Acoustofluidic phase microscopy in a tilted segmentation-free configuration
Julián Mejía Morales, Björn Hammarström, Gian Luca Lippi, Massimo Vassalli, Peter Glynne-Jones
BBiomicrofluidics , 014102 (2021); https://doi.org/10.1063/5.0036585 , 014102© 2021 Author(s). Acoustofluidic phase microscopy in a tiltedsegmentation-free configuration
Cite as: Biomicrofluidics , 014102 (2021); https://doi.org/10.1063/5.0036585Submitted: 06 November 2020 . Accepted: 17 December 2020 . Published Online: 05 January 2021 Julián Mejía Morales, Björn Hammarström, Gian Luca Lippi, Massimo Vassalli, and Peter Glynne-Jones
ARTICLES YOU MAY BE INTERESTED IN
Leveraging multimodal microscopy to optimize deep learning models for cell segmentationAPL Bioengineering , 016101 (2021); https://doi.org/10.1063/5.0027993Injectable biocompatible poly(2-oxazoline) hydrogels by strain promoted alkyne–azidecycloadditionBiointerphases , 011001 (2021); https://doi.org/10.1116/6.0000630Preface: A Two-Day Conference on Flexible Electronics for Electric Vehicles (FlexEV-2020)AIP Conference Proceedings , 010001 (2020); https://doi.org/10.1063/12.0001375 coustofluidic phase microscopy in a tiltedsegmentation-free configuration Cite as: Biomicrofluidics , 014102 (2021); doi: 10.1063/5.0036585 View Online Export Citation
CrossMark
Submitted: 6 November 2020 · Accepted: 17 December 2020 ·Published Online: 5 January 2021Julián Mejía Morales,
Björn Hammarström,
Gian Luca Lippi, Massimo Vassalli, and Peter Glynne-Jones AFFILIATIONS Institut de Physique de Nice, Université Côte d ’ Azur, CNRS, 06560 Valbonne, France Department of Experimental Medicine, University of Genova, 16149 Genova, Italy Engineering Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom KTH Royal Institute of Technology, 100 44 Stockholm, Sweden James Watt School of Engineering, University of Glasgow, G12 8LT Glasgow, United Kingdom a) Author to whom correspondence should be addressed: [email protected]
ABSTRACT
A low-cost device for registration-free quantitative phase microscopy (QPM) based on the transport of intensity equation of cells in continu-ous flow is presented. The method uses acoustic focusing to align cells into a single plane where all cells move at a constant speed. Theacoustic focusing plane is tilted with respect to the microscope ’ s focal plane in order to obtain cell images at multiple focal positions. As thecells are displaced at constant speed, phase maps can be generated without the need to segment and register individual objects. The pro-posed inclined geometry allows for the acquisition of a vertical stack without the need for any moving part, and it enables a cost-effectiveand robust implementation of QPM. The suitability of the solution for biological imaging is tested on blood samples, demonstrating theability to recover the phase map of single red blood cells flowing through the microchip. Published under license by AIP Publishing. https://doi.org/10.1063/5.0036585
I. INTRODUCTION
Quantitative Phase Microscopy (QPM) is a computationalapproach that utilizes bright field optics to generate cell phasemaps.
Each pixel of a phase map brings information on theoptical thickness of the sample, a convolution between the actualthickness and the refractive index (RI). For an homogeneous mate-rial of known RI, the QPM technique provides a direct measure ofthe volume. QPM has demonstrated to be effective in many appli-cations, and it offers significant advantages over traditional micros-copy when imaging transparent phase objects, such as live cells inculture medium. Two main families of QPM implementation exist, either basedon interferometry [as in Digital Holography (DH) ] or associatedwith the numerical processing of a stack of defocused bright fieldimages [making use of the Transport of Intensity Equation (TIE) ].The latter presents several advantages which render it simpler andless expensive than DH-based QPM: less stringent mechanicalstability and requirements on path length (since it avoids interference), computational simplicity, operation with partiallycoherent illumination sources, and the lack of constraints onhardware.QPM is a powerful label-free technique offering high sensitiv-ity, long term non-invasive imaging, and robust morphometricquantification of living cells. For example, QPM has been effec-tively used to measure the RI and the osmotic-induced volumechanges in erythrocytes, providing a precise morphometricdescription of cells. The same approach on white blood cellsallowed for the identification of robust biomarkers suitable for dis-criminating between healthy and diseased states. Moreover, fornonhomogeneous materials, such as living cells, QPM can be seenas a contrast enhancement technique to highlight organelles andstructures with different RIs. This perspective has been adopted todescribe intracellular motility and dynamic evolution.
