Birefringent Fourier filtering for single molecule coordinate and height super-resolution imaging with dithering and orientation.

Optical setup

The sample is excited by a laser (Coherent, Obis 488LS-20 for reference beads and single-molecule measurements; Coherent, Sapphire 488LP-200 for STORM measurements) in a wide field or TIRF illumination configuration (Fig. 1 b), and is held on a piezo nanopositioner (Mad City Labs Inc., Nano-Z200) to perform stacks along the z -axis with nanometric precision. Fluorescence light emitted by the sample is then collected by a ×60, NA 1.45 oil-immersion objective (Nikon, CFI Apo TIRF). A dichroic mirror (Semrock, DI02-R488) and a fluorescence filter (Semrock, 525/40) are used to select the emitted fluorescence and send it to the detection path. To adjust the field of view, a diaphragm is placed in a plane conjugate to the image. All the lenses are achromatic doublets: L 1 (125 mm) and L 3 (500 mm) are in a 4f configuration enabling us to locate the SEO in the back-focal plane; L 2 (400 mm) is used for back-focal plane imaging. To simulate emitters with different in-plane orientations, we put prior to the SEO a linear polarizer (Thorlabs, LPVISE100-A) mounted on a motorized rotation stage (Newport, PR50CC). To compensate unwanted polarization distortions introduced by the first dichroic mirror, we used another identical dichroic mirror (Semrock, DI02-R488), aligned along the plane where s and p polarization components of the incident fluorescence are inverted with respect to the incidence on the first dichroic mirror. Finally, the image is split into LHC and RHC polarization components by using a QWP followed by a quartz Wollaston polarizing 2.2° beamsplitter (Edmunds, 68-820), and each of these components is projected onto a different region of an emCCD camera (Andor iXon Ultra 897 for beads and single-molecule measurements; iXon Ultra 888 for STORM measurements). The total magnification provided by the lenses is 240, corresponding to a pixel size of 67 nm on the emCCD for the bead and single-molecule measurements, and 54 nm for the STORM measurements. Stress-engineered optic The term “stress engineering in optics” applies to the design and application of stress birefringence to achieve a desired retardance distribution. More specifically, the stress-engineered optic (SEO) used for this work was one of a collection of SEOs custom fabricated for the T.G. Brown research group at The Institute of Optics, University of Rochester. Details of the analysis and fabrication of the elements can best be found in the PhD dissertations of Alexis K. Spilman 48 and Amber M. Beckley 49 and summarized in several related publications 18 , 19 , 23 . To our knowledge, these elements are not yet commercially available, but can be readily manufactured by a skilled machine shop. The window material can be any transparent material with a nonzero stress optic coefficient; we have used both fused silica and BK7 glass windows. The material must also be strong enough to withstand approximately 100 MPa of peripheral pressure without fracture. For the SEO used in this experiment, commercial BK7 windows (10-mm diameter, 8-mm thickness) were first given a fine grind in order to ensure a cylindrical edge. A metal ring (steel) with inner diameter of about 25 microns smaller than the outer diameter of the glass was cut on a lathe. An end mill was then used to remove material at 0°, 120°, and 240°, leaving three contact points at 60°, 180°, and 300°. The assembly is accomplished by heating both the glass and metal to a temperature of 300 °C; at this temperature, the higher thermal expansion coefficient of the metal allows the insertion of the glass piece into the metal ring. Upon slow cooling, the ring then compresses the glass, applying force at three small regions around the perimeter in a way that is approximately uniform along the thickness.

