## 2 Materials and Methods
### Digital Holographic Microscopy  
DHM is a tool that has been gaining importance in different areas in the last three decades [28; 29] due to its ability to refocus different planes with a single hologram to its high precision in the measurement of up to 4 nm in the axial direction [30] due to its interferometric nature and in the lateral direction determined by the Rayleigh diffraction limit such as any optical microscope, DHM is an ideal tool for obtaining nanometric measurements in the axial direction. This method is based on acquiring a hologram created with the interference of a light beam that is reflected or passes through an object captured with a microscope objective and with a reference beam [31]. The complex amplitude of the object is recovered when the hologram is re-illuminated by the reference light beam. In this way, we can have access to phase and magnitude images that allow us to make real physical measurements of the specimen. The experimental optical arrangement used in this study was a Gates interferometer, as shown in Figure 3, which has previously been used in investigations by the authors [30; 32; 33]. A 5 mW laser diode with a wavelength (\(\lambda\)) of 640 nm was used as the illumination source. First, the beam of light is expanded and collimated by the lens (L). Subsequently, this beam is passed simultaneously through the sample and the substrate that does not contain deposited material (reference wave). In this manner, the object under test information is sent to the Gates interferometer through one window while the reference beam passes through the other. At the exit of the interferometer, the hologram was captured by a 10\(\times\) microscope objective with a long working distance and N.A. of 0.28. On the other hand, the camera used to capture the micro-holograms was a 1024 \(\times\) 1328-pixel monochrome StingrayTM with a pixel size of 6.4 \(\upmu\)m \(\times\) 6.4 \(\upmu\)m with an 8-bit depth. For more details about how the Gates interferometer works, consult the following references [32; 33]. Figure 2: Nanoparticles collecting setup. In Figure 4a it is possible to observe a hologram captured by the system, while in Figure 4b a photograph of the sample is presented under white light illumination. In the lower part of the photograph is the nanoparticles' deposition area. A dragonfly wing is shown in the upper part of the photograph, placed as a focus reference, clarifying that insect was found dead in the university facilities. The distance from the object to the camera plane was 38 mm, and the system configuration was devised to obtain off-axis holograms. As we can see in Figure 4a, the zoom area modulating straight vertical lines are present. In addition, it is important to mention that the maximum object dimensions that could be analyzed by the proposed equipment arrangement will depend on two factors, being the size of the beam splitter cube and the camera sensor. In other words, the larger the sensor and the beam splitter cube, the larger it would be the size of the object capable of being analyzed [33]. The Figure 4a shows an experimental digital hologram obtained by the optical setup proposed of the Figure 3. In order to obtain a digital hologram, it is essential to count with both, the object wave (red dash square) and the reference one (black dash square) (Figure 3). In addition, the illumination source must be coherent, being in this case a laser light. In contrast, to obtain a photograph, the illumination source is not required to be coherent, in this case the Figure 4b was illuminated with a simple LED and the reference wave was blocked. The Figure 4 is presented with aims of illustration. The intensity \(I(x,y)\) registered by the camera, is the interference distribution between the object wave \(O(x,y)\) and the reference wave \(R(x,y)\) that obeys the following expression:  
\[ \begin{array}{ll}I(x,y)&=|O(x,y)\,+\,R(x,y)|^{2}\\ &=O(x,y)^{2}+R(x,y)^{2}+R(x,y)O(x,y)^{*}+R(x,y)^{*}O(x,y)\end{array}  \tag{1}\]  
Figure 4: PLA nanoparticles deposited on a glass substrate.