1. Introduction
In situ particle measuring devices originally manufactured by Particle Measuring Systems, Inc. (PMS), and later by Particle Metrics, Inc. (PMI in Boulder, Colorado), have been used since the early 1970s to measure the microphysical properties of aerosol and cloud particles. Calibration procedures for both forward scattering spectrometer probes (FSSPs) and optical array probes (OAPs) have been reported by the manufacturers (PMS 1994; DMT 1994), and various issues related to calibration have been published by other authors (e.g., Cerni 1983; Dye and Baumgardner 1984; Korolev et al. 1985a, b, 1991, 1998; Heymsfield and Baumgardner 1985; Baumgardner et al. 1989; Brenguier and Amodei 1989; Brenguier 1989; Baumgardner and Spowart 1990; Hovenac and Hirleman 1991; Brenguier et al. 1993; Wendisch et al. 1996; Baumgardner and Korolev 1997; Strapp et al. 2001; Jensen and Granek 2002; Smedley et al. 2003). Procedures using glass beads and rotating glass disks with dots or images simulating spherical particles have become the standard for the absolute size calibration of scattering spectrometer probes and OAPs. The determination of the active sample volume is based on theoretical assumptions and laboratory measurements that are strongly influenced by the materials used as scattering sources. Mathematical algorithms have been developed to correct known systematic deficiencies and technical limitations of the probes. Nevertheless, discrepancies continue to exist in the overlap region between different probes, and between measured and theoretical values of microphysical properties of aerosols and cloud particles in the atmosphere, especially in radiative transfer calculations. Publications rarely provide estimates of probe measurement accuracy.
The main motivation for the development of the specific tools described in this article was to provide tools to characterize instrument performance in the laboratory and in the field, and to improve overall data accuracy. Three main error sources have been identified as follows: 1) device alignment and calibration, 2) electromagnetic interference (EMI) sensitivity, and 3) aerodynamic shape of the probe sample volume. A detailed analysis of all three subjects with their manifold problems is beyond the scope of this article, and we will concentrate here on the improvement of calibration and alignment. The results of our work are the product of extensive trial and error investigations, finally culminating in the most reasonable choice of mechanical and electronic calibration equipment and probe upgrades. The high cost for aircraft flight hours and subsequent data processing, and the importance of high-quality microphysical data in atmospheric research justifies the high level of effort necessary for the proper characterization and calibration of these probes.
While calibration and test equipment was developed in these studies for both scattering spectrometer probes and optical imaging probes, this article will focus only on their use for PMS FSSP calibration and alignment checks.
2. Laser beam characteristics
To determine the active sample volume of an FSSP for measurements in real clouds, the physical laser beamwidth in the so-called depth of field (DOF) was measured with a laser power meter masked with pinholes of different sizes. Figure 1 displays the energy distribution of the laser beam, measured with a 2-μm pinhole mask in 5-μm steps across the laser, at the approximate center position of the DOF. The measurements show that the laser does not have a “hat shaped” profile, as assumed by Hovenac and Lock (1993) for their laser beam simulation, but instead more resembles a Gaussian profile with several local intensity maxima. The region of energy within 90% of the maximum value is small for this particular probe, less than 25% of the total laser beamwidth. Similar energy distributions would likely be observed in other FSSPs. The contour plot of laser beam intensity published by Baumgardner and Spowart (1990) also shows the laser beam inhomogeneities. The area where the energy exceeds the 90% maximum value of their laser beam is also relatively small, less than 15%–20% of the measured beamwidth.
Figure 1 also compares the laser energy distribution to the measured response for a single 67-μm droplet produced by a monodisperse droplet generator (section 3) during its transition through the beam, as indicated by the input voltage of the probe peak-height analyzer (PHA). Both the laser beam energy curve and the PHA signal have been normalized to their maximum value. Although the measurements are not coincident in time, the shape of the water droplet signal reflects the characteristic changes in the laser beam intensity. The water signal contains many local features (see also Wendisch et al. 1996) at more or less the same positions as similar features in the laser energy intensity profile. Slight differences between the two are presumably caused by the random changes in the energy distribution of the laser.
