The use of laser diffraction is now common practice for the determination of an in situ particle size distribution in the marine environment. However, various imaging techniques have shown that particles vary greatly in shape, leading to uncertainty in the response of laser diffraction instruments when subjected to this diverse range of complex particles. Here we present a novel integrated system which combines both digital in-line holography and a LISST-100 type C, to simultaneously record in-focus images of artificial and natural particles with their small-angle forward scattering signature. The system will allow for further development of a reliable alternative to Mie Theory when using laser diffraction for the in situ measurement of complex suspended particles. A more detailed knowledge of the performance of laser diffraction when subjected to the wide variety of complex particles found in the marine environment will then be possible.
©2011 Optical Society of America
Characterizing particles suspended in seawater is important for several reasons. Suspended particles affect light penetration through the water column, causing a significant impact on radiative transfer and primary productivity [1, 2]. They can also influence the way in which sound propagates through water, affecting the performance of sonar equipment . Models of sediment transport require information on particle characteristics such as size, effective density and settling velocity. The distribution of pollutants can be predicted using these models because many pollutants attach to the surfaces of particles [4–6]. Understanding the distribution of organic carbon, (which may be in the form of particulate organic carbon) and how it sinks from the atmosphere to the ocean floor, is a key stage in the carbon cycle , and therefore has implications on large-scale climate prediction models. For all these cases it is vital to have an accurate measurement of suspended particle size and concentration.
One of the most widely used techniques for measuring the particle size distribution in situ is that of laser diffraction. This technique is adopted by the LISST (Laser In Situ Scattering Transmissometer) series of instruments (developed by Sequoia Scientific Inc.). The method for determining a particle size distribution (PSD) in this way relies on inversion algorithms based either on scattering theory or empirical measurement, and is described later in this section. Unfortunately the available inversion algorithms perform at different accuracies, depending on the type of particles under investigation. For a thorough understanding of the response of LISST instruments to the many complex particles found in the marine environment, it is necessary to capture detailed information on both particle size and shape, which may be done using imaging. However, standard imaging techniques encounter problems associated with limited depth-of-field in large sample volumes, and as a result, in-line holography is a preferred method for obtaining in-focus and high resolution particle images, regardless of their position within the sample volume. The method of extracting particle images from digital holography is described later in this section. Here, digital in-line holography is combined with the LISST-100 to allow for both particle images and forward-angle scattering measurement to be recorded simultaneously from within an identical sample volume.
1.1. Principles of laser diffraction & the LISST-100
The LISST-100 uses 32 ring-shaped detectors that measure a VSF (Volume Scattering Function) at logarithmically increasing angle ranges from ~0.05-10° (type C instrument). Agrawal & Pottsmith (2000) describe the way in which a LISST-100 uses the principles of laser diffraction to measure particles . The instrument consists of a collimated laser beam that passes through the sample volume onto a receiving lens and the 32 ring detectors are positioned at the focal plane of the receiving lens. This configuration allows scattering intensities to be recorded at varying angles, with larger angles being focused onto the outermost rings of the detector (Fig. 1 ).
The angular distribution of light scattered in the forward direction is primarily affected by the size of the particle. Using Mie Theory, it is possible to predict the intensity of light that would be recorded by each of the 32 ring detectors of the LISST-100, by integrating the theoretical VSF over the angle ranges covered by each of the rings. Figure 2 shows how the predicted intensities on each of the 32 detectors change with particle size. As particle size increases, the angle of the principal diffraction lobe (the largest peak in intensity at each size) decreases.
Substantial assumptions in the inversion of a VSF to an associated size distribution are that the particles in the sample volume are spherical and of a known refractive index. Agrawal et al. (2008) began to address these problems by producing an alternative kernel matrix for the inversion of scattering by random shaped particles, through empirical measurements of sand and ground coffee grains . However, unknown errors remain in the inversion when the LISST-100 is exposed to the wide range of complex particles and flocs that are common in marine environments. A number of studies have compared the performance of the LISST-100 with other particle sizing techniques, for example Mikkelsen et al. (2005)  and Reynolds et al. (2010) , both of which report comparable results between the LISST and other techniques. However, in regions in which large flocs were present, problems such as an overestimation of the volume of particles in the largest size bin were highlighted.
