The working principle of SmHOLIMO is based on digital in-line holography. Holography can generally be divided into two main parts: (1) the generation of holograms and (2) the numerical retrieval of single-particle information from the holograms.

To generate and record a hologram, a coherent light source (i.e., laser) and a digital camera are required. The beam of the coherent light source is first collimated (reference wave) before traversing the sample volume. If particles are present in the sample volume, they will cause diffraction, resulting in a secondary wave (diffracted wave) that interferes with the reference wave (see Fig. a). A digital camera records this wavefront as a two-dimensional hologram. A more complete and comprehensive description of holography can be found in and .

The three-dimensional location, shape, and size of the observed particles are numerically reconstructed from the hologram using the HoloSuite software package described in . The location is determined by the center voxel where the particle is in focus and the shape is a direct result of the given particle shadowgraph at this position. The particle size is inferred from the camera pixel sizes using a sizing algorithm described in Sect. . Only particles with a diameter larger than 3.7 µm (i.e., 2 px × 2 px) are analyzed (see Sect. ) to reduce the detection of artifacts due to camera sensor noise. The particles are classified into cloud droplets and artifacts based on their shape by a neural network . For more accurate classification, the neural network is fine-tuned using a subset of 512 hand-labeled particles and artifacts for each recorded data set.

SmHOLIMO's primary deployment sites are either ground-based locations (e.g., mountain tops) or balloon-borne platforms (e.g., TBS; see Sect. ), which typically experience highly variable wind conditions. Therefore, SmHOLIMO was specifically designed to be lightweight (≈5.3kg) and compact, measuring 45cm×40cm×13cm (height × width × depth). Due to the open-path configuration of SmHOLIMO, the effects of non-isokinetic sampling of cloud droplets are minimized, and the well-defined sample volume facilitates measurements with low and variable inflow velocities, which allows it to be used as a ground-based instrument (e.g., mountain tops). An image of the final instrument including its main components is shown in Fig. b.

A 409 nm

409 nm instead of 405 nm due to manufacturing tolerances.

A single-board computer (Raspberry Pi 4 Model B – 8 GB) synchronizes the triggering of the laser pulses with the acquisition of holograms and stores the recorded holograms on an external SSD hard drive. The computer also allows direct access via a VNC connection during measurement periods and yields live data of the measurements with information regarding their quality.

A uniform optical resolution across the whole sample volume is important to avoid a sampling bias linked to the size of cloud droplets. For SmHOLIMO, the optical resolution is limited by (1) the diffraction-limited resolution imposed by the working principle of digital in-line holography and (2) the pixel resolution limit of the camera pixel pitch.

The diffraction limited resolution Dres,rec(zrec)=2.44⋅λDcam,eff⋅zrec is derived from half the Rayleigh criterion and is a linear function of the reconstruction depth zrec (orthogonal distance from the camera sensor along the z direction; see Fig. a) and the laser wavelength λ. The effective camera sensor aperture is given by Dcam,eff=Dcam,x⋅Dcam,y with the camera sensor dimensions Dcam,x=7.44mm and Dcam,y=5.62mm along the two sensor dimensions. The diffraction limited resolution Dres,rec(zrec) for SmHOLIMO is shown in Fig.  as a solid black line.

The pixel resolution limit Dres,pix for SmHOLIMO is given by Dres,pix=2⋅dpix=3.7µm, with dpix=1.85µm the equilateral pixel size for our camera sensor. It is shown in Fig.  as a dashed black line. A more general and detailed derivation of both resolution limits can be found in .

The optical resolution Dres,exp of SmHOLIMO was verified by placing a 1951 USAF resolution test chart in different reconstruction depths 6<zrec<35 mm within the sample volume, as was done by , , and . The resolution was determined manually by identifying the smallest recognizable pattern (three bars) on the resolution chart, and the results are shown in Fig.  as red crosses. All measured resolutions are close to the theoretical limits and follow the expected increase for zrec>24 mm imposed by Dres,rec(zrec). Although the increase in resolution limit beyond zrec=25mm is known and could be corrected for, we restrict the SmHOLIMO reconstruction depth to this value. This ensures the highest and a uniform optical resolution across the entire sample volume while maintaining a sample volume that is independent of cloud droplet size.

To ensure that SmHOLIMO accurately measures cloud droplet diameters, we want to validate the particle sizing algorithm. The sizing algorithm is embedded within the HoloSuite software package and was introduced by . It is based on a brightness threshold between the observed droplet shadowgraph (dark) and the background (bright) within a hologram, which allows the particle sizing algorithm to be tuned.