Furthermore, QPM has been used to detect cell parasites such as
Plasmodium falciparum inside Red Blood Cells (RBCs).
Traditional bright field and phase contrast microscopy, including
Biomicrofluidics
ARTICLE scitation.org/journal/bmf
Biomicrofluidics15,
Biomicrofluidics15, ifferential Interference Contrast (DIC) microscopy, is less suitablefor identifying complex structures such as the mitochondrial net-works inside the cell due to the low absorption and scattering con-trast of the biological samples. On the other hand, QPM enablessuch structure visualization, together with their dynamics, withhigh contrast.
The main limit to the applicability of TIE-based QPM is theneed for acquiring a stack of images across the focal plane with welldefined focal offsets. Typically, this requires the mechanical transla-tion of either the camera or the object, introducing an expensivehardware component and requiring a longer and delicate imagingprocedure. This is particularly detrimental for the implementationof high throughput imaging procedures for diagnostic purposes.Some solutions have been proposed to achieve high throughputTIE-based QPM, either implementing strategies for fast scanningof the focal plane using tunable lenses or using smart optical con-figurations to obtain one-shot TIE imaging. – However, theseapproaches require rather expensive optical components or sub-stantial modifications to the standard bright field microscopyapparatus.In this work, we propose a simple and inexpensive techniquefor a fast, real-time implementation of TIE cytometry by combininga microfluidic channel, in a tilted configuration, with cell acousticfocusing. A transmission microscope is used to acquire images ofthe cells, levitated by the acoustic field, and translated by the fluidflow through the optical system ’ s focal plane, where the latterforms a controlled angle with the acoustic field ’ s focal plane locatedinside the microfluidic channel [cf. Fig. 1(b)]. Images are dividedalong the flow direction into stripes so that each stripe corresponds to a region of a similar amount of defocusing. Individual stripes areassembled into stacks for processing. Minimal registration isneeded, as the imaging rate is matched to the flow rate such thatobjects appear in the same position in each stripe.In a normal microfluidic channel, the parabolic flow profilewould cause flowing cells to move with a wide distribution of veloc-ities depending on their proximity to the walls. The acoustic focus-ing moves all cells to the same position in the flow profile, ensuringthat they all move at the same speed and maintain a fixed arrange-ment within the focused plane. The described configuration,therefore, allows for high throughput by retrieving the phase mapof several cells at once, leading to a performance increase withoutspecial optical elements.Cell orientation is also manipulated by the acoustic field.Previous work has shown that in an acoustic planar standingwave, RBCs are caused to rotate such that the disk of the cell lieswithin the pressure nodal plane. In our setup, this creates a “ flat ” view of the cells which exposes a maximal area of each cell to theoptics, and we conjecture that this leads to optimal informationfrom the image compared with other possible orientations.Additionally, by aligning cells to the center of the flow channel,where the shear stress gradients are at a minimum and symmetri-cal, the cells are not induced to “ tumble ” as would be found inother arrangements. This is important as the method describedhere relies on a lack of rotation between exposures.Our configuration, thus, enables the realization of an inexpen-sive device usable for cytometry-based diagnosis, a highly desirablegoal (particularly) in low-income countries, where access andquality of health care must be coupled to low costs.
II. MATERIALS AND METHODSA. Chip production
The microfluidic chip used in this work is based on a previ-ously proposed geometry.
