1. Introduction

Quantitative phase imaging (QPI) is a wide-field, label-free imaging modality that uses differences in optical path length to quantify cellular and sub-cellular structures with nanometer scale sensitivity [1]. Unlike other optical imaging methods used to visualize tissue structures with sub-cellar resolution (e.g., confocal microscopy [2], multiphoton imaging [3] and fluorescence microscopy [4]), QPI does not require labels, stains, or complex systems such as high-power lasers. Further, QPI yields unique quantitative biological information related to dry mass which can be used to assess cellular/tissue structure and dynamic activity to study fundamental biological processes, as well as diseases [1,5,6]. However, QPI requires a transmission-based system which sets important limitations on the thickness and transparency of the samples that can be analyzed with this method. The restriction to a transmissive geometry and thin samples has prevented the use of QPI in many medical/clinical applications, including endoscopic applications. Indeed, achieving quantitative phase contrast through a compact, flexible fiber-based system is highly desirable and could be transformative for many medical applications given QPI’s access to cellular and subcellular structures without labels or dyes.

To overcome the aforementioned limitations of QPI, we recently introduced a technique called quantitative oblique back-illumination microscopy (qOBM), which yields tomographic quantitative phase information of thick scattering samples with epi-illumination [5–8]. In this work, we develop a robust optimization method for a flexible fiber-optic-based qOBM system that can be applied as a handheld device or micro-endoscope for in-vivo imaging. The approach enables in silico optimization of the phase signal-to-noise-ratio (SNR) over a wide parameter space, including illumination fiber position (axial, lateral and tilt), illumination fiber numerical aperture (NA), and illumination wavelength. Sample specific scattering properties are also taken into account. Results show that a proper combination of these parameters is necessary for optimal imaging conditions, and that a single probe can be optimal for multiple tissue types. Simulations are verified experimentally using tissue-mimicking phantoms. We also correct for additional noise terms introduced by the fiber system to achieve a phase sensitivity of <20 nm with a single qOBM acquisition and a lower limit of ∼ 3nm using multiple averaged frames. The imaging capabilities of our system are further validated using fixed rat brain tissues from a 9L gliosarcoma tumor model [9–11] and fresh human brain tumor samples obtained directly from neurosurgery. Data show that our fiber-based qOBM system indeed recovers histological cellular information in excellent agreement with our free-space qOBM system [5–8] (without stains or labels) and with hematoxylin and eosin (H&E)-stained tissue sections (after tissue processing). The system’s ability to deliver quantitative phase contrast through a flexible fiber-based probe can be transformative for many biomedical applications, including micro-endoscopy, surgical guidance, and more. Further, the in silico optimization approach developed here—which would be extremely cumbersome to perform experimentally—can be widely applied for facile optimizations of other OBM/qOBM configurations in arbitrary environments.

2. Imaging setup and operation

2.1 Experimental apparatus

A schematic of our experimental setup is shown in Fig. 1(a). Our imaging system comprises a probe, a flexible fiber bundle, and a table-top camera recording setup. On the distal fiber end of the system, the probe is made of a micro-GRIN objective (GRINTECH, GT-MO-080-032-ACR-VISNIR-08-00), surrounded by four MMFs for epi-illumination (Thorlabs, FP1000ERT), all held in a fabricated aluminum metal holder. The GRIN lens has a ∼0.7 NA, with ∼2.2X magnification and an 80µm working distance in water [12]. In front of the GRIN lens, we attach a 50µm transparent polyester film to bring the focus of the GRIN lens closer to the surface of the tissue while the probe is in contact with the sample. Following fabrication protocols of Ref. [13], the GRIN lens is optically glued to a flexible fiber bundle comprising 30,000 core elements (Fujikura, FIGH-30-850N). The proximal end of the fiber bundle is then connected to an imaging setup, made of a 20X objective (Olympus, RMS20X), a 150mm achromatic doublet lens (Thorlabs, AC254-150-A), and an sCMOS camera (PCO, pco.edge 4.2 LT). For illumination, four multimode fibers (MMFs) are connected to 720nm LEDs (Luxeon Star, SinkPAD-II) through a pair of coupling lenses (Thorlabs, ACL2520U-A). The four LEDs are individually controlled by LabView and triggered sequentially in sync with the camera acquisition. Each MMF delivers ∼30mW of power on the sample, which is well within safe limits according to the IEC 62471 safety standard. As shown in Fig. 1(a), the four illuminating fibers are arranged 90 degrees apart in azimuthal angle around the GRIN lens. Captured images are then processed in real-time to obtain quantitative phase (data processing details are given in the next section).

