Results

Resolution quantification

To determine the effective PSF of the STED microscope under the pa-rameters of operation applied here, 20 nm fluorescent beads fixed in a

(1)Parts of this section are published as [331].

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spincoatedPVA⁽²⁾film were imaged with a pixel dwell time of 150 µs and a pixel size of (15×15) nm². Images of individual beads were manually identified and averaged. For STED imaging the measuredFWHM of the effective PSF was 77 nm in the beam scanning direction and 74 nm for the second lateral direction, for which stage scanning was used. For beads of 36 nm diameter (as used in the following experiments), the

FWHMof individual spots was predicted to be 83 nm and 80 nm, respec-tively. For the corresponding confocal imaging (i. e. without the deple-tion beam) the measured FWHM of the PSF was 249 nm. Thus, STED

microscopy provides, under the conditions used here, an about three times higher resolution than confocal microscopy.

The average background originating from stray light, measured with a blank sample, amounted to 0.3 counts per pixel, which can be ne-glected in comparison to the 10–20 counts per pixel from the beads.

Dynamic Imaging

A suspension of 36 nm particles in a glycerol film was prepared: 6 µl of 36 nm fluorescent bead suspension [≈4% (w/v),⁽³⁾ actual size according to the manufacturer (36±5) nm, Crimson, Invitrogen] were mixed with 200 µl glycerol and 1 µl of 10 M sodium hydroxide solution and spin-coated (KW-4A precision spin coater, Chemat Technology, Inc., North-ridge, CA,USA) onto cleaned (see in Methods on page 72) coverslips at 8000 rpm.⁽⁴⁾ Spincoating for 1 min gave (1–2) µm thick films. The beads were mostly confined to the glycerol surface, forming a two-dimensional sample simplifying particle tracking. The density of particles varied across the sample.

Movies of these diffusing nano-particles were filmed at 80 fps with the STEDmicroscope shown in Fig.2.4using four APDs for detection to augment the dynamic range. Each frame was recorded within 10 ms;

2.6 ms were needed for the reversal of the scan direction.

Throughout the whole movie, individual diffusing particles could be discerned in the STED images (Fig. 3.1 middle) but not in the confo-cal ones (Fig.3.1left). Linear deconvolution (Wiener filtering) acted as

(2)Poly (Vinyl Alcohol)

(3)weight per volume

(4)rotations per minute

Figure 3.1: Individual images (i. e. single frames of a movie) of fluores-cent 36 nm beads in glycerol recorded at 80 fps. Left: recorded via confocal microscopy. Middle: Recorded via STED microscopy. Right: Linear decon-volution with the effective PSFof the STEDmicroscope. The frame acqui-sition time was 10 ms with 2.6 ms used for reversal of the scan direction.

With 60×50 pixels per frame, the pixel dwell time was 1.9 µs. The color bars indicate the photon counts per pixel. Only in the STED movie, the individual beads can be discerned.

a noise filter for visualization while preserving the resolution (Fig.3.1 right). Despite the high density of the sample, it was possible to follow individual particles from frame to frame (Fig.3.2, the full movie is avail-able on the website of the New Journal of Physics athttp://www.iop.org/

EJ/mmedia/1367-2630/9/12/435/movie1.avi).

Brownian Motion

To quantify the distribution of the particle speeds, individual beads were localized and tracked (see also Methods on page72). The speed of the individually tracked particles was calculated asv=∆x_frame/∆t_frame with ∆x_frame denoting the displacement of the particle from frame to frame, and with∆t_frame = 12.6 ms denoting the time difference between two frames. In this experiment the particle density was nine times lower than in the sample of Figs 3.1 and 3.2, because this ensured that the maximal displacement of the particles between two frames was smaller than the average particle distance. The speed histogram of≈35 000 speed measurements taken from 2100 traces of individually

Figure 3.2: Rapidly diffusing 36 nm diameter fluorescent particles in a glycerol film shown in subsequent frames recorded at 80 fps. Data shown after linear deconvolution (upper panels). Some particles are marked to highlight their movement (the other particles move as well). All positions at which particles were automatically identified are marked by orange dots of 36 nm diameter (lower panels). Yellow traces show the movement of the particles that are marked in the upper panels. The 250 nm scale bar also indicates the resolution limit of a corresponding confocal system.

µ

Figure 3.3: Comparison of the measured speed distribution (dots) of dif-fusing nano-particles with the fitted χ-distribution (line) describing two dimensional particle diffusion. Error bars are the SEM(standard error of the mean) between different data sets.

resolved beads revealed close correspondence to a χ-distribution with two degrees of freedom which describes the two dimensional particle diffusion in space [85]:

vdv=β v exp

"

−β v² 2

#

dv. (3.1)

The constantβ depends on the viscosity of the medium and on the par-ticle diameter. A fit to the measured distribution with a single free parameter matched well for β = 0.33 (Fig. 3.3). The vast majority of speeds was significantly below 24 µm/s which was the maximum speed that could be tracked at this particle density. Fitting of Eq. (3.1) to the measured speed distribution gave a peak at 4.2 µm/s.

The standard deviation of bead displacement^ph∆x²iafter the time

∆t can be used to estimate the resolution degradation due to motion artifacts. The data underlying Fig.3.3yielded^qh∆x²_framei =72 nm be-tween consecutive frames; however, the relevant time for the blurring of a particle is the time ∆t_bead required to record a single particle. Be-cause each particle was imaged with five subsequent line scans,∆t_bead was 1 ms. Since^phx²iscales with√

∆t, it is^qh∆x²_beadi =20 nm, which can be neglected at a spot size of≈80 nm.

3.1.3 Methods