Super-resolution (SR) fluorescence microscopy has proved to be an incredible tool to advance science and technology in investigations of cellular or subcellular structures. It has essential applications in disease mechanisms^1-5 and image diagnosis^6-8. However, live-cell microscopy techniques have long been severely limited because photobleaching and phototoxicity are unavoidable as inherent properties of fluorescence imaging^9-12. Quantitative phase microscopy (QPM) is a significant advancement in the next generation of label-free imaging¹³, provides an alternative solution using refractive index as an endogenous dye, and has gained several significant advancements^14-16.

Imaging through scattering media remains a challenge in optical detection^17-19. These media, such as biological tissues, do not absorb light significantly; however, they scramble the light path and challenge even low-resolution resolution¹⁸. The high-contrast super-resolution imaging is mainly limited to imaging depths of 0.1 to 1 μm, such as total internal reflection fluorescence structured illumination microscopy (TIRF-SIM) and grazing incidence structured illumination microscopy (GI-SIM)^{20, 21}. The resolution and contrast are compromised inside the cell's deep layers²². Many approaches have been demonstrated to overcome the scattering effects and enable imaging or focusing capability through scattering media^23-25. The most direct method is ballistic optical imaging, which filters out the scattered light based on different characteristics, such as Kerr gate^{26, 27} and confocal microscopy^28-31. Confocal laser scanning microscopy (CLSM) has been demonstrated highly axial resolution and accurate phase contrast images, and one important milestone and promising frontier development is the Laser oblique scanning optical microscopy (LOSOM)³². Recently, laser-scanning gradient light interference microscopy (LS-GLIM) combined differential interference contrast microscopy with CLSM to achieve non-destructively confocal-level depth sectioning, sensitivity, and chemical specificity on unlabeled specimens³³.

However, due to motion artifacts of fast-moving subcellular structures in live cells, most increases in spatial resolution must be matched with an increase in temporal resolution³⁴. LS technique and the serial detection of several frames in phase-shifting methods suffer from low throughput, which limits many applications that require high temporal resolution, such as tubular endoplasmic reticulum and neural circuits, due to motion artifacts of fast-moving subcellular structures in live cells. Moreover, the precise imaging of anisotropic structures has remained a challenge for GLIM because two interfering fields are horizontal and vertical. It is worth noticing that many tissues and biological systems contain anisotropic structures^35-37.

In this letter, we present the principles of a label-free anti-scattering imaging method by integrating multiple waves to overcome the above limitation. Here, we have shown that conventional technique avoids photobleaching and phototoxicity in noise-free unlabeled images but fails in authentic microscopic images containing noise. Compared with normal optical imaging²⁸, we verify that the image quality of synthetic wave microscopy (SWM) has significantly improved, from a blurred image with no clear object features to super-resolution imaging. By exploiting the properties of synthetic waves to vary their phase slowly, the interferometric signal is decoupled from the incoherent, non-modulating background due to multiple scattering. This enables us to penetrate scattering media and successfully image areas of interest. Additionally, SWM shares the capability of numerous scattering suppression with LS-GLIM, delivers 4× faster imaging speed at an imaging speed of up to 10⁶ pixels/s, and has a more direct and integrated optical path by abandoning liquid crystal modulators. Moreover, SWM is unaffected by tissue polarization information and can achieve polarization-insensitive imaging. By introducing metalens, we demonstrate the SWM with the lateral resolution of 0.42 λ/NA. Therefore, our SWM can improve current anti-scattering techniques to push their spatiotemporal resolution limits and better resolve intricate, 3D, and fast dynamics in live cells.

The essence of our approach is based on the fact when two light waves with tiny wavelength differences transmit through the scattering media, the phase delay introduced by the scattering media is almost the same. Based on this, we design one technique with two closely positioned focused light waves to detect the material property at the focal point but ignoring the influence of the scattering media in its optical paths. (See Supplementary Section 1 for more information). The optical path and image processing are presented in Fig. 1(a) and 1(b). The synthetic wave source generation module comprises two laser scanning devices and a beam splitter. The amplitude of two input electric fields is equal to A. The frequencies of two input electric fields are ω1 and ω2, respectively. The initial phase of two input electric fields are φ1 and φ2, respectively. After combination, they form a synthetic wave pulse:

1E(t)=Aei(ω1t+φ1)+Aei(ω2t+φ2)=2Acos[(Δωt+Δφ)/2]ei(ω¯t+φ¯),

where Δω and Δφ are the frequency difference and phase difference of the two sources, respectively, ω¯ and φ¯ are the average frequency and phase of the two sources, respectively. The superimposed of two simple harmonics with little frequency difference allows us to enlarge the harmonics period from femtoseconds to picoseconds. Considering that the photomultiplier tube (PMT) already has accuracy at the picosecond level, the PMT can accurately record the synthesized wave's envelope intensity changes. It should be noted that the picosecond period is not the limitation of this technique. The period can be flexibly tuned by changing the frequencies of the two synthetic waves. Picosecond period is chosen to balance the performance of the detector and the scanning speed.

2I(r,t)=〈|E(r,t)|2〉=2A2[1+cos((Δωt+Δφ(r))]),

where r denotes the pixels in the sample, Δφ(r) denotes the phase difference between the two waves.

In this case, the phase image Δφ(r) is determined from four intensity measurements corresponding to t=0,T/4,T/2,3T/4, termed as four-step phase-measuring method. Here, T denotes the envelope period of the synthetic wave. It should be noted that for a more general case, more points in the harmonic period can be chosen to improve the accuracy of the phase detection：

3Δφ(r)=arg{[I(r,3T/4)−I(r,T/4)],[I(r,T/2)−I(r,0)]}.

We used the shear distance value δr, greater than or equal to the focal spot size.

4Δφ(r)=φ(r+δr)−φ(r)≈∇rφ(r)δr,

where ∇rφ(r) denotes the phase gradient along the r direction at a point r on the sample.

Now we convert the coordinate system to a cartesian coordinate system for data post-processing. We obtain the phase gradient along the direction of the shear (x-direction)：

5∇xφ(x,y)=φ(x+δx,y)−φ(x,y)δx,

where (x,y) denotes the pixels in the sample，δx denotes shear distance value along the x direction.

To integrate the measured phase map, we perform a cumulative sum along the direction of the shear direction:

6φ(x,y)=∫0x[∇xφ(x′,y)]dx′+φ(0,y),

where φ(0,y) is the initial value, which is obtained with some prior knowledge of the specimen. For example, if (0,y) is a background location, the phase φ(0,y) should be set to 0 radians (See Supplementary Section 2 for more information).

When imaged in a transmission configuration, the expected phase shift from a phase step object is

7φ(x,y)=2πλn(x,y)d(x,y),

where λ is the wavelength of the illumination, n(x,y) is the refractive index, and d(x,y) is the height. The wavelengths of the two sub-waves are nearly identical, so we refer to λ as 1064 nm. In modern laser technology, high-stability lasers can achieve highly narrow linewidths in the sub-hertz range^{38, 39}, and the corresponding wavelength linewidth (Δλ) can be converted to less than 10⁻²⁰ m using the formula Δλ=Δυ⋅λ2/c. This allows us to use two lasers with minimal wavelength differences.

Figure 1(a) illustrates the SWM system configuration, which comprises four main components: a synthetic wave source generation module, a metalens, a pinhole, and a PMT. The synthetic wave source generation module consists of two collimated continuous-wave (CW) lasers, two laser scanning modules and a beam splitter. Two CW lasers at 1064 nm and 1064.1 nm pass through the beam splitter and are focused by a metalens. For the imaging of bio samples, the laser power needs to be controlled to avoid damaging the samples, which is chosen to be ~1 mW. The scanning modules control the light source with different tilt angles to generate different beam shear distance values on the sample, the sample is placed at the focal plane of metalens. The pinhole is placed at twice the focal length of the metalens, and the size is chosen to be 40 µm. Then, the light source passes through a pinhole and is recorded by PMT with ps-level detection time accuracy (See Supplementary Section 6 for more information). In our experiments, each point of the sample is scanned over a total time length of Δt1=10−6s (the speed of the scanning module) with a step size of Δt2=10−12s (the rate of PMT), so imaging speed reaches 10⁶ pixel/s (1Δt1). In this condition, the limiting factor is the capability of the scanning module. It is possible to achieve ~10¹¹ pixels/s (>14Δt2) imaging if the scanning module's speed is further increased to match the rate of the PMT. Therefore, SWM is a suitable technique for observing living cells over long periods, in large areas, and with high temporal resolution. As shown in Fig. 1(b), four differential interference phase contrast (DIC) frames are used to reconstruct the quantitative phase image in post-processing. We obtain the phase gradient diagram using Eq. (3) with the four intensity maps provided. By utilizing the provided phase gradient, we integrate along the gradient direction using Eq. (6) to obtain the phase value. Notably, employing a greater number of frames enhances phase reconstruction accuracy (See Supplementary Section 2 for more information).

The Abbe diffraction limit refers to the minimum resolution distance expressed by λ/2NA⁴⁰. Rayleigh further pointed out that the Rayleigh criterion for physical two-point resolution is 1 Airy spot (0.61λ/NA)⁴¹. Consequently, the minimum distance that a focusing imaging system can resolve is nearly the radius of the Airy spot, which is the focal spot size of the optical system. Compared with the traditional optical lens, the metalens is much more attractive due to its distinct advantages of powerful focusing capabilities^42-48. Hence, we design a metalens to achieve super-resolution imaging. Si and Al₂O₃ are used considering large-area fabrication feasibility and their common usage in near-infrared (NIR) light. As shown in Fig. 2(a), the meta-atom comprises a Si nanopillar and a rectangular lattice Al₂O₃ substrate. Considering fabrication feasibility, the nanopillar height was chosen to be 700 nm. Then, we calculate the amplitude and phase delay of meta-atom using rigorous coupled wave analysis (RCWA) solver RETICOLO. As shown in Fig. 2(b) and Fig. 2(c), Lattice constant ranges from 400 to 700 nm to avoid higher order diffraction and duty cycle ranges from 0 to 1. As shown in Fig. 2(d), when we choose a constant period of P=500nm, the transmission efficiency is close to 100% and full 2π phase coverage is achieved as the width changes from 100 to 320 nm. After scanning the unit cell structure, we arrange the meta-atoms based on the ideal phase profiles. The calculated ideal phase profile of the designed metalens is shown in Fig. 2(e) and the schematic of designed metalens operating in transmission mode is shown in Fig. 2(f). The next step involves utilizing techniques such as super-oscillatory lenses⁴⁹ or microspheres^50-52 to further enhance the resolution, which is beyond the scope of this work. We investigate the influence of different size for metalens performance. (See Supplementary Section 3 for more information)

A commercial electromagnetic software (Lumerical FDTD solutions) analyzes electromagnetic properties based on the finite-difference time-domain method. In the simulations, the cutoff of convergence accuracy is set as 10⁻⁶. Considering rapidly changing spatial profiles and the feasible computation time, a medium size aperture of 20 μm (about 19λ) is chosen as the computation time increases significantly with the increment of metalens size. A commercial electromagnetic software (Lumerical FDTD solutions) analyzes electromagnetic properties based on the finite-difference time-domain method. In the simulations, the cutoff of convergence accuracy is set as 10⁻⁶. To achieve high spatial resolution, a focal length of 5 μm is chosen (NA = 0.89). The parameters in the text are designed for verifying the concept. However, metalens with a diameter of 2 inches is entirely feasible in actual production, has been demonstrated image qualities comparable to a state-of-the-art commercial objective⁴³. Note that, theoretically with the introduction of the scanning galvanometers (scanning angle of ±11 degrees) and the fabricated metalens (focal length of 200 mm), SWM would have an imaging field of 1224 mm². This can be further extended if the sample is mounted on a mechanical translational stage that can further shift the imaging area.

The focusing characteristics of metalens are characterized in detail. We start from the light incident in a normal direction. Figure 3(a) shows the normalized intensity distribution in the x-y plane and the 1D distribution along the x- and y-direction. The full width at half maximum (FWHM) along the x-direction is 0.42 λ/NA due to the intensity of the sidelobe increases, leading to the super-diffraction focusing phenomenon along the x-direction, which is due to its remarkable ability to manipulate electromagnetic waves at subwavelength dimensions^52-54. Figure 3(b) shows lateral resolution as a function of incident angles. In theory, the minimum resolution of SWM is achieved when the distance between the centers of the two focal spots is nearly equal to FWHM. Figure 3(c) presents the normalized intensity distribution in the x-y plane. Figure 3(d) presents the normalized intensity distribution in the 1D distribution along the x-direction. The synthetic wave source incident angles are 2.5°, 2°, 1.9° and 1.8°, respectively. It confirmed that the SWM achieves a super-resolution of 0.42 λ/NA when the metalens is illuminated by two x-polarized plane waves with incident angles of ±1.8°.

We test the anti-scattering capability by changing complexity of the scattering media and the dielectric layer distance from the sample. Firstly, we reconstruct phase without scattering media. The ideal phase difference ranges over 2π radians with a step size of 0.25π radians (Δφideal(i)=i*π4,i=0,1,...7). Figure 4(a) presents the normalized intensity curve recorded by PMT during one synthetic wave period for different ideal phase differences. Secondly, we establish a model for imaging through a scattering dielectric layer (Fig. 4(b)). On the left-hand side, the abrupt phase of the scattering phase plane is set to the maximum phase multiplied by a random number (0~1). It represents a scattering media with totally random distribution and full period phase disturbance, which stands for the worst imaging conditions for most cases. We change the complexity of the scattering media by varying the maximum phase. Figure 4(c) shows the reconstruction results (Δφtest(i),i=0,1,...7) when scattering media layer in the same focal distances. The reconstruction results closely match the real values represented by the red lines, when the maximum phase is 0.5π. Even when the maximum phase is π, there is only a minor discrepancy. It means that SWM can generate high-contrast images and are not affected by the scatter in the optical path. The reconstruction results deviate from the real values when the maximum phase is 1.5π. This phenomenon is due to less ballistic light and more multiple-scattered light reach the ideal focus point as the maximum phase increases.

Next, we assess the impact both of complexity of the scattering media and the dielectric layer distance from the sample. We establish a criterion to evaluate the anti-scattering capability of SWM, which is calculated as the average measurement error between the reconstructed phase and the ideal phase error=∑i|φideal(i|−φtest(i))8. In Fig. 4(d) and 4(e), it can be observed that as the scattering phase screen gets closer to the specimen, the error increases. This phenomenon occurs due to the reduction in the overlap area between the two beams. Even when the maximum interference phase is equal to 0.5π, the average error of different distance is less than 0.1 radians. In this case, it is possible to image the target object clearly (as demonstrated in Fig. 5). The anti-scattering capability achieved with the SWM is directly related to two effects. First, the wavelengths of the two sub-waves are nearly identical. Secondly, the two interference fields are also nearly identical except for a small transverse shift in spatial. Consequently, the two fields suffer equal degradation, and interferometry remains unchanged. We conduct an additional simulation to further demonstrate the capability of the proposed method under a realistic optical condition (See Supplementary Section 4 for more information).