The validation of the sizing algorithm is performed using a vibrating orifice aerosol generator (VOAG; model 3450, TSI, USA) that produces a jet of droplets from an isopropanol-polyethylene glycol emulsion. After the VOAG, the droplet jet was dispersed into a homogeneous plume by passing it through a ventilated cylinder (12cm×1m, flow rate of 50–70 Lmin-1). The residence time within the cylinder was ≈11s to ensure full evaporation of the isopropanol yielding nearly monodisperse droplets of polyethylene glycol. A total of six different droplet sizes were generated, with diameters ranging from ≈4 to ≈19 µm (see Table ). The six different validation experiments were conducted in a co-located measurement setup, using SmHOLIMO and an aerodynamic aerosol sampler (APS, model 3321, TSI, USA) serving as the ground truth instrument. The APS can measure droplets in the size range between 0.5 and 20 µm.

To validate the sizing algorithm of SmHOLIMO, the brightness threshold was varied between 0.40 and 0.75. The best agreement (minimum sum of squared errors) between the SmHOLIMO and APS measurements was found for a brightness threshold of 0.45. However, we decided to exclude the measurements with droplet diameters of 19 µm because this size is close to the upper observable limit of the APS. This likely leads to an underestimation of the droplet sizes due to a sampling bias toward smaller droplets. The best agreement was found with a threshold of 0.5 after removing the measurements at 19 µm.

The measured APS and SmHOLIMO droplet size distributions for a brightness threshold of 0.5 are shown in Fig.  and are normalized to their maxima. We see a general trend of SmHOLIMO slightly overestimating the droplet diameters compared to the APS except for the 6 µm measurements. The highest relative deviations are found for the 4 µm droplets with 6 % and the 19 µm droplets with 4 %, since these sizes are situated at the observable limits of SmHOLIMO and the APS, respectively. As mentioned previously, for the 19 µm experiment, we assume a sampling bias towards smaller droplet sizes from the APS. Conversely, for the 4 µm droplets, SmHOLIMO is assumed to overestimate the droplet size, as the diameter is just above the resolution limit of 3.7 µm. Overall, the droplet diameters measured by SmHOLIMO and APS are in good agreement without any significant deviations, and all measurements fully overlap within their respective uncertainties (see Table  and Fig. ).

Spatially resolved information on the homogeneity of the recorded droplets and the performance of the sizing algorithm is shown in the Appendix (Fig. ) for each droplet size individually. We observe a uniform droplet count distribution after trimming the sample volume to remove hologram edge effects. Furthermore, no dependence between droplet size and sample volume location can be inferred.

The measurement location is close to Eriswil (47°04^′14^′′ N, 7°52^′22^′′ E) at an altitude of 920 m a.s.l. For the in situ observations, we used a tethered balloon system TBS, HoloBalloon,, which can lift an instrumentation platform of around 80 kg inside the low stratus cloud. The platform carried SmHOLIMO and HOLIMO, mounted with a horizontal displacement of around 1.5 m, hanging 30 m below the TBS. The height of the TBS was adjusted using a winch, with a vertical velocity of 1.5 ms-1 during ascent and of 1 ms-1 during descent, which results in an average profile duration of 5 min.

The SmHOLIMO data were recorded and analyzed with a frequency of 5 Hz, and the reconstruction volume was trimmed to -3.2<X<3.2, -2.2<Y<2.2, and 7<Z<25 mm, yielding a sample volume of Vhol=0.5 cm3 and a sample volume rate of 2.5 cm3s-1. The primary objective of the measurements is to observe the large-scale temporal evolution of the cloud. Therefore, a recording frequency of 5 Hz was chosen instead of the maximum 10 Hz to enable continuous measurements for 4.6 h, constrained by the 1 TB storage capacity. Additionally, we average the SmHOLIMO data over 1 s, as our focus (in this specific measurement) is not on capturing small-scale fluctuations in cloud microphysical properties. This also ensures consistency in time resolution with HOLIMO while further improving the measurement accuracy through enhanced counting statistics.

The HOLIMO data were analyzed with a frequency of 1 Hz, and the reconstruction volume was trimmed to -6.5<X<6.8, -7.0<Y<6.5, and 40<Z<120 mm, resulting in an sample volume rate of 14 cm3s-1. The average vertical resolution for both instruments was 1.25 m.

