Holographic Imaging Model.
The readout of the signal corresponding to the biological approach A is based upon imaging E.coli on a single cell level. This is absolutely necessary since only then our algorithms will be capable of computing and detecting a change in the motility or tumbling frequency. Early experiments using scientific microscopes at our department showed that it is possible to image E.coli in a brightfield setup at a magnification of roughly 10x. However, as also described in the Hardware section, we first wanted to implement a simple setup that doesn’t involve lenses. Therefore at the very beginning of our project, we built our own lensless setup. After several improvements of our setup did not lead to the expected result, we decided to model our setup with the help of HoloPy - a python based tool for working with digital holograms and light scattering. HoloPy started as a project in the Manoharan Lab at Harvard University and the code can be found here.
With the help of Holopy we simulated whether our idea of the lensless setup would be feasible, i.e. would provide enough resolution to clearly resolve E.coli on a single-cell level and allows us to analyse their tumbling frequency. As described in the Hardware section our idea would be to use a setup as illustrated in figure below.
Since the incoherent illumination source is placed far away from the sample (especially when compared to the wavelength of the incident light), the approximation of having a plane wave illumination holds in such a setup [REF 2]. Therefore, this setting perfectly coincides with the functionality of HoloPy which performs a scattering calculation of an incoming plane wave with the specified sample and then displays the resulting hologram. This hologram is basically the interference pattern which was created through the fact that a part of the incoming wave (R) was scattered by our objects (O). Therefore at the image plane we effectively get:
$|R+O|^2 = |R^2|+|O^2|+R^*O+ RO^*$
The major limitation in this setting is the physical pixel size of our sensor as the magnification factor is 1 due to the sample being placed very close to the imaging chip. (For more details visit our Hardware section).
In the figure below, the results of different scattering calculations, performed in HoloPy are shown. For all of the scattering calculations we assumed to have a monochromatic blue light source (wavelength 405 nm) as well as a sensor pixel size of 1.2 um. The objects of interest were polystyrene beads and E.coli. We compared those two as they have comparable sizes. Nevertheless it should be easier to see the beads due to the higher contrast. In terms of refractive indices, we used a refractive index of 1.395 for E.coli, 1.59 for the beads, 1.3 for water and 1.338 for LB.
These modelling results show that a magnification of 10x drastically enhances the contrast and visibility of both the beads and the bacteria. The reason therein lies that when having a magnifying unit below the sample, one can choose the focus plane to be very close to the sample (e.g. 10um) through adjusting the objective lens. However, when using a lensless setup without this magnifying unit, one has to assume a bigger spacing between the sample and the sensor. When assuming this distance to be approximately 1mm, as shown in the lower row, it is almost impossible to see E.coli even in the simulation. This is due to the bacteria having very little contrast and multiple interferences due to the long path between the sample and the sensor. Unfortunately, the HoloPy simulation only provides the Signal Intensity in arbitrary units and therefore it is impossible to draw a final conclusion as one does not know how sensitive a real imaging chip is.
These theoretical results were in line with our experimental data and showed that a lensless setup would not be applicable with commercial sensors. Thus, we decided to primarily focus on the brightfield imaging. There was also no room for improvement in the pixel size of the sensor as our own with a pixel size of only 1.2um was already one of the smallest available. This decision was also in line with the literature available, as [REF1] and [REF3] were also using an additional magnification to successfully resolve E.coli.
- Wang, Anna, Rees F. Garmann, and Vinothan N. Manoharan. “Tracking E. Coli Runs and Tumbles with Scattering Solutions and Digital Holographic Microscopy.” Optics Express 24, no. 21 (October 17, 2016): 23719–25. doi:10.1364/OE.24.023719.
- Göröcs, Z., Ozcan, A., & Member, S. (2013). On-Chip Biomedical Imaging, 6, 29–46.
- Molaei, M., & Sheng, J. (2014). Imaging bacterial 3D motion using digital in-line holographic microscopy and correlation-based de-noising algorithm. Optics Express, 22(26), 32119. https://doi.org/10.1364/OE.22.032119