To validate the depth resolving performance of our multi-angle holographic imaging platform over a large field of view of ~60 mm2, we conducted an experiment with a mixture of 5, 10 and 20 µm diameter polystyrene beads (Monosized microsphere size standards, Thermo Scientific) suspended in DI water. The micro-particle suspension liquid was dispensed on a 0.5 mm thick glass substrate and covered by a No.1 glass cover slip (~150 µm thick) as shown in . To quantify the accuracy of our axial localization results over the entire imaging area of the sensor, before being imaged, the samples were kept still for >10 minutes, allowing the suspended micro-particles to fully settle on the substrates. This ensured that the recovered height (i.e., the axial position) of the particles can be related to the well-controlled radii of the micro-particles, enabling cross validation of our results. During this settlement time period, holograms of the samples were periodically recorded using the vertical illumination to track the trajectories of individual particles. These trajectories were then analyzed to ensure that the displacement had decreased to a stable level (below the Brownian motion limit).
To record the digital holograms of the micro particles distributed over ~60 mm2 field-of-view and their lateral shifts as a function of the illumination angle, three optical fibers with a core diameter of D = 50 µm each were utilized to illuminate the sample placed on the bare surface of a CCD image sensor chip with a pixel size of 5.4 µm (KAF-8300, Kodak). The protective glass of the sensor chip has been removed to minimize the distance between the sample and the sensor surface and maximize signal-to-noise ratio of the lensfree holograms. The fibers are individually butt-coupled to three cyan light-emitting diodes (LEDs, LXHL-LE3C, Luxeon) and their tips are placed approximately 6 cm away from the sample to provide one vertical and two other tilted illuminations with (ϕ= 0°; θ = 45°) and (ϕ = 180°; θ = 45°) as illustrated in . The center wavelength (λ) of the LEDs is 505 nm and the FWHM spectral width is ~30 nm.
Note that this fiber with a core diameter of D
= 50 µm introduces partial spatial coherence before its exit aperture. However, this is not a requirement for the presented approach, since the distance between fiber-end and the object plane (L
~6 cm) is sufficiently large to create a coherence diameter (Dcoh L
) that is significantly wider than the micro-object diameter (<50λ for all objects reported in this manuscript) for recording of their holograms individually. We further validated this by using an LED that is directly butt-coupled to a pinhole (D
= 0.1 mm) to effectively record similar holograms. Therefore, the fiber length and the degree of spatial coherence that the light picks up within the fiber is not of crucial importance in this study as the spatial coherence at the sample plane is sufficiently large even for a completely spatially incoherent source that is filtered by a similar aperture size of 0.05–0.1 mm.
Lensfree height characterization results of these particles are summarized in . illustrate the raw lensfree holograms that are captured under each illumination angle over an imaging FOV of >1 cm2
. Smaller focus on the individual holographic signatures, digitally taken from ; and the reconstructed amplitude images (created by iterative holographic reconstruction [25
]) of these representative particle holograms are also shown under different illumination conditions. As expected, in these figures the raw holograms of the tilted illumination conditions show an elongated texture, parallel to the tilt direction. Based on digital processing of these multi-angle lensfree holograms as described in the previous section, we recovered the height distribution of the micro-particles from the substrate surface as illustrated in , where for convenience the relative height
of the substrate surface is assumed to be 0 µm (the physical size and the height of the particles are coded by each spot size and the colormap, respectively). also reports the height histogram calculated from , which clearly resolves 3 different particle types from each other based on their relative heights (i.e., radii). For 20 µm and 10 µm particles our results estimate the mean height of these particles from the substrate surface as 9.83 µm and 5.06 µm, with a standard deviation of 0.32 µm and 0.37 µm, respectively, whereas for the smaller particle (5 µm diameter), the mean height from the surface was estimated to be 2.47 µm with a standard deviation of 0.97 µm. These results are in close agreement with the height values that one would expect from the radii of these particles, i.e., 10 µm, 5 µm and 2.5 µm, respectively. One could attribute the differences between our characterization results (9.83, 5.06 and 2.47 µm) and the known radii of the particles (10, 5 and 2.5 µm) to the unavoidable surface curvature of the substrate over the large imaging field of view (~60 mm2
) and to the standard deviation of the particle radii, which is reported by the manufacturer (Thermo Scientific) to be ± 1% for each particle type. The relatively worse performance (with a standard deviation of 0.97 µm) of the smaller sized particle (5 µm) is related to a reduced hologram signal-to-noise ratio (SNR) (refer to the individual hologram signatures and the SNR values that are provided in ). This is also a topic that we will also address in the Discussion Section.
