar 

  72. Wang, C. et al. Holographic characterization of colloidal fractal aggregates. Soft Matter 12, 8774–8780 (2016).

    ADS  Google Scholar 

  73. Altman, L. E., Quddus, R., Cheong, F. C. & Grier, D. G. Holographic characterization and tracking of colloidal dimers in the effective-sphere approximation. Soft Matter 17, 2695–2703 (2021).

    ADS  Google Scholar 

  74. Philips, L. A. et al. Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions. Water Res. 122, 431–439 (2017).

    Google Scholar 

  75. Cheong, F. C. et al. Holographic characterization of colloidal particles in turbid media. Appl. Phys. Lett. 111, 153702 (2017).

    ADS  Google Scholar 

  76. Mackowski, D. W. & Mishchenko, M. I. Calculation of the T matrix and the scattering matrix for ensembles of spheres. J. Opt. Soc. Am. A 13, 2266–2278 (1996).

    ADS  Google Scholar 

  77. Leahy, B. et al. Large depth-of-field tracking of colloidal spheres in holographic microscopy by modeling the objective lens. Opt. Express 28, 1061–1075 (2020).

    ADS  Google Scholar 

  78. Alexander, R., Leahy, B. & Manoharan, V. N. Precise measurements in digital holographic microscopy by modeling the optical train. J. Appl. Phys. 128, 060902 (2020). This review highlights the historic development of the generative modelling approach to holograms (the only review to our knowledge that does so) and discusses the current abilities and limitations of existing generative models.

    ADS  Google Scholar 

  79. Geyer, C. J. in Handbook of Markov Chain Monte Carlo (eds Brooks, S., Gelman, A., Jones, G. L. & Meng, X.-L.) 3–48 (Chapman & Hall/CRC, 2011).

  80. Hansen, N. & Ostermeier, A. Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. in Proc. IEEE Int. Conf. Evolutionary Computation 312–317 https://doi.org/10.1109/ICEC.1996.542381 (1996).

  81. Neal, R. M. in Handbook of Markov Chain Monte Carlo (eds. Brooks, S., Gelman, A, Jones, G L, & Meng, X L) 113–162 (Chapman & Hall/CRC Handbooks of Modern Statistical Methods, 2011).

  82. Earl, D. J. & Deem, M. W. Parallel tempering: theory, applications, and new perspectives. Phys. Chem. Chem. Phys. 7, 3910–3916 (2005).

    Google Scholar 

  83. Barkley, S. et al. Holographic microscopy with Python and HoloPy. Comput. Sci. Eng. 22, 72–82 (2019).

    Google Scholar 

  84. Crocker, J. & Grier, D. Methods of digital video microscopy for colloidal studies. J. Colloid Interf. Sci. 179, 298–310 (1996).

    ADS  Google Scholar 

  85. Krishnatreya, B. J. & Grier, D. G. Fast feature identification for holographic tracking: the orientation alignment transform. Opt. Express 22, 12773 (2014).

    ADS  Google Scholar 

  86. Parthasarathy, R. Rapid, accurate particle tracking by calculation of radial symmetry centers. Nat. Methods 9, 724–726 (2012).

    Google Scholar 

  87. Rotskoff, G. M. & Vanden-Eijnden, E. Trainability and accuracy of neural networks: an interacting particle system approach. Preprint at https://doi.org/10.48550/arXiv.1805.00915 (2018).

  88. Newby, J. M., Schaefer, A. M., Lee, P. T., Forest, M. G. & Lai, S. K. Convolutional neural networks automate detection for tracking of submicron-scale particles in 2D and 3D. Proc. Natl Acad. Sci. USA 115, 9026–9031 (2018).

    ADS  Google Scholar 

  89. Schneider, B., Dambre, J. & Bienstman, P. Fast particle characterization using digital holography and neural networks. Appl. Opt. 55, 133 (2016).

    ADS  Google Scholar 

  90. Klein, E. Structure and Dynamics of Colloidal Clusters. PhD Thesis, Harvard Univ. (2019).

  91. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://doi.org/10.48550/arXiv.1412.6980 (2014).

  92. Bottou, L. in Proc. COMPSTAT’2010 (eds Lechevallier, Y. & Saporta, G.) 177–186 (Physica-Verlag HD, 2010).

  93. Glorot, X., Bordes, A. & Bengio, Y. in Proc. Fourteenth Int. Conf. Artificial Intelligence and Statistics Vol. 15 (eds Gordon, G., Dunson, D. & Dudík, M.) 315–323 (PMLR, 2011).

  94. Redmon, J. & Farhadi, A. YOLOv3: an incremental improvement. Preprint at https://doi.org/10.48550/arXiv.1804.02767 (2018).

  95. Meng, G., Arkus, N., Brenner, M. P. & Manoharan, V. N. The free-energy landscape of clusters of attractive hard spheres. Science 327, 560–563 (2010).

