Characterising optical array particle imaging probes : implications 1 for small ice crystal observations 2 3

21 The cloud particle concentration, size and shape data from optical array probes (OAPs) are 22 routinely used to parameterise cloud properties and constrain remote sensing retrievals. This 23 paper characterises the optical response of OAPs using a combination of modelling, laboratory 24 and field experiments. Significant uncertainties are found to exist with such probes for ice 25 crystal measurements. We describe and test two independent methods to constrain a probe’s 26 https://doi.org/10.5194/amt-2020-265 Preprint. Discussion started: 26 August 2020 c © Author(s) 2020. CC BY 4.0 License.

Optical array probes are a family of instruments that have been widely used by the cloud physics 19 community for the last 40+ years. Primarily OAPs have been operated on research aircraft 20 (Wendisch and Brenguier, 2013). They collect images of cloud particles and are used to derive 21 cloud particle concentration, size and crystal habit (shape). Optical array probes operate by 22 recording a shadow image as a particle crosses a laser beam that is illuminating a 1-D linear 23 array of photodiode detectors. If the light intensity at any of the detectors drops below a 24 threshold value, the probe records an image of the particle and the corresponding timestamp. 25 A two-dimensional image of the particle is constructed by appending consecutive one 26 dimensional "slices" from the array of detectors as the particle moves perpendicular to the laser 27 beam due to the motion of air through the probe. 28 The rate at which data needs to be acquired from the detectors depends on the air speed through 29 the probe and the required image resolution. For example, when operated on research aircraft 30 at a typical airspeed of 100 m s -1 image slices from the detectors are acquired every 0.1 µs to 31 achieve an image resolution of 10 µm. Modern OAPs have 64 to 128 element detector arrays 32 with pixel resolutions ranging from 10 to 200 µm. Monoscale probes use a 50% drop in intensity 1 as a threshold for detection which results in 1-bit binary images (Knollenberg, 1970; Lawson 2 et al., 2006), while most greyscale OAPs have three intensity thresholds, which result in 2-bit 3 grayscale images (Baumgardner et al., 2001). 4 When particles pass through the object plane of a probe they are in focus and accurate digitized 5 images are recorded. When particles are offset from this plane the diffraction of light by the 6 particle alters the size and shape of the recorded image from its original form. When the distance 7 from the object plane (Z) is sufficiently large the reduction in light intensity at the detector will 8 no longer exceed the detection threshold. This distance is known as the probe's depth of field 9 (DoF). For large particle sizes the DoF is constrained by the physical separation between the 10 laser transmit and receive optics, which are in protruding structures referred to as "arms". The 11 following equation is generally used to define the DoF of monoscale probes using a 50% 12 intensity threshold for detection (Knollenberg, 1970)  correct. O19 show that greyscale information can be used to remove these fragments by 7 identifying the distance from the object plane of spherical particles in the range Zd = 3.5 to 8.5. 8 This allows a new DoF to be defined that excludes the fragmented images . 9 There has been significant discussion in the literature about the presence of high concentrations 10 of small ice particles (< 200 µm) observed by OAPs in cirrus and other types of ice clouds 11 (Jensen et al., 2009;Korolev et al., 2011). O19 shows that fragmented images near the edge of 12 the DoF have the potential to significantly bias OAP particle size distributions (PSDs) and result 13 in an artificially high concentration of small particles. 14 This paper quantifies the uncertainties in OAP size and shape measurements of non-spherical 15 ice crystals and presents corrections that removes large biases from OAP datasets. In Sect. 3.1, 16 3-D ice crystal analogs are repetitively passed through the sample volume of an OAP at 17 different distances from the object plane. These results are used to examine the ability of a 18 diffraction model based on angular spectrum theory to characterise the response of OAPs. In 19 Sections 3.2 to 3.5 a variety of ice crystals from commonly occurring habits are tested with the 20 diffraction model to quantify how OAP image quality degrades throughout a probe's sample 21 volume. Section 4 suggests and tests methods to improve OAP data quality. The impact these 22 results have on ice crystal PSDs is examined using field measurements collected during three 23 research flights in frontal cirrus. The impacts OAP measurement bias has on our understanding 24 of ice cloud microphysics are discussed in Sect. 5. . Images are recorded at three greyscale intensity thresholds. For this work 8 they were set to the manufacturer default settings of 25%, 50% and 75%. The 2D-S consists of 9 two optical arrays and lasers orientated at right angles to each other and the direction of motion 10 of the particles/aircraft. The laser beams overlap at the centre of the probe's arms, and each pair 11 of transmit/receive arms are separated by 63 mm. Each optical array has 128 elements and 10 12 μm pixel resolution. The 2D-S is a monoscale probe with a single 50% intensity detection 13 threshold. Both probes are fitted with anti-shatter tips to minimise ice shattering on the leading 14 edge of the probe during field measurements. This was further minimised by removing particles 15 with inter-arrival times less than 1x10 -5 s when calculating PSDs from field measurements 16 (Field et al., 2006). 17 Baumgardner & Korolev (1997) show that the electronic time response of older probes can 18 significantly reduce the DoF of small particles. This affect has been minimised in more modern 19 probes such as the 2D-S and CIP-15, which have an order of magnitude faster time response. 20 A range of definitions have been used to define the diameter of ice crystals from OAP images. 21 Here we test three metrics that have been widely used by the community. First, the mean of the 22 particle extent along the axes parallel and perpendicular to the optical array (mean X-Y 23 diameter). Second, the diameter calculated using D= (4A/π) 1/2 where A is the particle area 24 calculated as the sum of the pixels (circle equivalent diameter). Third the major axis length of 25 the ellipse that has the same normalized second central moments as the region (maximum 26 diameter). 27 An image frame from and OAP may contain more than one object, where individual objects are 28 defined as collections of pixels with 8-neighbor connectivity. This can be due to diffraction, 29 with a single particle appearing as more than one object as the structure and intensity of the 30 transmitted light degrades due to poor focus. However, it may also be due to shattering causing microscope image of each analog. This typically corresponded to a particle stage velocity of ~ 1 0.1 m s -1 .