The active laser beamwidth, that is, the fraction of the beam across the diameter of the laser in which particles are counted by the probe, is an important calibration measurement for the calculation of the sample volume. In a manner similar to that described by Hovenac and Hirleman (1991), pinholes of different sizes were mounted on a spinning disk and moved through the sample volume of the probe. In this study, additional scattering sources were used, such as a glass bead or a quartz fiber inside or in front of the pinhole, in order to extend the limited pinhole scattered-light amplitude to cover the entire size range of the FSSP. Measurements were performed at a velocity of 36 m s−1 in 5-μm steps across the laser beam in the center of the DOF. The velocity-averaging module of the probe was deactivated, because it would not operate properly in such constant-rate testing. Four different particle sizes were simulated, with 6.6-, 16.7-, 27.5-, and 43.7-μm diameters. Figure 2 summarizes the results together with the laser beamwidth as it was measured with the laser power meter. First, it is evident that the active laser beamwidth is a function of particle size and may be larger than the physical laser beamwidth. The effect of particle speed on the active width is yet to be investigated. From numerical simulations shown by Korolev et al. (1985a), we surmised that it would shrink in the same manner as DOF length (see section 4b). Second, relative to the size measured at beam center, one can see progressive undersizing away from the center, down to the first detection channel in the edge region of the beam. The fraction of total active laser beam that produces counts in the various size channels of the FSSP is given in Table 1 for the four simulated particle sizes. This can also be thought of as the probability distribution for sizing of monodisperse droplets of the sizes noted in the table, for a slice across the center of the DOF. These results also reflect the energy distribution in the laser beam cross section and its shape, especially in the edge region, as well as the collection efficiency of the detector diode as function of the location of the scattering source in the laser beam. In a manner similar to that depicted in Table 1, the energy profiles and the corresponding sizing distribution can be determined with such a calibration technique for every size channel, resulting in a distortion matrix for each channel that describes the expected probe response for monodisperse particles with sizes corresponding to the center of each FSSP size channel. This distortion matrix can then be used for the correction of the probe absolute sizing as described in section 3b.
3. The monodisperse droplet generator for absolute calibration
a. Instrumentation
Monodisperse droplet generators have been previously used in the study of FSSP probe, for example, by Bachert (1981), Dye and Baumgardner (1984), Keil (1995), and Wendisch et al. (1996). In the current study the overall design of probe absolute calibration with real water droplets is conceptually similar to that developed by Korolev et al. (1985b). A special droplet generator unit was developed based on a commercial product of microdrop Technologies GmbH, in Norderstedt, Germany, exploiting new technical advances in droplet generation used for ink jet printers. The principle of ink jet technology was developed much earlier and was described, for example, by Schneider and Hendricks (1964) or Lindblad and Schneider (1965). Activated by a voltage pulse, a piezo actuator surrounding a glass capillary forces a pressure wave in the enclosed liquid. In a nozzle at the end of the capillary, a small liquid column is expelled, breaks off, and forms a droplet. A more detailed description of the principle and the droplet generator itself is given by Meyer and Döring (1999) and de Gans et al. (2004). The droplet size is a function of nozzle dimension and can be controlled by the height, width, and frequency of the activating voltage pulse. Therefore, a size range between approximately 10 and 100 μm can be covered using several single dispensers (nozzles). The monodisperse stream of water droplets can be produced in a frequency range between about 90 and 400 Hz. The stability of the droplet size (as observed from video images) is in the range of ±1 μm over several hours.
The speed of the droplets depends on their size. It is mainly influenced by the pulse height (Meyer and Döring 1999) and the frequency of droplet production, and varies between 0.5 and 5 m s−1. The FSSP electronics were not designed for such low speeds. Even the 6-μs delay time board, which is offered by the manufacturer to elongate the time for signal processing for ground-based measurements, should not be used for speeds lower than 10 m s−1. Therefore, the stability of two key electronic signals was investigated in more detail. The first signal, the PHA input, is used by the probe for particle sizing. The second signal is used to define the time at which the particle exits the laser beam. The PHA input voltage (pulse height) is analyzed continuously by the probe while the particle passes through the beam, so that the PHA can latch the size channel corresponding to its maximum value. Meanwhile, the second signal is also continuously latched to the maximum PHA input. If the PHA input falls below the 50% level of this maximum, it is assumed that the particle has left the beam and a reset signal readies the electronics for the next particle. During the relatively long transit time across the laser for water droplets produced by the droplet generator, the latched maximum PHA input signal that determines whether the particle has left the beam decays about 1% of the maximum signal value for large droplets, and 8% for small droplets. This decay is only influencing the height of the 50% value, and therefore the time when the reset signal occurs; it is not influencing the absolute sizing by the probe. It follows that the slow movement of the water droplets does not affect the calibration measurements.
The dispenser is illuminated by a strobe diode. One of two microscopes with different magnifications and a working distance of about 2.5 or about 1.2 cm, combined with a charge-coupled device (CCD) camera and frame grabber, can be used to provide digitally recorded droplet images with a pixel resolution of 0.35 μm (width) × 0.37 μm (height) or 0.16 μm × 0.18 μm, respectively. It is estimated that droplet size can be determined from these images with an accuracy of about ±1 or ±0.5 μm. Korolev et al. (1985b, 1991) and Keil (1995) described the use of refractive glares produced by the illuminated drops, in addition to the size of the photographed drop image, to accurately deduce droplet diameter. Similarly, in this article, both the images of the droplet itself and of the glares produced when the droplet is moving through the probe laser beam are used for sizing (Fig. 3).