We further validated our multi-angle lensless holography approach by imaging a two-layered micro-channel containing red blood cells (RBCs) (see ). Whole blood samples were mixed with the anticoagulant EDTA at a ratio of 2 mg of EDTA per ml of blood (EDTA tubes, BD). The blood was kept still for ~20 minutes until the RBCs settled. After sedimentation, RBCs were extracted from the bottom of the sediment and diluted with cell culture medium (RPMI 1640, Invitrogen) to a concentration of ~15,000 cells/µL. A small number of polystyrene microbeads with a diameter of 20 µm were then added to the suspension (~40 beads/µL), serving as mechanical spacers in the multi-layer structure shown in .
Fig. 4 Lensless multi-angle characterization of RBCs located within two-layered micro-channels. (a)–(e) Lensfree holograms are captured with five different illumination angles. The magenta dashed rectangles in (a)–(e) are the regions corresponding (more ...)
The holograms of the cells were recorded by placing the samples directly on the image sensor chip as shown in . A CMOS image sensor with a pixel size of 2.2 µm and an active area of 24.4 mm2 (MT9P031, Aptina) was used for imaging the RBC suspension sample. After settlement for >10 minutes, the samples were illuminated from different angles sequentially and the lensfree holograms with different illumination angles were recorded separately as illustrated in . Alternatively, this image acquisition process could also be done in parallel by turning all the multi-angle sources on at the same time rather than sequentially. However the overall density of cells that can be imaged with parallel illumination is lower than sequential imaging, which is further quantified in the Discussion Section (–).
Fig. 7 The shadow overlap probability plotted as a function of both the shadow density (i.e., the throughput) and the multi-angle hologram recording method (parallel vs. sequential). The diameter of the holographic shadows for all the angles and all the vertical (more ...)
Fig. 8 Quantified performance comparison of the multi-angle lensfree holographic cell characterization platform as a function of the shadow density and the number of vertical layers on the sensor chip. (a) The true positive rate, (b) the false positive rate, (more ...)
To generate these lensfree cell holograms with different illumination angles, five optical fibers with a core diameter of 50 µm each were mounted with their tips approximately 6 cm away from the samples. Except the vertical illumination case, the illumination angles were 0°, 90°, 180° and 270° azimuthally and the polar angles were all 45° from the normal direction of the imaging plane, as shown in . The fibers are connected to a Xenon lamp (6258, Newport Corp.) filtered by a monochromator (Cornerstone T260, Newport Corp.), where the central wavelength of the monochromator was set to ~500 nm and the FWHM spectral width was ~10 nm.
By processing all these raw holograms acquired at different illumination angles as discussed in the previous section, we recovered the height distribution of the RBCs located at both of the vertical channels as illustrated in . also shows the histogram of the cell heights over the entire field of view, which exhibits a double peaked behavior, as expected, resolving the 2 vertical micro-channels. Because the cells were permitted to sediment on the surface of each micro-layer, we obtained a very narrow height distribution at each channel as a result of our fine depth resolving power. For the upper micro-channel, the standard deviation of the cell height (2.4 µm) is larger than the lower channel one (1.5 µm), which is due to the surface curvature of the spacer glass. In other words, because the spacer glass between the vertical channels is much thinner than the substrate of the bottom layer, it exhibits a significantly larger surface curvature over the imaging field of view which increased the height variations as observed in the upper channel cell height histogram (). Meanwhile, for the lower channel, the substrate was chosen to be >0.5 mm thick and therefore the cell height histogram showed a much better accuracy with a standard deviation of 1.5 µm in relative height of the cells.