SEO alignment

For the purpose of aligning the SEO and adjusting the parameter c , we used a sample of yellow highlighter’s fluorescent ink, embedded in a mounting medium (Sigma, Fluoromount). The fluorescence emitted by this sample is used as a bright and homogeneous illumination for the SEO. Circular polarization was produced by placing a linear polarizer and QWP before the SEO. Also, a lens (L 2 ) was inserted to image the SEO plane, leading to complementary rotationally symmetric intensity patterns whose radial dependence for the two emerging circular components is approximately proportional to documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${cos }^{2}(cu/2)$$end{document} cos 2 ( c u / 2 ) and documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${sin }^{2}(cu/2)$$end{document} sin 2 ( c u / 2 ) , respectively for c = π (Fig. 1 (c)). The system’s alignment and calibration is then fine-tuned by removing L 2 and keeping the polarizer and QWP, to image model nanoemitters under circular polarization conditions. We used for this purpose fluorescent nanobeads of 100 nm in size (yellow-green carboxylate-modified FluoSpheres), immobilized on the surface of a poly- l -lysine-coated coverslip and covered with a mounting medium (Sigma, Fluoromount). Ideally, the resulting images are complementary, nearly rotationally symmetric PSF shapes, one of them donut-like, the other a bright spot, as shown in Fig. 5 a, b 18 . These shapes are robust under defocus, but they are sensitive to polarization distortions, so they can also be useful for calibrating residual undesired birefringence. Once this stage of the calibration was complete, the polarizer and QWP prior to the SEO were removed.

Single-molecule imaging

To produce in vitro-reconstituted F-actin filaments, G-actin (AKL99, Cytoskeleton, Inc.) was polymerized at 5 μM in a polymerization buffer (5 mM Tris-HCl at pH 8.0, 50 mM KCl, 1 mM MgCl 2 , 0.2 mM Na 2 ATP at pH 7.0, and 1 mM DTT) in the presence of 5 μM phalloidin to stabilize the polymerization. To make the labeling sparse enough to isolate single molecules, we used a ratio of 1:200 phalloidin conjugated to Alexa Fluor 488. The filaments were then diluted to 0.2 μM, immobilized on the coverslip surface coated with poly- l -lysine, and covered with an imaging buffer containing an oxygen-scavenging system (5 mM Tris-HCl at pH 8.0, 50 mM KCl, 1 mM MgCl 2 , 0.2 mM Na 2 ATP at pH 7.0, 1 mM DTT, 1 mM Trolox, 2 mM PCA, and 0.1 μM PCD). The typical experimental conditions for single-molecule imaging were TIRF illumination, laser power of a few mW (at the objective plane), camera gain 300, and 1-s integration time. STORM imaging The F-actin filaments used for STORM imaging were obtained, as for the single-molecule images, from G-actin (AKL99, Cytoskeleton, Inc.) polymerized at 5 μM in a polymerization buffer (5 mM Tris-HCl at pH 8.0, 50 mM KCl, 1 mM MgCl 2 , 0.2 mM Na 2 ATP at pH 7.0, and 1 mM DTT). To fully label the actin monomers, the polimerization was done in the presence of 5 μM phalloidin conjugated to Alexa Fluor 488. The filaments were then diluted to 0.2 μM, immobilized on the coverslip surface coated with poly- l -lysine, and covered with a STORM buffer (100 mM Tris-HCl at pH 8.0, 10% glucose, 5 μ/ml pyranose oxidase, 400 μ/ml catalase, 50 mM β -MEA, 1 mM ascorbic acid, 1 mM methyl viologen, and 2 mM COT). Before taking images, the system was realigned, the value of c was adjusted to 1.2 π (in order to benefit from slightly more complex PSFs), and the SEO was aligned so that one of its stress points pointed in the y direction. The typical experimental conditions were TIRF illumination, laser power 150 mW, camera gain 300, and 200-ms integration time. For STORM imaging, a stack of 5000 images was used. For each frame, the approximate x , y positions of the fluorophores were detected. Since some fluorophores blinked for longer than the exposure time of one image, a routine was written to sum over all the relevant consecutive frames for each fluorophore in order to reduce SNR. Some fluorophores blinked for up to about ten frames, resulting in photon numbers of up to about 50,000. Pairs of arrays of 29 × 29 pixels containing each PSF set were then used to retrieve the parameters.

Supplementary information Supplementary Information Peer Review File Description of Additional Supplementary Files Supplementary Movie 1 Supplementary Movie 2 Supplementary Movie 3 Supplementary Movie 4 Supplementary Movie 5