The entire assembly of the dispenser and strobe diode is mounted on a three-dimensional positioning system that can be moved inside the sample volume of the probe with an accuracy of about 1 μm. The three-dimensional position can be recorded together with the probe response. During the calibration, the dispenser is placed right above the probe laser beam, but high enough to permit the oscillating droplet to relax into a sphere. The dispenser can be moved along the DOF and across the beam to map the entire active sample volume. To view the dispenser with the microscope, it was necessary to implement a cutout in the FSSP sample tube. A schematic of the arrangement is given in Fig. 4.
b. Results
Several FSSP-100 probes owned by the GKSS Research Center Geesthacht, Germany (hereafter GKSS), were used in all of the tests described in the next sections, including two standard four-range probes with a maximum size of 47 μm, and an extended four-range probe with a maximum size of 95 μm. The calibration size gain for all probes was adjusted at the outset so that water droplets passing through the center of the DOF and the center of the beam at low speeds were sized in the correct channel of the FSSP (with the exception of Figs. 8 and 9).
Droplets of different sizes were used to characterize the probe sizing at different positions across the laser beam. The PHA voltage was monitored with a special fast peak-height analyzer developed by GKSS and stored by the data acquisition system. The droplet generator position information and the probe response were also monitored and stored. Measurements were performed in 10-μm steps, starting at the beam center position and moving to one beam edge, and then starting again from the center and moving to the other beam edge. At every position, data were stored at a 50-Hz sampling rate for 10 consecutive seconds.
As an example, Fig. 5 demonstrates the PHA signal stability over a period of 10 s, as measured by the special GKSS peak-height analyzer for a droplet of 38-μm diameter. Although a few measured voltages exceed the threshold of size bin 6 for the 5–95-μm size range, the 10-s average of the voltage is 2.038 V with a standard deviation of 0.1 V, which is typical for droplets of this size. The standard deviation of long-term measurements (>10 min at one position) with several droplet dispensers producing various sizes is approximately the same. The probe response for the example presented in Fig. 5 corresponds to an average size and standard deviation of 38.6 and 1.9 μm, respectively. Because the standard deviation of the diameters of the droplets produced by the droplet generator is estimated to be smaller than 1 μm, typically 0.4–0.6 μm, it is evident from Fig. 5 that the probe response is introducing some sizing noise into the measured spectrum, although it is confined to within one 6-μm channel of the FSSP.
Averages and standard deviations have been calculated only for the stable 10-s time intervals to avoid any influence during motion of the droplet generator assembly from one position to the next one. Figure 6 shows the full measurement for the same droplet across the laser at the center of the DOF. Two conclusions can be reached from this figure.
Droplets that are introduced well outside the extension of the real laser beam edge, and whose straight trajectories should take them completely outside the beam, are still sized and counted by the probe. A more detailed investigation of this behavior revealed that the laser beam acts as a trap for charged droplets at low velocities. On several occasions, particles that were expected to stay outside the beam were observed to be “attracted” into the beam. This may be caused by the reaction of the so-called radiation pressure with air molecules and the particles themselves (e.g., Ashkin 1970; Ashkin and Dziedzic 1971; Roll et al. 1996). Because of this effect, droplet positioning with the monodisperse droplet generator system cannot be used to size the active laser beamwidth. Therefore, laser width measurements have been performed with pinholes mounted to a spinning disk as described in section 2.
Droplets are sized in the correct channel in the center of the laser beam (hashed area in Fig. 6), which is not surprising given the calibration method described above. Moving away from the center of the beam, droplets are increasingly undersized, to as low as the first channel at the beam edges. Measurements showing the artificial broadening of the spectrum caused by the droplet transition position within the laser beam were first reported by Dye and Baumgardner (1984). Our findings also corroborate the previous results by Wendisch et al. (1996), and are consistent with the rotating pinhole measurements of Fig. 2. Again, the energy distribution across the laser beam is reflected in the probe’s response to droplets in Fig. 6.
The above measurements were repeated at several positions along the laser beam from one edge of the DOF to the other. Figure 7 shows the resulting characterization of the entire sample volume. From this, it is concluded that droplets are sized correctly only in the central region of the DOF for an FSSP calibrated in the method described above. At the edges of the DOF, particles are still counted but are undersized. These edge areas, although small, can constitute 10%–20% of the total DOF depending upon probe alignment (see also Figs. 13 and 17).
