Characterization of active matter in dense suspensions with heterodyne laser Doppler velocimetry

We present a novel approach for characterizing the properties and performance of active matter in dilute suspension as well as in crowded environments. We use Super-Heterodyne Laser-Doppler-Velocimetry (SH-LDV) to study large ensembles of catalytically active Janus particles moving under UV illumination. SH-LDV facilitates a model-free determination of the swimming speed and direction, with excellent ensemble averaging. In addition, we obtain information on the distribution of the catalytic activity. Moreover, SH-LDV operates away from walls and permits a facile correction for multiple scattering contributions. It thus allows for studies of concentrated suspensions of swimmers or of systems where swimmers propel actively in an environment crowded by passive particles. We demonstrate the versatility and the scope of the method with a few selected examples. We anticipate that SH-LDV complements established methods and paves the way for systematic measurements at previously inaccessible boundary conditions.


Introduction
Active Matter is a rapidly evolving emergent field of Soft Matter Physics triggering intense experimental and theoretical activity [1][2][3].Catalytic Janus particles present a model system within the large class of self-propelled particles [4][5][6][7][8][9][10][11][12][13][14][15][16][17].Properties and performance of individual particles and small ensembles are readily accessible by (confocal or holographic) microscopy utilizing particle tracking and image analysis for structural and dynamical characterization [18][19][20].Particle image velocimetry or Dynamic Differential Microscopy (DDM) are suitable for studies of larger ensembles of individually propelling swimmers [17,21,22].Both approaches, however, reveal severe technical drawbacks (e.g.low statistics or the necessity for a fitting model), when more interesting situations are addressed.Swimming in crowded environments, collective swimming and density dependent phase separation have already received a lot of theoretical interest [1,2,[23][24][25][26][27][28][29], which, however is not yet fully complemented by experimental work.The main experimental challenges are reliable ensemble averaging and increased turbidity of concentrated or crowded samples.In particular, multiple scattering severely complicates acquisition of reliable information from the collected data in many optical approaches at large densities.In the present paper we present a simple alternative for characterizing the swimming performance of catalytic Janus nanoparticles in terms of their average velocities and directions.We based our approach on the recently introduced Super-Heterodyne Laser Doppler-Velocimetry (SH-LDV) allowing for the correction of multiple scattering [30].In the instrumental setup used here, we combine super-heterodyning (rendering the actual signal free of low-frequency noise and artefacts) with small angle scattering (allowing model-free access to the velocity distribution irrespective of the sample structure) and a large detection volume (providing excellent ensemble averaging).Moreover, we use a facile frequency-space correction scheme to isolate and subtract the multiple-scattering background and obtain high quality Doppler spectra for evaluation.This for the first time enables us to characterize the performance of catalytic self-propelled micro-swimmers in a turbid background bulk suspension of passive particles.