In short, three layers of double sidedadhesive transfer tape sheet (468MP, 3M, USA) were joined toproduce a bond film 320 μ m thick. Using a laser cutter, the joinedbond film was cut into 5 (cid:1) : (cid:1) (cid:1)
75 mm ),and access holes to the microchannel of 1 mm diameter weredrilled at both ends of the channel.Underneath a portion of the fluid channel, a piezoelectrictransducer of lead zirconate titanate (PZ-26, Ferroperm,Kvistgaard, Denmark) was attached with epoxy (Epotek-301,Epoxy Technology, Inc., USA). The size of the transducer was(1 (cid:1) (cid:1)
50 mm ), and a wrap-around electrode was created onthe top-surface, in contact with the glass, using conductive silverpaint (SCP Silver Conductive Paint, Electrolube Ltd., UK).To drive the piezoelectric transducer, a TTi TG1006 signalgenerator was used in conjunction with a custom amplifier basedaround a high frequency op-amp (linear technologies, LT1210).Frequency was set at 2.286 MHz with a voltage amplitude of 2 Vppto achieve the acoustic focusing. This results in an acoustic pressurenode along the device ’ s half-height center plane, which createsacoustic radiation forces that direct blood cells toward that plane. FIG. 1.
Experimental configuration. (a) A pulsed light emitting diode (LED)illuminates the inclined microfluidic channel equipped with acoustic focusing.The images are collected by using a microscope and acquired with a digitalcamera. (b) A cross-sectional view of the microfluidic chip. The red blood cells(RBCs) initially travel in random orientations before entering the acoustic fieldcreated by the transducer. The radiation forces rotate the RBCs to be parallel tothe chamber walls and align them into a plane in the device center where theymove with uniform velocity. (c) The device tilt, relative to the optical axis, causesthem to move diagonally through the focal plane defined by the microscopeobjective, thereby producing images with a controlled amount of defocusing.
Biomicrofluidics
ARTICLE scitation.org/journal/bmf
Biomicrofluidics15,
Biomicrofluidics15, . Microscopy setup
The microscopy setup in this work is based on an invertedtransillumination microscope equipped with an OlympusLMPLFLN 50X Objective, NA ¼ : (cid:3) , thus providing a totalchange in the field of view of Δ z (cid:4) μ m.With normal illumination, a particle traversing the field of viewcreates significant motion blur during the camera ’ s exposure time. Toavoid this effect, pulsed illumination was implemented to capture thecell images during short pulses of light. For this purpose, the originalfilament was replaced by a high intensity light emitting diode, LED(LZ1-00G102, LED Engin, CA, USA). This was driven by a customdriver circuit. The duration of the pulses of light and their synchro-nization with the camera triggering were controlled by a microproces-sor (Arduino Uno, Arduino). Pulse length was set to 10 μ s. C. Blood samples
Rat ’ s blood was mixed with lithium heparin at 20 IU/ml. Theblood was centrifuged at 2000 rpm for 5 min and the plasma andbuffy coat removed by using Pasteur pipet. 50 μ l of the centrifugedblood was diluted with 5 ml of a hypotonic solution of PBS buffer(Sigma Aldrich (cid:4) (cid:1) cells/ μ l,equivalent to dilute 3400 folds the mice blood ’ s original samples. Thediluted blood samples provided a suitable cell density for imaging, inour case 40 –
70 cells in each field of view (FOV). Experiments wereconducted at room temperature (around 20 (cid:3)
C) and carried outwithin 48 h of blood collection.A syringe pump (Harvard Apparatus Pump Elite 11) and a10 ml glass syringe were used to pump the samples through thedevice at 200 μ l/min. Our previous work had shown that the pulsedillumination used here with 10 μ s exposure time resulted in insignifi-cant motion blur at the flow rates we demonstrate. The optical resultspresented here are, thus, not significantly dependent on flow rates,and with the RBCs near the center of the channel, we do not antici-pate any significant shear stress induced changes in the RBCs. D. Image acquisition and processing
Images were acquired using a Hamamatsu Flash 4.0 C11440monochrome camera set at 90 fps and 12 bits depth. All parameterswere manually controlled, and any auto-balance feature wasswitched off. To eliminate artifacts due to partially uneven illumi-nation and fixed objects in the field of view (dust and debris), animage of the static background I BG was extracted from the medianover time of the first ten images. The adoption of the median(instead of the average) ensures that image features associated withparticles passing through the frame are not given significant weightin the average (image averaging leads to particle ’ s trails). The back-ground image I BG was then subtracted from every acquired image I CCD and the difference I ¼ I CCD (cid:5) I BG used to recover the phase.Each image I ( t ) was divided into five stripes I m ( t ), m ¼ (cid:5) (cid:5) (cid:6) (cid:6) (cid:6)
