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Abstract
Due to the multiple scattering effect, quantitative phase imaging of thick specimens is challenging in biomedicine research. Phase gradient methods with partially coherent illumination in the reflection geometry have significant potential. However, to reconstruct two-dimensional (2D) phase information robustly, these methods cannot avoid changing the shear direction orthogonally. Here we propose a rotation-free method named quadriwave gradient light interference microscopy (qGLIM). qGLIM excludes conventional shear components and uses an amplitude-type spatial light modulator (SLM) to perform lateral shearing and phase shifting. By displaying checkerboard gratings on the SLM, we can reconstruct phase gradient information in orthogonal shear directions simultaneously. We extract the phase quantitatively by applying the phase-shifting technique and deconvolution algorithm. We demonstrate this approach by standard samples, thin samples, and thick multiple scattering samples.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical imaging for turbid samples is a challenging issue in biomedical research. Due to the multiple scattering, complex refractive index variation, and light absorption from samples, the image quality suffers from low signal-to-noise ratio and low contrast.
For turbid sample imaging, the most common techniques include multiphoton fluorescence microscopy and optical coherence tomography (OCT). Multiphoton fluorescence microscopy realizes optical sectioning by exciting fluorophore on the focal plane with nonlinear interaction [1,2]. However, fluorophore-based microscopy suffers from photobleaching, phototoxicity, and information loss on the unlabeled area. OCT is a label-free and noninvasive technique with micrometer-scale axial resolution and several millimeters of imaging depth [3,4]. OCT measures path-length differences between the sample beam and the reference beam by low-coherence interferometry. Though OCT offers excellent depth-of-field, the transverse resolution is compromised. The full-field quantitative phase imaging technology was motivated by OCT to supply high lateral resolution.
Quantitative phase imaging (QPI) is a powerful label-free imaging approach in biomedicine with the characteristics of the phase sensitivity to nanoscale, the spatial resolution to the diffraction limit, and the field of view to hundreds of microns squared [5,6]. QPI has proved its application in live cell imaging [7,8], cell growth [9–11], hematological diagnosis [12,13], cancer prognosis [14,15] based on thin pathological section.
Regarding QPI methods of thick sample imaging, phase gradient methods with partially coherent illumination have a significant potential space. There are two main kinds of phase gradient methods. They are mainly based on differential phase-contrast imaging (DPC) and differential interference contrast imaging (DIC), respectively.
DPC-based methods control illumination angles to cause amplitude variation that implies phase information and refractive index information. Oblique back illumination microscopy (OBM) is the reflective variant of conventional DPC techniques [16–19]. The phase of one shear direction is reconstructed with the subtraction and deconvolution operations of two images illuminated under two asymmetric angles [20]. Other variants of the OBM for imaging blood cells or brain biopsies have also been developed, such as dual-wavelength OBM [21,22], scanning version of OBM [23] and tomographic OBM [24–26]. However, to reconstruct a 2D phase map, OBMs should light up illumination pairs sequentially and take frames under different azimuth angles [22,26,27].
DIC-based techniques are based on interferometry and transfer path-length difference between sheared wavefronts into amplitude variation. Orientation independent DIC can measure gradient magnitude and azimuth distribution without mechanical rotation [28,29]. Gradient light interference microscopy (GLIM) combines a conventional DIC microscope and a phase-type spatial light modulator (SLM) to measure phase quantitatively [30–33]. Recently, GLIM measures the dry mass of cell nuclei in spheroids with artificial intelligence [34]. Epi-illumination gradient light interference microscopy (Epi-GLIM) is a reflective variant of GLIM, which increases imaging depth and optical sectioning ability [35]. The epi-illumination accompanied with broadband light source brings Epi-GLIM good optical sectioning ability, as the fully opened illumination aperture ensures a large coverage area in axial frequency. However, GLIM and Epi-GLIM reconstruct phase maps with gradient information in one shear direction, which may not be robust as two-dimensional phase reconstruction.