Experimental
For our demonstrations, we chose SiO2/TiO2 Janus particles based on a SiO2 bead with hydrodynamic radius ah = 259±7 nm (SiO2-F-SC68, microParticles GmbH, Berlin, Germany) onto which TiO2 has been deposited.The Janus particles are fabricated similar to the ones described in [14].Briefly, a closed-packed monolayer of SiO2 beads is formed using the Langmuir-Blodgett technique and then transferred onto a Si-wafer, followed by a physical vapour only on one half of the particle, thus giving rise to a concentration gradient across the swimmers surface that will move the particle self-phoretically through the surrounding fluid [14].deposition of TiO2 under an oblique angle (85°) and continuous (fast) rotation of the substrate.
Afterwards the sample is annealed (450°C for 2h) in order to form anatase-TiO2 and subsequently immersed into solution via a sonication bath.The dry radius after coating is aSEM = (275±8) nm.The lab code for these particles is therefore JP550 where JP denotes the Janus Particle and the number denotes the Scanning Electron Microscope (SEM) diameter.Fig. 1 a) shows an SEM image of the TiO2-capped Janus particles on the wafer.Our fabrication scheme allows to manufacture a full wafer yielding a high number of particles (N~10 10 ) at once, giving us the freedom to create highly concentrated particle suspensions that are necessary to perform bulk light scattering experiments with larger sample volumes.
Under excitation with UV light ( =375nm) electron-hole pairs can be generated in the anatase-TiO2 cap which activate the decomposition of H2O2, causing a chemical gradient across the Janus particle.This gradient drives the self-phoretic motion as schematically depicted in Fig. 1b).In the present experiments, the peroxide concentrations ranged from 0.5% to 3%.By switching the illumination on and off, we can change the Janus particles' motion from purely Brownian passive to self-propelling active swimming.This type of catalytically active Janus particles are able to follow the direction of the incident UV light, and can even propel against gravity when illuminated from below [14].Low concentration samples of Janus particles in general [6,10] and in particular of light-switchable types have been extensively investigated elsewhere [7,9,12,14].However, the vast majority of experiments are measured in close proximity of a surface what could dramatically influence the propulsion [5] and interaction [13] characteristics.Moreover, most studies rely on particle tracking being subject to serious statistical issues [18][19][20].It's therefore highly desirable to have alternative measurement techniques that are able to measure the Janus particle propulsion in bulk, avoiding perturbative wall effects and yielding a much better statistical confidence.
Crowded environments were examined by suspending the active Janus particles in a dispersion of passive polystyrene latex micro-particles of radius ah = 167 nm and size dispersity PI= 0.08 (IDC Portland, USA, batch #1421, labcode PS310).Depending on the PS310 concentration this yielded samples with strongly reduced optical transmittance and substantial amounts of multiple scattering.Our systems are studied with an SH-LDV instrument (Fig. 2a) that has recently been described elsewhere with a detailed characterization of its performance [30].The technique employs super-heterodyning [31] to separate the desired super-heterodyne part from homodyne and low frequency noise contributions to the measurement signal.In short, light of an illuminating beam and a reference beam propagate through a cuvette containing the sample.
The reference beam and light scattered by the particles superimpose at the detector which monitors the resulting intensity.The frequency-shifted reference beam acts as a local oscillator generating a beat in intensity, which will be altered by the Doppler shift of the scattered light.
A hardware based Fourier transform analyser (OnoSokki DS2000, Compumess, Germany) provides the power spectrum of the measured intensity time trace as a function of linear frequency f = w / 2p.
In general, the measured intensity contains parts stemming from the homodyne scattering (scattered light mixing itself) and from the heterodyne scattering (scattered light mixing with the light from the local oscillator).These contributions are separated in frequency space via a shift of the heterodyne part by wBragg.In practice this shift between reference and illuminating beams is introduced with the help of an acoustic modulator.The present SH-LDV instrument further features small angle scattering, which allows an efficient correction scheme to isolate the single-scattering signal from undesired multiple-scattering contributions [30] (for a recently realized prototype for wide angle scattering see [31]).
