# Diatom Valve Three-Dimensional Representation: A New Imaging Method Based on Combined Microscopies

^{*}

## Abstract

**:**

## 1. Introduction

^{5}species have been identified so far, differing in dimensions (some microns up to 1 mm), shapes, pore diameters (from some nanometers to some microns) and pore distributions. In the 19th century, diatom frustules represented the standard objects to test the quality of microscope optics. Moreover, the frustule of some diatoms has showed very interesting photonic properties, generally related to its complicated and quasi-symmetric micro- and nano-structure, behaving as a natural photonic crystal [1,2,3]. In order to simulate light propagation inside these natural structures, to study the mechanical properties and to generate three-dimensional (3D) models for synthetic replica, it is important to determine their real 3D image with a high resolution. In this way, it is possible to model the natural microsystems in biomimicry or just for the understanding of physical phenomena occurring in biological organisms.

^{−9}m). In this case, the depth of field (D) in SEM images is D (mm) ≈ 0.2/αM, where α is the beam divergence, and M is the magnification. However, numerical three-dimensional information cannot be simply extrapolated by the SEM image: some algorithms reconstructing a 3D model of an object from SEM images have been recently presented in References [4,5,6,7,8]. In these works, the authors obtained a resolved and faithful 3D representation of the object by increasing the angular frequency and the angular interval (e.g., from −90° to 90°) of the acquired images. The main drawback is that these techniques require a calibration on a reference sample characterized with a different technique, such as atomic force microscopy (AFM). Moreover, the SEM microscope needs an eucentric goniometer with high definition in order to maintain the same field of view in all tilted images. Furthermore, when soft biological samples have to be imaged, a cooling stage is needed to immobilize them.

## 2. Results and Discussion

#### 2.1. Example 1: Creating a 3D Model of an Arachnoidiscus Diatom Valve

#### 2.2. Example 2: Creating a 3D Model of a Cocconeis Diatom Valve

#### 2.3. Example 3: Creating a 3D Image of a Porous of Coscinodiscus wailesii Diatom

## 3. Materials and Methods

#### 3.1. Sample Origin and Preparation

^{−2}·s

^{−1}. Organic content was then removed from the cells according to von Stoch’s method [17], which allowed also the separation of the various frustule components.

#### 3.2. Digital Holography Microscopy

#### 3.3. Scanning Electron Microscopy

#### 3.4. Atomic Force Microscopy

#### 3.5. Mathematical Procedure

^{®}or Mathematica

^{®}.

_{1DHM}and P

_{2DHM}, and the corresponding two points in the SEM image, P

_{1SEM}and P

_{2SEM}. The error in identifying the same points is related to the smallest in-plane resolution of the DHM. However, the in-plane resolution of the merging is improved by the SEM image and the axial resolution, given by the DHM reconstruction, is not affected by the choice of the points.

_{1DHM}, P

_{2DHM}, P

_{1SEM}and P

_{2SEM}points correspond to the a

_{i1M,j1M}, b

_{i2M,j2M}, elements in M matrix and a

_{i1N,j1N}, b

_{i2N,j2N}in N matrix.

_{1}in both images is usually placed on the center of the object and the points P

_{2}on the edge. Applying a mathematical procedure to one of the two matrices, it is possible to translate, rotate and magnify the object in one image with respect to the other one. In the following, the above-mentioned mathematical procedure is applied to the M matrix, without loss of generality. The final result is a new matrix, M”, created from M, so that the two selected points will have the same matrix indices both in the new M” matrix and in the other matrix N:

_{1M’’}= i

_{1N}, i

_{2M’’}= i

_{2N}

_{1M’’}= j

_{1N}, j

_{2M’’}= j

_{2N}

_{1}points of the two matrices Δi and Δj are calculated as follows:

_{1M}− i

_{1N}

_{1M}− j

_{1N}

_{1}by α with respect to the other. The angle α is calculated as:

^{−1}(i

_{2M}/j

_{2M}) − tan

^{−1}(i

_{2N}/j

_{2N})

_{f}. is given by the ratio between these two distances. A number of elements have to be added, in order to magnify the less magnified image. The values of these added points are calculated using the nearest neighbor interpolation.

## 4. Conclusions

^{®}). As examples, we presented the developed methodology and the combined final reconstruction applied on elements of biological interest, i.e., marine diatom valves belonging to three different species.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) SEM image; (

**b**) Amplitude map obtained by means of DHM of an Arachnodiscous single valve. The P

_{1SEM}, P

_{2SEM}and P

_{1DHM}, P

_{2DHM}points (see main text for definition), useful for image alignment, are shown by blue and red crosses, respectively.

**Figure 2.**(

**a**) Transparent overlay of the SEM and DHM images after their centering. The pictures underline the different orientation (given by the angle α and sizing of the same valve in the two images; (

**b**)Transparent overlay of the images after rotation; (

**c**) magnification adjustements.

**Figure 3.**Final reconstruction by the SEM and DHM merging of the Arachnodiscus valve. In the inset, a zoomed view of the center of the diatom reconstruction is shown.

**Figure 4.**(

**a**) SEM image; (

**b**) Amplitude map obtained by means of DHM of the Cocconeis diatom. The P

_{1SEM}, P

_{2SEM}and P

_{1DHM}, P

_{2DHM}points (see main text for definition), useful for image alignment, are shown by blue and red crosses, respectively.

**Figure 5.**Final reconstruction by the SEM and DHM merging of the Cocconeis diatom. In the inset, a zoomed view of the region of the diatom reconstruction highlighted is shown.

**Figure 6.**Final reconstruction by AFM and SEM merging of single pores of a Coscinodiscus wailesii valve. In the insets, zoomed views of a particular part of the reconstruction are shown.

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**MDPI and ACS Style**

Ferrara, M.A.; De Tommasi, E.; Coppola, G.; De Stefano, L.; Rea, I.; Dardano, P.
Diatom Valve Three-Dimensional Representation: A New Imaging Method Based on Combined Microscopies. *Int. J. Mol. Sci.* **2016**, *17*, 1645.
https://doi.org/10.3390/ijms17101645

**AMA Style**

Ferrara MA, De Tommasi E, Coppola G, De Stefano L, Rea I, Dardano P.
Diatom Valve Three-Dimensional Representation: A New Imaging Method Based on Combined Microscopies. *International Journal of Molecular Sciences*. 2016; 17(10):1645.
https://doi.org/10.3390/ijms17101645

**Chicago/Turabian Style**

Ferrara, Maria Antonietta, Edoardo De Tommasi, Giuseppe Coppola, Luca De Stefano, Ilaria Rea, and Principia Dardano.
2016. "Diatom Valve Three-Dimensional Representation: A New Imaging Method Based on Combined Microscopies" *International Journal of Molecular Sciences* 17, no. 10: 1645.
https://doi.org/10.3390/ijms17101645