    ADS  Google Scholar 

  96. Szegedy, C., Vanhoucke, V., Ioffe, S., Shlens, J. & Wojna, Z. Rethinking the inception architecture for computer vision. in Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR) 2818–2826 (IEEE, 2016).

  97. Pickering, S. U. Emulsions. J. Chem. Soc. Trans. 91, 2001–2021 (1907).

    Google Scholar 

  98. Xiao, J., Li, Y. & Huang, Q. Recent advances on food-grade particles stabilized Pickering emulsions: fabrication, characterization and research trends. Trends Food Sci. Tech. 55, 48–60 (2016).

    Google Scholar 

  99. Yoon, K. Y. et al. Core flooding of complex nanoscale colloidal dispersions for enhanced oil recovery by in situ formation of stable oil-in-water Pickering emulsions. Energ. Fuels 30, 2628–2635 (2016).

    Google Scholar 

  100. Bhargava, A., Francis, A. V. & Biswas, A. K. Interfacial studies related to the recovery of mineral slimes in a water–hydrocarbon liquid-collector system. J. Colloid Interf. Sci. 64, 214–227 (1978).

    ADS  Google Scholar 

  101. Aveyard, R., Binks, B. P. & Clint, J. H. Emulsions stabilised solely by colloidal particles. Adv. Colloid Interfac. 100–102, 503–546 (2003).

    Google Scholar 

  102. Dinsmore, A. D. et al. Colloidosomes: selectively permeable capsules composed of colloidal particles. Science 298, 1006–1009 (2002).

    ADS  Google Scholar 

  103. Rahmani, A. M., Wang, A., Manoharan, V. N. & Colosqui, C. E. Colloidal particle adsorption at liquid interfaces: capillary driven dynamics and thermally activated kinetics. Soft Matter 12, 6365–6372 (2016).

    ADS  Google Scholar 

  104. Fung, J. & Manoharan, V. N. Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters. Phys. Rev. E 88, 020302 (2013).

    ADS  Google Scholar 

  105. Perry, R. W., Meng, G., Dimiduk, T. G., Fung, J. & Manoharan, V. N. Real-space studies of the structure and dynamics of self-assembled colloidal clusters. Faraday Discuss. 159, 211–234 (2013).

    ADS  Google Scholar 

  106. Zia, R. N. Active and passive microrheology: theory and simulation. Annu. Rev. Fluid Mech. 50, 371–405 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  107. Style, R. W. et al. Traction force microscopy in physics and biology. Soft Matter 10, 4047–4055 (2014).

    ADS  Google Scholar 

  108. Cheong, F. C. & Grier, D. G. Rotational and translational diffusion of copper oxide nanorods measured with holographic video microscopy. Opt. Express 18, 6555 (2010).

    ADS  Google Scholar 

  109. Makarchuk, S., Beyer, N., Gaiddon, C., Grange, W. & Hébraud, P. Holographic traction force microscopy. Sci. Rep. 8, 3038 (2018).

    ADS  Google Scholar 

  110. Moerner, W. E. & Fromm, D. P. Methods of single-molecule fluorescence spectroscopy and microscopy. Rev. Sci. Instrum. 74, 3597–3619 (2003).

    ADS  Google Scholar 

  111. Steelman, Z. A., Eldridge, W. J., Weintraub, J. B. & Wax, A. Is the nuclear refractive index lower than cytoplasm? Validation of phase measurements and implications for light scattering technologies. J. Biophotonics 10, 1714–1722 (2017).

    Google Scholar 

  112. Liu, P. Y. et al. Real-time measurement of single bacterium’s refractive index using optofluidic immersion refractometry. Procedia Eng. 87, 356–359 (2014).

    Google Scholar 

  113. Molaei, M. & Sheng, J. Imaging bacterial 3D motion using digital in-line holographic microscopy and correlation-based de-noising algorithm. Opt. Express 22, 32119 (2014).

    ADS  Google Scholar 

  114. Wang, A., Garmann, R. F. & Manoharan, V. N. Tracking E. coli runs and tumbles with scattering solutions and digital holographic microscopy. Opt. Express 24, 23719–23725 (2016).

    ADS  Google Scholar 

  115. Bozzuto, G. & Molinari, A. Liposomes as nanomedical devices. Int. J. Nanomed. 10, 975–999 (2015).

    Google Scholar 

  116. Deamer, D. The role of lipid membranes in life’s origin. Life 7, 5 (2017).

    Google Scholar 

  117. Schwille, P. & Diez, S. Synthetic biology of minimal systems. Crit. Rev. Biochem. Mol. 44, 223–242 (2009).

    Google Scholar 

  118. Spustova, K., Köksal, E. S., Ainla, A. & Gözen, I. Subcompartmentalization and pseudo-division of model protocells. Small 17, 2005320 (2021).