The optical axis of the setup coincides with the propagation direction of the reference beam, i.e., kref.The sample is further illuminated by a widened parallel UV laser (IUV = 19.5 mW) to UV-activate the catalytic particles and that is covering both reference and illumination beams, as shown in Fig. 2a).The propagation direction of the UV beam encloses an angle a with the optical axis.Typically, we chose | | = 15° with the possibility to switch the direction of the UV illumination from +a to -a.In the present experiment, the detection optics ensure that only the light scattered with the same wave vector as of the reference beam ks = kref is collected.It is convenient to base the definition of the scattering vector q on the momentum transfer from the ticles move co-linear with the wave vector of the UV illumination, kUV.c) A photograph of the sample cell filled with dense suspension of beads make the pronounced multiple-scattering halo of the reference as well as the illumination beams visible so they can be seen by the naked eye.
moving particles to the scattered photons: q = ks -kill pointing in positive z-direction [32].Its magnitude S 0 4 sin( /2) n q p l == q depends on the scattering angle q, the laser wave length l0 and the suspension refractive index nS.Note that the light scattered by moving particles is Doppler shifted with a frequency (,,) (,,) s i n 2 , where v(x,y,z) is the (spatially-dependent) velocity of the particles.Here a denotes the angle between the UV and reference beams, and vz is the velocity's z-component, which is parallel to q.During a measurement an individual frame covers a duration of tframe = 32 s, with overlap adjustable between 0 and 16 s.The signal gets averaged over successive frames for a total measurement time, T, typically a few thousand seconds.
A detailed scattering theory was already worked out elsewhere [33].Briefly, we consider the case of scattered light with Gaussian statistics and particles drifting with a constant velocity v.In addition, we assume the particles to undergo Brownian motion with an effective diffusion coefficient, Deff, which may depend on direct and hydrodynamic particle interactions, as well as on activity.The super-heterodyne power spectrum Cshet(q,w), is the time Fourier transformation of the super-heterodyne mixed-field intensity autocorrelation function, Cshet(q,t), that generally contains homodyne and heterodyne contributions: Here w is the circular frequency and t the correlation time.In [33] we had derived its form in detail accounting for all components arising from singly scattered and reference light.Parasitic scattering at optical surfaces, multiple scattering and noise terms were not considered, as they are simply superimposing and can conveniently be removed from the raw data [30].The corresponding single scattering power spectrum reads: where Iref is the reference beam intensity, and <Is(q)> is the time-averaged single scattering intensity for the chosen q.The subscript shet stands to specify the case of super-heterodyning, i.e. including the frequency shift between illuminating and reference light.The super-heterodyne power spectrum contains three terms: a trivial static background, the super-heterodyne Doppler signal and the homodyne signal (for examples of typical raw-spectra see e.g.[30,33,34]).Due to the super-heterodyning these terms are well separated in central frequencies.Both the static d-peak and the homodyne signal are insensitive to the particle drift motion and are centred at zero.The super-heterodyne parts are centred at ±wD.For a positive Doppler shift, both parts of the spectrum are shifted further outward from the origin.In the present integral mode, scattered light is collected from the complete cross section of the cell which is illuminated by the central part of the widened UV beam that is activating the self-propulsion of the particles.The super-heterodyne signal thus averages over the projection of all velocities present in the detection volume.In fact, writing a normalized particle velocity distribution, p(v) ~ dx/dv [35] in terms of the normalized distribution of Doppler frequencies p D), the spectrum can be written as convolution integral: Both homodyne and background terms of Eq. 2, stay unaffected by the convolution with the particle velocity distribution.The two parts of the super-heterodyne Doppler spectrum, now, are diffusion-broadened distributions of Doppler frequencies about the averages, determined by the mean particle velocity.Note, that for any given UV illumination, the shape of Cshet(q,w) is determined by a convolution of the intensity distribution across the detection volume with the distribution of catalytic activities.Thus, for dilute suspensions of large particles with weak Brownian motion and weak spatial variation of UV intensity, we should be able to obtain valuable information about the catalytic activity via the catalytic self-propulsion.

