Shaping light beams, namely the process of engineering the irradiance and the wavefront of an optical radiation, is fundamental to many, if not all, optical applications. This is traditionally implemented with conventional free-space and bulky optics such as mirrors, optical lenses, and diffractive diffusers and more advanced components such as spatial light modulators [1,2]. The bulky nature of these components and of their combinations, the size of which is more than five orders of magnitude larger than the wavelength of the beam, imposes harsh alignment and stability constraints, which leads to limited performance even for applications where the cost is not a real limiting factor. In this context, photonic integrated circuits (PICs) are promising solutions to outperform conventional optical systems and provide new opportunities for beam shaping by taking advantage of their compatibility with complementary metal oxide semiconductor (CMOS) technology. PICs are able to shape and control optical beams in a compact and robust way. When optical phase arrays [3,4] are included in the PICs, they can be used, for instance, for reliable, low-power, and affordable light detection and ranging (LiDAR) applications [5] for image classification [6] or spaced-based optical communications terminals [7]. PICs designs that are less demanding in terms of the impact of residual fabrication errors than the aforementioned examples can already offer new functionalities, as recently unveiled for super-resolved near-field [8,9] and far-field [10,11] structured illumination microscopy, on-chip ion trapping for quantum computing [12], laser beam scanning [13], and optogenetic probes [14]. Here, we present a novel conceptual application of PICs that allows us to significantly outperform state-of-the-art coherent light source-based quantitative phase imaging (QPI) techniques that make use of bulky optical components or of compact metasurfaces. Our technique that works with coherent light provides a phase noise level comparable to the best one obtained with incoherent light sources. We take advantage of the integration and design flexibility of photonic integrated circuits to dynamically match their far-field emission pattern with specific positions at the aperture stop of a given imaging microscope objective. This approach allows us to implement low-phase noise quantitative phase imaging that makes use of the space-domain Kramers-Kronig (KK) relations, which was first implemented in electron microscopy [15] and recently extended for two-dimensional light microscopy [16]. The photonic integrated circuit provides the illumination beam required for taking advantage of the KK relations without any reshaping of the exit pupil of the collecting microscope objective. As a main result, we show that the compact nature of the PICs leads to a seven times improvement of the phase noise compared to the KK-based approach using conventional free-space optics and enables to image graphene monolayers with high contrast.

One of the main challenges to make quantitative phase imaging a powerful label-free method for investigating the morphology and refractive index of transparent objects is the phase stability of the instrument [17]. Any mechanical vibrations or air fluctuations along the optical path result in phase noise that spoils the image contrast. To mitigate this problem, several common-path approaches [16,18–21] have been proposed. In these configurations, the illuminating beam that is incident on the sample serves as the phase reference and follows the same optical path as the field scattered by the object. As the reference and scattered beam are subject to almost the same phase fluctuations, the noise resulting from these fluctuations is canceled out during the interference process at the camera sensor. In practice, even a common-path configuration is not fully immune to phase noise as the relative position of the illumination beam and of the scattered field has to be stable, as in the KK-based QPI technique discussed below.

Considering an optical microscope objective of a given numerical aperture (NA) and a plane wave illumination of the object with an incident scalar field Ein(r→), as in Fig. 1(a), the scalar spatial field E(r→) in the image plane at a location defined by the position vector r→=xx→+yy→ can be described as the sum of the unscattered Eu(r→) and scattered Es(r→) fields. Eu(r→) corresponds to the fraction of the field that is transmitted through the object with the same transverse wave vector k→in as the incident field. The transverse wave vector is defined as the projection of the wave vector in a plane perpendicular to the optical axis (Oz). Es(r→) results from the scattering process induced by the object. Its angular spectrum includes all the transverse wave vectors k→s=k→x+k→y other than the incident one and is limited to the spatial bandwidth of the microscope, which is represented, for a wavelength λ, as a disk of radius kmax=2πλNA in the k-space diagram in Fig. 1(b). The field E(r→) conveys important information about the object, for instance, its shape. In standard quantitative optical microscopy, a digital image sensor records the intensity map I(r→) of the field. It follows that the phase information is lost—and with it the information related to the object’s morphology. Many experimental and numerical QPI techniques have been implemented to circumvent this problem, including phase-shifting digital holography microscopy (DHM) [22,23], Fourier phase microscopy [24], gradient light interference microscopy (GLIM) [21], ptychography [25], quantitative oblique back-illumination microscopy [26], and phase retrieval based on the transport-of-intensity equation (TIE) [27]. These approaches rely in general on bulky optical setups that are not ideal for minimizing the phase noise. Recently, miniature QPI interferometric setups have been explored by designing metal gratings on coverslips [28], gratings on fluidic chips [29], and Si-based metasurfaces on fused silica substrates [30,31]. However, the gain in compactness comes at the expense of the general phase noise performance.