    Google Scholar 

  119. Wang, A., Chan Miller, C. & Szostak, J. W. Core-shell modeling of light scattering by vesicles: effect of size, contents, and lamellarity. Biophys. J. 116, 659–669 (2019).

    ADS  Google Scholar 

  120. Tran, L. H. A. et al. Measuring vesicle loading with holographic microscopy. Preprint at https://doi.org/10.48550/arXiv.2204.13068 (2022).

  121. Quinn, M. K. et al. How fluorescent labelling alters the solution behaviour of proteins. Phys. Chem. Chem. Phys. 17, 31177–31187 (2015).

    Google Scholar 

  122. Hughes, L. D., Rawle, R. J. & Boxer, S. G. Choose your label wisely: water-soluble fluorophores often interact with lipid bilayers. PLoS ONE 9, e87649 (2014).

    ADS  Google Scholar 

  123. Markel, V. Introduction to the Maxwell Garnett approximation: tutorial. J. Opt. Soc. Am. A 33, 1244–1256 (2016).

    ADS  Google Scholar 

  124. Zagzag, Y., Soddu, M. F., Hollingsworth, A. D. & Grier, D. G. Holographic molecular binding assays. Sci. Rep. 10, 1932 (2020).

    ADS  Google Scholar 

  125. Altman, L. E. & Grier, D. G. Interpreting holographic molecular binding assays with effective medium theory. Biomed. Opt. Express 11, 5225 (2020).

    Google Scholar 

  126. Snyder, K., Quddus, R., Hollingsworth, A. D., Kirshenbaum, K. & Grier, D. G. Holographic immunoassays: direct detection of antibodies binding to colloidal spheres. Soft Matter 16, 10180–10186 (2020).

    ADS  Google Scholar 

  127. Draine, B. T. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848–872 (1988).

    ADS  Google Scholar 

  128. Ruffner, D. B., Cheong, F. C., Blusewicz, J. M. & Philips, L. A. Lifting degeneracy in holographic characterization of colloidal particles using multi-color imaging. Opt. Express 26, 13239–13251 (2018).

    ADS  Google Scholar 

  129. Rawat, S., Wendoloski, J. & Wang, A. cGAN-assisted imaging through stationary scattering media. Opt. Express 30, 18145–18155 (2022).

    ADS  Google Scholar 

  130. Abadi, M. et al. TensorFlow: large-scale machine learning on heterogeneous distributed systems. Preprint at https://doi.org/10.48550/arXiv.1603.04467 (2015).

  131. Bradbury, J. et al. JAX: composable transformations of Python + NumPy programs. GitHub http://github.com/google/jax (2018).

  132. Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A. & Blei, D. M. Automatic differentiation variational inference. J. Mach. Learn. Res. 18, 1–45 (2017).

    MathSciNet  MATH  Google Scholar 

  133. Jouppi, N. P. et al. In-datacenter performance analysis of a Tensor Processing Unit. in Proc. 44th Annual Int. Symp. Computer Architecture 1–12 (Association for Computing Machinery, 2017).

  134. Leith, E. N., Upatnieks, J. & Haines, K. A. Microscopy by wavefront reconstruction. J. Opt. Soc. Am. 55, 981–986 (1965).

    ADS  Google Scholar 

  135. Schnars, U. & Jüptner, W. Direct recording of holograms by a CCD target and numerical reconstruction. Appl. Opt. 33, 179–181 (1994). This paper represents another major development in the field of holographic microscopy: the application of the digital camera, which allows holograms to be reconstructed numerically rather than optically.

    ADS  Google Scholar 

  136. Hickling, R. Holography of liquid droplets. J. Opt. Soc. Am. 59, 1334–1339 (1969).

    ADS  Google Scholar 

  137. Slimani, F., Grehan, G., Gouesbet, G. & Allano, D. Near-field Lorenz–Mie theory and its application to microholography. Appl. Opt. 23, 4140–4148 (1984).

    ADS  Google Scholar 

  138. Trujillo, C., Castañeda, R., Piedrahita-Quintero, P. & Garcia-Sucerquia, J. Automatic full compensation of quantitative phase imaging in off-axis digital holographic microscopy. Appl. Opt. 55, 10299–10306 (2016).

    ADS  Google Scholar 

  139. Popescu, G. et al. Fourier phase microscopy for investigation of biological structures and dynamics. Opt. Lett. 29, 2503–2505 (2004).

    ADS  Google Scholar 

  140. Joo, C., Akkin, T., Cense, B., Park, B. H. & de. Boer, J. F. Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging. Opt. Lett. 30, 2131–2133 (2005).