Results and Discussion
We now turn to various demonstrations of the data obtainable in SH-DLV experiments and the scope of the present instrument.First, we investigated the SiO2/TiO2 Janus particles (JP550) at a number concentration of n JP550 = 5 10 m -3 suspended in a 2.5% aqueous H2O2 solution.Their typical Doppler spectra with and without UV illumination are displayed in Fig. 3a).
Without UV-illumination (yellow data) a central Lorentzian indicates purely Brownian motion.
With UV-illumination a slightly asymmetrically broadened Doppler peak shifted to the right indicates particle propulsion in the direction of kref and allows for an easy discrimination between passive and active motions.At wB = 3 kHz, a sharp line is visible.This line is also present in the reference experiment performed in particle free 2.5% aqueous H2O2 solution (Fig. 3b).
We attribute it to parasitic scattering of illumination beam light at the cell surface and data from the immediate peak region are therefore neglected in the subsequent evaluation.
In turbid systems of decreasing transmission, the actual signal becomes drowned in a broad multiple scattering background.This sets the typical limit for signal detection to a transmittance of about 40% [30].In Fig. 4a), a typical Doppler-spectrum of a moderately concentrated suspension (red data) and one taken in a multiple scattering environment (black data) is presented.
Note the presence of a broad symmetric background in the latter signal obtained at a transmittance of 60%.To isolate the actual signal we fit a Lorentzian (yellow solid line) to the outer wings of the broad background signal using the Levenberg-Marquardt algorithm implemented in Origin9.0 (OriginLab, Northampton, MA, USA), and subtract it from the data.Also the spectrum of the moderately concentrated sample is corrected, here by subtracting a constant background stemming e.g. from detector shot-noise.In Fig. 4b) the background corrected SH-LDV spectra are shown for both cases.The signal shape due to the velocity distribution is now clearly recognized in both data sets and the thus isolated single scattering signals can be subjected to a further evaluation [34].Next, we demonstrate how to reliably obtain quantitative information from our SH-LDV instrument by comparing it to standard Dynamic Light Scattering (DLS).Remember that in SH-DLV we measure the Fourier transform of g (1) (q,t), retaining full information of both the individual particle velocity and diffusion.DLS, by contrast, measures the intensity autocorrelation function, g (2) (q,t).Using the Siegert-relation to obtain the field autocorrelation function, g (1) (q,t), the information on any directed motion is removed, but changes in mutual distances of particle pairs as caused by diffusion are retained.Thus, for measuring the diffusion constant of passive particles a long time DLS measurement was done as a high-precision benchmark for comparing our method.Non-interacting JP550 (number concentration n JP550 = 8 10 m -3 ) suspended in pure water, i.e., particles in the passive Brownian state in a singly scattering suspension were used.For precision determination of the diffusion coefficient by DLS, we follow the protocol in [36].The autocorrelation functions extending over several orders of magnitude in time after the decay into the baseline were recorded and the data was fitted with the 2 nd order cumulant expansion under the assumption of purely Brownian motion (Fig. 5a).Fig. 5b) shows the SH-LDV spectrum taken by our instrument at n JP550 = 10 m -3 .For the experiments shown in Fig. 5a) and 5b), we obtain DSH-LDV = (8.41± 0.30) ´ 10 -13 m 2 s -1 and DDLS = (8.49± 0.21) ´ 10 -13 m 2 s -1 , respectively.Both values agree quantitatively within their small experimental error and yield an average hydrodynamic radius of ah = (289 ± 9) nm slightly larger than the dry SEM radius aSEM = (275±8).
The main purpose of SH-LDV, however, is the determination of velocities.For this, it is advantageous to switch between two different modes of data acquisition: frame by frame and continuous averaging.In sufficiently dilute systems, the former case measures small ensembles of individual particles, i.e., their scattering contribution remains separated in frequency space.
Examples of individual frames are shown in the stacked panel of Fig. 6a).Note the "noisy" appearance of the spectra due to summation over very few particles.This mode allows direct discrimination of runs that contain artificial perturbations when showing strongly deviating spectra, e.g.stemming from bubble formation or scattering by dust.Such data is readily distinguished and can be omitted before further evaluation.Moreover, any trend in velocities (e.g. a slowing from peroxide exhaustion or other systematic influences) will readily become observable this way.Hence, by employing the frame-wise acquisition mode we always assured that any systematic variation of velocities is caused by catalytic activity of the JP only.Fig. 6b) displays the corresponding histogram of observed velocities.The distribution is rather symmetric.Assuming a Gaussian distribution of velocities, the fit to the histogram returns an average velocity of v = 7.9 µm s -1 and standard deviation normalized to the mean of s = 0.23.We come back to this observation and its relation to the distribution of catalytic activities below.To prove the consistency between the aforementioned acquisition modes the same data as in Fig. 6 is plotted again in Fig. 7a) and b) (down triangles).Fig. 7a) displays the typical smooth spectral shape obtained from continuous averaging, whereas in Fig. 7b) the velocities obtained from different acquisition modes are plotted frame-wise.The additional data in b) was taken during