Demonstration of TSOPC in Biological Tissues
The salient features of TSOPC are well illustrated in the first experiment. We employed a photorefractive 45°-cut 0.075% Fe-doped Lithium Niobate (LiNbO3) crystal as the OPC light field generator or phase conjugate mirror (PCM); the recording-and-playback scheme  is detailed in the Method section. In this study, our target was a 0.46 mm thick chicken breast tissue section. Light at 532 nm, 3.5 mW power and 1/e2 beam size of 0.7 mm was transmitted through a standard negative USAF resolution target. The patterned light was then imaged onto the front face (face 1) of the tissue section using a 1:1 imaging relay lens. The forward scattered light traversed the tissue sample, exited from face 2, and arrived at the photorefractive crystal for holographic recording. The recording geometry is highlighted in . In the experiment, the separation between the crystal facet and the tissue section was 0.5 mm. The 7.8 mm 1/e2 diameter 6.5 mW reference beam employed during the recording process crossed the crystal at 1 mm distance from the crystal facet facing the tissue section. This implies a nominal maximum recording angle range of 66°. The hologram recording time was ~2 minutes for this experiment. Upon completion, the USAF resolution target was replaced with a compensation glass plate and an OPC light field was generated with a conjugate reference beam of 12 mW. This light field retraced the path of the original transmission and recreated an image of the USAF target on face 1 of the tissue . This image was then relayed onto a CCD camera (DMK 31BF03, The Imaging Source).
Schematics of TSOPC setup and scattering medium
Mathematically [see ], the interaction of incident light field
with a scattering medium can be expressed as 12
is the scattering matrix associated with the medium,
is the output light field and a2
= 0. The subscript denotes the terminal face 1 or 2 of the scattering medium. In this case, the light field impinging on the PCM is given by 21a1
. The OPC light field traveling back towards face 2 of the tissue section can be expressed as:
represents the reduction in angular range of the reconstructed wave due to the incomplete recording and playback of the transmitted wave. The reconstructed light field on face 1 of the tissue section can be written as:
Since the relationship between any two points on the medium's surface is symmetrical we get 21
In an ideal case, 1) the capture of the initial light transmission is complete; this leads to a reduction of Ā
to a unitary matrix, 2) medium is lossless and backscattering is absent; this leads to 1212†
= I by energy conservation, where 12†
is the complex conjugate of 12T
. The reconstructed light field expression can then be written as:
The extent to which an experimental realization approaches this ideal is verified in our experiment. shows the reconstructed USAF image through the 0.46 mm thick tissue section. For comparison, show USAF target imaging through 0.46 mm thick agarose and tissue section, respectively, using plane wave illumination. At 532 nm, the chicken breast tissue scattering coefficient was 38 mm−1 (quantified through interferometric measurement of ballistically propagating transmission through tissue) and the sum of the reduced scattering coefficient and the absorption coefficient was 0.45 mm−1 (quantified through transmission measurement). This implies that, on average, a photon is scattered 17 times in a 0.46 mm thick tissue sample, and 19% of the input light did not reach face 2 of the 0.46 mm thick tissue section. The high quality of the reconstructed image in demonstrates that the conjugated signal beam can indeed retrace its initial trajectory through the tissue to a good degree, in spite of these issues.
Demonstration of the TSOPC phenomenon through 0.46 mm thick chicken breast tissue section
TSOPC Experiments using Point Source Illumination
The next set of experiments studied the TSOPC phenomenon in a more quantitative fashion. In this case, we focused 0.65 mW signal beam to a 1.4 μm 1/e2 diameter spot via L3 (Olympus PLAN 10×) at the face 1 of the tissue section [see ].
TSOPC using point source illumination
Each experiment consisted of the following. The transmitted light through the tissue section was first holographically recorded in the photorefractive crystal for 30 sec with a reference beam power of 33 mW. Next, a conjugate reference beam (3.3 mW) was used to generate the OPC light field, which traveled back through the tissue section and reconstructed the original light spot at face 1 of the tissue section. We displaced the tissue sample laterally in incremental steps to a limit of 8 μm and acquired an image of the reconstructed spot for each displacement. Four targets were employed – a 0.23 mm thick clear agarose section (non-scattering control) and chicken breast tissue sections of thickness 0.23 mm, 0.46 mm and 0.69 mm. The experiment was repeated 8 times for each sample thickness. For the agarose section, the average return power through the sample was measured as 0.4 nW. This value was a function of the readout reference beam power and the crystal's recording efficiency. To eliminate contributions of these two experimental parameters from our analysis, we normalized our data with respect to our measurements from the agarose control.