Rencently, harmonically decoupled gradient light interference microscopy (HD-GLIM) measures phase difference under orthogonal directions and calculates two-dimensional phase with spiral integration algorithm [36,37]. Unlike other methods [38,39], HD-GLIM works without traditional shear optics and expensive phase-type SLMs. In HD-GLIM, an amplitude-type SLM displays sinusoid patterns to introduce optical shearing and phase shifting [40]. The sinusoid patterns are rotated in orthogonal directions. A similar SLM-based structured illumination microscope is developed to enhance resolution [41]. The SLM generates sinusoid patterns for illumination and phase shifting. However, both of them need multiple frames to recover one phase map, which is time-consuming.
As an alternative solution, quadriwave lateral shearing interferometry (QLSI) is a powerful approach that enables orthogonal phase gradient measurement simultaneously with a modified Hartmann grating [42,43]. To realize the continuous shear distance variation of the grating, researchers proposed randomly encoded hybrid grating [44,45]. A phase-type SLM-based QLSI has been developed to overcome manufactory residuals and to avoid diffraction order filters [46]. A metasurface based QLSI also have been developed [47]. However, the phase gradient in orthogonal directions is retrieved by cropping the Fourier spectrum of the wavefronts [48]. The crop window should be set appropriately for different samples.
According to the methods above, many of them are in transmission mode, in which the imaging depth is limited in nature, as the light source cannot reach the camera if the samples are bulky or otherwise opaque.
In this work, we propose a quadriwave gradient light interference microscopy (qGLIM). qGLIM is based on bright-field microscopy and applies traditional epi-illumination and a 4f system. The amplitude-type SLM is placed at the center of the 4f system, which introduces light shearing and phase shifting. The SLM displays two-dimensional gratings to get phase gradients in orthogonal directions simultaneously. We realize phase-shifting by adding the initial phase of the grating. The shear distance can be modified by adjusting the grating pitch. We reconstruct the phase map by phase-shifting and the Wiener deconvolution algorithm. In summary, qGLIM is the reflective variant of HD-GLIM and combines two-dimensional grating used in QLSI. qGLIM avoids DIC optics, shear rotation, and filter window chosen in previous methods.
2. Principle
The setup is shown in Fig. 1. The system consists of Koehler illumination, imaging optics with an objective and a tube lens, a 4f system accompanied with SLM, and a CMOS. To improve the thick sample imaging ability of the system, LED (Thorlabs M780LP1) at 780nm with 30nm bandwidth is used as the light source, the power of which is 800mW. The spatial coherence of the light source can be adjusted by the aperture diaphragm in the Koehler setup, which enables changing optical sectioning depths. The temporal coherence of the light remains still, as the bandwidth maintains. The light is directed by the beam splitter and the objective (Nikon CFI Plan Fluor 20X, NA 0.5) to illuminate the sample. The light reflected from the sample carries unknown phase information and passes through the objective and tube lens to the imaging plane. In order to reconstruct phase information in a linear way, an amplitude type SLM (UPOLabs HDSLM80RA) is set at the Fourier plane of a 4f system, consisted of L3 and L4 (Thorlabs, LA1509-B), to perform four-step phase shifts. The SLM contains two linear polarizers (P1 and P2) to help modify the amplitude. P1 makes the polarization of incident light aligned to the slow axis of the SLM. The polarization of P2 is perpendicular to P1, which maximizes the modulation range of the amplitude. By displaying 2D diffraction gratings on the SLM, the incident wave diffracts into four replicas along x and y directions symmetrically (Fig. 2) [46,48], and they interfere with each other to create an interferogram on the CMOS (Basler acA1300-60gmNIR). Eq. (1)–Eq. (5) can express the diffraction process.
Fig. 1. Schematic representation (a) Schematic of the optical setup. (b) 2D diffraction grating with phase shifts $\phi _\delta$ displayed on the SLM.
