Imaging of fluorescent microspheres

As described in section 2.2, the applied STED laser power is easily accessible experimentally.

However, it is not the only relevant parameter which governs the fluorescence depletion and thus the achievable resolution enhancement. The influences of e.g. the fluorophore properties (STED cross-section), the laser parameters (repetition rate, wavelength) and the microscope (NA) can be merged into a single parameter, the saturation power P_sat. It is given by the power necessary to deplete the fluorescent signal to half, can be determined experimentally and allows to compare the performance of different STED patterns regardless of the utilized microscope.

Therefore, a STED focus with a Gaussian intensity profile is utilized to deplete fluorescence

and determinePsat. The measurements are conducted for fluorescent microspheres at varying STED laser power (for all sample protocols refer to appendix B). In order to compensate for bleaching artifacts, a confocal scan is performed before and after each STED acquisition and the average of both scans is taken for the further analysis. The sum of the signal count over the area of 700 nm×700 nm is determined for both confocal scans and the STED acquisition. Sub-sequently, the respective quantity for the STED image is divided by the average signal count for the confocal images, yielding the ratio of the signal counts at each STED laser power. The results are averaged over several beads and displayed in figure 4.1. An exponential fit is used to approximate the data and allows to determine the saturation powerPsat= (0.497±0.018) mW from the fit parameters.

The suitability of the suggested STED depletion pattern generated by conical diffraction is ex-perimentally verified. Both the depletion pattern generated by conical diffraction forρ₀ ≈1.3 and a pattern generated conventionally by a 0/π phase plate (data taken from [Krü17]) are employed for imaging fluorescent microspheres for different STED laser powers. Exemplary measurements with a depletion pattern generated by conical diffraction for two pattern ori-entations are depicted in figure 4.2(a) and (b): The upper left corner of each image shows a confocal image, the lower right corner a STED image with one-dimensional resolution

enhance-0 1 2 3 4 5

0.0 0.2 0.4 0.6 0.8

1.0 data

fit

normalized intensity

P_STED (mW)

y = A*exp(-x*ln(2)/Psat)+y0 Value Standard Error

y0 0.032 0.005

A 0.968 0.005

Psat 0.497 0.018

Figure 4.1:Utilizing a Gaussian shaped STED intensity distribution and circular polarization, images of Crimson 40 microspheres are recorded for different STED laser powers. The resulting signal count as sum over the area of 700 nm×700 nm is compared to the respective quantity in confocal mode. To account for bleaching, the signal count for the confocal mode is determined as average of a confocal scan before and after the STED acquisition. The average of this ratio over 10 microspheres is shown here together with an exponential fit. The saturation power can be determined asP_sat= (0.497±0.018) mW.

ment. The corresponding STED PSFs measured on gold beads are depicted in the insets.

A quantitative analysis is conducted by measuring and averaging the FWHM in the direction perpendicular to the orientation of the 1D STED pattern, i.e. the high-resolution direction.

The measurements are done for the two different pattern orientations shown in figure 4.2(a,b) as well as for one orientation of the 0/π phase plate (data taken from [Krü17], a homogeneous resolution increase for different orientations in this case is demonstrated therein) for varying STED laser power. The measured FWHM is corrected for the size of the microspheres (cf.

[Krü17]) to obtain the effective resolution ∆STED as a function of the saturation factor ζ, de-termined by scaling the applied STED laser power with the saturation power. The data shown in figure 4.2(c) are fitted according to equation (2.11) by

∆STED= ∆conf· 1

q1 +_{8 ln 2}¹ ∆²_conf·a·ζ (4.1)

(a) ^{0 max}

x y

(b) ^{0 max} (c)

0 20 40 60 80

0 50 100 150 200 250

300 conical diffraction, 0°

conical diffraction, 90°

1D phasemask Fit model:

Fit con. diff. 0°: ∆_conf= 269nm; a = 4.9E-5 1/nm² Fit con. diff 90°: ∆_conf= 278nm; a = 5.0E-5 1/nm² Fit phasemask: ∆_conf= 261nm; a = 4.38E-5 1/nm²

∆ STED (nm)