Synthetic data (Angular spectrum theory) 8
Theoretical shadow images of 2D non-spherical shapes were calculated using a diffraction 9 model based on Angular Spectrum Theory (referred to as the AST model). Several previous 10 studies describe this model in detail (Vaillant de Guélis et al., 2019a, 2019b). We initialised the 11 model using a 2-D binary image of an opaque shape at the object plane (Z = 0) and calculate 12 the wave field for different positions between the probe arms in the Z axis. This model has been 13 shown to give good agreement with OAP images of several types of 2D rectangular columns 14 In this study, we use a variety of different shapes to initialise the model. In Sect. 3.1, the 1 diffraction model is compared to CIP15 images of 3D ice crystal analogs. To initialise the model 2 for the comparisons with ROS250 and ROS300 the CIP-15 image of them at Z=0 is used. Due 3 to the smaller size of ROS118 and coarse pixel size of the CIP-15, a microscope image of the 4 analog is used to initialize the model. This image converted to a binary image. 5 In Sect. 3.2 the quality of OAP images of commonly occurring ice crystal habits is explored. (rosette, column/bullet, plate, quasi-spherical, column-aggregate, rosette-aggregate and 12 plate-aggregate). To initialise the model each CPI image was converted to a binary image. 13 Shadow images were calculated every 2 mm for the range Z = 0 to 100 mm. These images were 14 averaged to 10 µm pixel resolution, which is typical of modern OAPs. All simulations were 15 performed using a light wavelength of 0.658 µm. 16 An example simulation for a rosette crystal is shown in Fig. 3 and a column in Fig. 4, the top 17 left panels show the images at Z=0 that are used to initialise the model. The other panels show 18 images of the crystals at different distances from the object plane. Green, blue and black pixels 19 correspond to decreases in detector intensity of 25 to 50%, 50 to 75% and > 75%, respectively. 20 plane, which will impact derived properties such as particle size, number and habit. This 22 compares to many 10s of mm for the typical arm separation of modern OAPs. and 20 mm). Green, blue and black pixels correspond to decreases in detector intensity of 25 5 to 50%, 50 to 75% and greater than 75%, respectively.  Therefore, a minimum size threshold of 35 μm is applied, above which it is estimated that the 5 probe's detection rate is greater than 90% (Schlenczek, 2017). Shattered particles were 6 minimised by removing all particles with inter particle distances less than 10 mm ( All three analogs have a general trend of diameter initially increasing with Z. The full DoF was 26 sampled for ROS118 and shows the images fragmenting and diameter decreasing near the edge 27 of the DoF. In addition to these general trends there is a significant amount of fine scale 28 structure that is specific to each sample. There is a general trend of the greyscale ratio A75-100 29 decreasing with Z, while both A25-50 and A50-75 initially increase for all 3 analogs. Like the diameter vs Z plots there is a significant amount of fine scale structure overlaying these general 1 trends. 2 In general, the AST model can capture the large-scale structure in these measured parameters, 3 although some discrepancies are present in the finer detail. For ROS118 the DoF from the 4 experiments and the model agree to within ±1 mm (Fig. 5). The size and greyscale parameters 5 calculated from CIP-15 images are not completely symmetrical about Z=0. The reason for this 6 is unclear, potential causes are if the CIP-15 laser beam is not perfectly collimated, additional 7 refraction caused by the optical window used to mount the sample, or changes to the CIP- 15 8 background/dark current calculation due to attenuation by the optical window. 9