The phase noise level depends on the degree of coherence of the light source. Although coherent laser sources offer advantages such as high brightness, low power consumption, and ease of alignment, their high spatial coherence results in strong light speckles that currently limit the phase noise level to ∼30mrad [32]. The state-of-the-art records of phase resolution are achieved with incoherent white light source based QPI techniques, such as diffraction phase microscopy (DPM) [33], quadriwave lateral shearing interferometry (QSLI) [34], and spatial light interference microscopy (SLIM) [35], for which the phase noise is as low as ∼3mrad. Our approach that uses a PIC to shape a coherent light beam in a compact and robust way achieves phase noise levels comparable to those obtained with incoherent light, as demonstrated below.

Among the different QPI techniques, the KK-based approach has several advantages: the illuminating beam acts as the phase reference in a common path configuration and the phase shifting is replaced by beam steering. As unveiled below, combining a PIC-based illumination with this technique can drastically improve the performance. The underlying principle of the technique is based on the following observation: E(r→) can be entirely described either by its intensity I(r→) and phase φ(r→) and written as E(r→)=I(r→)eiφ(r→) or by its quadratures, namely its real Re(E(r→)) and imaginary Im(E(r→)) parts. If the Fourier transform of the field is square integrable, holomorphic, and nonzero only in the upper half plane of the complex plane, the quadratures are deduced from each other by a Hilbert transform [36]; the corresponding relationships are also known as the KK relations. It is reasonable to expect a similar link between the intensity and the phase, which is obtained by considering the function ln(E(r→))=12lnI(r→)+iφ(r→) as discussed in the 1970s for electron microscopy in Ref. [15].

Two different microscopy configurations have been implemented up to now to fulfill the necessary conditions to apply KK relations, i.e., the conditions to make ln(E) an analytical signal; see Appendix A for more details on these conditions. The first one consists in illuminating the sample at normal incidence kin=0, which leads to a k-space bandwidth centered at the origin, and in reshaping the aperture at the back focal plane [15]. The main challenge is to match precisely the mask with the optical axis in order to cancel one of the half-planes in the back focal plane. In addition the mask must be rotated or flipped around the optical axis in order to reconstruct the whole bandwidth of the aperture. Instead of reshaping and moving a mask in the back focal plane, the other approach relies on oblique plane wave illuminations [16]. A plane wave illumination with a given angle θ defined by kin=2πλsinθ implies a k→in shift of the bandwidth in the k-space. The main condition to apply KK relations then fulfilled for kin=kmax as illustrated in Fig. 1(b). Using Cauchy theory and the Cauchy principal value P, the KK relations between the phase and the image follow. For instance, for an illumination along k→in=kinx→, the phase is given by φ(x,y)=−1πP∫−∞∞lnI(x′,y)x′−xdx′+kinx.(1)

Repeating this phase retrieval methodology for several directions of illumination allows determining the complex Fourier spectrum E^(kx,ky), from which the amplitude and phase images are deduced.

