4.1. Experimental Setup
The characterizations of the sensor are performed in the same fashion as for the lens-less setup [31
], by using the Creapyx motherboard that drives the holed retina, and a calibrated aerosol test bench (Constant output atomizer model 3076 by TSI) that provides a continuous flow of calibrated particles, which are commercially available monodisperse PSL beads in our case.
A photography of the characterization setup is given in Figure 14
a. The optical piece is sitting on the cloaker that properly aligns it with the holed retina below. As explained earlier, the downward illumination is provided by the illumination module (standard 0.5 inch lens tube, with a LD and aspheric lenses, see Appendix B
), and redirected horizontally toward the muzzle of the air channel using a 45° mirror.
In the photography we see that, despite the diaphragm, a large portion of stray light comes toward the optical piece, hitting some of its diopters. Then, we take a reference image, using the holed retina when no aerosol is injected in the channel. Such a reference is presented in Figure 14
b, and is automatically subtracted from future images. We notice that a portion of the second sub-retina is impacted by stray light (FS and BS ROIs), but not to a great extent.
Given the visible amount of stray light hitting the optical piece, and the reasonable amount that ends up on the retina, one might argue that the anti-stray-light designs were successful, at least for our given illumination setup.
We record bursts of 32 images, in global shutter (GS) mode, and we follow the standard deviation of the full image (with its reference subtracted). Then, an image is saved when its standard deviation reaches a given threshold. More information on the experimental setup, notably in terms of the sampled aerosol and the driving of the retina, is reported in reference [31
4.2. Experimental Images of Scattering Signatures
We were able to detect single PSL particles of 3 µm and 830 nm. Examples of representative signatures that can be experimentally recorded are given in Figure 15
a,b. The images obtained seams quite repeatable for a given aerosol, both in terms of brightness and patterns. A precise study on repeatability should be conducted in the future (in order to quantify the deviation), but this can already give us confidence that the signature is weakly impacted by particle position, due to the Fourier-domain imaging setup.
We observe three separated areas that correspond to the S-ROI on the first sub-retina (rows 76 to 150); the BS and FS-ROIs on the second sub-retina (rows 1 to 75). We notice that the positions of such ROIs are slightly translated compared to what was expected, due to the small alignment problems that will have to be addressed in the future. The white pixels correspond to pixels from the reference image that reached a certain threshold, that were removed from the image processing, in order to be less sensitive to Poissonian-type noises.
The scattering signatures of large spheres, such as the 3 µm PSL, exhibit a number of Mie’s oscillations, whereas the 830 nm PSL does not (at least within the evaluated FoV). This effect is predicted by the Lorenz–Mie theory (spheres with refractive index
]), and be can be found on the RT simulations for the associated PSL diameters (see, subfigures (c,d)).
Note that the images were normalized, but the same color axis was kept between (a,b) on the one hand and (c,d) on the other hand, in order to compare the relative brightness of scattering signatures obtained with different diameters.
4.3. Reconstruction of Scattering Signatures
The oscillations of 3 µm PSL signatures facilitate the interpretation of such a recorded signature. For didactic reasons, we are going to focus in particular on the specific image shown in Figure 15
a. We observe several vertical oscillations on the S-ROI, whereas those on the BS and FS ROIs are slanted by
, which was expected by design. Those oscillations follow what we call the iso-
, which are defined as the trajectories on the retina that correspond to the rays scattered with the same scattering angle
The procedure to reconstruct a signature is relatively simple: let us first consider one of the three ROI separately. First, every pixel in the ROI is normalized using the simulated intensity map calculated previously using a RT simulation (intensity map in Figure 11
a). Then, by using an angle map, also computed by RT (see, Figure 11
a), one can associate each pixel of the retina to a scattering angle. For a given scattering angle (with a tolerance of 1°), a mean value of the intensity carried by those associated pixels can be calculated which then results in a sub-scattering signature reconstructed within the sub-FoV of each ROIs. In this case, the ROIs are misaligned with respect to the retina, thus, we had to manually translate the angle map to best fit with the recorded image. Due to this effect, the BS ROI was cropped, resulting in a loss of FoV for very high angles. Still, the total FoV is relatively wide, at about 85°.
Before plotting those sub-signatures together, we had to perform a correction that consists in having a multiplicative factor for each sub-signature. This step is motivated by the fact that the relative brightness of the ROIs are not consistent to what was expected: this can be seen especially with the BS-ROI (see Figure 15
a) that is much brighter than expected (see Figure 15
c). Hopefully, this correction appears to be very repeatable between the different recorded images, and could be easily found through a calibration campaign. We believe that it could be attributed to misalignment errors of the apertures of the cloaker with respect to the subsystems’ pupils, which may create an uneven loss of photometry between the ROIs.
One notices that the sub-signatures are not perfectly overlapping: the edges of the individual curves correspond to the blind field and should not be over-trusted. Again, this overlapping mismatch will not overly affect results as it appears to be very repeatable, and thus easy to correct in post-process; for example, with a single calibration. To connect the curves, we make averages on the overlapping regions. The averaging weight varies linearly from 1 to 0, dropping at the edge of each curve. With this step, one can have a continuous merged curve (drawn in black), which is more representative of real scattering signatures.
We insist on the fact that the reconstruction step is particularly resource-efficient in terms of computing capabilities, especially when applying only matrix operations (which are optimized by MATLAB, our data processing tool), at least compared to the planar projection set-up (see, reference [31
]). This gives us confidence that procedure is compatible with low-energy portable applications.
In Figure 16
, we plot the merged scattering signatures alongside the theoretical signature of a 3 µm PSL sphere (refractive index
]) illuminated by a 637 nm wavelength beam, computed using the Lorenz–Mie theory.
Based on such a representative plot, we find that the reconstructed signature is surprisingly faithful to the theoretical one, especially with the position and frequency of the Mie’s oscillations in the plot (which were not corrected).
This gives us confidence that such an architecture of the sensor and reconstruction procedure is well suited for our application. However, to conclude on this point, we will have to conduct a proper statistical study, over a wide number of PSL diameters, with blind reconstructions. To do so, we will have to make our setup more robust. In the near future, the 3D printing of the cloaker will be optimized; then, the next step would be to integrate directly both the cloaker (with its optimized apertures) and the optical piece on-top the CMOS at wafer scale, in order to achieve optimal alignments.
Note that a study on a larger number of particles, and on a larger diameter range, could allow us to conclude on the detection limit in terms of particle size. We can already determine with which SNR (Signal to Noise Ratio) we have detected 3 µm and 830 nm PSL. The PSL of 3 µm were detected with an SNR of about 825, while the PSL of 830 nm (which scatter less intensely) were detected with an SNR of about 145 (these values were quite constant between images obtained from the same PSL diameter, meaning that the brightness and patterns of the recorded signatures are very repeatable).
Those values are quite high already, and thus we can realistically expect that we can measure smaller particle sizes using such a setup. In addition, the SNR should be further improved by optimizing the illumination system so that the amount of stray light is minimized.