OAP ice crystal sizing 3
Having investigated the performance of the AST model using 3-D analogs of complex ice, we 4 will now use the AST model to examine the ability of OAPs to correctly determine the size of 5 commonly occurring ice crystals. Figure 9 left panels show the ratio of the measured diameter 6 (D) to the true diameter (D0) vs Zd for diffraction simulations of 1060 ice crystals. The data for 7 each individual ice crystal is shown as grey lines, while the coloured lines are the median for 8 each habit. Top panels show plots using the circle equivalent diameter, while the middle panels 9 use the mean X-Y diameter and maximum diameter. Right panels show histograms of D/D0 for 10 each habit calculated for the Zd range from 0 to 10. 11 Figure 9 shows large differences in these relationships depending on whether the mean X-Y, 12 maximum or circle equivalent diameter is used to define the particle size. For the 1060 ice 13 crystal images used in this study the median D/D0 over the Zd range from 0 to 8 is 1.1 using 14 circle equivalent diameter, 1.0 using the mean X-Y diameter and 1.0 using the maximum 15 diameter. However, there is significantly less variability between crystals using circle 16 equivalent diameter, which has an inter-quartile range D/D0 of 0.2 compared to 1.1 and 1. 3 17 using the mean X-Y and maximum diameters, respectively. This is also shown in Table S1-S3,  18 which gives the median and inter-quartile range D/D0 at selected Zd for each habit using the 19 three different size metrics. 20 https://doi.org/10.5194/amt-2020-265 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.
There is a general trend of increasing size with distance from the object plane. Over-sizing is 1 up to approximately 100%, 200% and 50% using mean X-Y, maximum and circle equivalent 2 diameters, respectively. However, the degree of oversizing is dependent on habit, with quasi-3 spherical and plate aggregates most significantly over-sized using all D definitions. In 4 agreement with O19, once D reaches a maximum, further increases in Z cause the images to 5 fragment and their size to decrease until they are no longer visible. 6 K07 uses the size of the internal voids within images of droplets to determine their Zd and 7 correct their size. O19 shows that this algorithm is effective using modern OAPs for droplets 8 with Zd < ~6. For Zd > 6 the images are too fragemented for their size to be corrected. The K07 9 approach was derived by considering Fresnel diffraction from opaque discs, and has only been 10 tested for images of spherical droplets. However, previous studies have applied K07 to images 11 of ice crystals (e.g. Davis et al., 2010). To examine the efficacy of this approach, Fig. 9 bottom 12 panels shows the mean X-Y diameter of the simulated images of ice crystals once K07 has been 13 applied. The ratio of their K07 corrected diameter to their true particle diameter is shown as a K07 is not able to remove the small image fragments that occur when a particle is near the edge 20 of the DoF.  where a particle is no longer detected by the OAP. If a single c value is used this would need 12 to be independent of particle shape. Table 1 shows the median and inter-quartile range Zd where 13 particles are no longer visible for each habit using the maximum, mean X-Y and circle 14 equivalent diameters. Using mean X-Y the habit median DoF varies between Zd = 5.0 and 9. 9 15 for rosettes and quasi-spherical particles, respectively. Using the maximum as the particle 16 sizing metric the median DoF varies by a similar amount ranging between Zd = 3.4 to 7.8 for 17 bullets and quasi-spherical crystals. In addition, particles have significant intra-habit variability 18 using both maximum and mean X-Y, with most habits DoF inter-quartile ranges greater than 2 19 Zd. The variability is lower using circle equivalent diameter, with median DoFs ranging 20 between 8.2 and 10.2 for plates and bullets, respectively with habit inter-quartile ranges near 1 21 Zd. As a result, derived physical quantities such as number concentration will have lower 22 uncertainty if circle equivalent diameter is used to define the particle size compared to 23 maximum and mean X-Y diameter.