    ADS  Google Scholar 

  141. Piliarik, M. & Sandoghdar, V. Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites. Nat. Commun. 5, 1–8 (2014).

    Google Scholar 

  142. Young, G. et al. Quantitative mass imaging of single biological macromolecules. Science 360, 423–427 (2018).

    ADS  Google Scholar 

  143. Mahmoodabadi, R. G. et al. Point spread function in interferometric scattering microscopy (iSCAT). Part I: aberrations in defocusing and axial localization. Opt. Express 28, 25969–25988 (2020).

    ADS  Google Scholar 

Download references

Acknowledgements

Work at Harvard is supported by the National Science Foundation under grant DMR-2011754 and by the Department of Defense through the National Defense Science & Engineering Graduate Fellowship Program. Work at UNSW Sydney was supported by the Human Frontier of Science Program Grant (RPG0029/2020 to A.W.), and A.W. was supported by the Australian Research Council Discovery Early Career Award (DE210100291). Work at NYU was supported by the National Science Foundation under grants DMR-2104837, DMR-1420073 and DMR-0922680, and by the National Institutes of Health under grant R44TR001590.

Author information

Authors and Affiliations

Authors

Contributions

Introduction (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Experimentation (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Results (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Applications (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Reproducibility and data deposition (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Limitations and optimizations (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Outlook (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.); Overview of the Primer (C.M., L.E.A., S.R., A.W., D.G.G. and V.N.M.).

Corresponding author

Correspondence to Vinothan N. Manoharan.

Ethics declarations

Competing interests

D.G.G. is a founder of Spheryx, Inc., which manufactures instruments for holographic particle characterization. The remaining authors declare no competing interests.

Peer review

Peer review information

Nature Reviews Methods Primers thanks Radim Chmelik; Laurence Wilson, who co-reviewed with Sam Matthews; and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related links

CATCH: https://github.com/laltman2/CATCH

HDF5: https://www.hdfgroup.org/solutions/hdf5/

HoloPy: http://holopy.readthedocs.io/

pylorenzmie: https://github.com/davidgrier/pylorenzmie

Glossary

Holograms

2D intensity patterns resulting from the interference between light scattered from an object and a reference beam.

Fringes

The bright or dark bands in an image that are produced by the interference of light.

Holographic microscopy

The use of a microscope with a coherent or semi-coherent light source to record holograms of microscopic objects.

Reconstruction

The process of illuminating a hologram with a beam such that the hologram acts as a diffraction grating.

Tomograms

Images recorded by a penetrating wave that represents a cross section of a 3D object.

Colloidal particles

Nanoparticles or microparticles suspended in a fluid or other medium.

Scattering

The interaction of electromagnetic radiation with an object resulting in a change in the direction of the light.

Coherent

Light that has a narrow distribution of frequencies and a well-defined phase, such that interference can be observed.

Collimated

A beam of light with parallel rays.

Objective lens

A lens or collection of lenses that focus and magnify light to form an image.

Tube lens

A lens or series of lenses that focus parallel rays to form an image on a sensor or eyepiece.

Speckle

Fluctuating bright and dark regions in an image that arise from extraneous scattering and interference.

Spherical aberration

A type of optical aberration in which rays nearer the edge of a lens are deflected more than those near its axis.

Capillary action

Flow driven by interfacial tension.

Syringe pumps

Volumetrically controlled pumps that deliver fluid by moving a syringe piston, typically resulting in a constant flow rate.

Pressure pumps

Pumps that are pressure-driven and have controllers to maintain constant pressure.

Dynamic range

The range of intensities that a sensor can record.

Quantum efficiency

A measure of the sensitivity of a detector, determined by how many incident photons are converted into electrons.

Dark count

The intensity recorded by a sensor or camera in the absence of a signal.

Bayesian parameter estimation

A statistical inference technique yielding the probability distribution of the parameters of a model given the data.

Marginalized uncertainties

The uncertainties in a model parameter determined by accounting for correlations with other parameters.

Markov-chain Monte Carlo

(MCMC). A numerical method that uses a biased random walk through the parameter space to both estimate a probability distribution and integrate it.

Convolutional neural networks

(CNNs). Machine-learning algorithms that use convolution layers to process higher-dimensional image data.

Support vector machines

Machine-learning algorithms that distinguish data points using hyperplanes in a high-dimensional parameter space.

ReLU

The rectified linear activation function, a piecewise function that returns zero for negative inputs and returns the input for positive inputs.

Brownian motion

The random motion of particles suspended in a medium due to collisions with the surrounding molecules.

Polydispersity

The distribution of sizes within a sample.

Graticule

A set of parallel lines with known spacing used for measuring scale.

Lossy encoding

Methods of compressing or transferring data that approximate or down-sample the data.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Martin, C., Altman, L.E., Rawat, S. et al. In-line holographic microscopy with model-based analysis. Nat Rev Methods Primers 2, 83 (2022). https://doi.org/10.1038/s43586-022-00165-z

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s43586-022-00165-z

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing