Marker-free phase nanoscopy

We introduce a microscopic method that determines quantitative optical properties beyond the optical diffraction limit and allows direct imaging of unstained living biological specimens. In established holographic microscopy, complex fields are measured using interferometric detection, allowing diffraction-limited phase measurements. Here, we show that non-invasive optical nanoscopy can achieve a lateral resolution of 90 nm by using a quasi-2p-holographic detection scheme and complex deconvolution. We record holograms from different illumination directions on the sample plane and observe subwavelength tomographic variations of the specimen. Nanoscale apertures serve to calibrate the tomographic reconstruction and to characterize the imaging system by means of the coherent transfer function. This gives rise to realistic inverse filtering and guarantees true complex field reconstruction. The observations are shown for nanoscopic porous cell frustule (diatoms), for the direct study of bacteria (Escherichia coli), and for a time-lapse approach to explore the dynamics of living dendritic spines (neurones). In the field of optical nanoscopy, image resolution at the subdiffraction scale has been obtained through saturation of fluorophore transitions1 and has been demonstrated to work well with certain fluorescent proteins. Subdiffraction resolution has also been shown without using saturated fluorescence2. Although both techniques rely on phase structuring, it is used only in excitation. On its own, phase analysis provides a complementary means to fluorescence of measuring the morphology and composition of a specimen; additionally, quantitative phase analysis allows the study of the sample-induced optical path length (OPL) and the refractive index3–5. Recently, the determination of these parameters has become increasing important throughout the life sciences6–9. Here, we present marker-free and time-lapse phase nanoscopy, which allows lateral phase resolution below the 100 nm barrier. This can deal with the complex electromagnetic wave field scattered by a specimen, for example as obtained from the reconstruction of digitally recorded interferograms in digital holographic microscopy (DHM)10 or, more generally, by various quantitative phase microscopy methods11–13. An appealing feature of reconstructed complex wave fields is the direct synthesis of the aperture of a virtual microscope14–17; that is, scattered light beyond the numerical aperture (NA) of the microscope objective (MO) can be detected, as described in Fig. 1a,b. Figure 1c shows a suitably engineered scanning concept for such a synthetic aperture. An inclined beam sequentially illuminates the specimen from various directions, thereby measuring the scattered field in the far-field regime for all possible directions of incidence. The goal is to match the 2p concept completely up to the free propagation limit (Fig. 1d–f) of the maximal wavenumber18 kmax1⁄4 2k1⁄4 4pni/l for a given wavelength l and immersion medium ni. In the spatial frequency domain (SFD) of wave vector k, each measurement of the scattered field represents a low-pass filtered (LPF) sub-aperture (Si) as it suffers convolution with the system’s three-dimensional coherent transfer function (CTF), depicted in Fig. 1g–i. Diffraction tomography14 can be performed by synthesizing all three-dimensional SFD components Si to obtain the LPF approximation (Fig. 1e) of the object’s scattering potential19, hereafter referred to as ‘synthetic DHM’. In contrast to this LPF approach, the proposed method, termed 2p-DHM, uses complex deconvolved20,21 sub-apertures Oi to effectively synthesize the scattering potential as far as kmax (Fig. 1f ). In the 2p-DHM scanning concept, with two opposed high-NAMOs, complex deconvolution has the advantage of directly correcting (in the SFD) for any aberration22,23 in phase (Fig. 1i) and apodization24 in amplitude (Fig. 1h). Thanks to the combination of the physical detection of frequencies and the direct complex deconvolution model, 2p-DHM does not require any assumptions to be made concerning noise, iteration or sparsity8. If the synthetic bandpass is effectively enlarged up to the free propagation limit, then the resolution should improve significantly. The lateral resolution potential is determined by the total SFD content of the microscope (2kc in Fig. 1g), related to Abbe’s formula hmin1⁄4 a(l/NA), where a yields 0.5 for the diffraction limit24. The effective resolution power between two scatterers at a distance h from one another is limited by the pointspread function (PSF), which implies a contrast of 27% (Rayleigh criterion24 where acoh yields 0.82 for coherent light) or 0% (Sparrow criterion 24), as summarized in Supplementary Fig. S1 for different imaging modalities. With either criterion, the effective resolution of 2p-DHM is expected18,25 to reach beyond the Abbe limit. The setup for providing experimental proof for our method was based on a Mach–Zehnder interferometer10, which provides quantitative phase images from a single-shot hologram for each illumination angle. A diode laser beam (l1⁄4 405 nm) was divided into sample and reference arm paths by a beamsplitter. A wedge prism in imaging condition with an upright MO was used to rotationally scan the sample (positioned between the two matched oil-immersion MOs, NA1⁄4 1.4) at a steep angle of illumination (angle a in Fig. 1c). A second beamsplitter recombined the sample and reference laser beams, forming an off-axis interference pattern at the image plane. For each rotational angle of illumination (Euler angle w in Fig. 1c, with angular sampling Dw≈ 1.58), a chargecoupled device (CCD) camera (Basler 102f) recorded a hologram at 13.3 frames per second, providing a total of 240 holograms in 18 s for 3608. Phase images were then calculated by applying Fresnel reconstruction10,26. For complex deconvolution (see Methods), the CTF was derived experimentally by means of a complex point source (see Methods and Supplementary Figs S2,S3). All the deconvolved spectra were used consecutively for tomographic data processing (see Methods).