Greyscale information 5
Greyscale information in OAP imagery has previously been used to filter severely mis-sized 6 images and enforce a DoF threshold that improves data quality (O19). Figure 10 shows 7 combinations of simple greyscale ratios as a function of Zd for the simulation of 1060 ice crystal 8 images described in the previous section. Left panels use the size metric mean X-Y diameter in 9 the Zd calculation, whereas the right panels use circle equivalent diameter in Zd calculation. 10 Like the ratio D/D0 (Fig. 9), the greyscale ratios also show significant variability between habits 11 as a function of Zd. Figure 10 shows this variability is greater if mean X-Y diameter is used to 12 calculate Zd, though it is still significant using circle equivalent diameter. The variability is 13 larger still using maximum diameter (not shown). 14 O19 uses simple greyscale ratios to determine Zd for spherical liquid droplets near the edge of 15 the DoF (3.5 < Zd < 8.5). This allows a new DoF to be defined that excludes fragmented images, 16 removing significant biases in the PSD. This is possible since all spherical droplets independent 17 of size have the same greyscale ratios at a given Zd. Figure 10 shows that this is not true for ice 18 crystals where the initial shape of the ice crystal has an impact on the greyscale ratios at a given 19 Zd. As a result, O19 cannot be used to determine Zd in the same way. where P is the particle perimeter, and A is the particle area including any internal void. Crosier 13 et al. (2011) used a threshold of 1.25 to discriminate between these two categories. When 14 images are manually selected to train habit recognition algorithms only images that can be 15 identified 'by-eye' as a specific habit will be included. For OAPs this is likely to be images that 16 are 'in-focus'. However, the shape of an OAP image and therefore the geometrical features that 17 are used in habit recognition algorithms depend on where in the probe's sample volume a 18 particle is detected. For example, Figure 3 shows a simulated 190 µm rosette at different 19 distances from the object plane. It is only in the top left panel (Z=0) that it can be identified as 20 a rosette from its image alone. Figure 11 shows how this particle's circularity changes with Z 21 and Zd. At Z=0 its circularity is near 4, while at Z=20 mm it is near 1 and may be confused with 22 a spherical droplet. Figure 11 demonstrates that the measured particle shape is highly dependent 23 on the position in the sample volume Zd (and Z) with the circularity decreasing by a factor 2 by 24 Zd=1; in comparison the particle size has only changed by 15%. 25 The variance in geometrical features for each habit will not only be due to natural variability in 26 the shape of ice crystals, but also due to their position in the sample volume when measured. 27 To date, this second effect has not been accounted for by habit recognition algorithms. 28 Therefore, currently the results of habit classification algorithms on OAP datasets cannot be 29 considered quantitative. 30 1 Figure 11. The circularity (Eq. 4) of the rosette shown in Fig. 3 as function of distance from the 2 object plane Z and Zd. Depending on where in the sample volume a particle is observed the OAP image size can range 6 between being as small as a single pixel or up to twice the true particle diameter (see Fig. 9). 7 Algorithms such as K07 and O19 have been derived using spherical shapes and are therefore 8 not directly applicable to OAP PSDs of non-spherical shapes. However, there are several 9 possible approaches that could be used to correct OAP ice crystal size distributions. 10 11

Greyscale filtering 12
Unlike for liquid droplets, O19 does not accurately determine Zd for non-spherical ice crystals. 13 We now describe a new technique to use greyscale information to remove the most severely 14 mis-sized ice crystals and constrain the sample volume with a reasonable uncertainty using 15 circle equivalent diameter as the particle sizing metric. For example, if the diffraction 16 simulations are filtered to only include images that have at least one pixel with a greater than a 75% drop in light intensity (Fig. 7) then the median position where particles are no longer 1 visible (using a 50% intensity threshold) is Zd = 4.6 (interquartile range 1.1 in Zd). This removes 2 the fragmented images that begin to occur at approximately |Zd| > 6. The median ratio D/D0 for 3 Zd < 4.6 is 1.2 (interquartile range = 0.1), however, particles may still be oversized by 4 approximately 40% even with this filter applied (Fig. 7). Other greyscale thresholds may be 5 used to provide a more or less restrictive DoF constraint. Table 2 shows the median 6 (interquartile range) c values for various greyscale thresholds between 65 and 85%. Using a 7 65% threshold the median c value is 6.2 (interquartile range = 1.3), while for 85% it is 3.2 8 (interquartile range = 0.9). It should be noted that the lower the greyscale threshold the higher 9 the probability of a fragmented image being observed, and the small particle concentration 10 being biased.   This flight has previously been discussed by O19. Figure 13  at the 75% intensity threshold. This threshold significantly reduces the concentration of small 25 particles (<200 µm) compared to when this filtering is not applied (grey lines) and generally is in much better agreement with HALOHolo a holographic imaging probe (blue markers). This 1 suggests that for these cases using current data processing techniques, a significant fraction of 2 the ice crystal number concentration at sizes < 200 um is an artefact due to optical effects.