 

Fig. 1. Experimental setup and imaging mechanism of fiber-based qOBM system. (a) The setup comprises of an optimized probe, a flexible fiber bundle, and a table-top camera recording setup. Front of the probe is shown on the bottom right inset, with a GRIN lens surrounded by four MMFs arranged at 90 degrees from each other. Each MMF is connect to an LED. (b) Epi-illumination, used for qOBM, where multiply scattered photons within a thick sample (brain) form a banana-shaped path from the source (MMF) to the detector (GRIN lens) and effectively produce a virtual, oblique light source at the focal plane. ${D_L}$ and ${D_A}$ are the lateral and axial separations, respectively, between MMF and GRIN lens. $\theta $ is the fiber tilting illumination angle. The bottom-right inset shows a simulated photon illumination in the spatial-frequency (k_x, k_y) domain. (c) 2D optical phase transfer function of the qOBM system. The inset shows the profile along the central dashed line, where the slope, $m,$ near the center of the transfer function, scales with the phase sensitivity of a particular probe design.

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2.2 Image processing

To retrieve quantitative phase information with qOBM, four raw intensity images are captured, one from each LED. From the two pairs of opposed illuminations, two orthogonal differential phase contrast (DPC) images are computed via [14–20]

Figure 2(a) illustrates the fiber-based qOBM image processing algorithm, which has an additional step from the description above. To illustrate the effects of each processing step (Fig. 2(b)–2(e)), we present images of a phantom consisting of 10µm polystyrene microspheres (Polysciences, Polybead 17136-5) immersed in water atop a glass slide, with a piece of paper placed underneath to serve as the scattering medium for oblique back-illumination. As illustrated in Fig. 2(b), the measured raw intensity images contain a strong honeycomb pattern—a consequence of light traveling through the fiber cores but not through the cladding, which obscures the structures of interest. Numerous algorithms have been developed to suppress/remove this pattern [24]: here we choose an efficient low-pass Fourier filtering approach to remove the high-frequency honeycomb pattern while passing low-frequency components corresponding to the imaged scene. Specifically, a low-pass radial Butterworth (9 pole) filter is applied with a cut-off frequency of ∼500mm^-1, approximately corresponding to the inverse of fiber core spacing projected to the focal plane (∼2µm). An example of a filtered intensity image of the beads (one of four such images) is shown in Fig. 2(c), which shows that the fiber-bundle honeycomb pattern has been effectively suppressed.

 

Fig. 2. Quantitative phase retrieval in qOBM. (a) Flow chart to process four raw intensity images, into two DPC images, and finally into one qOBM image representing the quantitative phase. First, low-pass filtering is applied to the intensity images to remove the honeycomb pattern from the fiber bundle. Then, DPC images are deconvolved with the optical phase transfer function and averaged to recover the full quantitative phase. (b) Raw intensity of 10µm beads in water atop a glass slide, under one LED source illumination (from the left). Beads are illuminated through oblique back-scattered light from a piece of paper under the sample. (c) Low-pass filtered intensity image. (d) DPC image obtained from opposite horizontal illuminations. (e) qOBM image showing quantitative phase. Bottom-right insets of (b)-(e) show zoomed-in areas, marked by the dashed red squares in the main plots.

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Next, Fig. 2(d) shows one of two DPC images obtained by subtracting two intensity images from opposed LEDs and normalizing by their sum, following Eq. (1). As mentioned earlier, the subtraction and normalization processes remove out-of-focus content and absorption-related effects, thus enhancing the phase contrast. Lastly, because each DPC image only contains phase gradient along one direction, we deconvolve two orthogonal DPC images (DPC 1 and DPC 2 as in Fig. 2(a)) and average the retrieved results to recover the full quantitative phase. Figure 2(e) shows the final quantitative phase image of the phantom. Note that the lateral spatial resolution for our fiber-based qOBM system is dictated by the fiber core spacing projected onto the focal plane (4.5µm spacing/2.2 magnification= ∼2µm) [25], instead of the NA of the GRIN lens (∼0.7). The axial resolution is 6µm in air, experimentally assessed following a similar approach to Ref. [12] using 2µm beads. Also, note that near the edge of the field-of-view (FoV, 300µm), there is a noticeable deterioration of image clarity due to field-curvature from the GRIN lens. This effect is noticeable in flat sample (e.g., beads on a microscope slide) but it is imperceptible in thick samples, such as biological tissues.

3. Results and discussion

3.1 Probe design optimization framework

To optimize the probe performance, we consider several degrees of freedom in our design, including the illumination wavelength, lateral separation distance (${D_L}$) and axial separation distance (${D_A}$) between MMF and the GRIN lens (see Fig. 1(b)), MMF illuminating angle, and MMF NA. Experimental optimization can be extremely cumbersome to perform over this wide parameter space, and as we show below, can easily miss optimal conditions. Thus, here we use Monte Carlo simulations to model the effects of the system design on the final qOBM phase image. Multiple tissue types are also modeled.