The phase retrieval approach is illustrated in Fig. 1 with finite-difference time-domain simulations (FDTD, Lumerical) in the case of a simple 5μm×5μm square phase object of height 50 nm and refractive index 1.547. Four directions of illumination labeled d1 to d4 and symmetric by a 90 deg rotation around the optical axis (Oz) are considered. For all of them, the illumination angle is set at θ=26.74deg to match a numerical aperture of NA = 0.45 in line with our experimental setup. The intensity image of the field E(r→) produced by the microscope is simulated with FDTD for the d1 illumination in Fig. 1(a). From this intensity image, the phase map of E(r→) is obtained by solving Eq. (1), and the outcome is identical to the FDTD simulated phase as it should be; see Fig. 7 in Appendix A. Knowing the intensity and the phase, the Fourier transform of the field E^(kx,ky) is determined within the spatial frequency bandwidth that is defined by the aperture stop of the collecting microscope objective and by the direction of illumination d1 and is represented in Fig. 1(c) by the disk labeled d1. After processing the images for the four consecutive illuminations, the total phase domain of E^(kx,ky) is retrieved as shown in Fig. 1(c) where the contribution of each illumination is identified by di. The different contributions have overlapping k-areas that are averaged to avoid doubling the signal. An inverse Fourier transform finally leads to the amplitude and phase images in Fig. 1(d). The recovered phase map reproduces the expected phase profile of the object very well, although some ripples are present due to the sharp edges and limited spatial bandwidth of the microscope.

Rotating the illumination beam to reconstruct the synthetic aperture certainly avoids the motion of a mask in the back-focal plane but still requires stringent dynamical mechanical alignments to match the illumination angle with the aperture stop, which is a tour de force with bulk optics. Using a photonic integrated circuit made of single-mode waveguides such as the one illustrated in Fig. 1(e) alleviates this problem. The illumination is here provided by four first-order Bragg gratings that diffract the light propagating in the circuit out of the chip at a diffraction angle matching the maximal angle collected in the aperture stop of the microscope objective, i.e., satisfying kin=kmax. During phase imaging, the gratings are excited one after the other with an integrated 1×4 optical switch made of three Mach–Zehnder interferometers (MZIs), which avoids any mechanical displacement. Each MZI is made of one 1×2 multimode interferometer (MMI) at the input to split the light into the two arms of the MZI, one thermal phase shifter in each arm driven by current sources, and one 2×2 MMI at the output. All the gratings can also be excited at the same time with a proper setting of the driving current of the different thermal phase shifters in order to align the photonic chip with the microscope objective. Such an alignment is carried out by imaging the exit pupil of the latter and the far-field of the diffracted beams [see Fig. 2(d)] or by looking at the intensity in the imaging plane. The PIC has a typical compact size of 2 cm by 2 cm on a photonic chip that can be used with any standard optical microscope without modification of the collecting part. In the following, after presenting the properties of the beam shaping and switching of our PICs, we discuss their performances for quantitive phase imaging on test objects. As key examples, we investigate the phase images of monolayer graphene patches and bacterial cells.

Achieving and maintaining the proper matching conditions between the illuminating beam and the pupil of the collecting lens is demanding. A key advantage of the PIC-based approach is the opportunity to fabricate on a single chip several replicas of the same photonic integrated circuit with a parameter tuning sweep assisted by numerical simulations. Such a sweeping strategy effectively mitigates the effects of residual fabrication errors and allows us to select the best circuit post fabrication. Figure 2(a) provides an example where six PICs of identical design but of different grating parameters are present on the same chip.

The circuits are here made of aluminum oxide AlOx deposited on thermal silicon oxide wafers with an atomic layer deposition technique (ALD). AlOx thin-films exhibit very good transparency across a broad wavelength range spanning from ultraviolet-C (UVC) to infrared wavelengths [37–39]. Fully etched single-mode AlOx waveguides with propagation losses of 3 dB/cm at a wavelength of 360 nm [10,11] are used to guide the light towards the grating out couplers; see Fig. 1(e).

The diffraction gratings play a crucial role in the accuracy of the retrieved phase. The four identical gratings are located on a circle, the center of which corresponds to the position of the optical axis of the microscope objective. The circle has a radius of 2.5 mm. To align the center with the optical axis, the four gratings are simultaneously activated by the guided light, and their far-field emission patterns are imaged in the back-focal plane of the microscope objective; see Fig. 2(b). In the far field, the light diffracted by each grating is similar to a plane wave, which ideally results in a point in the k-space. Each point is indicated in Fig. 2(b) with the corresponding direction of illumination di on the image of the exit pupil. The exit pupil is nothing else than a mapping of the k-space. Positioning the four far-field points at the edge of the aperture stop by adjusting the photonic chip guarantees a proper centering of the chip with the collecting microscope objective. With a designed illumination angle corresponding to an excitation numerical aperture of NAex=0.45, i.e., equal to the specified numerical aperture of the current microscope objective, all the diffracted beams overlap in a plane that is located 4.96 mm above the photonic chip and where the object to be imaged is positioned.