2, of identical width ξ ¼ L =
5, where L is the image ’ s length along the direction of the flow [cf. Fig. 2(a)]. Thefloating objects are acoustically focused in the same plane so thatthey all move with the same speed v . If a series of five images isacquired with a delay τ ¼ ξ = v , the same objects imaged in a stripe m at time t will be in the stripe m þ t þ τ but at a differ-ent vertical position. Thus, if we call z m ( x , y ), the distance fromthe focal plane of each point of the stripe m , we can write z m ( x , y ) (cid:5) z m þ ( x , y ) ¼ δ =
5, where δ is the maximum defocusing[see Figs. 1(c) and 2(a)]. Taking this into account, a virtual inten-sity stack ^ I ( x , y , z ) can be constructed using the five intensitystripes I m (cid:5) ( t (cid:5) τ ) (cid:6) (cid:6) (cid:6) I m þ ( t þ τ ) containing the same field ofview at different heights. Little deviations might arise in the align-ment of the stripes by simple translation, mainly due to opticalaberrations. To correct for this deviation, the position of the stripeswas finely tuned based on a strict registration procedure. E. Solution of the TIE
The solution of the TIE, based on the two-dimensional FastFourier Transform (FFT), is fast and computationally simple.
First, the right hand side of Eq. (1), which represents the change ofintensity along the z axis, is computed by taking the forward deriv-ative evaluated at the in-focus plane z ¼
0, the standard procedurein the QPM TIE-based approach.
Then, a two dimensionalFFT is applied, to the obtained derivative, to retrieve the phase gra-dient ∇ ? f ( x , y ). A periodic boundary condition was applied to thestack when calculating the 2D FFT, which was useful to convert therectangular symmetry of the stack to a squared one. Indeed, a FIG. 2.
Schematics of the experimental setup. (a) Acoustic focusing forcesfloating particles to flow along a plane (in gray) that is tilted with respect to thefocal plane (in cyan). Samples in different regions of the image will be at differ-ent distances from the focal plane. If z is the coordinate along the optical axis,objects in the central stripe (black frame) will correspond to z ¼
0, while objectsin the first and last stripe (green and red, respectively) will sit at a higher dis-tance from the focal plane, z ¼ + δ for them. The image of length L wasdivided in five stripes of identical width ξ . (b) Images from each strip, takensequentially, to show the distribution of particles acquired at each vertical posi-tion, as defined by the stripes. The time series is converted into a series of ver-tical stacks by aligning the requisite stripes from images. Biomicrofluidics
ARTICLE scitation.org/journal/bmf
Biomicrofluidics15,
Biomicrofluidics15, quare symmetry is more favorable for 2D FFT calculations and isless prompt to artifacts of high frequencies. In addition, the 10thpercentile of the frequencies with larger amplitude j f ( u , ν ) j wasremoved to eliminate the periodic noise, regardless of its high- orlow-frequency nature. Finally, a second 2D FFT was applied toobtain the desired phase map f ( x , y ). The computational TIEsolution was based on the Numpy Pyhton library. III. RESULTS
The acquired ^ I ( x , y , z ) stack can be exploited to calculate theoptical thickness of the sample (phase reconstruction) using theTIE, ∇ ? I ( x , y ) ∇ ? f ( x , y ) ½ (cid:7) ¼ (cid:5) k @ I ( x , y , z ) @ z (cid:1)(cid:1)(cid:1)(cid:1) z ¼ , (1)where k is the wavenumber, ∇ ? is the in-plane gradient, I ( x , y ) ¼ ^ I ( x , y , 0) is the image in the focal plane, f ( x , y ) is the phase (to bereconstructed), and @ z indicates the derivative along the optical axisevaluated at z ¼
0. Under the assumption of a homogeneous and par-tially coherent illumination, this equation can be numerically solvedto finally obtain a quasi-3D real-time reconstruction of the object.The numerical solution of the TIE has been described in Sec. II E.The proposed approach has been adopted here to study asample of murine blood. Figure 3(a) shows reference images ofRBCs acquired with this method. For each sample, the in-focusbright field stripe (first column, m ¼