To analyze the impact of these parameters on the probe performance, we take into account both phase sensitivity and photon detection efficiency to estimate the SNR of the phase measurement. Phase sensitivity in our measurement is proportional to the central slope m of the optical phase transfer function (see inset of Fig. 1(c)). One may also choose to use the total energy (area under the curve of the absolute value of the transfer function) or the maximum value. All these metrics yield similar results and can be used as a surrogate for the phase sensitivity of a particular configuration Thus, the signal produced by a given configuration is proportional to $mN$, where N is the number of photons collected at the detector using a consistent set of initially launched photons for all numerical simulations (∼1 billion). Then, the noise level, corresponding to the Poisson noise, is given by $\sqrt N $. Therefore, the phase SNR can be estimated by $SNR\,\propto\,m \times \frac{N}{{\sqrt N }} = m\sqrt N $.

3.2 Wavelength-dependent optimization factors

We first consider the impact of illuminating wavelengths. Figure 3(a) shows the calculated SNR values as a function of wavelength for brain white-matter (similar results are obtained for other tissues including grey matter and are thus not shown). For these simulations we use a lateral and axial separations of ${D_L}$ = 2.5mm and ${D_A}$ = 4mm, respectively, between the GRIN lens and illuminating MMFs. As expected, the collected photon-count (upper-left inset of Fig. 3(a)) falls sharply at wavelengths below 600nm due to hemoglobin absorptions, and remains largely unchanged over longer wavelengths. Interestingly, this behavior is reversed for the phase sensitivity (slope $ m$ of the transfer function). As shown in the bottom-right inset of Fig. 3(a), the slope m is much larger at shorter wavelength, and falls rapidly around 600 nm. This behavior results from the fact that under large absorption (under 600nm), photons reaching the imaging focal plane have traveled a shorter path on average (scattered fewer times), and thus possess a larger oblique angle compared to photons in less absorptive media (above 600nm, under otherwise identical conditions). At longer wavelengths, however, the scattering coefficient decreases monotonically with respect to wavelength, resulting in a slight increase in the slope m. A lower scattering coefficient produces less diffused light, which increases the average oblique angle of photons at the focal plane, and hence increases phase sensitivity. Thus, after a local SNR peak at 600nm, the SNR continues to increase with wavelength.

 

Fig. 3. Wavelength-dependent optimization of SNR in probe design by Monte Carlo simulations. (a) SNR vs. illumination wavelength (simulated in white matter). Upper-left inset (red curve): logarithm of photon-counts ($N$) vs. wavelength. Bottom-right inset (blue curve): central slope m of optical phase transfer function vs. wavelength. (b) System SNR obtained by multiplying SNR in (a) with the square root of QE of our camera. Bottom inset (green curve): QE vs. wavelength (data from vendor).

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Another wavelength-dependent factor that affects the SNR is the wavelength-dependent photon detection efficiency. The most influential factor in our setup is the quantum efficiency (QE) of the camera (pco.edge 4.2 LT, inset curve in Fig. 3(b)). In Fig. 3(b), we plot the overall system SNR, obtained by multiplying the sample-specific SNR curve in Fig. 3(a) by the system-specific factor √QE. Note that the detected photon-count N scales with QE, thus the SNR scales with √QE. As a result, when the wavelength increases from 600nm to 1000nm, the falling QE lowers the overall system SNR, and leaves a relatively high-SNR region from ∼600nm-950nm with a maximum around 800nm. Our operating wavelength is at 720nm, which resides well within the high-SNR region.

3.3 Geometrical optimization factors

Next, we investigate probe geometrical factors that affect SNR, including lateral and axial separation distances (${D_L}$ and ${D_A}$, respectively, as in Fig. 1(b)) between the illuminating MMF and the GRIN lens. We also consider the MMF illumination angle and NA. Simulations are performed using optical properties of brain tissues (white and grey matter), breast tissue, and epidermis [23,26]. Due to physical size constraints of the probe (GRIN lens metal housing of 1.4mm in diameter and MMF bare fiber of 1mm in diameter) and the fact that GRIN lens works in contact mode, we simulate conditions with ${D_L}$ $\in$ [1.5mm - 5mm] and ${D_A}$ $\in$ [0mm - 6mm]. Fiber illumination angles of 0 to 90 degrees and NAs of 0 to 1 are considered.