The detected particles were classified into cloud droplets and reconstruction artifacts using a neural network that has been fine-tuned using the respective data set (see Sect. ). Cloud droplets with diameters >20 µm for SmHOLIMO and >30 µm for HOLIMO were manually classified into the same categories. The derivation of cloud microphysical variables, i.e., liquid water content (LWC), cloud droplet number concentration (CDNC), and cloud optical depth τc, was constrained to LWC >0.01 gm-3 (“in cloud” definition). The derivation of the cloud droplet mean diameter is further constrained to CDNC >20 cm-3 for statistical reasons. The uncertainty in retrieving the diameter of a single droplet with SmHOLIMO is defined by the pixel pitch, yielding Δds=1.85µm . When measuring N independent droplets, the total uncertainty decreases according to the central limit theorem due to random error reduction, resulting in ΔdN=Δds⋅N-1. The uncertainty associated with CDNC follows counting statistics and is thus described by N, where N represents the total number of detected droplets. Exemplary CDSDs, including their corresponding uncertainties, are presented in Fig. . Additionally, reconstruction quality in in-line holography decreases at higher hydrometeor concentrations due to speckle formation on the hologram. Following the approach of and assuming a particle diameter of 20µm, SmHOLIMO and HOLIMO can reliably detect number concentrations up to 25 800 and 6450 cm⁻³, respectively.

On 29 February 2024, a low stratus cloud was present over the field site which dissipated over the course of the measurement period, as visible in the height–time indicator (HTI) radar reflectivity measurements shown in Fig. a, along with the flight level of the TBS showing the 30 profiles. A stable Bise situation (cold, dry, northeasterly winds), which generally facilitates the formation and the persistence of low stratus, weakened during the previous afternoon, due to a change in the synoptic weather situation. The wind direction and wind speed over the last 2 d (weather station on ground at field site) were ≈70°N and ≈5 ms-1 and changed to variable wind directions and wind speeds between 1 and 2 ms-1. The lack of solar radiation supported the low stratus to persist for another night, before the increase in radiation on the next morning led to its dissipation after 2 d of persistence. A more comprehensive work on the climatology and life cycle of wintertime low stratus in Switzerland can be found in and .

During the measurements, the cloud top decreased from 1500 to 1400 ma.s.l., while the cloud base increased from 1150 to 1250 ma.s.l. Around 09:00 UTC we observe a strong thinning of the cloud, and at about 09:45 UTC, the previously uniform cloud layer became increasingly patchy, visible in the HTI radar reflectivity measurements of Fig. a. Figure b and e show vertical profiles of meteorological parameters recorded by two radiosondes (RSs), RS1 and RS2, launched from the measurement site. A strong and stable temperature inversion is visible above cloud top (Fig. b and c). Due to the weakening/breakdown of the Bise situation, the wind speed was low, at about 2 ms-1 below the inversion layer (Fig. d). The wind direction was variable over the measurement time period and altitude, covering directions from 0 to 150°N (Fig. e).

The measured CDSDs of the 30 profiles are shown over time in Fig. a and b for SmHOLIMO and HOLIMO, respectively. Some exemplary profile numbers are shown, with odd numbered profiles being ascending and even numbered ones being descending (see Table ). As intended, SmHOLIMO is capable of extending the observable size spectrum down to 3.7 µm, well below the resolution limit of HOLIMO at 6 µm (horizontal black dashed line), while still capturing the full upper end of the CDSD. Furthermore, SmHOLIMO observed the expected shift of the CDSD maxima towards larger cloud droplet diameters with increasing height inside the cloud, which is only faintly visible in the CDSDs measured with HOLIMO.

In Fig. c–v, we show averaged CDSDs of SmHOLIMO and HOLIMO for the four profiles P4, P5, P18, and P19, each divided into the five sections: cloud base, lower center, cloud center, upper center, and cloud top. The section ranges are based on the total vertical extent of the clouds (defined by LWC >0.01 gm-3) divided by 5 and are determined individually for each profile. The interpretation of the smallest size bins of the CDSD, for SmHOLIMO and HOLIMO, should generally be treated with caution as it is close to the respective resolution limit.