0) and the phase reconstruc-tion (third column) are reported, together with the phase gradient(central column). The phase gradient ∇ ? f ( x , y ) is calculatedfrom the last column and offers a high contrast qualitative representation. The effectiveness of the method is highlighted inFig. 3(b), where two phase profiles are shown, one obtained on aclump of cells (blue dotted profile) and the second on an isolatedRBC (red dotted profile). This picture demonstrates the quantitativeinformation carried by the TIE reconstruction. Aggregated cells(blue) are, in fact, higher than the single RBC (about twice asmuch) and present a rounded shape. In contrast, the red profileclearly highlights the expected donut-like shape of the isolatedRBC, which is acoustically trapped in a planar configuration. IV. DISCUSSION AND CONCLUSION
A simple chip geometry was utilized, with a rectangular crosssection where the width was much larger than the thickness. In thisconfiguration, the flow was laminar with a parabolic velocity profile(objects close to the center of the chip flow faster than objects nearthe walls). This geometry was previously adopted to perform imagecytometry on single algae, demonstrating a strong focusing effi-ciency, also resulting in a narrow velocity distribution of the float-ing objects. The adoption of a tilted configuration to obtain motion-freevertical stacks of floating objects has been previously suggested as alow-cost method to perform TIE-based QPM reconstruction.
Here, we propose a substantial improvement, provided by the inte-gration of the acoustic focusing mechanism. Two main advantagesare associated with this configuration. First, all objects flow throughthe field of view in the same plane so that an efficient stacking withcontrolled distances between planes is achieved for all objects, notonly for those that were by chance in the correct region. The abilityto finely control the distance between planes is crucial for thequality of the reconstruction, which is based on the calculation of thederivative. Moreover, focusing objects to a single plane means thatthey all move with the same velocity, and the motion can be effi-ciently approximated as a rigid translation. The majority of RBCswere observed to have rotated in the acoustic manipulation region toorient themselves within the pressure nodal plane and present a “ flat ” view. Furthermore, due to the absence of significant shearstresses at the channel half-height, no significant cell rotation wasobserved between the successive exposures required to build up theQPM image. To reconstruct the virtual stack in this condition, weare not required to isolate and track the motion of individual cells,resulting in a more rapid and efficient image processing that canincorporate aggregates and objects of unexpected size.The proposed device offers a low-cost approach to obtain physi-cal maps associated with the refractive index and thickness of thesample that can be further manipulated and exploited for differentaspects depending on the needs of the specific application. QPMmaps can be rendered as 3D-like images of the sample, in whichsingle objects can be effectively segmented using simple and fastthreshold-based algorithms, thus enabling effective extraction of real-time morphological features (see image 3 and Ref. 31). Moreover, thesame setup is suitable for addressing high throughput recognition ofinfected cells, where the presence of an intracellular parasite isknown to directly impact the phase map, as in the case of malariainfections. While QPM is primarily considered an imaging techni-que, it measures a physical quantity that relates to the refractiveindex, and this offers the possibility of using the system as a
FIG. 3. (a) The left column shows the stripe of the brightfield image of theRBCs in the focal plane; the center column shows the gradient of the phase r f ( x , y ) and the right column shows the phase of the images f ( x , y ). (b)Phase profile for a single RBC and for a clustered group of RBCs. Biomicrofluidics
ARTICLE scitation.org/journal/bmf
Biomicrofluidics15,
Biomicrofluidics15, pectroscopic device for the identification of the sample ’ s materialproperties, as recently proposed for the recognition of microplastics insea water. The method is based on the acquisition of image stripesthat can accommodate more than one cell at the time ( (cid:4)
10 cells atthe same time were mapped during experiments), thus increasingthe overall potential throughput (in terms of cells/s).In conclusion, the segmentation-free TIE-based setup pro-posed in this paper demonstrates a robust high throughputlow-cost single cell in-chip QPM. The simple implementationoffers a nonexpensive solution, suitable for environments where thecost is a core requirement, but where throughput and accuracy aremandatory. Examples include the identification of rare infectedcells in tropical diseases, screening applications in veterinary orfood science, or the identification of specific micrometrictargets in environmental samples. AUTHORS ’ CONTRIBUTIONS
J.M.M. and B.H. contributed equally to this manuscript.