For comparison between glass bead calibrations (as recommended by the manufacturer) and the calibration with real water droplets, the following simplifications were made.
During glass bead calibrations, beads move through the entire active sample volume. Therefore, a certain unknown fraction of beads is undersized at the edges of the sample volume. In addition, an also unknown fraction of the glass beads is oversized resulting from bead shape quality, coincidence, and clustering. This well-known behavior is independent of whether the velocity-averaging module of the probe is activated or not. Without velocity averaging, the number of counts in the lower channels 1 and 2 will be larger than with velocity averaging, and the mean diameter calculated as the arithmetic average of all counts in all channels will theoretically be lower due to the stronger influence of particles away from the center of the beam. Figure 8 shows the typical result of a glass bead calibration of the FSSP on the 2–47-μm size range for beads with a mean diameter of 31.5 μm (water equivalent is ∼25.6 μm). The bead response is compared to the FSSP distribution expected to be produced by a pinhole simulating a 27.5-μm particle, as described earlier in Table 1. That means because of its laser energy distribution the probe would size 21% of those particles in channel 9, 19.8% in channel 10, . . . and 15.8% in channel 1. If one takes into account the slight difference in the water-equivalent diameter and the maximum size of the simulated particles, the curves are very similar. This indicates that for the most part, the wide spectrum of sizes observed during an FSSP calibration, without the velocity-averaging card activated, is largely a result of the variation in sizing resulting from the uneven laser beam intensity cross section. This also holds for other probes with a calibration size-gain setting, for example, for glass beads or latex particles.
To compare the response of glass beads and water droplet response, the following method is employed to deduce an “average diameter” for a glass bead calibration. The average water-equivalent particle size is calculated using only the channel with the maximum counts and one channel on either side of the maximum-count channel. For the example in Figure 8, these would be channels 7–9. All counts in smaller and larger size bins are neglected. The mean particle size is calculated by multiplying the channel mean size by the counts, summing up that product for the three channels, and then dividing the sum by the total number of counts in the three channels.
For a water droplet calibration, only droplets moving through the laser beam center region are considered. To achieve this, the exit of the droplet generator nozzle was positioned above the geometric center of the laser beam at the center of DOF. This guarantees a probe response for the droplets within the 90% energy level of the beam.
As an example Fig. 9 shows the results for both calibration techniques for an extended range FSSP (FSSP-ER) in size range 1 (i.e., 2–47 μm) before the gain setting of the probe electronics was set for proper water droplet sizing. While the glass bead calibration gives the impression that the probe is nearly perfectly calibrated for sizing (all data points are close to the one-to-one line) the water droplet calibration suggests an oversizing by the probe by more than one size bin (>3 μm). Similar differences have also been observed for other probes. One explanation for this discrepancy may be the fact that the conversion of the glass bead mean size to “water equivalent” (glass beads scatter more light than water, and thus an adjustment must be made) is calculated from “simple” Mie theory considering only the difference between refractive indices.
Glass beads manufactured by Duke Scientific, Corp., are used worldwide for this kind of calibration. They are not always ideal spheres and may have surfaces of different roughness, as illustrated in Fig. 10. Both properties have an influence on the scattering behavior of the beads and may distort the measurement. In addition, glass bead calibration results are influenced by human handling and delivery to the probe, the equipment, the speed of the beads and, last but not least, the calculation procedure used.
4. High-speed calibrations
All in situ particle measurement devices, including the new generation of products recently appearing on the market, may suffer from degradation of response at high aircraft speed, particularly when the particles move through the sample volume at more than 150 m s−1. Cerni (1983) reported the airspeed influence on FSSP sizing based on his investigations with glass beads. Baumgardner et al. (1989) noted that the FSSP electronic response time is insufficient to resolve the electronic pulses for particles transiting the probe at 200 m s−1 and the roll-off in sizing even at 100 m s−1. Dye and Baumgardner (1984) recognized the velocity influence on the sample volume of an FSSP. Korolev et al. (1985a) investigated the dependence of the FSSP volume diameter on particle velocity based on a numerical model and measured the dependence of the PHA signal amplitude on particle velocity. Based on model calculations they found that the sample volume is a function of particle size and decreases with increasing particle velocity. Therefore, it is necessary to characterize probe behavior at real aircraft speed.