For the descending profiles, i.e., P4 and P18, we observe a deviation between the CDSDs measured by SmHOLIMO and HOLIMO, with SmHOLIMO measuring lower concentrations of larger cloud droplets and HOLIMO measuring higher concentrations of small droplets, especially in the cloud center and cloud base regions (e.g., Fig. k, m, o, q, and u). Our main hypothesis is that there are two interrelated reasons for this underestimation, namely the low atmospheric wind speed (≈2 ms-1; see Fig. d) and the non-ideal mounting of SmHOLIMO on the measurement platform. The descending velocity of the TBS of ≈1 ms-1 is close to the ambient wind speed, and SmHOLIMO was mounted on the measurement platform in the same orientation as shown in Fig. b with the sample volume above the electronics box. This combination resulted in non-isokinetic sampling of cloud droplets for descending profiles because the electronics box prevented an undisturbed airflow. In hindsight, the non-isokinetic sampling could easily have been avoided by turning SmHOLIMO by 90°, resulting in an unobstructed sample volume from above and below, as is the case for HOLIMO. Another hypothesis is that in the lower cloud and cloud base regions, some of the smaller cloud droplets may have been incorrectly sized by HOLIMO due to resolution limit effects, causing them to be assigned to a larger size bin, e.g., Fig. q and u. This feature persists across all cloud base region CDSDs (Fig. s–v), where HOLIMO generally measures higher concentrations in the smallest size bin compared to SmHOLIMO. However, as noted earlier, measurements in the smallest size bin should be interpreted with caution. Since the descending profiles are not trustworthy, we will discard them from the following analysis and focus on the data from ascending profiles only. To better assess the source of this discrepancy we conducted an intercomparison campaign at Mt. Sonnblick Observatory, Austria, between SmHOLIMO, HOLIMO, and the Fog Monitor (FM-120, Droplet Measurement Techniques, USA). The data are currently being analyzed.

The ascending profiles, i.e., P5 and P19, show very good agreement in CDSDs between SmHOLIMO and HOLIMO (Fig. , columns 2 and 4). The locations of the CDSD maxima show the expected shift from smaller sizes at the cloud base to larger sizes in the cloud top region. For the cloud top and upper center region (Fig.  row 1 and 2), both HOLIMO and SmHOLIMO are able to capture the full CDSD. We also want to emphasize that SmHOLIMO sufficiently captures droplets in the size range larger than 20 µm, despite the sample volume rate of 2.5 cm3s-1 that is more than 5 times smaller compared to HOLIMO's rate of 14 cm3s-1. However, starting from the cloud center region towards the cloud base (Fig.  row 3–5), we clearly see the importance of SmHOLIMO's ability to measure smaller cloud droplets down to 3.7 µm compared to 6 µm. As an example, in Fig. n in the cloud center region, we see how the CDSD measured with HOLIMO is truncated right at the maximum, giving a misleading location of the maximum at larger cloud droplet diameters, and this trend further intensifies toward the cloud base (see Fig. p and r). In the cloud base region (Fig.  row 5) it is particularly difficult to capture the full CDSD. Here, cloud droplets are formed and tend to have initial diameters in the submicron range, so even the low resolution limit of SmHOLIMO is not sufficient to capture the full CDSD, as can be seen in Fig. v. Nevertheless, and despite the seemingly marginal difference of 2.3 µm in resolution between HOLIMO and SmHOLIMO, SmHOLIMO provides a much more complete image of the CDSD.

The necessity of capturing a broad range of the CDSD becomes even more evident if we compare the derived quantities of CDNC, cloud droplet mean diameter, LWC, and cloud optical depth (τc) between SmHOLIMO and HOLIMO. They were obtained during the vertical profiles P5 and P19 (see Fig. ) and are shown as absolute values in Fig. a–d and as ratios between SmHOLIMO and HOLIMO in Fig. e–h. P5 was measured while the cloud was still in a more stable phase, while P19 was obtained just before the breakup of the uniform cloud layer. Therefore, the trends over height for P5 are more consistent with the theory of an adiabatic cloud profile than the trends observed in P19. From an adiabatic cloud profile, we expect a rapid increase in CDNC near cloud base until it stabilizes to a more constant value after the height of maximum supersaturation is reached. We see how SmHOLIMO captures these features well during P5, while HOLIMO significantly underestimates the CDNC at lower cloud levels, measuring concentrations up to 4 times lower (Fig. a and e). Simultaneously, we expect a steady increase in cloud droplet mean diameter with height above cloud base. The increase in cloud droplet diameter from cloud base to cloud top is around 2.5 µm for SmHOLIMO and 1.3 µm for HOLIMO (Fig. b and f). Also, the retrieved mean diameters are up to 1.6 times smaller for SmHOLIMO in the cloud base region. Finally, we observe an almost linear increase in LWC with cloud height for both instruments during P5 (Fig. c), as expected for shallow clouds with vertical extents less than 1 km . The LWC measurements of SmHOLIMO and HOLIMO show an overall good agreement, with SmHOLIMO having slightly higher values in the cloud center and cloud top region. The similar LWCs indicate that it is mainly defined by the higher mass of the larger cloud droplets for the sampled low stratus, with small droplets having only a minor influence. In the cloud top region with larger mean diameters, with SmHOLIMO we observe a LWC that is 1.5 times higher (Fig. g). In contrast to the LWC, more and smaller droplets can have significant effects on the cloud optical depth already at cloud base (Fig. d and h). The optical depths τc,P5∗ and τc,P19∗ retrieved for the full cloud profiles are more than 10 % higher for SmHOLIMO. The differences would translate into attenuation of radiation that is 2.7 times and 1.2 times (Beer–Bouguer–Lambert law) higher obtained with SmHOLIMO for profile P5 and P19, respectively. The comparison between SmHOLIMO and HOLIMO measurements unequivocally shows the importance of capturing small cloud droplets in order to retrieve accurate cloud microphysical quantities to confirm or establish new hypotheses.

