# Study of Marine Particles Using Submersible Digital Holographic Camera during the Arctic Expedition
## 2 Methods and Equipment
### Data Analysis
#### 2.3.1 Integral DHC data  
The integral data for plankton usually include the concentration (\(\rm{ssp/m^{3}}\)) and biomass (1 mg/m\({}^{3}\)) for each taxon. Some literature sources [48; 49] provide various methods to determine plankton biomass, including those based on images of plankton individuals [50; 51]. The DHC software can be adapted to the requirements of the chosen biomass counting technique. This study determines the maximum size \(H\) of the rectangle circumscribed around the reconstructed image of each plankton particle suspended in water, i.e., in its wet state. In this case, the density of a plankton individual of any taxon can be taken as equal to the density of water: g \(\approx\) 1 mg/mm\({}^{3}\)[52]. To calculate the biomass by wet weight, each plankton particle is represented as an ellipsoid, whose volume is as follows:  
\[V=\frac{4\pi abc}{3}=\frac{1}{6}\pi\cdot H^{3}\cdot M^{2}, \tag{1}\]  
\[c=\frac{H}{2},M=\frac{b}{c},a\approx b=\frac{HM}{2}\]  
where \(a,b,c\)--semi-axis of the ellipsoid circumscribed around the particle, \(M\)-- morphological parameter, and \(H\)--maximum size of the rectangle circumscribed around the reconstructed image of a plankton particle. The total biomass of \(k\) taxon particles by wet weight will be as follows:  
\[Biomass_{k}=\frac{\sum_{i=0}^{n}WW_{i}^{k}}{V_{0}}, \tag{2}\]  
where \(WW_{i}^{k}=gV_{i}^{k}=\frac{1}{6}\pi\cdot H_{i}^{k3}\cdot M_{i}^{k2}\)--wet weight (mg) of the i particle of the \(k\) taxon in the DHC measured volume--\(V_{0}\). The total biomass of all particles is the sum of the biomass of planktonic individuals of certain taxa. Turbidimetric and sedimentological measurements are typically performed to clarify the hydrological state of the water area (for example, turbidity measurements). According to the DHC data, turbidity can also be estimated by making a histogram of the _Suspension_ particle size distribution (Figure 6). Figure 6: Example of a histogram of the _Suspension_ particle size distribution at AMK-82 station No. 6939. Turbidity is taken equal to the total fraction of the volume section area covered by the sections of the _Suspension_ particles:  
\[\alpha=\frac{\sum_{i=0}^{n}S_{i}}{S_{DHC}}, \tag{3}\]  
where \(S_{DHC}\)--area of the DHC entrance pupil, \(S_{i}\)--area of the image of the \(i\)-particle section, and \(n\)--number of particles of the _Suspension_ taxon. Data on the size and number of particles in the _Bubble_ taxon are used to determine the volume content of methane. A laboratory bubble test was performed to verify the correct bubble size. The test used square test particles with a size of 500 \(\times\) 500 \(\upmu\)m for calibration (test objects in Figure 2). The Hailea ACO-5501 tank compressor was used as the bubble generator during the test. Capacity: 80 L per hour. Outlet pressure: 0.10 bar. The Hailea ACO-5501 is designed to ensure the effective aeration of water tanks. Digital holograms of bubbles were registered against the background of test particles. A 2D display of holographic images of the water volume with bubbles was obtained from the focused images of particles and bubbles reconstructed from digital holograms using the DHC technology (Figure 7). The size of the bubbles studied in the laboratory experiment was established by comparing the size of the bubble images with the known size of the test particles (model particles), and a histogram of the distribution along the bubble diameter was compiled (Figure 8). The formula for calculating the volume density of the _Bubble_ taxon is used to calculate the volume content of bubbles:  
\[V=\frac{\sum_{i=0}^{n}\frac{1}{6}\pi H_{i}^{3}}{V_{DHC}}, \tag{4}\]  
where \(V_{DHC}\)--studied volume by the DHC, \(H_{i}\)--size of the \(i\) particle (bubble) of the _Bubble_ taxon, and \(n\)--number of particles of the _Bubble_ taxon. Figure 7: A 2D display of holographic images of the water volume with bubbles.