a. Instrumentation
Water droplets produced by any of the droplet generators described earlier cannot be accelerated to aircraft speed in the laboratory. For this reason, a spinning-disk device was developed to simulate water droplets at high velocities. A similar method was first mentioned by Korolev et al. (1985a) for this purpose. In our equipment, a small tube (0.5-mm diameter) is mounted radially on the circumference of the disk with a thin wire or fiber (6–300-μm diameter) protruding from its end. This wire or fiber is moved through the sample volume of the probe by rotating the disk. With special motors on an oscillation-dampening mount, velocities up to 250 m s−1 can be reached without significant vibration. The size of the “artificial” particles can be reduced by introducing a neutral density glass filter positioned into the optical path directly in front of the laser output. The entire setup is moveable in all three dimensions with micropositioners to an accuracy of ±5 μm. Again, all three positions can be stored together with the probe response by the data acquisition system. To access the sample volume of the FSSP, a special cutout in the FSSP sample tube was implemented as described earlier. A schematic of the high-speed tool is given in Fig. 11.
b. Results
Of course, the scattering behavior of a wire or a fiber with scattering edges of the length equal to the laser beamwidth is very different from that of a spherical water droplet. However, the electronic signals produced by the detecting diodes (signal and annulus/acceptance) and their relationship to each other are the most important criteria for the assessment of probe behavior. More than 30 different materials, including different metals (e.g., gold, silver, copper, tungsten, platinum, etc.), and carbon, quartz, and glass fibers, were investigated to find something with an FSSP response similar to that of water droplets. Figure 12 compares the FSSP electronic signal produced during the movement of a tungsten wire and a glass fiber (right) through the laser beam to the signal produced by a water droplet of similar speed (left). This figure again illustrates the variations observed in the response across the laser mostly induced by the laser energy distribution. In the end, signals produced by glass fibers were found to be most similar to the water droplet signal.
The spinning wire/fiber method was also used to measure the length of the FSSP DOF, as defined electronically by comparison of the signal measurement to the annulus measurement. For comparison, the FSSP DOF was measured with water droplets of different sizes. Figure 13a displays the result for a 61-μm water droplet. The droplets were produced at a frequency of 113 Hz and a velocity of 1.8 m s−1. The DOF was mapped by moving the dispenser along the laser beam between probe arms, but always in the center of the beam. The probe counted the droplets in channels 9 and 10 (5–95-μm size range). The sum of all counts in all channels (sum counts) should be equal to the droplet frequency. The measurements show that this is true for the main part of the DOF. We now define the edges of the DOF as those points where the total counts drop below two-thirds or 66% of the true droplet frequency. For the example contained in Fig. 13a, a DOF of 2.1 mm was calculated between the intersection points between the sum counts curve and the dashed line. The latter represents 66% of the droplet frequency of 113 Hz.
Similar measurements were performed with the rotating wires and fibers at a velocity of 2 m s−1, which is comparable to that of the average water droplet velocity. Figure 13b shows the result for a glass fiber at 17 revolutions per second (rps). The simulated particles were also counted by the probe in channels 9 and 10 (56 and 62 μm, respectively). The length of the DOF was calculated in the same way as for water droplets, and the same value of 2.1 mm was achieved. A summary of all DOF measurements is given in Fig. 14. It is evident that the DOF calculated from water droplet measurements decreases somewhat with increasing droplet size (large dots and function-fit dashed line), an observation previously reported by Dye and Baumgardner (1984). They also compared the DOF size for water droplets of different sizes with the DOF measured by moving different materials (metal wire, nylon fiber, and frosted tape) along the laser beam, but not across the beam as performed in this study with the spinning disk tool. The water droplet–generated DOF differs for this particular probe from the value determined with the usual tape scattering source (dotted line) by about 5%–10%. As in Dye and Baumgardner (1984), we also observed the material dependence of DOF size. Metal wires (squares) produce DOF lengths that are much larger than those of water droplets. Quartz fibers (triangles) produce better results than metal wires, but measured values depend on the position of the quartz fiber in the laser beam, and therefore have low reproducibility. Values exceed the corresponding values for water droplets by 20%– 30%. The best comparisons to water droplet–derived values are obtained from glass fibers (stars), particularly those with a special brown glass. The electronic signal of the same glass fiber was presented in Fig. 12.
For this reason, all further characterization requiring a high-speed spinning scatterer has been accomplished with a brown glass fiber. The length of the FSSP DOF was next measured as function of particle speed. The results illustrated in Fig. 15a reveal that the DOF shrinks with increasing airspeed, by about 5% from 2 to 155 m s−1. At 100 m s−1 the difference from the “static value,” which represents the measurement with a tape as a scattering source, is about 10%. In addition, particles are increasingly undersized with increasing speed (Fig. 15b), an effect first noted by Cerni (1983). Depending on the probe and particle size, the amount of undersizing can reach 10%–20%. In this example the probe is sizing a 70-μm particle at 61.5 μm and 100 m s−1. That would result in an underestimate of at least 32% in the calculated liquid water content (Fig. 15c) if the probe had been calibrated at a low airspeed.