two subsequent runs, one averaging over N = 57 non overlapping frames (green circle) and the other ranging over N = 47 frames with 50% overlap (blue square).Using the latter parameters allowed for the reduction of the total measurement time.The average velocity of the frame by frame measurement coincides quantitatively with the velocities obtained in two independent runs using continuous averaging but different overlap conditions.Thus, if interested in obtaining only the average speed, the experiment duration can be considerably shortened.This also helps to avoid artefacts due to detection of unwanted long time effects like fuel exhaustion, coagulation and sedimentation.In Fig. 6b we had shown that the velocity distribution of frame-wise averaged spectra is only approximately Gaussian.We now discuss, how additional information may be extracted from this distribution and the spectral shape of the averaged spectra.In particular, we may identify the normalized distribution of average velocities (Fig. 6a) with the distribution of average activities if certain assumptions are fulfilled: i) a homogeneous UV-illumination, ii) a homogeneous and constant peroxide concentration and iii) no significant additional particle flows inside the observation volume due to the locally induced collective swimmer flux.The first assumption is uncritical, since in our setup we only observe the homogeneously lit central region of the widened UV beam.The assumption of constant and homogeneous fuel concentration is difficult to test, but in principle could be feasible via additional fluorescence microscopy measurements using suitable dyes or by taking changes in pH as proxy.We performed preliminary measurements using micro-photometry [37] on JP550 particles in 3% peroxide solution in a horizontally placed microscopy cell lit homogeneously by UV light from below.
Only a gradual change of overall pH but no significant spatial variation in pH was detected.
This indicates a homogeneous distribution and consumption of peroxide which however decreased in time.The absence of convective solvent flows is the least reliable assumption.In  [30,34,33], but also from patterning experiments with light sensitive swimmers [38].Due to the illumination/observation geometry in our experiment, solvent convection in negative zdirection along the cell walls will be monitored and readily yield a spectral contribution also for frequencies smaller than wB.Aligning the UV-laser counter-linear to the illumination beam kref and simultaneously increasing Q should minimize this effect and further increase the magnitude of recorded Doppler shifts.Both expectations can be checked by analysing the corresponding spectral shapes.Thus, also the determination of activity distributions based on a large numbers of simultaneously measured UV-activated swimmers is doable with SH-LDV.
In the present experiment, UV-sensitive particles show motion away from the light source, i.e. motion along kUV [14].However, this can change under altered preparation conditions or be unknown for other types of self-propelling particles [6].Therefore, it is a useful feature, to be able to explicitly discriminate the propulsion direction.SH-LDV offers this feature due to the fact that in the two branches of the spectrum the Doppler frequency enters as ±(wB + wD), c.f. Eq. (2).For the set-up shown in Fig. 2a), motion along kUV translates to a positive Doppler shift with respect to wB.By switching the angle of the incident UV light (with respect to kref) from +a to -a the corresponding switch of Doppler shift was demonstrated (Fig. 8a).We obtain two spectra that are mirrored around the Bragg frequency wB.Thus, upon change of the illumination direction, the projection of the swimming velocity onto the z-axis changes its sign.
Finally, we demonstrate the usefulness of SH-LDV for measurements under systematic changes of experimental boundary conditions and their simultaneous control.Fig. 8b) displays the results of (preliminary) measurements of the average swimming speed (here expressed in terms of the centre of mass Doppler frequency) as a function of peroxide concentration.From literature, an increase of velocities with increased peroxide concentration is well documented [5,14], but its functional form for specific types of swimmers remains under debate.The data in Fig. 8b) was obtained by evaluation of continuously averaged spectra (N = 50 ± 5) for each peroxide concentration.In this set of experiments, the measurements were deliberately performed without any specific care about constant experimental boundary conditions.The UVillumination intensity was approximately tripled and the peroxide concentrations were derived from added amounts of concentrated peroxide solution, but not checked via reaction with standard chemicals.Moreover, samples were investigated at different times after their preparation (sonicating a wafer piece and mixing the suspension with peroxide).As before, each run reliably determined the respective average swimming velocity, which increased as expected from literature.However, the data contains significant outliers, and a unique functional dependence cannot be inferred reliably.Both is attributed to systematic errors due to the reproducibility of experimental boundary conditions.Hence, due to its excellent statistics SH-LDV allows not only the precise determination of average swimmer velocities and directions but, moreover permits immediate identification of insufficiently stabilized or less-controlled systematic investigations.Systematic measurements of the peroxide concentration dependence for differently sized Janus particles (including JP550) under well controlled boundary conditions are under way and will be reported elsewhere.