The amplitude transmittance of a perfect 2D diffraction grating on the Fourier plane is given by:
In Eq. (1), $k=\dfrac {2 \pi }{\lambda _{0}} \cdot \dfrac {r}{f}$ denotes the transverse spatial frequency, where ${\lambda }_{0}$ is the central wavelength, $\boldsymbol r$ is the spatial coordinate, $f$ is the focal distance of L4. ${{\phi }_{\delta }}=0,\dfrac {\pi }{2},\pi,\dfrac {3\pi }{2}$ is the additional phase shifts introduced by SLM, ${x}_{0}$ and ${y}_{0}$ are shear distances along ${x}$ and ${y}$ directions respectively. According to Eq. (2), We can estimate the shear distance ${x}_{0}$ by determining the grating period ${d_{x}}$. $M$ is the magnification of the system. The calculation is the same for shear distance ${y}_{0}$. We can adjust the shear distance by changing the grating period, in case of a steep change in the sample to cause phase wrapping.
The pattern displayed on the SLM is the projection screen of the computer. So, the pattern itself will not introduce extra diffraction orders. But the SLM pixel itself have diffraction effect, as the pixel is not full filled. The $DC$ component can be canceled through the following calculations. Other diffraction orders will not interfere with the modulated light, because the shear distance caused by the SLM pixel exceeds the field of view, according to Eq. (2).
The image field passing through L3 is Fourier transformed, denoted as $U(\boldsymbol {k})$. After being modulated by the SLM, the image field with DC component induced by the SLM becomes:
The wave is inverse Fourier transformed on the back focal plane of L4:
We assume the amplitude of the four diffracted waves is uniform over the shear distance: $\left |U\left (x \pm x_{0}, y \pm y_{0}\right )\right | \cong |U(\boldsymbol {r})|$. The assumption is commonly used in differential phase-sensitive methods, as the shear distance is smaller than the diffraction limit and biological specimens rarely have steep changes in phase.
The intensity on the CMOS is given by:
After modulating the four-step phase shift by SLM, we can get the sum of differential phase in the $x$ and $y$ directions.
By Fourier transforming the sum of the differential phase and using Wiener deconvolution, we can obtain $\phi _{0}(x, y)$ directly. The calculation progress is shown as follows:
To reconstruct the phase gradient in x and y directions separately, we define:
3. Experiments and discussions
The experimental setup is presented in Fig. 1. The aperture diaphragm is closed to the minimum. Firstly, to validate the system, we image 5$\mu \mathrm {m}$ polystyrene beads embedded in immersion oil with a $\times$20/0.5 objective (Nikon). A reflective surface is set behind the beads as the background. We can calculate the phase of the beads theoretically as [35]:
where $\lambda _{0}\ (780\mathrm {~nm})$ is the central wavelength, $n\ (1.5788)$ is the refractive index of the bead, $n_{0}\ (1.515)$ is the refractive index of the oil, $d\ (5 \mu \mathrm {m})$ is the height of the bead. By fitting the experimental result and the simulation value $\left (\phi _{0}=5.139 \mathrm {rad}\right )$, as is shown in Fig. 3(b), we obtain the actual shear distance value, $x_{0}=y_{0}=586 \mathrm {~nm}$.Fig. 3. Imaging a 5$\mu \mathrm {m}$ polystyrene bead. (a) The phase gradient maps reconstructed by four intensity frames with 90$^{\circ }$ phase shift as an increment. (b) Comparison between red dashed line section in measured phase map and ideal phase profile.
Secondly, in order to quantify the spatial-temporal phase noise of the system, a glass slide without a sample is continuously imaged 256 times. The phase distribution of a hologram shows spatial phase sensitivity. The phase fluctuation of the red dot (Fig. 4(a)) among 256 frame stacks is shown in Fig. 4(c), which represents temporal phase sensitivity. The phase fluctuation between two consecutive holograms shows the spatial-temporal noise distribution (Fig. 4(b)). The standard deviation of spatial-temporal phase noise is 0.0435 rad between two consecutive phase maps in a $200 \times 200\ \mu \mathrm {m}^{2}$ area (Fig. 4(d)). The noise level is transferred to $d\ (5.297\ \mathrm {nm})$ by Eq. (18), which is far lower than the diffraction limit. The noise level can be affected by the stability of SLM and the noise induced by the CMOS. All these noises can be further suppressed.