To avoid such sizing errors, a high-speed calibration is recommended for all size bins of the probe. First, the probe response should be measured in the center of DOF at about 2 m s−1 with a rotating glass fiber. Neutral density glass filters can be used to simulate smaller particles to cover all size bins of the probe. A 10-s average is taken to represent the “real size” of the artificial particle. Then, the same measurements are taken at the expected operating true airspeed, and the channel shift is monitored for every particle size. This results in a correction equation for the airspeed effect on probe sizing at the given operating speed. An example for an FSSP-ER is shown in Fig. 16. The corrected (or “true”) particle diameter Dt is a linear function of the measured diameter at 75 m s−1 D(75 m s−1) within acceptable accuracy. A more general correction algorithm could be designed by incorporating variations in airspeed. Korolev et al. (1985a) have reported on such a general form of this correction based on their rotating glass fiber measurements as a function of measured signal rather than droplet size.
5. Instrument performance characterization
Probe characterization is an important part of maintaining and improving probe measurement accuracy. It is necessary to have calibration and diagnostic tools to check probe accuracy and functionality that are easy to handle, especially during field experiments. With the modular tools described earlier, one can derive much useful information. A few recommended field checks will be described in the following sections. The use of the rotating wire for these checks (sections 5a and 5b) was independently suggested about the same time at GKSS and the Meteorological Service of Canada (MSC) laboratories (A. Korolev 2002, private communication).
a. Basic FSSP field check
A glass fiber rotating at low speed (e.g., 20 m s−1) inserted into the same position in the sample volume will produce a repeatable probe response, both in counting and in sizing, and can be used as a quick check in the field. If results in the field change from the previously determined well-calibrated values, this may indicate a misalignment or a need to clean optical parts. If the signal and annulus are monitored at the same time with an oscilloscope, it is also possible to judge the quality of the optical alignment (see section 5c).
b. Alignment check of both optical systems of the FSSP
In a perfectly aligned FSSP, the focal plane of both optical systems (the condensing lens for the laser and the detecting optic system) must be at the same geometrical position. This would guarantee the maximum energy right at the center of the DOF. As discussed in section 4b, a rotating fiber can be used to measure the particle sizing inside the DOF. This method can be used to check whether there is an asymmetry in the sizing across the DOF, as might be caused by a misaligned probe. Figure 17 shows examples before (Fig. 17a) and after (Fig. 17b) alignment of an FSSP. Before alignment the focus of the laser beam was slightly shifted to the laser side, resulting in an asymmetric counting with the maximum in channel 10 at that side. After realignment, the probe counts the particles more or less symmetrically in the DOF, with the characteristic undersizing at the edges of the DOF here indicated by the increasing number of counts in channel 9.
c. Checks of the FSSP detector diodes
The capillary alignment inside a HeNe laser tube may change depending on temperature and the mounting position of the probe. For this reason, the probe alignment should always be performed with the probe in the same position that will be used during the field measurements. It is also important to make sure that all optical elements are aligned properly to one optical axis. Otherwise, the probe will not produce good signals, and that may result in the improper sizing and counting of particles.
In a well-aligned FSSP, the output signals of the detecting diodes should change symmetrically away from the center of the DOF in either direction. In the center of the DOF, the signal must rise to its maximum absolute value in the center of the beam and drop down again to its baseline at the edges, while the annulus remains constant at its baseline (Fig. 18a). At a position somewhat away from the center of the DOF, the signal shows the same behavior as in the central region. However, the annulus absolute voltage rises when the particle is passing the first beam edge, drops down to baseline when the particle is moving through the beam center, and rises again symmetrically to the same absolute voltage as before when it approaches the other beam edge (Fig. 18b). Near the edge of the DOF, both signals rise to about the same maximum absolute value at the center of the beam. Here, the counting of the probe depends on the noise level of both signals and is therefore random (Fig. 18c).
With the help of the spinning fiber or the spinning pinhole and a micropositioner, it is possible to monitor both signals with an oscilloscope while moving a well-defined number of monodisperse particles through the DOF at different positions. If the signals show a different behavior than that described above, the alignment can be optimized while the spinning disk is producing simulated particles inside the sample volume.
6. Estimation of achievable accuracy
The GKSS calibration tools described in this article offer the possibility of recognizing and reducing systematic and randomly occurring errors. The undersizing of particles moving through the edge of DOF and/or the laser beam edges, the shrinking sample volume and the undersizing with increasing speed, and the influence of aerodynamic shape of the probe sample volume on the measured spectrum are all permanent systematic error sources. Based on the calibration techniques described earlier, these errors can be minimized. Further systematic errors, such as the ambiguity resulting from Mie oscillations, coincidence undercounting and oversizing, the influence of ice crystals in mixed-phase clouds, or disturbance of the particle spectra by the nonaerodynamic shape of the probe, cannot be mitigated by the methods described in this paper. Error sources that produce randomly occurring effects, such as probe manufacturing tolerances, misalignment, contamination of the optics, or EMI, can be detected in the laboratory and during field campaigns and can be corrected.