For the rigorous implementation of the KK relations [see Fig. 1(b)] and a subsequent accurate extraction of phase information from the intensity images, precise control of the illumination beam angle is essential as quantified in Fig. 2(d). Simulating images as in Fig. 1(a) with the FDTD method for different angles of illumination and implementing the KK phase imaging approach, it follows that the ratio between the retrieved height hretrieved of the object and its ground truth value hGT is already increased by more than 20% for a ±1% NA mismatch between the excitation and the collection; see the red curve in Fig. 2(d). A much better accuracy, namely an error of 0.8% between the actual object height and the retrieved height, is obtained experimentally. To achieve such a result we have swept the grating parameters including grating pitches (Λ=181, 182, or 183 nm) and filling factors (ff = 0.6 or ff = 0.8) on a single chip with a targeted 20-nm-etch depth in a 120-nm-thick AlOx layer for all gratings. Mapping the grating surface with an atomic force microscope (AFM) (Park Systems NX20) reveals a grating groove depth he of 18.1±0.7mm in line with the designed value. With the parameter sweep, the illumination angle is tuned from NAex=0.44 to NAex=0.46 with a step ΔNAex=0.005; see simulation in Fig. 14 in Appendix A.

For each grating, the excitation numerical aperture is experimentally investigated by imaging the exit pupil of the microscope objective. To be able to locate the aperture stop corresponding to the collection numerical aperture NAco=0.45, a light emitting diode (LED) with a central wavelength of 370 nm (LED370E, Thorlabs) illuminates the object in a Köhler configuration. The reflection of the LED illumination by the object provides a signal within all the spatial frequency bandwidth of the microscope objective, which allows relative positioning of the beam diffracted by the grating with respect to the aperture stop; see Figs. 2(d) and 2(c). The 20 μm-wide and 1000-cycles-long diffraction gratings illuminate the object plane over a field of view (FoV) of 210μm×187μm; see Fig. 11 in Appendix A. The corresponding divergence is 0.45 deg, which is retrieved from the beam width δNA=NAδkkmax=0.007 in the back focal plane; see inset in Fig. 2(c). The current value of the beam divergence is sufficiently small to avoid any bias in the phase retrieval process as discussed with Fig. 8 in Appendix A.

Note that the beam width at half maximum δNA=0.007 is larger than the designed numerical aperture step ΔNAex=0.005 between the different circuits, which makes it difficult to experimentally distinguish the difference in illumination angle, i.e., in NAex, between two consecutive grating designs. In addition, determining the absolute value of NAex with the accuracy required for the NA mismatch that is here targeted is challenging. Moreover, the actual numerical aperture of the microscope objective might slightly deviate from its specified value of 0.45, which adds another uncertainty. To circumvent these difficulties and provide an experimental value of the NA mismatch, ΔNA=(NAex-NAco)/NAco, between the illumination and collection, we have determined the phase image of a test phase object and compared the experimentally retrieved height of its profile with the simulated one for different ΔNA. The phase object is made of 5μm×5μm square pillars etched in a 500-nm-thick silicon oxide (SiOx) layer on a 170-μm-thick microscope cover glass. The nominal etch depth of the pillars is 25 nm. The experimental height of the pillars, hAFM=24.9nm, is determined with an AFM measurement and is considered here as ground truth; see Fig. 2(e).