We begin with an analysis of SNR as a function of ${D_L}$ and ${D_A}$ using a constant 0.5 NA fiber without tilting the illumination MMF angle. SNR results are plotted in Fig. 4 for four different tissue types. Points denoted by ①, ②, and ③ indicate geometries that are experimentally validated in Section 3.4 using scattering phantoms that mimic brain white and grey matter. Insets plot the detected photon-count $ N$ (in logarithm scale) and central slope m of the optical transfer function.

 

Fig. 4. SNRs simulated over the lateral separation distance ${D_L}$ and axial separation distance ${D_A}$ between GRIN lens and MMF. SNRs of (a) white matter, (b) grey matter, (c) epidermis, and (d) breast tissue. The insets show photon-count log(N) and central slope m variation over ${D_L}$ and ${D_A}$. Red circled numbers indicate three different geometries we investigated experimentally. All SNR values are normalized to geometry② value in grey matter.

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As shown in the insets of Fig. 4, detected photon-counts N are higher in the low-${D_L}$/high-${D_A}$ regions. This is because (1) with a lower ${D_L}$, the MMF (light source) and GRIN lens (detector) are closer to each other and more photons are thus detected; and (2) with a higher ${D_A}$, more photons from the MMF will be illuminating regions closer to the detected focal plane area. Meanwhile, the phase sensitivity assessed via slope m (Fig. 4 insets) shows a significantly different behavior with a set of maxima near the edges of the high photon-count regions and with decreasing values elsewhere. This behavior can be explained as follows: when the MMF light source is far from the GRIN lens (low photon-count region), detected photons will have a more randomized angular distribution, thus lowering the average angle of detected photons and the slope m, which indicates a lower phase sensitivity. On the other hand, when the source is too close to the detector (high photon-count region), photons will not experience enough scattering to significantly alter their original forward propagation direction. Therefore, there is an optimal region of operation where (1) sufficient photons are collected and (2) incident light has had sufficient opportunity to scatter such that photons change trajectory and illuminate the focal plane obliquely.

It is important to highlight that all four tissue types simulated here (white matter, grey matter, epidermis, breast tissue) form an optimal peninsula-shaped high-SNR region with slightly different shapes and optimal regions. However, optimal regions for these tissues do show substantial overlap. This indicates that a single probe geometry can be produced with fairly optimal conditions for a wide variety of biological specimens. However, given that optimal regions can be narrow and not necessarily in intuitive configurations, this type of analysis is warranted when optimizing probes for use in tissues with different optical properties.

We now consider the SNR dependence with MMF illumination angle and NA, with varying separation distances ${D_A}$ and ${D_L}$. Note that, in practice, manipulating the fiber angle in the probe design may be more difficult than changing the axial and lateral separation distances. Keeping the fiber angle at zero degrees (parallel to GRIN lens) provides the simplest geometrical configuration, with the least chance of breaking a fiber. If fiber polishing is used to alter the initial illumination angle (as in Ref. [27]), the available angular range is quite limited (∼0 to 15 degrees) due to total internal reflections. Similarly, there are few options to fine tune the fiber NA, with 0.1, 0.3 and 0.5 NAs being the most common commercially available options. Nevertheless, it is still instructive to show how these factors influence the SNR. Given the large parameter space, we only show simulated imaging conditions in grey matter, but the same approach can be readily implemented for other tissue types (indeed white matter, epidermis and breast tissues show similar behavior).

The first row of Fig. 5 (with ${D_A}$=0) shows that SNR has little to no dependence with the fiber illumination angle or NA. However, as ${D_A}$>0, both illumination angle and fiber NA have a significant influence over the SNR. The second and third rows of Fig. 5 show two examples with ${D_A}\; $= 4 mm and 6mm, respectively. The SNR, as a function of fiber NA and lateral separation (second column in Fig. 5), show peninsula-shaped high-value regions, similar to the axial and lateral separation plot in Fig. 4. This indicates that changing NA has a similar effect on SNR as changing the axial separation. The SNR dependence with fiber illumination angle, however, is more complex (first column in Fig. 5). Figures 5(c) and 5(e) show that as the angle increases, the SNR goes from positive to negative, reaching zero at around ∼30-60 degrees (teal color region). After reaching its most negative value (dark blue region) the SNR approaches zero again as the angle increases further. This behavior is a result of two factors: (1) From 0-30 degrees the slope m drops from its highest value into a relative uniform-value region, due to the loss of overall illumination obliquity. After the illumination passes ∼30-60 degrees, however, the net angular distribution of the illuminating light at the imaging focal plane appears to come from the opposite direction, resulting in a negative slope m of the transfer function (hence the negative SNR). After reaching a minimum slope (which corresponds to high sensitivity but with an opposite shear direction in the DPC image), the slope begins to approach zero again (low sensitivity) resulting from a loss of light obliquity of light at the focal plane due to more scattering. (2) The second factor affecting SNR is the detected photon count (shown in Fig. 5(c) and 5(e) insets as log($N$)). At illumination angles below ∼60 degrees, detected photon counts are relatively high, but beyond this region counts decrease sharply due to the overly large tilting angle preventing adequate collection of photons within the acceptance angels (NA) of the GRIN lens.