Stereoscopic imaging 1
A second method that could be used to constrain the DoF of an OAP is to use the stereoscopic 2 imaging that is possible with the 2D-S. The 2D-S in effect consists of two OAPs (known as 3 channels) orientated perpendicular to each other and the direction of motion of the 4 particle/instrument. Under normal operation the probe is oriented so that one laser beam is 5 horizontal and the other is vertical. The two lasers overlap at the centre of each channel's arms. 6 As well as increasing sampling statistics by having two channels which can be 7 merged/averaged, this design also allows some ice crystals to be viewed from two orientations 8 to study their aspect ratios. In this study we use this feature to constrain the probe's DoF, which 9 greatly limits the magnitude of diffraction artefacts, and represents the first implementation of 10 stereoscopic analysis on an ambient OAP dataset. The 2D-S was designed so that Z= 0 on both 11 channels is in the region where the two lasers overlap. We refer to particles observed by both 12 channels as co-located particles. Co-located particles have tightly constrained Z position and 13 should not be subject to significant mis-sizing due to diffraction. For the 2D-S this is likely to 14 be true for D0 > 20 µm. For a hypothetical stereoscopic probe with larger optical arrays (NR) it 15 may be necessary to restrict the distance a particle can be from the centre of the optical array. 16 For the case where channel 0 is used for particle sizing and channel 1 is used to constrain the 17 particle Z position, the sample volume of co-located particles is given by, 18

Equation 5 20
Where TAS is the true air speed, E is the number of array elements, R is the resolution of the 21 probe, D is the measured particle diameter and DCH0 is the particle diameter measured along the 22 axes of the channel 0 optical array. This requires that particles in contact with the edge of the 23 channel 0 optical array have been removed. If channel 1 is used for particle sizing instead of 24 channel 0 then particles in contact with the edge of the channel 1 optical array are removed 25 instead of channel 0, and DCH0 is replaced by DCH1 in Eq. 5. 26 For this method to be applicable it is important to validate that Z=0 on both channels is in the 27 laser overlap region. If it is significantly offset this would prevent small co-located particles 28 from being observed, since the DoF from one channel would not overlap with the optical array 29 of the other channel. Increasingly large offsets between the channels prevent increasingly large 30 co-located particles from being observed. It is therefore important to check that this offset is not significant by regularly sampling in environments where small particles are present (i.e. in 1 liquid cloud or using a droplet generator in a laboratory as in O19). 2 Co-located particles could be confused with shattered particles since they are also associated 3 with short inter-arrival times. Figure 14  shattering events, each channel was independently filtered for particles using an inter-arrival 6 threshold of 1x10 -5 s. It may still be possible to mistakenly detect shattered particles as co-7 located particles if one shattering fragment splits into two particles, triggering each channel 8 simultaneously but in spatially independent parts of the sample volume. However, examination 9 of co-located images suggest that this is rare. 10 To identify co-located particles, we use the difference in arrival time between a particle on one 11 channel and their closest neighbour on the other channel. Figure 14 shows a histogram of co-12 location times for measurements in cirrus on 7 February 2018. This distribution is bi-modal 13 with a larger mode centred at approximately 1x10 -3 s. and a smaller mode at 1x10 -7 s. The larger 14 mode is associated with the typical spatial separation between ambient particles, with its 15 position dependent on the particle concentration. Examining pairs of images from the smaller 16 mode suggests these images are the same ice crystal viewed from different orientations. Figure  17 15 shows example pairs of co-located images, with channel 0 images shown in yellow and 18 channel 1 images shown in blue. In addition to overall consistency in the geometrical shapes 19 between channel 0 and channel 1 images, there is also excellent consistency in the particle size 20 along the airspeed direction (x-axis in Figure 15) between these two channels. 21 Figure 14 shows that most co-located particles don't trigger both channels simultaneously 22 within the time resolution of the data acquisition system but are offset by a few hundred 23 nanoseconds. At 100 m s -1 data slices from the detectors are acquired every 1x10 -7 s, which 24 corresponds to a spatial separation of 10 µm. Using the laboratory droplet generator system 25 described in O19, we were able to generate a continuous stream of droplets of known size, 26 velocity, rate, and with precise control over the position within the sample volume. These 27 experiments with particle velocities of 1 m s -1 resulted in a 1x10 -5 s mode time delay in detection 28 events between the two channels of the 2D-S. This also corresponds to an offset of 10 um in 29 the sample volume in the axis of airflow through the probe (Y axis). These two sets of analysis 30 provide a robust independent verification of the spatial offset between the two channels of the 2D-S. Therefore, when considering ambient data, we classify co-located particles as those with 1 time separations less than 5x10 -7 s.  When determining the particle size from co-located images it is advantageous to use the largest 1 object in the image frame. Occasions where a single particle have been imaged as two objects 2 in the same image frame due to diffraction are removed by restricting the sample volume to a 3 narrow Z range. When sampling in environments with very high concentrations of small 4 particles (e.g. in liquid cloud) it is possible that two ambient particles could occur in the same 5 image frame. Under these circumstances using the largest particle in the image frame prevents 6 significant particle mis-sizing. 7  However, these high concentrations of small ice particles are not present in the co-located and 8 the HALOHolo size distributions. This suggests using only co-located particles on the dual 9 channel 2D-S probe is effective at removing significant biases at small particle sizes. At larger 10 sizes (>300 µm) the 2D-S data processing using conventional and stereoscopic methods are in 11 good agreement, however the latter method is limited by sampling statistics. 12 Stereoscopic data processing has the advantage of removing out-of-focus artefacts that bias the 13 PSD at small sizes, while at larger sizes traditional processing methods offers significantly 14 improved sampling statistics. Therefore, a hybrid approach using stereoscopic processing for 15 small sizes and traditional processing methods for larger sizes is advantageous. The choice of 16 size threshold to switch between the two methods is dependent on the arm width of the probe 17 and the level of mis-sizing that is deemed acceptable. To give an idea of a suitable threshold, 18 we will choose a size limit that prevents all particles with Zd > 2 from being included in the 19 PSD. The maximum Z that the 2D-S can observe a particle is Z=31.5 mm (2D-S armwidth/2) 20 This corresponds to a 222 µm particle at Zd = 2. However, since particles can be mis-sized by 21 a factor 1.4 then a size threshold of 300 µm is needed to ensure that no particle with Zd> 2 is 22 included. Figure 17 dashed lines shows 2D-S PSDs processed using this hybrid approach.