The experimental height hretrieved retrieved from the KK QPI image in Fig. 2(b) is expected to approach the value hAFM for a given grating design, which is verified by the black dots in Fig. 2(d): hretrieved=25.1nm corresponding to a minimum value of |1−hretrieved/hAFM| is achieved for a grating pitch Λ=182nm and a fill factor ff = 0.8. By varying the grating period or the fill factor, FDTD simulations predict that NAex reaches NAco for a grating pitch of Λ=183nm and a fill factor of ff = 0.8; see Fig. 15(a) in Appendix A. A 1 nm grating pitch step corresponds to a 0.01 NAex step. This 1-nm-pitch deviation between the simulated and the experimental values results from the combined effect of a 1 nm uncertainty in the AlOx layer thickness, the 2 nm grating etched depth deviation from the nominal value corresponding to a 0.002 NAex shift, and a possible uncertainty on the specified NAco value of 0.45. The difference between the simulated grating pitch to obtain the optimal NA matching for KK QPI and the actual experimental value is remarkably less than 0.6%.

The value of hretrieved is the difference between the average of the distribution of the low heights and the average of the distribution of the high heights in the phase image of Fig. 2(e). The error bars in Fig. 2(d) correspond to the pooled standard deviation σp of these two distributions. Taking into one σp uncertainty at the minimum NA mismatch and the simulated variations of |1−hretrieved/hGT|, a ΔNA accuracy of less than 0.5% is obtained with a height measurement accuracy of 0.8%.

The theoretical spatial transverse resolution of a standard optical microscope is given by Λmin=λNAco+NAex for a coherent plane wave illumination. Λmin corresponds to the smallest period of the optical index modulation that is observable in the imaging plane. At normal incidence, i.e., NAex=0, and for NAco=0.45, Λmin=800nm at an operating wavelength of 360 nm. Under an NA matching condition as used here to implement the KK relations, Λmin decreases to λ2NAco=400nm, namely, two times smaller than that of the conventional normal illumination.

To verify whether the current photonic chip based illumination allows us to reach the 400 nm resolution performance, we have imaged a series of strips with different line spacings that are patterned on a standard cover glass with a nominal height of 46.7 nm. The amplitude and phase images of the strips can be clearly retrieved up to a strip pitch of 400 nm, whereas the three strips with a 300 nm pitch appear as a single strip; see Figs. 3(a) and 3(b). As an important result, the PIC-based illumination allows us to resolve spatial features with the theoretical resolution of the microscope. The current theoretical value can be further improved by using higher NA objectives and by adjusting the PIC design. For instance, decreasing the pitch of the gratings to 150 nm, the diffracted beams will illuminate the object with a high NAex of 0.9, which suggests that imaging phase objects with a spatial resolution of 200 nm is feasible. Theoretically, the maximum achievable NA is constrained by the NA of the microscope objective, which is 0.95 for a dry objective. Achieving a larger illumination NA is possible by using diffraction gratings with a smaller pitch, but it might pose challenges for large-scale fabrication in current foundries, where the typical minimum feature size is 150 nm. Additionally, as the grating pitch decreases, the radius of the circle where the diffraction gratings are positioned must increase to keep the current working distance of 4.96 mm between the sample and the photonic chip. Decreasing further the illumination wavelength will also improve the spatial resolution.

A crucial key performance indicator for the current quantitative phase imaging technique is the standard deviation of the spatial phase noise σφ, which determines the minimum detectable phase variation. We have used an unpatterned 500-nm-thick silicon oxide layer on top of a flat microscope cover glass to infer σφ; see Fig. 3(c). The SiOx layer induces spatial phase fluctuations, the phase distribution of which has a standard deviation as low as σφexp=6.3mrad for the entire image. Such a value is up to 7× performance improvement over methods using bulky optics based on KK relationships [40] and up to 13× performance improvement over metasurface-based miniature QPI modules [30].

To disentangle the phase noise contribution intrinsic to the QPI technique from the phase fluctuations induced by the surface roughness of the object, we have mapped the surface topography with an AFM tool and simulated the corresponding KK-based phase image with FDTD; see Fig. 3(d). The AFM scanning of the SiOx surface provides a root mean square of the height fluctuations of 0.4 nm [see height map histogram in Fig. 3(d)] for an AFM axial resolution of 0.1 nm. It follows that the actual standard deviation of the roughness of the SiOx layer is σφSiOx=0.42−0.12=0.39nm. Using the experimental correlation length lcSiOx=125nm and standard deviation σφSiOx=0.39nm of the surface roughness that are retrieved with the AFM, and simulating the KK-based phase image produced by such a roughness, provides a theoretical standard deviation of the phase fluctuations of σφsim=3.0mrad, which is two times smaller than the experimental data σφexp=6.3mrad measured in Fig. 3(c). Assuming that the phase noise contribution coming from the sample roughness and the one coming from residual imperfections of the experimental setup are uncorrelated, the one-sigma uncertainty on the phase noise that is intrinsic to the QPI technique is σφ=6.32−3.02=5.5mrad. To confirm this low noise value and demonstrate the ultimate performance of our approach, we have investigated two-dimensional (2D) materials consisting of a single atomic monolayer.