 

Fig. 5. SNRs simulated over initial fiber illumination angle or fiber NA, and over lateral separation. (a),(c),(e): SNR as a function of lateral separation ${D_L}$ and illumination angle, at axial separation ${D_A}$= 0mm, 4mm, 6mm, respectively, and NA = 0.5. (b),(d),(f): SNR as a function of lateral separation ${D_L}$ and fiber NA, at axial separation ${D_A}$= 0mm, 4mm, 6mm, respectively, and illumination angle of zero degrees. In all cases, the circled numbers indicate selected geometries as in Fig. 4 before. All SNR values are normalized to geometry② value in grey matter.

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These results demonstrate that designing the probe and finding its optimal operation requires a thorough understanding of a wide parameter space and the physics behind the photon ensemble distribution inside thick samples. Again, experimentally performing this optimization would be extremely cumbersome, and could lead to less than optimal designs. Finally, note that geometry② continues to show fairly optimal performance over the large parameter space considered here.

3.4 Experimental validations using tissue mimicking scattering phantoms

We verify our simulations experimentally using scattering phantoms that mimic brain white and grey matter [28]. Our scattering phantoms use polydimethylsiloxane (PDMS) (Dow, Sylgard 184, with a 10:1 curing agent ratio) as the substrate, titanium dioxide (TiO₂, Atlantic Equipment Engineers, Ti-602) as the scattering agent, and India ink (Pro Art, PRO-4100) as the absorbing agent [29]. The concentration of TiO₂ is set to 3.94g/L for white matter and 1.57g/L for grey matter, while the concentration of the India ink is 0.218g/L for both (the absorption coefficients of white and grey matter are approximately equal at 720nm) [23]. On top of these scattering phantoms, we place 10µm polystyrene beads in water which serve as the phase target to image.

We fabricate three probes with different lateral and axial separations (${D_L}$, ${D_A}$), namely, geometry①: (2mm, 0mm), geometry②: (2.5mm, 4mm), and geometry③: (2.5mm, 6mm) as marked in red circles in Figs. 4 and 5. These three geometries are specifically chosen to test the validity of our model, which has an unusual peninsula-shaped high-SNR region, and has a slight level of tissue dependence (Figs. 4(a) to 4(d)). Note that geometry③ is out of the peninsula-shaped high-SNR region and geometry② is well within the optimal SNR region for white and grey matter ((Figs. 4(a) and 4(b), respectively)), while geometry① is outside the optimal region only for white matter but not for grey matter. For each probe geometry and phantom type, we measure 10 beads and 10 featureless areas in the FoV, and then compute the experiment SNR using the average phase value of the beads, divided by the average phase-standard-deviation of the featureless areas. Figure 6(a) compares experimental SNRs to simulation. For ease of comparison, all SNR values are normalized to geometry② value in the grey matter phantom.

 

Fig. 6. SNR experimental validation of Monte Carlo simulations by measuring 10µm beads in white and grey matter scattering phantoms. In (a) experiment SNRs for 3 distinct geometries (defined in Fig. 4) are drawn with solid bars and error bars, and simulations are drawn with dashed bars. In (b) experiment SNRs as a function of illumination angle and axial separation distance ${D_A}$ are given in solid lines, and simulated results are in dashed lines, for the grey matter phantom. The lateral separation distance ${D_L}$ is fixed to 2.5 mm. Experiment SNR in all cases is calculated by dividing the average measured phase of 10 beads by the phase standard deviation of 10 featureless areas. We normalize all SNRs to geometry② value in the grey matter phantom.

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As Fig. 6(a) shows, the experiment and simulation SNR values are in good agreement for all configurations and tissue types. Geometry② exhibits the highest SNR and geometry③ has the lowest SNR among all cases. As expected, geometry① yields a tissue-type dependent SNR, with the configuration providing a better SNR for grey matter compared to white matter. Indeed, these experimental results validate our numerical treatment, including the peninsula-shaped high-SNR region and the slight tissue dependence. These results also clearly show the importance of careful probe optimization to achieve optimal operation conditions (for brain imaging in this case). For instance, the most intuitive geometry of ${D_A}$= 0 with a small ${D_L}$, as with geometry①, leads to vastly sub-optimal performance in white matter, which can be remedied with a slightly less obvious geometry, using small offset in ${D_A}$ as with geometry②.