Other potential methods 1
There are several other potential methods that could be used to improve OAP PSD 2 measurements. First reducing a probe's arm width to physically limit a distance a particle can 3 be from the object plane would reduce out-of-focus particles. The amount the arm width would 4 need to be decreased depends on the level of mis-sizing that is deemed acceptable for a given 5 particle size, with more accurate sizing and smaller particles requiring smaller arm widths. 6 However, as well as decreasing the sample volume, reducing the probe's arm width is likely to 7 increase the proportion of shattered artefacts particles compared to ambient particles that the 8 probe measures, since shattered artefacts are thought to cluster near the probe's arms. 9 Second, statistical retrievals have been applied to particle size distribution measurements where 10 the instrument response is a distorted version of the true ambient distribution. These methods 11 are reliant on knowing or empirically approximating the instrument function that distorts the 12 ambient distribution. These methods have been applied to OAP measurements of spherical 13 droplets (Korolev et al., 1998;Jensen & Granek, 2002). For non-spherical particles the 14 distortion function is dependent on the ice crystal habits present and therefore the derived size 15 distributions would have greater uncertainty, unless the particle shape is known a priori. 16 However, this methodology may still result in an acceptable level of uncertainty if circle 17 equivalent diameter is used, since its intra-and inter-habit D/D0(Zd) variance is smaller than for 18 the mean X-Y and maximum diameter. 19 20

Implications for small ice crystal observations 21
In-situ measurements of ice clouds have consistently observed a mode in particle size 22 distributions at small sizes (< 200 µm). This would imply that ice nucleation occurs at all cloud 23 levels, since small ice particles would rapidly grow in regions of ice super-saturation or sublime 24 in sub-saturated regions. Particle shattering on the leading edge of a probe has previously been 25 identified as a possible explanation (Korolev et al., 2005;Korolev et al., 2011). However, the 26 impacts of shattering are thought to have been minimised by modifying the leading edges of 27 probes (Korolev et al., 2013) and using particle inter-arrival time algorithms (Field et al., 2006). 28 Yet even with these improved measurements a small ice mode has been found to be ubiquitous This work has shown that depending on where in the OAP sample volume a particle is observed 1 its image size can be as small as a single pixel or up to a 200% overestimate of the true particle 2 diameter (see Fig. 9). Only a relatively small proportion of undersized larger particles are 3 required to generate a significant bias in number concentration at small sizes (< 200 µm) due 4 to the size dependence of the DoF (Eq. 1) (O19). We have tested two methods that could be 5 used to remove out-of-focus artefacts: greyscale filtering (Sect. 4.1) and stereoscopic imaging 6 (Sect. 4.2). Both methods either remove or significantly reduce the concentration of small ice 7 crystals observed in specific cirrus cloud cases (Figures 12, 13 and 17). 8 To further explore the impact OAP mis-sizing has on the measured PSD shape we use the results 9 from the AST model. Consider the ambient ice crystal PSD N(D0) with units L -1 µm -1 . If this 10 distribution is observed by an OAP with size dependent sample volume SVol(D0) (units: L -1 s -11 1 , Eq. 2) then the number of ice crystals observed by the probe as a function of true particle 12 diameter C(D0) (units: µm -1 s -1 ) is given by, 13 D0) is the probability distribution that a particle of measured size D has true size D0. These 20 probabilities are dependent on the particle shape, the particle sizing metric, probe characteristics 21 (e.g. armwidth, laser wavelength) and the data processing protocols used (e.g. greyscale 22 filtering, co-location). The PSD observed by the probe N(D) can then calculated by, 23