SUPPLEMENTARY MATERIAL
Supplemental material provides a detailed description for thereconstruction of virtual stacks for transport of intensity equationQPM implementation.
ACKNOWLEDGMENTS
The authors would like to thank Dr. Stéphane Barland (UCANice) and Dr. Marco Sartore (ElbaTech SRL) for fruitful discus-sions. J.M.M. acknowledges the funding for international mobilityFrance – Italy provided by the Université Franco Italienne (UFI,Project No. C2-1031) and the Mexican Council of Science andTechnology (CONACyT) scholarship (No. 471712). P.G.J. gratefullyacknowledges fellowship funding by the UK EPSRC (No. EP/L025035/1). This work has also been supported by the French gov-ernment through the UCAJEDI Investments in the Future projectmanaged by the National Research Agency (ANR) with ReferenceNo. ANR-15-IDEX-01.
DATA AVAILABILITY
The data that support the findings of this study are availablefrom the corresponding author upon reasonable request.
REFERENCES A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. , 817 (1998). Y. Park, C. Depeursinge, and G. Popescu, Nat. Photonics , 578 (2018). C. L. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent,and L. M. D. Delbridge, Cell. Physiol. Biochem. , 193 –
200 (2006). W.-J. Zhou, X. Guan, F. Liu, Y. Yu, H. Zhang, T.-C. Poon, and P. P. Banerjee,Appl. Opt. , A229 – A234 (2018). S. Zhang, J. Cheng, and Y.-X. Qin, PLoS ONE , e38343 (2012). I. Vasilenko, V. Metelin, M. Nasyrov, V. Belyakov, A. Kuznetsov, andE. Sukhenko, Quant. Phase Imaging , 2078661 (2015). C. Martinez Torres, B. Laperrousaz, L. Berguiga, E. Boyer Provera, J. Elezgaray,F. E. Nicolini, V. Maguer-Satta, A. Arneodo, and F. Argoul, Quant. PhaseImaging II , 97182C (2016). T. Yamauchi, H. Iwai, and Y. Yamashita, Opt. Express , 5536 (2011). J. Jung, L. E. Matemba, K. Lee, P. E. Kazyoba, J. Yoon, J. J. Massaga, K. Kim,D.-J. Kim, Y. Park, and Y. Park, “ Characterizations of erythrocytes from individ-uals with sickle cell diseases and Malaria infection in Tanzania using a portablequantitative phase imaging unit, ” in International Conference on Photonics andImaging in Biology and Medicine (Optical Society of America, 2017),p. W3A.115. M. T. Rinehart, H. S. Park, K. A. Walzer, J.-T. A. Chi, and A. Wax, Sci. Rep. ,1 – Y. Ma, S. Guo, Y. Pan, R. Fan, Z. J. Smith, S. Lane, and K. Chu,J. Biophotonics , e201900011 (2019). S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, Opt. Lett. ,447 –