To further validate our model, we experimentally measure the SNR as a function of fiber illumination angle at multiple axial separation distances (Fig. 6(b)). The fiber angle is varied from 0 degree to 40 degrees, with respect to the GRIN-lens. Similar to Fig. 5, here we also consider three different axial separations (${D_A}\; $=0mm, 4mm, 6mm) with a fixed lateral distance ${D_L}$ = 2.5mm. Once again, we measure the 10µm polystyrene beads immersed in water atop a grey matter mimicking scattering phantom. For each experimental SNR, we measure the phase value obtained from 10 beads and divide by the phase standard deviations from featureless background areas to estimate the SNR. As shown in Fig. 6(b), the measured experimental SNRs are in excellent agreement with the simulation results. Importantly, geometry② (orange curve in Fig. 6(b) with zero-degree fiber illumination angle) shows an optimal SNR configuration. This is also in agreement with the unique optimal behavior predicted by our model in Figs. 5(a), 5(c), and 5(e), in which an axial separation distance of 4mm shows an optimal SNR at zero-degree illumination angle, but then falls-off sharply (i.e., SNR worsens) as the illumination angle is increased. In comparison, the other axial separation distances (0mm and 6mm) with fixed ${D_L}$ = 2.5mm show a weaker dependance with illumination angle. Again, this unique behavior predicted by our model is in excellent agreement with the experiments.

In subsequent sections of this work we adopt geometry② since this configuration achieves optimal conditions (i.e., highest SNR) for white and grey matter (as well as other tissue types) as shown in Fig. 4–6.

3.5 Characterization of probe phase sensitivity

We quantify the phase sensitivity of our system using a photo-lithographic quartz target consisting of letters of different heights (“OIS”: 300nm, “LAB”: 200nm, and “GT EMORY BME”: 100nm). In this case, we use a 1% intralipid agar phantom as the scattering medium below the phase target (this mimics our previous experimental conditions to assess sensitivity in Ref. [5] and permits direct comparison to the free-space qOBM system). As shown in Fig. 7(a), the phase target contains letter structures that are comparable in phase-values to the featureless background. To characterize the spatial fluctuations and obtain a quantitative estimate of phase sensitivity, we select 4 rectangular featureless areas (40µm-by-40µm) across the FoV and characterize their average phase standard deviations. This results in a phase sensitivity of ∼0.58rad which translated to a ∼67nm sensitivity for this sample. However, while the background phase structures appear to be random, the pattern is mostly static and is a result of phase irregularities among fiber cores in the fiber bundle. Figure 7(b) shows an image of a blank area which has a high degree of similarity to the background in Fig. 7(a). We also observe that the pattern does not fluctuate significantly as the fiber bundle is moved. Thus, to eliminate the static phase noise, we take a qOBM image of a blank region (Fig. 7(b)) and subtract it from subsequent acquisitions. Figures 7(c) and 7(d) illustrate the drastic improvements achieved by the simple background subtraction. Using the same regions as before, we obtain a phase sensitivity of ∼0.17rad or ∼19nm for this sample, which is over a three-fold improvement.

 

Fig. 7. Characterization of phase sensitivity. A photolithographic quartz phase target with letters of 300nm, 200nm, and 100nm in height is measured. (a) Phase measurement of the target. (b) Phase measurement of a blank area. (c) Phase retrieved after background subtraction. (d) Phase mapped to quartz height in air. (e) Measured phase standard deviation over the number of averaged frames, ${N_f}$. The dotted green curve follows a ${\propto} 1/\sqrt {{N_f}} $ dependence, corresponding to a Poisson noise distribution, while the dashed blue curve (fitted curve) follows a relation: $15.03nm/\sqrt {{N_f}} + 3.05$ nm. The shaded area indicates the measured data ± standard deviation of the four featureless areas. (f) Measured single-pixel phase fluctuation over time (3 minutes). Measured phases are from 4 selected pixels in the phase target measurement, as shown in the upper-left inset.