1.2 Digital in-line holography
A digital hologram takes the form of an interference pattern recorded by a CCD (Charge-Coupled Device) of a camera. This interference pattern is produced from constructive and destructive interference between coherent background light (laser light) and the scattered light from particles within the sample volume (Fig. 3 ). The resulting hologram can be numerically reconstructed to produce in-focus images of every particle recorded, eliminating the problems associated with depth-of-field and focussing that occur when using conventional imaging methods. The details of holographic reconstruction are explained by Owen & Zozulya (2000) and Graham & Nimmo Smith (2010) [12, 13].
The holographic images shown in Figs. 4(a) and 4(b) show a bright centre and dark edges, created from the Gaussian beam. The reason for the chosen beam diameter, and resulting dark areas in the holograms, was to allow the holographic camera to capture the entire sample volume recorded by the LISST-100 when combining both instruments (Section 2). The background image of Fig. 4(b) was subtracted from the raw image (a) in order to remove any stationary objects and reduce noise. An example of the resulting clean image is shown in Fig. 4(c). This is a similar process to the ZScat (background scattering data) which is subtracted from LISST-100 data before analysis. Once a clean holographic image was calculated, the reconstruction procedure explained by Owen & Zozulya (2000)  was then implemented, producing a stack of reconstructed images. Following this, each particle within the reconstructed image stack was manually focused and binarised to allow for errors in the automatic focusing and thresholding to be reduced, and for overlapping or poorly resolved particles to be excluded from the analysis. This procedure resulted in a binary image of all in-focus particles in the sample volume. Each particle in the binarised image was then analysed independently to return their geometrical properties, such as equivalent spherical diameter, perimeter and major axis length.
An advantage of digital holography over laser diffraction for sizing particles is the ability to view a projected area for each particle in the sample, a result which is not possible without imaging technology. Unfortunately, the computational storage demands of imaging techniques greatly reduce sampling durations and increase processing times when compared with laser diffraction.
2. Combined LISST-100 and holographic camera system
The combination of digital holography and a LISST-100 should allow for a greater understanding of how forward scattering signatures are affected by various types of particle. This is because the system simultaneously records in-focus images of particles and their light scattering signature from within the same sample volume. Further development of a reliable alternative to Mie Theory when using laser diffraction for the in situ measurement of complex suspended particles will then be possible.
The new laboratory-based system allows for the forward-angle VSF, recorded by the LISST-100, to be compared with an accurate measurement of particle characteristics, obtained with holographic imagery. The system consists of a purpose-built settling column that allows for a collimated laser beam (658 nm wavelength) to be passed through the sample volume, and for measurements to be taken simultaneously by the LISST-100 ring detectors and a holographic camera. This is achieved using a beam splitter positioned on the far side of the settling column, between the two instruments. A schematic illustration and photograph of the system is shown in Fig. 5 and 6 respectively. The collimated laser beam is passed through a first beam splitter to allow for a reference of laser power to be measured. A kinematic mount is positioned between this beam splitter and the sample volume to allow for precise alignment of the laser to the LISST-100 ring detector. Once light has passed through the settling column it is split again with a larger beam splitter. The purpose of this is to enable the holographic camera to record images of the interference pattern, while simultaneously allowing the LISST-100 focusing lens to receive the same light and record the VSF.
The use of a 35 mm beam splitter and a sample volume length of 20 mm, allowed for a gap of 3.9 mm between the 10 degree scattering angle and the outer-most edge of the focusing lens of the LISST-100. This gave reassurance that there was no vignetting whilst recording LISST-100 scattering measurements, within the angle ranges covered by the type C instrument. A schematic illustration of the triggering cycle used for the two instruments is shown in Fig. 7 . The LISST-100 measurement is an average of the scattering by particles in the laser beam over a period of approximately 100ms. In contrast, the holographic camera takes a near-instantaneous snapshot of the particles in the sample. In order to accurately quantify the particles that are recorded during the period in which the LISST is recording, two holograms are recorded - one at the start of the LISST exposure (i.e. when the laser is turned on), and one at the end of the LISST averaging period (when the measurement is taken). After this period the laser is turned off until the LISST-100 ring detectors reset to zero. This ensures that each cycle obtains data restricted to the period in which that laser was switched on. The resulting sequence allows for a time series to be recorded, during which samples of particles may be introduced into the settling column and passed through the sample volume. Faster sampling is possible, but is limited by the time taken for the LISST rings to reset and the camera speed, which requires a minimum of 67 ms between consecutive holograms. A frame length of 0.2 seconds was used for this work.