Equation 8 25
The probe armwidth limits the maximum Zd that a particle of given D0 can be observed. By shows plots using mean X-Y diameter and the right panels shows circle equivalent diameter. 7 The ambient PSDs (blue lines) are compared to simulated OAP observations using different 8 data processing methodologies. The grey lines represent an OAP with armwidth of 70 mm using 9 conventional data processing methods. The red markers represent a 2D-S using only co-located 10 particles, which has the effect of limiting the maximum Z a particle can be observed to 0.64 11 mm. The blue markers show simulated OAP measurements from a greyscale probe with 70 mm 12 arm width when the data has been filtered to only include particles that have at least one pixel 13 with a greater than 75% decrease in light intensity. 14 It should be noted that these simulated distributions only include mis-sizing due to diffraction 15 and do not include other sources of OAP measurement uncertainty (e.g. counting statistics). 16 Counting statistics will be responsible for a larger uncertainty for the co-located PSDs 17 compared to conventional data processing methods. 18 Figure 18 top panels show an ambient distribution (blue lines) dominated by small particles (µ= 19 -1, λ =1000 cm -1 and N0 = 10 L -1 cm -1 ), with concentrations increasing with decreasing size 20 over the displayed size range 10 to 1280 µm, which is representative of modern OAPs. The 21 grey lines show the simulated OAP observations of this PSD, which have a similar 22 characteristic shape. The total particle concentration observed by the simulated OAP over the 23 size range 10 to 1280 µm is 3% and 13% higher than the true PSD using mean X-Y and circle 24 equivalent diameter, respectively. Figure 18 top left panel show the PSD that a 2D-S would 25 observe when only co-located particles are included (red markers). The total particle 26 concentration from the co-located PSD differs from the ambient distribution by less the one 27 percent. The total particle concentration when greyscale filtering is applied is 2% lower that the 28 true distribution. 29 Figure 18 middle panels show an ambient distribution with mode near 100 µm particles (µ = 2, 30 shape with much higher concentrations of particles <100 µm. Here the OAP overestimates the 1 total particle concentration over the size range 10 to 1280 µm by 74% and 80% using mean X-2 Y and circle equivalent diameter, respectively. When stereoscopic imaging is used to constrain 3 the OAP sample volume (red lines) the small particle mode is removed. The true and simulated 4 OAP total particle concentration differ by < 1%. Greyscale filtering again removes the small 5 particle mode, though underestimates the total particle concentration by 11%. 6 Figure 18 bottom panels show an ambient PSD with mode near 400 µm particles (µ = 4, λ =100 7 cm -1 and N0 = 1x10 6 L -1 cm -1 ), like the previous case the simulated OAP PSD significantly 8 overestimates the small particle concentration. The simulated OAP PSD is bi-modal, while the 9 true PSD is mono-modal. However, in this case the artificial small particles contribute a 10 relatively small proportion to the total number concentration in the 10 to 1280 µm size range, 11 as a result the simulated OAP only overestimates this by 4% using both particle size metrics. are rosettes. The red markers show simulated 2D-S measurements using only co-located 1 particles, which has the effect of limiting the maximum Z a particle can be observed to 0.64 2 mm. The blue markers show simulated OAP measurements from a greyscale probe with 70 mm 3 arm width when the data has been filtered to only include particles that have at least one pixel 4 with a greater than 75% decrease in light intensity. 5 6 A significant amount of our understanding of clouds microphysics is based on OAP 7 measurements, with the small particle artefact being present and manifesting in some manner. 8 This includes how PSDs are parameterised in numerical models and remote sensing retrievals. 9 Generally in the literature some formulation of exponential or gamma funtion has been used to where the number concentration (N(D)) and diameter are normalised using the second (M2) 2 and third (M3) moments of the PSD and x is equal to DM2/M3. The 2D-S PSD in Fig. 19 has  3 been calculated using only co-located particles for D <300 µm and all particles for D > 300 µm. 4 Both the tropical and mid-latitude parameterisations show rapidly increasing concentrations 5 with decreasing size. At larger sizes the 2D-S and these parameterisations are in good 6 agreement, while they diverge at smaller sizes. The green line in Fig. 19 shows the gamma 7 component of the mid-latitude F07 parameterisation (Eq. 12), which is in much better 8 agreement with the observations at small sizes. This work suggests that the data used for derived PSDs parameterisations is subject to 12 significant artefacts. As a result, the parameterisations are likely to have incorrect fundamental 13 shape for ice cloud PSDs. The impacts of these artefacts can be expected to propagate to 14 inaccuracies in remote sensing retrievals, which will be assimilated into weather forecast 15 models, and to incorrect radiative properties due to a bias towards small particle sizes. Future 16 work is needed to quantify the impact on retrievals and our understanding of ice microphysics 17 and cloud radiative properties using the improved measurement methodologies presented in 18 this paper. This paper quantifies the optical response of OAPs to non-spherical particles for understanding 7 ice crystal observations, expanding the work of O19. We make the following comments and 8 recommendations on the use of OAP data: 9 https://doi.org/10.5194/amt-2020-265 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.
• The shape and size of an OAP image depends significantly on where in the OAP sample 1 volume a particle is observed. Particles < 200 µm are the most significantly mis-sized. 2 The measured size of a particle can range between being as small as a single pixel up to 3 being as large as a 200% overestimate of the true particle. The persistent mode of small sizes observed in many previously studied cases is likely 8 artificial. However, the importance of this artefact is strongly influenced by the true 9 shape of the ambient PSD. 10