Fig. 4. Spatial and temporal noise distribution. (a) Spatial noise distribution. (b) Spatial-temporal noise distribution. (c) Phase fluctuation in temporal domain. (d) Histogram of spatial-temporal noise and its standard deviation.
Thirdly, to show the imaging performance of the system on cells and tissues, we use red blood cells and stained esophagus section as specimens. Fig.5 shows red blood cells on the blood smear. We can obtain DIC like features by subtraction between corresponding interferograms, as illustrated in Fig. 5(a-b). The biconcave structure of normal red blood cells can be seen clearly in Fig. 5(c). Fig. 5(d-e) shows the phase gradient information in x and y directions.
Fig. 5. Human blood smear. (a-b) Interference data used for phase reconstruction. (c) The integrated phase map of the cells, the unit is $radian$. (d-e) The phase gradient of the cells in x and y directions, the unit is $radian/ \mu \mathrm {m}$.
In Fig. 6(a), we can easily distinguish four different layered structures from the cross-section of the esophagus contains, as is marked with dotted lines in Fig. 6(b). The lower left of Fig. 6(b) is the magnified basal layer of the epithelium, the purple arrow points out the stem cell, and the red arrow shows the proliferative basaloid cell. The lower right of Fig. 6(b) is the magnified myenteric plexus, and the orange arrow shows the neuron. Overall, these results indicate that the system can identify cells at 20$\times$ magnification fuzzily, but has sufficient imaging quality to identify characteristics of tissues, which would be helpful for pathological diagnosis.
Fig. 6. Cross section of the stained esophagus under 20$\times$ magnification. (a) Phase gradient of the tissue. (b) The reconstructed phase of the tissue and its details. Layers of the esophagus: (I) Nonkeratinized stratified squamous epithelium, (II) Lamina propria, (III) Muscularis mucosae, and (IV) Submucosae.
Finally, the system can suppress multiple scattering light, which is essential in thick sample imaging. We image the bee mouthparts at depths of 0, 30, 60, 90 $\ \mu \mathrm {m}$, as shown in Fig. 7. When the aperture diaphragm is closed to the minimum, the phase map shows the background of near layers and sample details (Fig. 7(a)). To maximum the optical sectioning ability, we open the aperture diaphragm fully, and thus we can get high condenser illumination numerical aperture. As shown in Fig. 7(b) and Visualization 1, the out-of-focus light is suppressed apparently, and the phase values decrease. Due to the optical sectioning ability, only a thin layer in the sample is detected. We scan the bee mouthparts deep into 139.5 $\mu \mathrm {m}$ with 94 frames of phase map at a step of 1.5 $\mu \mathrm {m}$ in the Z direction and put them into a 3D phase stack, as is shown in Fig. 8 and Visualization 2. The morphology of proboscis is clearly shown in these phase gradient maps. These results show the excellent optical sectioning ability of the system and show the potential for thick sample imaging.
Fig. 7. Phase maps ($radian$) of the bee mouthparts at different depth: 0, 30, 60, 90 $\mu \mathrm {m}$. (a) Imaged when the aperture diaphragm is closed to the minimum (condenser $\mathrm {NA}_{\mathrm {c}}=0.125$). (b) Imaged when the aperture diaphragm fully opened (condenser $\mathrm {NA}_{\mathrm {c}}=0.5$). The deep scanning video (see Visualization 1).
Fig. 8. Phase stack of the bee mouthparts from 0 $\mu \mathrm {m}$ to 139.5 $\mu \mathrm {m}$ in $3 \mathrm {D}$ view. The phase stack video (see Visualization 2).
4. Summary
We propose a quadriwave gradient light interference microscopy (qGLIM) by modulating 2D grating patterns with SLM. Firstly, the system combines the ideas of previous work and makes extensions: (1) from conventional DIC optics components combined with phase modulation to purely amplitude modulation based on SLM, (2) from shear direction rotation to rotation-free, (3) from transmission setup to reflection setup, which breaks the limit for thick sample imaging.