Two-dimensional (2D) materials, featuring atomic thickness and van der Waals layered structures, have recently attracted much attention in microelectronics and optoelectronics due to their broadband high absorption, ultrafast carrier dynamics, strong mechanical durability, and dangling-bond-free surface nature [41–44]. Importantly, the band structure and electronic and optical properties of graphene and 2D semiconductors are critically dependent on the number of the layers, offering additional freedom for device tunability and scalability. It follows that quantifying precisely the number of layers of a few-layer 2D material is fundamental for understanding its physical properties and practical applications. The two typical ways to distinguish spatially monolayer from bilayer materials are Raman spectroscopy imaging and thickness measurement using AFM. Both techniques involve a time-consuming scanning technique. In contrast, using quantitative phase imaging to characterize 2D materials offers significant time and simplicity benefits provided that the detection limit is sufficient. In Fig. 4(a) we show that the spatial phase noise of our PIC-based QPI approach is low enough to image with high contrast monolayer graphene. With the spatial phase noise of 5.5 mrad previously determined, the QPI one-sigma axial resolution that varies according to the refractive index value and the illumination angle (see Appendix A.6) reaches 0.14 nm for monolayer graphene, the refractive index of which is 3.10 [45].

The monolayer graphene was grown by chemical vapor deposition (CVD), patterned, and transferred to cover glass; see details in Appendix A. The contrast in Fig. 4(a) allows us to clearly identify the patterned monolayer graphene. The high-phase value at the horizontal edges of the graphene patch may be caused by an imperfect adhesion on the glass substrate. The cross section along the dashed black line in Fig. 4(a) is plotted in Fig. 4(b) to quantify the thickness of the layer. We retrieve a thickness of 0.45±0.15nm that agrees very well with the non-contact AFM measurement, namely 0.43±0.25nm; see Figs. 4(c) and 4(d). The uncertainty of 0.25 nm, which is comparable to the AFM noise level of 0.2 nm, is determined from the analysis of 510 data points measured at a substrate position without graphene. The contrast of the AFM image [see Fig. 4(a)] is lower than the one of the phase image due to a 1.7× larger noise. In addition to being at least 20× faster, the PIC-based QPI offers better noise performance compared to a standard AFM tool for this measurement. The theoretical thickness of the monolayer graphene specified by the supplier (Graphenea) is 0.34 nm, which corresponds to the interlayer spacing in graphite [46]. The value reported here is 30% larger, which is commonly observed with AFM measurement due to organic residues coming from the processing, adsorption of water molecules, and roughness of the substrate surface [47].

An important biological application of QPI is the identification of pathogens such as fungi cells or bacteria based on their shape and refractive index [48]. The optical throughput of our miniature PIC-based QPI approach in terms of lateral spatial resolution and field of view is sufficiently high to discriminate different types of bacteria cells among large numbers as illustrated with Escherichia coli bacteria cells in Fig. 5. The lateral spatial resolution is large enough to distinguish individual cells from dividing cells for which a typical spacing between the nucleoids is 735 nm; see Fig. 5(b). Approximately 50 cells are visible within the field of view, a large majority of which exhibit a similar maximum phase; see Fig. 5(d). Lower phase entities are attributed to dead bacteria cells that have lost a fraction of their inner biological material. The miniature nature of the photonic chip and its phase imaging capability demonstrated on bacteria cells are promising for the deployment of compact imaging sensors to monitor the presence of pathogens in outdoor environments.