11
• Algorithms to correct OAP size distributions such as K07 and O19 that have derived 12 using spherical particles are not applicable to non-spherical ice crystal images without 13 significant uncertainty. 14 15 • New methods that may be used to filter OAP ice crystal size distributions were tested, 16 including filtering using grayscale, and the use of stereoscopic imaging. 17

18
• For greyscale instruments (such as the CIP-15), filtering images so that they must 19 include one pixel with at least a 75% decrease in detector intensity removes the most 20 severely fragmented particles near the edge of the DoF. This approach constrains the 21 DoF to c = 4.6 (interquartile range 1.1) using circle equivalent diameter. 22

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• Using the stereoscopic imaging that is possible with the 2D-S can constrain the sample 24 volume to only 'in-focus' images. A hybrid approach using stereoscopic processing for 25 small sizes and traditional processing methods for larger sizes is advantageous, as it 26 limits any negative impacts on sample volume and therefore counting statistics. The 27 choice of size threshold to switch between the two methods is dependent on the arm 28 width of the probe and the level of mis-sizing that is deemed acceptable. For the 2D-S 29 we suggest that 300 µm is a suitable threshold for particle sizing using the mean X-Y 30 diameter. 31 • These new methodologies were tested using data from three research flights sampling 1 cirrus. In these cases, they significantly improved agreement with a holographic 2 imaging probe compared to conventional data processing protocols and either removed 3 or significantly reduced the concentration mode at small particle sizes (<200 µm). This 4 raises the question over the interpretation of many existing datasets such as those used 5 to parameterise PSDs (e.g. Delanoë et al., 2005;2014;Field et al, 2007), and the 6 persistent observation of small particles throughout the entire vertical extent of ice 7 clouds which has been difficult to reconcile with concepts of ice nucleation. 8 9 • Past datasets from OAPs need to be revisited, where possible the filtering and sample 10 volume adjustments described in this paper should be applied. The impact these 11 corrections have on how PSDs are parameterised in numerical models; remote sensing 12 retrievals and radiative calculations of ice clouds need to be examined. 13 14

Data availability 15
The data presented here can be provided on request to the contact author. 16 17 18

Acknowledgements 19
We would like to thank Thibault Vaillant de Guélis for his help with the AST model. We are 20 grateful to Jacob Fugal for assistance with HALOHolo. The authors wish to thank Hannakaisa Centre for Atmospheric Science provided support for the ice crystal analog experiments. This 27 work was supported by the NERC grants NE/P012426/1 and NE/L013584/1. 28