We found that, under these experimental conditions, the strength of a recorded hologram decreased minimally over the experimental time frame of ~2 minutes for each TSOPC experiment (see Supplementary Fig. 1) and, as such, does not impact on our findings significantly. We also note that the efficiency of the TSOPC reconstruction is expected to drop as the biological samples change in time, but experimentally, we did not observe a significant change over the time in which each experiment was conducted.
illustrate the average radial light intensity distribution in the reconstructed spot for 0 μm, 2 μm, 4 μm, 6 μm and 8 μm displacements, respectively, of the 0.23 mm thick agarose sample (magenta) and the tissue sections of thickness 0.23 mm (black), 0.46 mm (red), and 0.69 mm (blue). Two observations are noteworthy. First, while a significant tissue section displacement leads to a mismatch between the scattering structures and the returning OPC light field, and results in no turbidity suppression, it can be observed from that this phenomenon is tolerant to small sample displacements, particularly for thinner samples. Second, illustrates that the width of the fully reconstructed spot appears surprisingly similar for all tissue thickness.
shows normalized peak intensity as a function of sample lateral displacement. Several observations are worth noting: 1) The reconstructed peak intensity falls as a sample is displaced. This is predictable, as displacements of the sample disrupt the light trajectory retracing condition and deteriorate the reconstruction. 2) The extent to which the reconstructed peak appeared to be reconstructed is remarkable. For the 0.69 mm thick tissue section, the reconstructed peak intensity difference between zero sample displacement (optimal reconstruction condition) and large sample displacement of 8 μm (mismatched sample and OPC light field) is more than 3 orders of magnitude. 3) The rate of reconstructed peak intensity drop due to sample lateral translation is a function of the sample thickness; for a 0.69 mm thick chicken tissue section, a displacement of ~0.7 μm results in peak intensity reduction by one order of magnitude. 4) Finally, the reconstruction appears surprisingly robust. With our thickest tissue section of 0.69 mm, the reconstructed peak intensity was still a respectable (17 ± 3) % of the agarose reconstructed peak intensity.
Strength of the reconstructed light field under OPC and non-OPC conditions
The dependence of specific reconstruction efficiency on tissue thickness can be seen from . We plotted the relative reconstructed peak intensity on the same scale for zero sample displacement. We can realistically expect the loss of scattering information from light being absorbed by the tissue and/or scattered away from the crystal to deteriorate the reconstruction. Simplistically, we can conjecture that the reconstructed peak height with no sample displacement will follow a Beer's Law-type dependency on tissue thickness for thin tissue sections. In other words, the reconstructed peak intensity Ipeak is proportional to exp(−αL), where α is the coefficient associated with the drop in reconstruction efficiency and L is the thickness of the tissue section. reveals that such a dependency does indeed hold well for the thin tissue sections (~0.46 mm or less), for which an experimental fit for α is (1.45 ± 0.05) mm−1. For thicker tissues, the drop-off in reconstruction efficiency appears to deviate from this trend. The exact behavior of the reconstruction efficiency is an important subject that deserves further in depth study. For comparison, we have added a line in that shows the unscattered light attenuation as a function of tissue depth; this line shows an expected signal drop associated with coherence based interference detection methods. We can see from that the rate of TSOPC efficiency drop occurs at a much slower rate, which clearly indicates that the TSOPC phenomenon is able to make good use of multiply scattered light components.
shows the change in normalized transmission collected through the objective as a function of sample lateral displacement. This parameter is different from the reconstructed peak intensity in that it tracks the total amount of light that is returned from the sample (and falls within the collection angle, 29°, of the objective) even if the reconstruction is imperfect. The data trace for the 0.69 mm thick section is particularly revealing. Comparing the normalized transmission between when TSOPC is present (zero sample displacement) and absent (~2.5 μm sample displacement), we can see that TSOPC pushes the total light transmission up by a factor of 3.8. This clearly indicates that TSOPC can be used to achieve enhanced light transmission through biological tissues.
plots the 1/e2 width of the reconstructed spot as a function of sample displacement. Under optimal reconstruction condition (zero sample displacement), the reconstructed spot is tight for all the sample thicknesses, as also shown in and . However, as the displacement increases, the 1/e2 spot size widens. The results in also indicate that the rate of 1/e2 width increase with sample displacement is a function of sample thickness or scattering extent. Further, we can see from the plots in as well as , the reconstructed light spot appeared to consist of two components – a sharp well-reconstructed spot and a more diffused spot. The more diffused spot grew in strength as the sample was displaced and likely consisted of light components that were weakly reconstructed. In comparison, the well-reconstructed spot dropped in intensity with sample displacement but did not appear to increase in width significantly.
Quality of the reconstructed light field under OPC and non-OPC conditions
More intriguingly, revealed that the 1/e2 width for all tissue thicknesses at zero tissue displacement is approximately the same (1.5 μm). This is in good agreement with the estimated 1/e2 spot size of 1.4 μm for perfect reconstruction. The insensitivity to tissue thickness and the good fit to the theoretically predicted width for ideal reconstruction suggest that there exists a phase conjugate component that can retrace the initial light trajectory optimally even if the phase conjugation process as a whole is necessarily imperfect due to experimental constraints.