Secondly, by imaging red blood cells, the cross-section of the esophagus, and the bee mouthparts, the qGLIM shows the ability to image label-free cells, thin and histologically samples, thick samples, which is suitable for various occasions. qGLIM can combine with fluorescence microscopy for observation of specific substances, since they work in the same optical channel. Moreover, as DIC optics introduce polarized illumination, fiber bundle-based endoscopic probes can disturb the polarization statement and disrupt the phase information. qGLIM may find utility where DIC optics cannot be used, but widefield imaging is available, such as endoscopic probes.
Finally, there is still room for improvement. In our case, the camera exposure time is 10ms, the overall qGLIM frame rate is 2 phase frames per second. The computational time is overlapped with acquisition time. The frame rate is mainly limited by the SLM stabilization time that is 100ms. Moreover, like other DIC-based methods, qGLIM contains polarizing components that are invalid for birefringent samples. In further work, we will use DMD to replace the amplitude-type SLM to eliminate polarization and further enhance the imaging speed. Developing a single-shot microscope is also an important issue in live specimen observation. Recently, a single-shot quantitative phase gradient microscopy based on metasurfaces is proposed [49,50]. It uses two layers of metasurface to introduce lateral shearing and phase shifting. This method shots three images simultaneously and minimizes a DIC-based microscope into a few-layer scale device. Developing a single shot and fiber bundle-based endoscopic qGLIM for in-vivo imaging is also a meaningful topic in further research.
Funding
National Natural Science Foundation of China (51875227, 51975233); Natural Science Foundation for Distinguished Young Scholars of Hubei Province of China (2019CFA038); Shenzhen Technical Project (JCYJ20210324141814038).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7(3), 205–209 (2013). [CrossRef]
2. A. Escobet-Montalbán, F. M. Gasparoli, J. Nylk, P. Liu, Z. Yang, and K. Dholakia, “Three-photon light-sheet fluorescence microscopy,” Opt. Lett. 43(21), 5484–5487 (2018). [CrossRef]
3. W. Yuan, D. Chen, R. Sarabia-Estrada, H. Guerrero-Cázares, D. Li, A. Qui nones-Hinojosa, and X. Li, “Theranostic OCT microneedle for fast ultrahigh-resolution deep-brain imaging and efficient laser ablation in vivo,” Sci. Adv. 6(15), eaaz9664 (2020). [CrossRef]
4. H. Kawagoe, M. Yamanaka, and N. Nishizawa, “Axial resolution and signal-to-noise ratio in deep-tissue imaging with 1.7-μm high-resolution optical coherence tomography with an ultrabroadband laser source,” J. Biomed. Opt. 22(8), 085002 (2017). [CrossRef]
5. H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017). [CrossRef]
6. X. Chen, M. E. Kandel, and G. Popescu, “Spatial light interference microscopy: principle and applications to biomedicine,” Adv. Opt. Photonics 13(2), 353–425 (2021). [CrossRef]
7. N. Lue, W. Choi, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Quantitative phase imaging of live cells using fast fourier phase microscopy,” Appl. Opt. 46(10), 1836–1842 (2007). [CrossRef]
8. Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19(2), 1016–1026 (2011). [CrossRef]
9. G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Physiol. 295(2), C538–C544 (2008). [CrossRef]
10. S. Sridharan, M. Mir, and G. Popescu, “Simultaneous optical measurements of cell motility and growth,” Biomed. Opt. Express 2(10), 2815–2820 (2011). [CrossRef]
11. S. Aknoun, M. Yonnet, Z. Djabari, F. Graslin, M. Taylor, T. Pourcher, B. Wattellier, and P. Pognonec, “Quantitative phase microscopy for non-invasive live cell population monitoring,” Sci. Rep. 11(1), 4409 (2021). [CrossRef]