Our experimental results demonstrate that photonic integrated circuits are able to shape light beams to precisely match their far field with the numerical aperture of a microscope objective. The accuracy and robustness are such that quantitative phase imaging based on KK relations can be implemented with unprecedented performance for coherent light illumination. The PIC-based approach combines not only low phase noise of 5.5 mrad and high spatial resolution of 400 nm but also high compactness. As highlighted in Table 1, it outperforms recently reported state-of-the-art miniature modules for QPI based on metasurfaces [30,31], patterned microscope slides [29], or lensless optical fibers [49] by ∼2 times for spatial resolution and 15 times for phase noise. Besides, the detection limit of our PIC-based QPI is ∼7 times better than that obtained with the bulky optics approach based on the KK relations [40], is more than five times lower than that obtained with QPI techniques using a coherent light source (∼30mrad), and is comparable to the best phase noise level obtained with the incoherent light sources (∼3mrad) [32,34].Table 1.

Comparison of Miniature Modules for Quantitative Phase Imaging

The performance of the PIC-based QPI represents a significant improvement compared to bulk optic approaches in view of the values of the temporal and spatial coherent length. The current laser linewidth of 50 pm and the spatial frequency broadening δk=0.122μm−1 correspond to a temporal coherence length of 2.6 mm and to a spatial coherence length of ls=10μm, respectively. With such values, Shin et al. have reported a phase noise around 100 mrad with a bulky optic setup [50], which is 18 times larger than the value achieved here with a photonic chip.

Shifting the working wavelength deeper into the UV can further improve the optical resolution, but with the appearance of more phototoxicity effects in biological samples. Phototoxicity effects, which cause irreversible damage to the DNA of biological cells [51], can be circumvented by decreasing the illumination dose and implementing a Hilbert–Huang transform. As recently demonstrated [52], the Hilbert–Huang transform is more robust to noise than the standard Hilbert transform, which allows reducing the UV photon budget without degrading the quality of the phase image.

The photonic chip used as a simple add-on miniature module provides the illumination of a standard wide-field optical microscope and upgrades the imaging system to a quantitative phase microscope. As a key result, topological profiles of quantitative phase images of graphene patches are obtained with a signal-to-noise ratio larger than 3 [see Fig. 4(b)], which enables us to clearly identify a single atomic monolayer. The phase image is retrieved from four single shot images with a 10 ms acquisition time. In this experiment, the thermal switch is stabilized for 30 s between each acquisition. The stabilization time is currently limited by the relative low efficiency of the thermal phase shifters, which can be further improved. The thermal phase shifter is one of the standard components in photonic integrated circuits and is well-developed in the silicon (Si) and silicon nitride (SiN) platforms where the switching rate can reach sub-kilohertz [53]. The AlOx platform is at its early stage, and the thermo-optical coefficient of AlOx is similar to that of SiN; consequently we expect significant improvement of the switching time of the phase shifters by engineering the heat dissipation or by developing UV compatible electro-optic approaches [39]. In addition to the temporal throughput, the spatial throughput of PIC-based QPI can be further enhanced by increasing the size of the diffraction gratings.

Dense integration of diverse optical functionalities is a key asset of photonic integrated circuits. The laser source integration on a single chip will make the system even more compact and stable, which has been demonstrated at telecom wavelengths [54]. In addition, a large number of diverse modalities can be integrated on a single photonics chip. For instance, simultaneously implementing on the same chip structured illumination microscopy (SIM), which we have demonstrated in Ref. [10], and quantitative phase imaging, as described here, will offer new imaging opportunities. Such multimodality imaging has the potential to improve the identification of pathogens in a lot of industrial processes or healthcare environments.

To conclude, the low phase noise demonstrated here with a compact photonic chip compatible with CMOS technology should accelerate the deployment of on-site quantitative phase imaging for a large number of biosensing and biomedical applications. In particular, the PIC-based QPI is expected to play a crucial role in hematological diagnosis and cancer pathology [55] by accelerating the diagnostic period and improving the diagnostic accuracy.

Acknowledgment. C.L. and N.L.T. acknowledge Christophe Detavernier’s research team for providing the ALD AIOx layers, Nico Boon for providing biological samples, and Tom Vandekerckhove for helping to measure the samples with the AFM.