We compare the temporal resolution of LS-GLIM and SWM. The acquisition time of each frame depends on the dwell time and pixel numbers set for the image acquisition. Given an image case with the same acquisition time of ~1 s and the same dwell time of 1 µs/pixel: In LS-GLIM, we obtain an image with 500 × 500 pixels for 1 frame. In SWM, we obtain an image with 1000 × 1000 pixels for 1 frame. As shown in Fig 5(a), we image a neuron cell without the scattering layer using LS-GLIM and SWM, respectively. The temporal resolution of SWM surpasses that of LS-GLIM, and SWM offers a fourfold greater field of view compared to LS-GLIM. This phenomenon occurs due to LS-GLIM needs the liquid crystal to modulate the phase shift between the two orthogonal polarizations after each intensity frame is recorded³² and SWM abandons liquid crystal modulators by leveraging the temporal variation of intensity in synthesized waves.

We image a neuron cell over a 90 μm×90 μm field of view to compare the anti-scattering capability of traditional QPM¹³ and SWM. It is important to note that we did not actually perform experimental tests with biological samples, but rather used data from the literature¹³ for imaging comparisons for proof-of-concept of the superiority of our imaging. Conducting imaging experiments on biological samples is the next step in our work, and all sample preparation procedures involving animals need to be reviewed and approved by the ministry of health. The scattering layer maximum phase is set to 0.1π, 0.25π and 0.5π, respectively. SWM could achieve anti-scattering imaging because the two interfering fields are almost identical except for a small transverse spatial shift. The two fields suffer equal degradation due to multiple scattering, so interferometry remains unchanged, thus allowing it to resolve high-quality images with greater depth and accuracy compared to traditional imaging techniques. As shown in Fig. 5(b), at a maximum phase ~0.1π, a substantial fraction of the light has been scattered, resulting in a blurry background, obscuring the object features. At a maximum phase of ~0.5π, essentially all of the light has been scattered, and the conventional image degrades to the point where no sharp object features can be seen. As depicted in Fig. 5(c), SWM allows for clear visualization of the nucleolus and the dendrites of the neuron cell. Supplementary Video 1 and Section 7 illustrate the anti-scattering capability of SWM on unlabeled dynamic neurons for 10 s time-lapse imaging. The SWM image records the dynamic changes of neuronal cells and does not suffer from scattering medium, phototoxicity, or photobleaching while maintaining a super-resolution image with high contrast. As a result, SWM is suitable for the non-destructive study of living cellular systems over long periods of time. We make a comprehensive comparison among 5 different optical imaging techniques in spatial resolution, temporal resolution, live-cell compatibility, and anti-scattering capability level. (See Supplementary Section 5 for more information)

In summary, we present a label-free anti-scattering imaging method by the integration of multiple waves. In comparison to the most advanced QPW techniques, SWM excels in extending the temporal resolution and is not influenced by polarization information. Under the same measurement time, SWM enables a fourfold expansion of the imaged field of view. Most importantly, SWM exhibits superior anti-scattering performance in comparison to traditional QPW techniques, such that it resolves high-quality images with greater depth and accuracy. We anticipate that SWM can be potentially adopted at a broad scale because a SW source generation module can be readily added to many existing microscopy systems, such as structured illumination microscopy and confocal microscopy. We hope that the results presented here can serve as an important step toward the field of optical detection, which has significant implications for various fields, including medical imaging, industrial inspection, and scientific research.

We are grateful for financial support from CAS West Light Grant (xbzg-zdsys-202206) and National Key Research and Development Program of China (2021YFA1401003).

YT Xiao refined methodology, performed simulations, and write original draft. LW Chen proposed the original idea and supervised the project. MB Pu and XG Luo participated in idea discussions that shaped the objectives of the paper. MF Xu, Q Zhang, and YH Guo provided detailed proofreading and editing for the manuscript, ensuring its language fluency and structural clarity. TQ Chen revised the figures to present experimental results and data in a more visually intuitive manner.

The authors declare no competing financial interests.

Supplementary information for this paper is available.https://doi.org/10.29026/oes.2023.230037