449 (2010). P. K. Poola, V. Jayaraman, K. Chaithanya, D. Rao, and R. John, OSA Contin. , 1215 (2018). C. Zuo, Q. Chen, W. Qu, and A. Asundi, Opt. Express , 24060 – K. Lee and Y. Park, Opt. Lett. , 3630 (2014). L. Waller, S. S. Kou, C. J. R. Sheppard, and G. Barbastathis, Opt. Express ,22817 (2010). W. Yu, X. Tian, X. He, X. Song, L. Xue, C. Liu, and S. Wang, Appl. Phys. Lett. , 071112 (2016). R. Zmijan, U. S. Jonnalagadda, D. Carugo, Y. Kochi, E. Lemm, G. Packham,M. Hill, and P. Glynne-Jones, RSC Adv. , 83206 (2015). O. Jakobsson, M. Antfolk, and T. Laurell, Anal. Chem. , 6111 (2014),pMID: 24863098. F. Merola, P. Memmolo, L. Miccio, R. Savoia, M. Mugnano, A. Fontana,G. d ’ Ippolito, A. Sardo, A. Iolascon, A. Gambale, and P. Ferraro, Light Sci. Appl. , e16241 (2016). P. Glynne-Jones, R. J. Boltryk, and M. Hill, Lab Chip , 1417 (2012). C. Willert, B. Stasicki, J. Klinner, and S. Moessner, Meas. Sci. Technol. ,075402 (2010). S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne,J. D. Warner, N. Yager, E. Gouillart, and T. Yu, and the scikit-image contribu-tors, PeerJ , e453 (2014). T. Sun, Z. Zhuo, W. Zhang, J. Lu, and P. Lu, Laser Phys. , 125601 (2018). S. S. Gorthi and E. Schonbrun, Opt. Lett. , 707 (2012). E. Bostan, E. Froustey, M. Nilchian, D. Sage, and M. Unser, “ Variational phaseimaging using the transport-of-intensity equation, ” IEEE Trans. Image Process. (2), 807 –
817 (2016). C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen,D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus,S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Río, M. Wiebe,P. Peterson, P. Gérard-Marchant, K. Sheppard, T. Reddy, W. Weckesser,H. Abbasi, C. Gohlke, and T. E. Oliphant, Nature , 357 (2020). B. Hammarström, M. Vassalli, and P. Glynne-Jones, J. Appl. Phycol. , 339(2019). N. C. Pégard and J. W. Fleischer, J. Biomed. Opt. , 040503 (2013). V. K. Jagannadh, M. D. Mackenzie, P. Pal, A. K. Kar, and S. S. Gorthi, Opt.Express , 22144 (2016). N. O. Loewke, S. Pai, C. Cordeiro, D. Black, B. L. King, C. H. Contag, B. Chen,T. M. Baer, and O. Solgaard, IEEE. Trans. Med. Imaging , 929 (2018). N. R. Patel, V. K. Chhaniwal, B. Javidi, and A. Anand,
Advanced MicroscopyTechniques IV; and Neurophotonics II (OSA, 2015). V. Bianco, P. Memmolo, P. Carcagnì, F. Merola, M. Paturzo, C. Distante, andP. Ferraro, Adv. Intel. Syst. , 1900153 (2020). T. Go, J. H. Kim, H. Byeon, and S. J. Lee, J. Biophotonics , e201800101(2018). F. A. M. Ramírez, E. M. Rodriguez, C. A. O. Castelblanco, and M. Camacho,in
Optical Methods for Inspection, Characterization, and Imaging of BiomaterialsIII , edited by P. Ferraro, M. Ritsch-Marte, S. Grilli, and C. K. Hitzenberger(SPIE, 2017). B. Rappaz, B. Breton, E. Shaffer, and G. Turcatti, Comb. Chem. HighThroughput Screen. , 80 (2014). Biomicrofluidics
ARTICLE scitation.org/journal/bmf
Biomicrofluidics15,