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Lastly, we explore how averaging multiple frames helps to mitigate noise and improve the phase sensitivity. The phase sensitivity in Fig. 7(e) is calculated using the same 4 rectangular featureless areas (40um-by-40um) as before. As Fig. 7(e) illustrates, the phase sensitivity (in nm) of the probe first decreases (i.e., improves) quickly with increasing number of averaged frames (${N_f}$), roughly following a ${\sim} 1/\sqrt {{N_f}} $ Poisson-noise distribution (dotted green line). However, after averaging more than ∼10 frames, the sensitivity improvement slows down and begins to deviate from the expected shot noise behavior. We designate this deviation to persistent noise from the fiber bundle that is not completely eliminated by the background subtraction correction. By fitting the data to a slightly different model following $\alpha /\sqrt {{N_f}} + \beta $, with $\alpha $ being a proportionally constant and $\beta $ a lower sensitivity limit set by the fiber bundle, we obtain a much better fit (dashed blue line). We find that $\beta $ = 3.05nm which effectively represents the best-case-scenario sensitivity (when large averaging can be tolerated). It is likely that different fiber-bundles will show different lower sensitivity limit coefficients (β). By averaging 70 frames, the probe sensitivity is ∼0.05rad or ∼5.4nm, which is comparable to our previous free-space qOBM system’s sensitivity [5–8].

Finally, we consider how the power stability of the light source (LEDs) can lead to noise in the measured phase value. To estimate the effect, we use a power meter (Thorlabs, PM100D) to measure the delivered LED power from one single illumination fiber. We find its standard deviation is ∼0.030mW or ∼0.1% power fluctuations over a period of 3 minutes. The impact of the power instability on the measured phase can be analyzed by investigating at measured phase values from single-pixels over time. In Fig. 7(f), we include our measurements on 4 independent pixels, and analyze their measured phase values over a period of 3 minutes. The temporal phase standard deviations as measured by these 4 representative background points is ∼12nm. Recall that the spatial phase variations (assessed from 40µm-by-40µm featureless areas) are ∼19nm, which indicates that the temporal phase noise is a slightly less severe noise factor than the spatial phase noise (i.e., fixed pattern noise from fiber bundle, remaining even after conducting the background subtraction).

3.6 Probe validation using fixed rat brain and freshly excised human brain tumor samples

To demonstrate the imaging capability of the fiber-based qOBM system on biological samples, we measure formalin-fixed, excised rat brain samples from a 9L gliosarcoma rat tumor model. All our animal experimental protocols are approved by the Institutional Animal Care and Use Committee (IACUC) of Georgia Institute of Technology and Emory University. Figure 8 shows the measurements of a cortex structure (choroid plexus) in a healthy rat brain (Figs. 8(a)–8(d)) and a dense tumor region of the 9L tumor model (Figs. 8(e)–8(h)). Specifically, Figs. 8(a) and 8(e) show the low-pass filtered, single-frame intensity images (from one LED), where little or no identifiable detail of the tissue can be seen. In Figs. 8(b) and 8(f), a DPC image (with no frame averaging) is shown where some tissue structure starts to appear with horizontal phase gradient information. Figures 8(c) and 8(g) show the retrieved quantitative phase (qOBM image) with background subtraction (no frame averaging). Here tissue structures are more conspicuous with appreciable detail of the folded structures of choroid plexus (Fig. 8(c)) and the characteristic granular cellular structures of the 9L tumor model (Fig. 8(g)). Figures 8(d) and 8(h) show the same structures after averaging over 40 qOBM images which clearly has a higher SNR but this is only possible for still samples.

 

Fig. 8. Measurement of formalin-fixed rat brains from a 9L gliosarcoma tumor model. Top row: healthy cortex area (choroid plexus). Bottom row: dense tumor cellular area. (a), (e): Low-pass filtered single-frame intensity image; (b), (f): DPC image under horizontal illumination; (c), (g) retrieved quantitative phase (qOBM image) without frame averaging; and (d), (h): retrieved quantitative phase by averaging 40 frames.

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As a final demonstration of the capabilities of the fiber-based probe, we acquire qOBM images of freshly excised human brain tumor samples (astrocytomas) discarded from neurosurgery. All human samples are de-identified and obtained through the Winship Cancer Institute of Emory University using approved protocols. For comparison, we also acquire qOBM images using our free-space qOBM system [5,8]. After imaging with qOBM, samples are furthered processed for histology to obtain the “gold-standard” H&E-stained bright-field images for comparison.

Our measurements are shown in Fig. 9. The first column shows the fiber-based qOBM images (no averaging, single qOBM acquisition at 10Hz), and the second and third columns show images from our free-space qOBM system and H&E, respectively. Images in each row are from the same specimen (and hence patient and tissue type). Note that, while the three types of images (probe-qOBM, free-space-qOBM, and H&E) capture similar structures from the same specimen, they are not necessarily from the exact same spot. Figures 9(a)–9(c) present an area with a capillary blood vessel (single blood cells inside) and some tumor cells around/along it. Figures 9(d)–9(f) show a larger blood vessel with many blood cells inside and some astrocytoma (tumor) cells nearby. Figures 9(g)–9(i) show a densely packed tumor cell area, with highly myelinated processes present, which are more prominent in qOBM than H&E. Our fiber-based qOBM system can measure clear histological structures from unstained, thick, fresh samples comparable to the free-space qOBM and H&E, which illustrates the potential use of our flexible probe for in-vivo, intraoperative diagnosis of human brain tumors, among many other applications.