12. G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells, Mol., Dis. 41(1), 10–16 (2008). [CrossRef]
13. N. T. Shaked, L. L. Satterwhite, G. A. Truskey, A. P. Wax, and M. J. Telen, “Quantitative microscopy and nanoscopy of sickle red blood cells performed by wide field digital interferometry,” J. Biomed. Opt. 16(3), 030506 (2011). [CrossRef]
14. Z. Wang, G. Popescu, K. V. Tangella, and A. Balla, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16(11), 116017 (2011). [CrossRef]
15. V. Dubey, A. Ahmad, A. Butola, D. Qaiser, A. Srivastava, and D. S. Mehta, “Low coherence quantitative phase microscopy with machine learning model and Raman spectroscopy for the study of breast cancer cells and their classification,” Appl. Opt. 58(5), A112–A119 (2019). [CrossRef]
16. X. Ma, M. Yao, Z. Zhang, J. Peng, S. Li, and J. Zhong, “Computational oblique illumination microscopy with isotropic high resolution,” IEEE Trans. Comput. Imaging 6, 317–327 (2020). [CrossRef]
17. S. B. Mehta and C. J. Sheppard, “Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast,” Opt. Lett. 34(13), 1924–1926 (2009). [CrossRef]
18. L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23(9), 11394–11403 (2015). [CrossRef]
19. M. Chen, Z. F. Phillips, and L. Waller, “Quantitative differential phase contrast (DPC) microscopy with computational aberration correction,” Opt. Express 26(25), 32888–32899 (2018). [CrossRef]
20. T. N. Ford, K. K. Chu, and J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9(12), 1195–1197 (2012). [CrossRef]
21. T. N. Ford and J. Mertz, “Video-rate imaging of microcirculation with single-exposure oblique back-illumination microscopy,” J. Biomed. Opt. 18(06), 1 (2013). [CrossRef]
22. P. Ledwig, M. Sghayyer, J. Kurtzberg, and F. E. Robles, “Dual-wavelength oblique back-illumination microscopy for the non-invasive imaging and quantification of blood in collection and storage bags,” Biomed. Opt. Express 9(6), 2743–2754 (2018). [CrossRef]
23. J. Mertz, A. Gasecka, A. Daradich, I. Davison, and D. Coté, “Phase-gradient contrast in thick tissue with a scanning microscope,” Biomed. Opt. Express 5(2), 407–416 (2014). [CrossRef]
24. P. Ledwig and F. E. Robles, “Epi-mode tomographic quantitative phase imaging in thick scattering samples,” Biomed. Opt. Express 10(7), 3605–3621 (2019). [CrossRef]
25. P. B. Ledwig and F. E. Robles, “3D refractive index tomography with quantitative oblique back-illumination microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XXVII, vol. 11245 (International Society for Optics and Photonics, 2020), pp. 1–8.
26. P. C. Costa, Z. Guang, P. Ledwig, Z. Zhang, S. Neill, J. J. Olson, and F. E. Robles, “Towards in-vivo label-free detection of brain tumor margins with epi-illumination tomographic quantitative phase imaging,” Biomed. Opt. Express 12(3), 1621 (2021). [CrossRef]
27. P. C. Costa, P. Ledwig, A. Bergquist, J. Kurtzberg, and F. E. Robles, “Noninvasive white blood cell quantification in umbilical cord blood collection bags with quantitative oblique back-illumination microscopy,” Transfusion 60(3), 588–597 (2020). [CrossRef]
28. M. I. Shribak, J. LaFountain, D. S. C. Biggs, and S. Inoue, “Orientation-independent differential interference contrast microscopy and its combination with an orientation-independent polarization system,” J. Biomed. Opt. 13(1), 014011 (2008). [CrossRef]
29. M. Shribak, “Quantitative orientation-independent differential interference contrast microscope with fast switching shear direction and bias modulation,” J. Opt. Soc. Am. A 30(4), 769–782 (2013). [CrossRef]
30. T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017). [CrossRef]