2.1 Instrument validation
To validate the accuracy of measurements taken using the combined holographic camera and LISST-100, samples of Basalt spheres ranging from 90 to 500 µm in diameter were used. They were sieved into ¼Φ size ranges to reduce the width of the particle size distribution of each sample that was measured. The first method for validation was a cross-comparison between the adapted LISST-100 (type C) in the combined system, and a standard LISST-100 (type C). Secondly, a comparison between scattering predictions, informed through measurements of particle sizes from the holographic camera, were compared with the LISST-100 scattering.
The optical configuration of the system does not interfere with the principles of measuring the angular scattering of light that are adopted by commonly used LISST-100 instruments described in Section 1.1. However, the wavelength of the laser used for the combined holographic camera and LISST-100 system was 658 nm as opposed to 670 nm adopted by a typical LISST-100. Figure 8 demonstrates that the 12 nm difference in wavelength between the two instruments was near-indistinguishable in both the scattering predicted by Mie Theory and the associated inverted volume distribution.
For reassurance that the LISST-100 scattering from the combined system was representative of a standard LISST-100, tests were carried out using the same samples of Basalt micro-spheres used in subsequent tests. An example of the agreement between the two LISST instruments is shown in Fig. 9(a) . Some deviations between the two characteristic scattering functions that were recorded are present, and are as expected from slight changes in the width of the particle size distributions between the two sub-samples used. When comparing median sizes (D50) from the holographic camera with the D50 from the inverted LISST-100 scattering, a near 1:1 fit is observed (Fig. 9(b)). It was possible to account for small deviations below the 1:1 line by comparing the observed results with inverted numerical predictions of scattering from Mie Theory, and comparing the size used in the calculation of scattering, with the D50 from the inverted size distribution (solid line of Fig. 9(b)). The width of each of the LISST-100 ring detectors and associated size bins resulted in slight oscillations in the predictions of D50, which were amplified in the larger size classes (with larger size ranges). The observations shown in Fig. 9 illustrate the reliability of the combined laboratory system for reproducing both observations of a VSF and inverted particle sizes that are within close agreement with those of a standard LISST-100.
3. Combined system results
The data used for background removal for both the LISST-100 and holographic camera was taken from the region at the start of each time series, before particles were introduced into the sample volume. For the LISST-100, the ZScat was taken from the frame containing the highest transmission value (i.e. the cleanest frame). The background image used for correction of the holograms was taken as the average of frames that were used to find the ZScat values. This background image was subtracted from each hologram before processing to reduce background noise, as per Fig. 4.
Data from each time series were filtered to leave only the frames that contained enough particles to produce a clear scattering response on the LISST-100 detectors, and few enough particles to allow for reliable reconstruction of holograms. This allowed for a comparison between the VSF measured by the LISST-100 and the PSD measured by the holographic camera. Multiple scattering is likely to contaminate the LISST scattering measurement with transmissions less than 40%. All data analyzed here contained transmissions greater than 80%, and is therefore unlikely to be contaminated with multiple scattering.
To predict the scattering intensities recorded by the LISST-100, it was first necessary to calculate scattering from every particle recorded by the holographic camera using Mie Theory and integrating the Mie scattering intensities across the angle ranges covered by each of the 32 ring detectors of the LISST-100. The predicted scattering intensities of each particle were then scaled relative to the average pixel intensities of the background image from the same location in which the particle was recorded. This is illustrated by Fig. 10 , where the intensities of each of the particles in the binary image have been scaled according to the intensity of the background image in the same location. This scaling of scattering intensities accounted for the differences in scattering due to the particle location within the Gaussian beam. For example, particles in the centre of the beam will scatter more intensely than particles towards the edges. This was an important effect to consider due to the near-instantaneous sample time for each hologram – a problem that is removed through averaging during the LISST-100 sampling time. Predicted scattering intensities for each frame are then calculated from the sum of the predicted scattering from each particle, as predicted by Mie Theory. This “predicted scattering function” can then be compared with the recorded scattering from the LISST-100 from the same point in time.
The progression from Figs. 11(a) to 11(d) shows that as particle size increases, the angle of the principal diffraction lobe (PDL) decreases. The relative scattering intensities recorded by the LISST-100 fit closely to intensities of the “predicted scattering function” from Mie Theory, informed by the particle size information from the digital holography. Scattering from the Basalt spheres also shows well-resolved peaks and troughs at angles larger than the PDL – a pattern that is expected from spherical particles. An examination of an electron micrograph of the Basalt spheres (Fig. 12 ) reveals that some of the particles have variations in their surface roughness, suggesting that many of the deviations between predictions of scattering using Mie Theory and the observed scattering is likely to be due to these slight deviations from perfect spheres. The relative amplitude of the second and third peaks and troughs in the scattering was resolved very well by the predicted scattering function described earlier in this section. A single Mie Theory prediction (integrated over the angles of each of the LISST-100 ring detectors) using only the mean particle size, consistently overestimates the amplitudes of these second and third peaks and troughs in the scattering. This is due to the slight smoothing of the scattering signature caused by the width of the particle size distribution.