 

Fig. 9. Images of unstained, freshly excised, thick human brain tumor samples using the fiber-based qOBM system (first column), in comparison to free-space qOBM images (second column) and H&E stained slices (third column; after fixation and processing. (a)-(c): A capillary blood vessel with single blood cells inside, and tumor cells around. (d)-(f): A large blood vessel, where blood cells are closely packed, and astrocytoma tumor cells are nearby. (g)-(i): A densely packed tumor area, where cell nucleus and myelin sheath of neurons (with higher phase contrast) are visible.

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4. Conclusion

We have presented a robust optimization and characterization of a flexible, fiber-based qOBM system and have shown its capability to retrieve quantitative phase from thick scattering samples with high sensitivity. Our system design is compact (∼8mm in diameter), light-weight (∼40g for the probe head), low-cost, flexible, and robust; and it achieves 2µm lateral resolution, 6µm axial resolution, 300µm field of view, and a 10Hz imaging rate. Indeed, OBM has been previously demonstrated through a fiber-based system [14,17] and we have previously presented a similar fiber-based qOBM system [8]. However, none of the previous studies presented an optimization of the probe, which is the crux of this work. This work has three critical and novel points: (1) It presents the first optimization for qOBM (and OBM) for a fiber-based system (however, the approach is also universal and can also be applied to non-fiber-based systems, including free-space qOBM and OBM systems). Optimization of DPC illumination has been presented [20], but that was in transmission using thin samples—epi-mode OBM and qOBM imaging require drastically different considerations, as discussed here. (2) Our approach to estimate the phase SNR, using the slope of the optical phase transfer function as a measure of phase sensitivity and photon count from Monte Carlo as a measure of noise, is unique and critically important for facile optimization in arbitrary environments. Importantly, this approach obviates the need for tedious experiments and allows for efficient in silico optimization over a wide parameter space. (3) We show the importance of performing the analysis for various samples of interest (namely, white matter, grey matter, epidermis, and breast tissue). Indeed, we show that certain “sweet spots” exist, but some of the most intuitive geometries may not work universally across different samples. However, we also show that certain geometries may provide near optimal performance across a variety of tissue types.

In addition, the numerical treatment presented here was validated experimentally. We showed the approach is able to faithfully model the SNR and phase sensitivity of the probe under numerous conditions. With optimization, we achieved a sensitivity of <20 nm for a single qOBM capture, with a lower limit of ∼3nm when averaging. To demonstrate the utility of the probe and illustrate a potential application, we presented qOBM images of thick fixed brains from a 9L gliosarcoma rat tumor model and fresh human brain tumor samples. QOBM images, taken with our probe, clearly show cellular structures which are in agreement with those observed with a free-space qOBM system and H&E. These results strongly suggest that the probe is well-suited for applications ranging from image-guided surgery to micro-endoscopy.

While this fiber bundle design is simple to implement, there are some important limitations worth discussing. The resolution of the system is not limited by the NA of the GRIN lens; instead, it is dictated by the core-to-core pitch in the optical fiber bundle. Improvements of about 30% in resolution can be achieved with tighter-bound fiber bundles (i.e., with smaller core pitch), but this comes at the price of a smaller FoV [25,30]. Also, the number of cores in the fiber bundle dictates the total number of useful pixels in the image. Even with the largest-count commercially-available fiber bundle of ∼100,000 elements, the effective pixel count is still far less than conventional CMOS cameras. Moreover, each core effectively serves as a “cone receptor” (0.30∼0.35NA) with a certain level of manufacturing irregularity [24], which further contributes to noise. Finally, even though GRIN lenses have the advantages of being compact and light-weight, they also suffer from more severe optical aberrations than normal microscope objectives. In our future work, we will test new designs of micro-objectives, and explore ways to increase the resolution and the total number of effective pixels.

In conclusion, qOBM is an exciting new label-free imaging method that offers unique 3D, tomographic quantitative phase contrast with subcellular resolution in real-time. Here we have developed a robust and facile method to optimize the phase SNR of a flexible and compact fiber-based qOBM system, and presented a careful characterization of the probe. The approach is universal and can be applied to other qOBM (and OBM) systems in arbitrary environments. This novel technology can help improve many areas of biomedicine, including micro-endoscopy, surgical guidance and more.