# A Brief Review of Mueller Matrix Calculations Associated with Oceanic Particles
## 4 Computational Results and Discussion  
### Dinoflagellate Simulation Using ADDA  
Phytoplankton are one of two main categories of oceanic organisms and a significant component of the marine ecosystem that travel along the ocean currents. Many phytoplankton are positioned with preferred orientations due to the ocean flow [64]. Most phytoplankton are single-celled, such as dinoflagellates, diatoms, and coccolithophores. The bloomed phytoplankton can cause huge economic losses and influence environmental health, such as the red tide bloom of dinoflagellates in Florida [65]. Optical properties of an individual or bulked phytoplankton are essential to study phytoplankton populations (e.g., [66]). As mentioned in Section 3, dinoflagellates, diatoms, and coccolithophores have been simulated using the DDA and IITM [11; 41; 42; 43; 54]. Dinoflagellates have a large group of species so we take them as an example to describe the application of a scattering method.  
Laboratory observation using transmission electron microscopy showed that the nucleus of dinoflagellates contains cylindrical chromosomes [67; 68; 69] and the chromosomes are arranged by ordered helical structures [69; 70]. The helical structures are responsible for the strong circularly polarized effect that was observed in dinoflagellates [43; 71; 72]. The Mueller matrix element P\({}_{14}\) reflects the circular polarization of a scattering particle and can be used as an index to indicate the strong circularly polarized effect [16; 20]. [PERSON] and [PERSON] employed the ADDA code to fully simulate a single cell of a dinoflagellate and compute the 16 Mueller matrix elements [43], where the chromosomes are constructed using the plywood model [73]. For computational efficiency, only the nucleus with dozens of randomly positioned chromosomes is simulated. A chromosome is modeled as a cylindrical capsule with many layers, where every layer with fixed diameter contains parallel fibrils and the helical structure is described by making two adjacent layers with a constant rotation angle between them. The height with one period of rotation for the parallel fibrils is called the pitch. The chromosome simulation in the DDA method was performed by constructing fibrils in terms of dipoles and these fibrils were then arranged in layers and each layer was twisted a certain amount to make a helical shaped capsule to represent the chromosome. The diameter, the constant rotation angle, the number of helical periodicities, the pitch, the incident wavelength, and the incident directions can be changed to examine the circularly polarized effect of the helical structure. The important conclusions while using the ADDA code are given by [PERSON] and [PERSON], as follows [43]:  
* Strong back scattering signals from Mueller matrix element S\({}_{14}\) are indeed from the helical structures of the chromosomes.  
* Strong S\({}_{14}\) back scattering signals are observed when the incident wavelength in the ocean is matched with the pitch of the helical structure, even if the chromosomes are under the random orientation condition.
* Strong S\({}_{14}\) back scattering signals are observed when the incident direction is close to the main axis of the helical structure.
* The helical structure with constant rotation angle has stronger S\({}_{14}\) back scattering signals than the helical structure with random rotation angle.  
These conclusions suggest potential applications on the detection of the dinoflagellate and also the appropriate incident wavelength to match the pitch of helical structure.