The accuracy of absolute sizing of water droplets for a well-calibrated FSSP is mainly influenced by
the accuracy of the distortion matrix, which represents the laser beam energy distribution for each size bin;
the accuracy of the monodisperse droplet generator;
the precision of the fit function as a result of the water droplet calibration, which can be used to correct the sizing of water droplets in the center of the laser beam if the electronic gain setting of the probe causes an over- or undersizing; or
the precision of the correction function for the undersizing with increasing airspeed.
On average, application of the methods above yields a sizing accuracy of about 10%, with the caveat that the further systematic errors noted above (e.g., Mie oscillations) undoubtedly may degrade this accuracy.
The correct determination of the active sample volume (DOF, active beamwidth, and airspeed) is very important for the calculation of particle concentration, and thus other derived spectral parameters such as the liquid water content. The sample volume accuracy determined by the methods described in this paper primarily depends on how precisely the position measurements can be made with the high-speed tools along and across the laser beam. With high-quality micropositioners, the relative error in the determination of the active sample area can be estimated to be of the order of 5%–10%. In the future, the use of spinning pinholes of different sizes at aircraft speeds will help to improve the accuracy of active laser beamwidth measurements and will further reduce the relative error. Uncertainties resulting from differences between the true airspeed of the aircraft and at the mounting position of the probe have not been examined.
7. Summary
In principle, every particle probe has its own sizing and counting characteristics. This is due to the probe-specific laser beam characteristics, optics, and electronics. The general results presented in this article from specific probes of a certain type can be applied to all probes of that type, but calibration details must be recreated for each specific probe for a high-quality calibration.
The electronic signal produced by an FSSP from a water droplet moving through its sample volume primarily reflects the laser energy distribution in the beam cross section. The response variation across the beam shows some local variation and noise, and is never a smooth, continuous function. The energy distribution of the HeNe laser used in the FSSP does not have a “top hat” shape. The part of the beam producing counts in the maximum size channel is a small fraction of the total active beam sample volume. The active laser beamwidth is a function of particle size and may be larger than the physical laser beamwidth.
When using the size of the particle in the center of the DOF to calibrate the FSSP, particles are then only properly sized in this central DOF region and in the widthwise center of the laser beam. The undersizing of particles at the edges of DOF and in more than 50% of laser beamwidth outside the central region cannot be neglected. The knowledge of this undersizing is important, because hardware features like the velocity-averaging module in an FSSP-100 or the slit mask in the FSSP-300 may not reliably avoid counting the undersized particles moving through the sample volume in those regions of the laser beam. The artificial broadening of the spectrum resulting from the variable laser energy intensity across the beam can be avoided by the size correction method described in this article using the measured response matrix. Glass bead calibration also suffers from the same type of errors introduced by the uneven energy distribution in the laser beam cross section.
It is concluded that absolute calibration with monodisperse water droplets is fundamentally superior to glass bead calibrations, because
no theoretical adjustment for the increased light scattered by glass is required;
the effect of the variations introduced by the human operator can be minimized, including the speed of the particles;
the influence of the individual calculation procedure can be mostly avoided; and
calibration with the same “material” to be later sampled eliminates any unknown material effects.
The electro-optical systems of most probes currently on the market do not adequately compensate for airspeed effects up to aircraft velocities. As already shown by others, it has been demonstrated here that both the probe DOF and the size response decreases with increasing airspeed. The high-speed calibration technique with glass fibers simulates particles similar to water droplets or ice crystals up to speeds of 250 m s−1; it can be used for the characterization of probe behavior, for diagnostic purposes, and for probe maintenance in the laboratory and in the field.
In summary, the methods shown for the calibration of absolute sizing and for determination of the active sample volume can significantly improve the measurement accuracy of PMS FSSPs and OAPs. The methods can be used for other in situ optical measurement devices as well.
Acknowledgments
This work was completed within the scope of cloud physics research in the GKSS Research Center Geesthacht, Germany. The authors thank the staff in the GKSS machine shop and electronic shop for their excellent support in building all the components that made our work easier and even possible. We also like to thank Dr. Alexei Korolev of Environment Canada for the helpful discussion on theoretical and practical questions related to the development of our calibration technique. We are grateful to the German Ministry for Research and Development (BMBF) for partially funding the work in the framework of the bilateral program for German–Canadian collaboration (CAN-ENF-00/08).