Conclusion
We presented SH-LDV as a facile and versatile approach to measure velocities of active systems in the bulk and away from a wall.In particular, it was shown to reliably measure selfpropelling Janus particles while they undergo purely passive Brownian motion as well as in their catalytically active state.The motion was characterized by extracting the hydrodynamic radius and for the active swimmers the directionality, the average speed and the determination of the activity distribution could be obtained additionally.Most importantly, we could measure the swimming performance not only on isolated, non-interacting swimmers, but also in bulk environments crowded by passive particles.Working in frequency space allows us to remove the multiple scattering contributions occurring in turbid systems by a facile correction scheme.
This leads to a statistically trustworthy method, highly sensitive to environmental changes.The system chosen for demonstration were photocatalytic active Janus particles of SiO2/TiO2 type.
However, the method is not restricted to this specific system, and we anticipate that SH-LDV opens access to characterize the swimming properties for a wide variety of swimmer classes and types.

Fig. 1
Fig. 1 a) SEM image of the as prepared SiO2/TiO2 Janus particles JP550 (scale bar 200nm).b) Schematics of the photo-catalytically active Janus particle.Upon UV irradiation electron-hole pairs are generated in the anatase-TiO2 that will drive the decomposition of H2O2.The decomposition occurs

Fig. 2 a
Fig. 2 a) Experimental setup and scattering geometry in top-view.Illuminating (Iill, ill = 0) and reference (Iref, ref = 0 + Bragg) beams, cross under a scattering angle qS = 7.6° inside the suspension filled sample cell with thickness d = 10 mm (refraction at cell walls not drawn here).The reference beam is collinear with the observation direction.Scattered light is focused by lens (L) at f = 50 mm onto a small circular aperture (CA), collected by a gradient-index lens (GL) and fed into an optical fibre leading to the detector (not shown).Precise location of CA selects the detected vector of scattered light and restricts it to ks = kref.The distance CA-GL defines the diameter of the cylindrical detection volume (VD, boxed area inside the cell) adjusted to contain the complete path of the illuminating beam inside the cell.Note that it covers the central region of the widened UV beam activating the catalytic swimmers.A horizontal slit aperture (SA) rejects any light travelling outside the x-z plane and a polarizer (P) assures V/V scattering geometry.b) Wave vectors of the illumination beam, kill, and of the reference beam, kref = ks, yielding a scattering vector q parallel to the cell axis.The scattered light is Doppler shifted by = v = (k s k ill ) v z , which is positive, if the par-

Fig. 3
Fig. 3 Typical spectra obtained by a SH-LDV experiment.a) Power spectra obtained by averaging over N = 54 individual frames (total measurement time T = 1500 s) for JP550 with w(H2O2) = 2.5% without (yellow) and with (black) UV illumination.The spectrum for particles that are not catalytically active is a Lorentzian, centred at the Bragg frequency B = 3 kHz.Active motion towards the detector results in a positive Doppler shift.The signal change in shape reflects the diffusion broadened velocity distribution appearing under UV-illumination.b) Particle-free signal measured in pure water (yellow) and 2.5% hydrogen peroxide solution (black).No signal, except for the delta peak at the Bragg frequency, is detected.