The in situ observations are now compared against the remote sensing observations, i.e., a microwave radiometer (MWR, RPG-HATPRO-G5, RPG Radiometer physics GmbH, Germany) and a vertically pointing W-band Doppler cloud radar (RPG-FMCW-94, RPG Radiometer physics GmbH, Germany). In order to have a fair comparison between all data sets, we will only use SmHOLIMO and HOLIMO observations acquired during ascending profiles due to the sampling bias described in Sect. . The MWR and cloud radar are located at a horizontal distance of 100–150 m away from the in situ measurements see.

Figure a shows a time series of the liquid water path (LWP) measured by the MWR. The LWPs for SmHOLIMO and HOLIMO are determined by integrating the LWC over height for each ascending profile. The LWPs measured by SmHOLIMO and HOLIMO are in good agreement with the LWP observed by the MWR (i.e., they lie within the given uncertainty). Furthermore, all three measurements independently observe a sharp decrease in LWP around 09:30 UTC. The two linear regressions for SmHOLIMO and HOLIMO shown in Fig. b are in good agreement with the MWR data. Since their 95 % confidence intervals overlap and their respective slopes (SmHOLIMO: (1.12±0.07)g-1m2; HOLIMO: (1.05±0.03)g-1m2) agree within the given uncertainties, no significant differences can be inferred.

Finally, we compared the in situ observations of SmHOLIMO and HOLIMO with the equivalent reflectivities measured by the cloud radar. To do this, we approximate the equivalent in situ equivalent reflectivities (in dBZ) by converting the measured CDSDs first into the radar reflectivity Z using the discretized radar equation Z=64∑iN(ri)⋅ri6, with N(ri) the cloud droplet size distribution as concentrations per bin, ri the mean radius of each size bin, and i the number of size bins. The equivalent reflectivity Ze is then calculated using Ze=|K|20.93⋅10⋅log⁡10Z1mm6m-3, with |K|2=0.93, the square of the absolute value of the complex index of refraction for liquid particles.

The temporal evolution of the Ze is shown in Fig. a–c for the radar, SmHOLIMO and HOLIMO. For the in situ observations only values Ze>-60dBZ are shown, which corresponds to the lower limit for the cloud radar. A qualitative comparison of Fig. b and c with the HTI radar measurements in Fig. a shows a good agreement for all ascending profiles and a clear underestimation of the Ze for the descending profiles of SmHOLIMO due to the sampling bias described in Sect. . Correlation plots of the calculated in situ Ze vs. the measured radar Ze are shown in Fig. d and e for ascending profiles. Based on linear regressions we observe better agreement for the SmHOLIMO data with a slope of 0.82±0.03 compared to HOLIMO 0.66±0.02. In general, one observes a larger spread of data points below the 1 : 1 line, indicating a more pronounced underestimation of Ze by the in situ measurements, in particular for SmHOLIMO. This bias arises directly from the large difference in the observed cloud volume, which is more than 7 orders of magnitude higher for the radar data points with >1000 m3 compared to <0.1 L for the in situ measurements. Since Ze is dominated by the largest droplets (∝ri6), we believe that this underestimation results from the lower probability of observing large droplets since they occur less frequently.