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Energy distribution of an FSSP HeNe laser measured with a laser power meter and a 2-μm pinhole mask, and the electronic signal for a 67-μm water droplet moving through the beam center at the DOF center. Both curves have been normalized to their maximum value.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Measurement of sizing of an FSSP as a function of the position in the laser beam cross section for rotating pinholes (partly with additional scattering sources) simulating particles of different sizes. The physical laser beamwidth of 290 μm is bounded by the two vertical lines.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Image of (a) a droplet and (b) the glares produced during its transit across the probe laser beam.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Schematic of the droplet generator assembly inside the sample tube of an FSSP, with microscope and positioning system.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
FSSP particle pulse signal peak voltages for a 10-s time interval, measured by the fast peak-height analyzer developed at GKSS. The signals were produced by monodisperse water droplets with 38-μm diameters. The dashed lines mark the threshold values of the size bins of the probe.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
The 10-s average pulse signal peaks for 38-μm water droplets in 10-μm steps across the laser beam in the center of the DOF of an FSSP. Measurements were made by the fast peak-height analyzer developed at GKSS. Error bars represent the ±1σ spread in data. The dotted lines correspond to the threshold values for the size bins of the probe. The hashed area marks the fraction of the beam in which the water droplets were sized in the correct channel of the probe.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Characterization of probe sizing in the entire sample volume of an FSSP by measurements with 38-μm water droplets along and across the probe laser beam.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Result of a glass bead calibration for beads with a 31.5-μm mean diameter (approximate water equivalent of 25.6 μm), and the percentage of the beam counting particles in the respective channels of the probe from a 50-μm pinhole producing a signal equivalent to a 27.5-μm particle at the center of the probe sample volume (Table 1).
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Size calibration results with water droplets (open symbols) and glass beads (filled symbols) for an FSSP-ER (size range of 2–47 μm) before the gain setting of the probe electronics was set for proper water droplet sizing in the center of the probe sample volume. The glass bead true diameter has been adjusted to a water-equivalent value using Mie calculations to allow for direct comparison of the water and glass results.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Scanning electron microscope photographs of glass beads manufactured by Duke Scientific, Corp., with a mean diameter of (a) 60 and (b) 40 μm.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Schematic of the high-speed tool with spinning disk in the probe laser sample volume.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Oscilloscope signals of a water droplet of 70-μm diameter, a glass fiber, and a tungsten wire, as produced by the FSSP electronics and as measured at the PHA input.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
(a) Determination of the size of the DOF for 61-μm droplets at 1.8 m s−1, and a droplet frequency of 113 Hz; the calculated DOF is 2.1 mm. (b) DOF for particles simulated by a rotating glass fiber at 2 m s−1 and 17 rps; the calculated DOF is 2.1 mm. The edges of DOF are defined as the positions where the percentage of particles counted by the probe drops to 66% of peak values.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
DOF measured at low speed with water droplets of different sizes (large dots and fitted function) and with several other materials that have been moved through the FSSP sample volume with the spinning disk tool. The “static value” is the standard manufacturer’s DOF produced with frosted tape as the scattering source.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
(a) FSSP DOF and (b) probe sizing for a 70-μm particle, as function of airspeed, simulated with a rotating glass fiber. The “static DOF size” measured with frosted tape as the scattering source is included. (c) In addition, the normalized liquid water content is given.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
High-speed size response for a typical aircraft speed of 75 m s−1 relative to that at 2 m s−1, which is the typical droplet velocity produced by the droplet generator. The resulting linear fit function describes the diameter shift resulting from airspeed and may be used for data correction; Dt is the “true” droplet diameter, D(75 m s−1) is the diameter measured by the probe at the airspeed of 75 m s−1.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Examples of a (a) poorly and (b) well-aligned FSSP probe. In (a) the shift of maximum counts in channel 10 to the laser side of the DOF indicates that the focus plane of the laser condensing lens is not in the center of DOF; (b) shows the probe response after realignment.
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Oscilloscope images of the FSSP signal (dark gray) and annulus (light gray) for a 55-μm droplet (a) passing through the laser beam at the center of the DOF, (b) at a position somewhat away from the center of the DOF, and (c) at the edge of the DOF. The grid scale is 20 μm (x axis) and 0.5 V div−1 (y axis).
Citation: Journal of Atmospheric and Oceanic Technology 24, 5; 10.1175/JTECH2006.1
Beam fraction (%) for sizing of four different “artificial” monodisperse particles by an FSSP-ER in the 2–47-μm size range. It is assumed that the particles have been sized correctly in the center of the beam in the highest observed channel (shown in bold).