ζ

Figure 4.2: (a,b) Confocal (upper left corner) and STED (lower right corner) images of fluorescent microspheres (Crimson 40, 48 nm diameter) with one-dimensional resolution enhancement for a depletion pattern generated by conical diffraction enclosing an angle of 0^◦ (a) and 90^◦ (b) with thex-axis. The scale bar indicates a length of 2µm. Here, PSTED = 38 mW, Pexc = 3.2µW, the pixel dwell time is set to pT = 30µs and the pixel size to px = 20 nm. The insets show the respective STED PSFs visualized by gold bead measurements (scale bar 0.5µm). (c) Dependence of the resolution on the STED laser power for a conically diffracted intensity distribution with orientation of 0^◦ (black), a conically diffracted intensity distribution with orientation of 90^◦(red) and an intensity distribution generated by a 0/π phase mask (blue). The experimental data are well described by equation (4.1). The respective Levenberg-Marquardt fits have fitting parameters ∆conf = (269±15) nm, a = (4.9±0.4) 10⁻⁵nm⁻² (black curve), ∆conf = (278±12) nm, a = (5.0±0.5) 10⁻⁵nm⁻² (red curve), ∆conf = (261±4) nm, a= (4.38±0.12) 10⁻⁵nm⁻² (blue curve).

with ∆STED, ∆conf being the FWHM for the effective STED and the confocal PSFs, respec-tively and a the depletion pattern steepness. The fitting parameters are given by ∆conf = (269±15) nm,a= (4.9±0.4) 10⁻⁵nm⁻² for the horizontally oriented conical diffraction STED pattern, ∆conf = (278±12) nm, a = (5.0±0.5) 10⁻⁵nm⁻² for the vertically oriented conical diffraction STED pattern and ∆conf = (261±4) nm, a= (4.38±0.12) 10⁻⁵nm⁻² for a verti-cally oriented 0/π phase plate. Hence, the parameter a is similar for the two orientations of the depletion pattern generated by conical diffraction and even larger than for the reference measurement with the 0/π phase plate. This is also expected from the simulation results pre-sented in figure 3.3.

Consequently, depletion patterns generated by conical diffraction are, in terms of resolution enhancement, comparable to or even slightly more efficient than the pattern generated by a 0/πphase plate. Exploiting the high switching rates possible with Pockels cells, a rotation on

0 2582

Figure 4.3: TomoSTED microscopy on Crimson 40 microspheres: Comparison of maximum-value reconstruction and Richardson-Lucy deconvolution. (a) Confocal scan of Crimson 40 microspheres at an excitation power ofPexc= 7.9µW, a pixel size ofpx= 20 nm and a pixel dwell time ofpT = 90µs.

(b,c) Reconstructed images for the tomoSTED acquisition with 6 pattern orientations at a STED laser power of PSTED = 46 mW. The individual images for the six orientations are displayed in (d-i). The maximum-value reconstruction (b) has a significantly lower signal count than the Richardson-Lucy deconvolution (c), which takes full advantage of all available signal. The Richardson-Lucy deconvolution was conducted with 20 iteration steps andα_Rch = 0.0001. Closeups of (j) the confocal, (l) the sub-image with according pattern orientation, (k) the maximum-value reconstruction and (m) the Richardson-Lucy deconvolution are shown with the respective line profiles (n) averaged over 3 neighboring lines. The scale bar indicates a length of 1µm (a-i) and 200 nm in the closeups (j-m).

a single-pixel level can thus be realized. Such a pixel-wise acquisition is demonstrated on fluo-rescent microspheres, with the results shown in figure 4.3. Sub-images for six different pattern orientations (d-i) are displayed alongside with the confocal image (a) and the reconstructed images (b,c). The maximum-value reconstruction (b) is performed as described in section 3.4.

It shows artifacts due to the insufficient sampling with pattern orientations (cf. figure 2.5) for the here applied resolution enhancement of k ≈ 6, corresponding to an optimum number of 10 pattern orientations. The under-sampling yields a slightly larger FWHM in the image, as can be seen from line profiles drawn over a single bead. The corresponding profile is indicated in the closeups (j-m) and quantitatively shown in (n). The Richardson-Lucy deconvolution (c,m), performed as described in section 3.4 for 20 iteration steps and regularization parameter α_Rch = 0.0001, can compensate for the insufficient sampling, as shown in [Krü17]. It yields the same image FWHM of 50 nm as in the raw data, corresponding to a FWHM of 42 nm of the effective PSF.

As a consequence of the results shown in figure 4.2, tomoSTED microscopy with the here presented depletion pattern yields the same advantages over 2D STED microscopy as for the variant presented in [Krü17]. Namely, the same resolution enhancement for each sub-image is obtainable at only half of the STED laser power compared to 2D STED microscopy. For an adequate comparison of the light dose employed on the sample, the pixel dwell time per sub-image for tomoSTED microscopy needs to be scaled such that the total pixel dwell time amounts to the respective quantity utilized for 2D STED microscopy. As shown in [Krü17], the necessary light dose for image acquisition can be reduced even further by imaging withN_opt/2 number of pattern orientations, yielding an artifact-free reconstruction when employing the Richardson-Lucy deconvolution. In this way, imaging with only one fourth of the light dose compared to 2D STED microscopy is possible, as demonstrated in the following on cellular structures.