The problem of a known particle refractive index is also clear in Fig. 12. The rising tail at larger angles of the scattering function (ring numbers greater than 22), typical of particles with refractive properties such as sand (evident in Fig. 10 of Agrawal et al. 2008 ), was not resolved with the basalt spheres. This was due to the relatively high refractive index of basalt (1.95 relative to air). Because forward angle scattering is dominated by diffraction, a variable refractive index only affects the shape of the scattering function at larger angles, and therefore the predicted position of the PDL is not affected.
Finally, the LISST-100 scattering data was inverted into a PSD and compared with the PSD obtained from the holographic camera. This allowed for a comparison between sieving, imaging and laser diffraction, as shown in Fig. 13 . The “sharpen” option was used in the Sequoia Scientific Inc. inversion of scattering data because of the narrow ranges in size distributions that were used. The particle volume information from the holographic camera was binned into equivalent size classes to the LISST-100 (type C) for a reliable comparison. For each of the size ranges, the peak in volume distribution obtained from both holography and the inverted LISST-100 scattering is clearly within the sieved ranges. The shapes of the size distributions matched well from the 90-106 µm (a), 125-150 µm (b) and 180-212 µm (c) samples, although a consistent underestimation of particle volumes from the LISST-100 is observed in the coarse tails of the distributions (i.e. sizes greater than the sieved ranges) when compared to that from the holographic camera. This is possibly a result of a slight over-sharpening during the inversion of the LISST-100 scattering. While the peak in volume distribution for the sample of 425-500 µm spheres (d) is correctly placed in the correct size bin of both instruments, there is, however, a substantial increase in the number of smaller particles (< 400 µm) inverted by the LISST-100.
As the focus of this work is in comparing the determination of particle size measurement using a holographic camera and the LISST-100, the distributions in scattering intensities presented are relative to their peak, and are subsequently independent of total particle concentration. With a mono-disperse sample of varying numbers of particles, the intensity of scattered light recorded by the LISST is proportional to the concentration of particles present. This allows the inversion of scattering from the LISST to give an estimate of particle concentration, in addition to particle size. However, the conversion of the inverted size distribution to a true volume concentration requires calibration of the LISST-inverted distribution using a known concentration of particles. The performance of this calibration constant for determining true volume concentrations will be assessed in future publications using the system described here.
4. Summary and conclusions
The new system, comprising of a combination of digital in-line holography and a LISST-100 type C, is able to simultaneously record in-focus images of particles and their small-angle forward scattering signature. This is achieved using an additional beam splitter, positioned on the detector-side of the sample volume. The beam splitter allows for both the LISST-100 and holographic camera to simultaneously receive scattering data from particles within the sample. The combination of the LISST-100 and holographic camera, will allow for an accurate measure of particle geometry to be compared with the forward angle light scattering signature recorded by the LISST-100.
Comparison between scattering recorded by the combined system and that of a standard LISST-100 shows good agreement. It can therefore be assumed that accurate scattering measurements are possible using the adapted LISST-100 set-up described. When results from spherical particles recorded by the system are compared with Mie Theory, a very good agreement is clear between the theoretical predictions of scattering, informed by the holographic camera, and observed scattering from the LISST-100. When ranges of particle sizes are present, the use of Mie Theory at only the mean particle size is not sufficient to accurately resolve the relative amplitudes of the peaks and troughs in scattering. It is therefore necessary for scattering to be predicted for each particle recorded in the holographic images before an accurate comparison can be made.
The combination of digital holography and a LISST-100 will allow for further development of a reliable alternative to Mie Theory when using laser diffraction for the in situ measurement of more complex suspended particles. This will in turn allow for a greater understanding of the effect of particle shape and composition on the volume scattering function at forward angles. A detailed investigation of scattering from flocs and how they are interpreted by the LISST-100 will now be possible using the combined system described here.
E. Davies is funded by the Natural Environment Research Council (NERC grant number NE/H525070/1). Staff at Sequoia Scientific Inc. have provided support with instrument set-up and configuration. We would also like to thank Dr. George Graham and for his valuable feedback on improving the manuscript, and reviewer comments which were extremely helpful and gratefully received.
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