Structured detection microscopy

Abstract

Super-resolution microscopy is crucial for imaging sub-wavelength biological structures. However, most techniques rely on nonlinear saturation or stochastic switching of emitters, limiting imaging speed and increasing phototoxicity. Here, we achieve deep super-resolution without employing saturation or stochastic dynamics, instead using a form of spatial mode demultiplexing. By shaping the point-spread function of the emitted light, our Structured Detection Microscope (SDM) redistributes information away from high shot-noise regions of the image, enhancing sensitivity to sub-diffraction emitter separations in two-dimensions and without mode-sorting optics. Implementing SDM within a high-numerical aperture total internal reflection fluorescence microscope, we demonstrate imaging of fluorophores attached to DNA nanorulers with separations as small as 50 nm at resolutions surpassing 40 nm - fivefold below the diffraction limit. This shows that spatial mode demultiplexing can achieve far sub-wavelength resolution and is applicable to biologically relevant samples. By enabling super-resolution biomolecular imaging without emitter saturation and stochasticity, our work opens the door to better understanding biological structure, function and dynamics.

Figures (8)

• Figure 1: Theoretical advantage of higher-order light modes in imaging. (A) small shifts of the emitters from the centroid below the diffraction limit (indicated by the arrows on the emitters in the dPSF row) causes a signal change (indicated by the red/blue regions) in the point-spread function (PSF). The top-left diagram is the conventional microscopy signal, whose signal change is largest where shot noise (which is proportional to PSF intensity) is largest; the top-right diagram is the structured detection signal, whose change is largest where shot noise is smaller. (B) the effect on the Fisher information: for separations below a critical point of approximately 0.45$\sigma$, (with $\sigma$ the diffraction limit), SDM has a larger Fisher information (FI) and hence 'wins' in imaging precision over conventional microscopy (vice versa for above 0.45$\sigma$). The inset shows the ratio of FI for SDM to conventional microscopy. There is a slight variance in the FI depending on emitter orientation for SDM, explained by the lack of circular symmetry in the structured detection PSF, however its impact is negligible compared to the gain in FI and makes structured detection effectively emitter-orientation independent.
• Figure 2: Schematic of SDM experiment. The illumination beam totally internally reflects off a glass coverslip with many DNA nanorulers affixed. The evanescent field excites the fluorophores attached to the ends of the nanorulers. A long-pass dichroic mirror then reflects the illumination beam and transmits the fluorescence emission. In the Fourier plane, the emission beam is shaped by a quadrant waveplate which has a $\pi$ phase shift on diagonally opposite quadrants (indicated by the arrows). In the image plane, the imaged PSFs show the expected mode shape. The quadrant waveplate can be removed to allow a comparison with conventional microscopy.
• Figure 3: Example (experimental) data and data analysis pipeline. The left column is conventional microscopy, and the right SDM. (A) Example imaged PSFs. These photon intensity distributions include 32,851 and 43,419 photon detection events for the conventional and structured detection images, respectively. (B) The $n$ likelihood functions we construct from the imaged PSFs (the blue point is a photon's separation from the centroid, and the red point is the diagonally opposite separation; therefore, this represents the likelihood of the emitter separations from the centroid given a photon's separation). (C) The resultant probability densities for the emitter separations obtained by multiplying and normalising the $n$ likelihood functions. The maxima are taken to obtain the estimated emitter separations. These are substituted into bias correction functions, obtained via simulation under imaging conditions matching the actual image. (D) Corrected separation estimates. The black dashed line indicates the actual separation (50 nm).
• Figure 4: SDM and conventional microscopy results. In this figure, blue is conventional microscopy and red is SDM. The outline of the coloured bands represent the Cramér-Rao bounds (CRBs) for the separation estimates from each method, with their width the theoretical resolution limit for any unbiased estimator. The SDM CRB is entirely subsumed within the conventional microscopy CRB under our imaging conditions. At each imaged separation, an overlay shows experimental data with identical vertical scaling to the figure. Error-bars represent the resolutions, and crosses are the means of each method. Individual separation estimates are represented with triangles for conventional microscopy (17, 58 and 31 estimates at 50, 120 and 180 nm length rulers, respectively), or circles for SDM (likewise, 15, 17 and 7 estimates). The dashed black line is where the actual separation equals the estimated separation. The $x$-axis maximum is approximately the ideal diffraction limit. A grey dashed line crosses the vertical axis at $y = 0$, and shows that with an ideal estimator, the two emitters cannot be reliably resolved below 49 nm (conventional) or 39 nm (SDM).
• Figure S1: Quadrant waveplate fabrication. (A) A cemented zero order waveplate with two sides produces a total phase retardation of half a wavelength with a fast axis pointing vertically on one side and horizontally on the other side. (B) The waveplate is cut into four equal pieces, and the top-right and bottom-left pieces are flipped over a 45$^\circ$ axis and exchanged. (C) The result is the rearranged pieces have a phase shift that corresponds to a fast axis oriented vertically on the top-left and bottom-right quadrants, and horizontally on the top-right and bottom-left.