31. M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, and K. G. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Microsc. 199(1), 79–84 (2000). [CrossRef]
32. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005). [CrossRef]
33. B. Heise, A. Sonnleitner, and E. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66(6), 312–320 (2005). [CrossRef]
34. M. E. Kandel, Y. R. He, Y. J. Lee, T. H.-Y. Chen, K. M. Sullivan, O. Aydin, M. T. A. Saif, H. Kong, N. Sobh, and G. Popescu, “Phase imaging with computational specificity (PICS ) for measuring dry mass changes in sub-cellular compartments,” Nat. Commun. 11(1), 6256 (2020). [CrossRef]
35. M. E. Kandel, C. Hu, G. N. Kouzehgarani, E. Min, K. M. Sullivan, H. Kong, J. M. Li, D. N. Robson, M. U. Gillette, C. Best-Popescu, and G. Popescu, “Epi-illumination gradient light interference microscopy for imaging opaque structures,” Nat. Commun. 10(1), 4691 (2019). [CrossRef]
36. M. R. Arnison, K. G. Larkin, C. J. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004). [CrossRef]
37. I. Choi, K. Lee, and Y. Park, “Compensation of aberration in quantitative phase imaging using lateral shifting and spiral phase integration,” Opt. Express 25(24), 30771–30779 (2017). [CrossRef]
38. T. J. McIntyre, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Differential interference contrast imaging using a spatial light modulator,” Opt. Lett. 34(19), 2988–2990 (2009). [CrossRef]
39. T. J. McIntyre, C. Maurer, S. Fassl, S. Khan, S. Bernet, and M. Ritsch-Marte, “Quantitative SLM-based differential interference contrast imaging,” Opt. Express 18(13), 14063–14078 (2010). [CrossRef]
40. Y. Wang, M. E. Kandel, M. J. Fanous, C. Hu, H. Chen, X. Lu, and G. Popescu, “Harmonically decoupled gradient light interference microscopy (HD-GLIM),” Opt. Lett. 45(6), 1487–1490 (2020). [CrossRef]
41. P. Gao, G. Pedrini, and W. Osten, “Phase retrieval with resolution enhancement by using structured illumination,” Opt. Lett. 38(24), 5204–5207 (2013). [CrossRef]
42. P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009). [CrossRef]
43. D. Fu, S. Oh, W. Choi, T. Yamauchi, A. Dorn, Z. Yaqoob, R. R. Dasari, and M. S. Feld, “Quantitative DIC microscopy using an off-axis self-interference approach,” Opt. Lett. 35(14), 2370–2372 (2010). [CrossRef]
44. T. Ling, D. Liu, X. Yue, Y. Yang, Y. Shen, and J. Bai, “Quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating,” Opt. Lett. 40(10), 2245–2248 (2015). [CrossRef]
45. T. Ling, J. Jiang, R. Zhang, and Y. Yang, “Quadriwave lateral shearing interferometric microscopy with wideband sensitivity enhancement for quantitative phase imaging in real time,” Sci. Rep. 7(1), 9–14 (2017). [CrossRef]
46. T. Fordey and Z. Bouchal, “Phase measurement by quadriwave lateral shearing interferometry using spatial light modulator,” in Fourteenth International Conference on Correlation Optics, vol. 11369 (International Society for Optics and Photonics, 2020), p. 1136912.
47. S. Khadir, D. Andrén, R. Verre, Q. Song, S. Monneret, P. Genevet, M. Käll, and G. Baffou, “Metasurface optical characterization using quadriwave lateral shearing interferometry,” ACS Photonics 8(2), 603–613 (2021). [CrossRef]
48. G. Baffou, “Quantitative phase microscopy using quadriwave lateral shearing interferometry (QLSI): principle, terminology, algorithm and grating shadow description,” J. Phys. D: Appl. Phys. 54(29), 294002 (2021). [CrossRef]
49. H. Kwon, E. Arbabi, S. M. Kamali, M. Faraji-Dana, and A. Faraon, “Single-shot quantitative phase gradient microscopy using a system of multifunctional metasurfaces,” Nat. Photonics 14(2), 109–114 (2020). [CrossRef]
50. Y. Baek and Y. Park, “Scaling down quantitative phase imaging,” Nat. Photonics 14(2), 67–68 (2020). [CrossRef]