Fig 4
Fig 4 Multiple scattering correction in SH-LDV.a) Raw data taken for JP550 at n JP550 = 5 10 m -3 in 2.5% hydrogen peroxide solution (red) and at n JP550 = 2 10 m -3 with the same peroxide concentration, but now in a suspension of passive PS310 at n PS310 = 10 m -3 .Note the presence of a broad, peaked background in the latter case.A Lorentzian (yellow) is fitted to the wings of the signal and subtracted while in the first case, only a constant background is subtracted.b) Comparison of background corrected spectra.Now, the peak shape is clearly discriminated also for the case of the crowded, multiply scattering environment.

Fig. 5
Fig. 5 Determination of diffusion constants for particles suspended in pure water i.e. in the passive state.a) Autocorrelation function measured by Dynamic Light Scattering (DLS) of non-interacting JP550 at a number concentration of n JP550 = 8 10 m -3 and evaluated following [36].A second order cumulant fit returns a diffusion constant of DDLS = (8.49± 0.21) ´ 10 -13 m 2 s -1 .b) SH-LDV power spectrum the same particles at n JP550 = 10 m -3 .Fitting a Loretzian to the data returns a diffusion coefficient of DSH-LDV = (8.41± 0.30) ´ 10 -13 m 2 s -1 .

Fig. 6 a
Fig. 6 a) Selected individual frames collected for the actively propelling JP550 under UV illumination.Each frame duration is tframe = 32 s with the overlap set to zero.b) Velocity distribution of 57 frame-wise averaged swimming speeds yielding a total average velocity of 7.9 µm s -1 .The solid curve is a fitted Gaussian assuming a normal distribution of catalytic activity with a standard deviation normalized to the mean of s = 0.23.Given a homogeneous illumination and fuel distribution, and the absence of solvent flows, such a histogram corresponds to the distribution of average activities.

Fig. 7
Fig. 7 Quantitative determination of velocities at a peroxide concentration of w(H2O2) = 2.5%.a) Power spectrum obtained by continuous averaging over 57 non-overlapping frames in one go.The centre of mass frequency fCoM = 3000.46Hz (dashed line) corresponds to a number averaged particle velocity v = 7.9 m s .b) Extracted velocities from different acquisition modes are shown to be within good agreement (Black down triangles: individual frame data; Orange down triangle: average of 54 individual frames; Light green circle: subsequent independent run over 57 successive frames without overlap.Light blue square: subsequent independent run over successive 47 frames with 50% overlap).

Fig. 8 a
Fig. 8 a).UV-activated JP550 Janus particles with changing incident direction of the UV laser beam (a = +15° (black data) and a = -15° (yellow data)).Both spectra appear to be mirrored, with almost equal amplitudes, but Doppler shifts opposite in sign.The centre of mass frequencies are shifted by = 0.65 and = 0.72 , respectively.b) Preliminary measurement on the H2O2 dependence of the swimmer velocity.The velocity increases with peroxide concentration.Note the large scatter of data and indicating the importance of precise control of experimental boundary conditions.fact, closer inspection of the spectra in Figs.7a) and 8a) reveals that the distribution of velocities tends towards negative values.We attribute this finding to solvent convection induced by the locally enforced swimmer flux along the illumination direction in combination with solvent volume conservation.Similar flows are well known from phoretic experiments in closed cells