Once the axial and lateral locations of the cells are accurately determined within this multi-layered structure (), we can also characterize other properties of the cells in 3D such as the thickness or the volume of each cell. report the thickness and the volume maps, respectively, of each one of the red blood cells that are characterized in . In these figures the colormaps code the measured thickness (µm) and volume (fL) of each cell. also plot the thickness and volume histograms of the red blood cells at each vertical channel, which predict a mean RBC thickness of 1.74 µm and 1.68 µm for the bottom and top channels, respectively; and a mean RBC volume of 95.7 fL and 91.1 fL for the bottom and top channels, respectively. These results are in good agreement with standard values of healthy red blood cells, further validating our results [33
]. The computation time required to generate the presented results in and is ~30 minutes on a 2.2 GHz Opteron CPU. However, this computation time can be significantly reduced by further optimizing the code and performing the tasks on a graphic processing unit (GPU) since most computations in this technique can be highly parallelized [26
Fig. 5 Thickness and volume of each cell within the two-layered micro-channels are calculated over a field of view of >15 mm2. (a) The 3D distribution of the RBCs in both of the vertical channels is illustrated with their cell thickness value coded by (more ...)
The key to estimate each cell’s thickness and volume properties individually over the entire imaging FOV is the iterative twin image elimination algorithm that permits digital reconstruction of the phase and amplitude images
of each cell from its lensfree hologram [25
]. To relate the recovered optical phase of each cell to a physical thickness, we assumed that red blood cells are phase only objects with an average refractive index of 1.40 in a solution with refractive index 1.33 [34
]. Under these assumptions the thickness of the RBC is directly proportional to its phase recovered from the iterative twin-image elimination algorithm. The areas of the cells were estimated by a simple global thresholding of the recovered phase images, and the volume of each cell was estimated by the product of its thickness and area. These imaging results are quite important as they enable lensfree on-chip characterization of a 3D distribution of cells over a much larger volume than a regular microscope could enable (note that the lateral scale bars and grid size in , are all 1 mm).
For the experiments reported in –, the cell density at each layer was ~15,000 cells/µL. To achieve the reported depth accuracy in 3D for such a high concentration of cells, we made use of two key factors: (1) we used 5 illumination angles (see ) which reduced the likelihood of the events where all the shadows corresponding to a single cell were overlapping with other cells for all the illumination angles. And (2) the image reconstruction process enabled resolving densely packed cell shadows from each other. A good example of the success of this digital reconstruction process is illustrated in , where 3 red blood cells from the top micro-channel overlap at the sensor plane with the holograms of 3 different red blood cells located at the bottom micro-channel (refer to the holograms within the white dashed rectangle of which correspond to these 6 RBCs at both layers). illustrate the reconstructed amplitude images at the bottom and top channel surfaces, respectively. also illustrates the digital reconstruction results at an intermediate plane between the bottom and the top micro-channels. To independently confirm our reconstruction results, two microscope images of the bottom and top micro-channels (corresponding to the same FOV as in ) are also provided in , respectively. Here we would like to also emphasize that the lensfree holographic image and its reconstructions that are reported in are digitally taken from a much larger field of view shown in , which illustrates ~2 orders of magnitude increased FOV of our approach when compared to conventional optical microscope images ().
Fig. 6 Demonstration of overlapping RBCs from two vertical micro-channels being digitally resolved by the holographic reconstruction process. (a) The raw lensfree hologram of the digitally zoomed region specified with the yellow rectangle in is illustrated. (more ...)