3.1.

Signal Processing

The intensity detected at the n'th row of the CCD represents the spectrum of sample signal scattered at angle [TeX:] $\theta _{\it n}$ ${\theta }_{\mathit{n}}$ , and can be written as

The signal processing begins with the subtraction of [TeX:] $I_{\rm r} (\lambda, \theta _{n})$ $I_{\mathrm{r}}(\lambda ,{\theta }_n)$ and [TeX:] $I_{\rm s} (\lambda, \theta _{n})$ $I_{\mathrm{s}}(\lambda ,{\theta }_n)$ , which are recorded separately using two computer-controlled mechanical shutters in the reference and sample arms. Because [TeX:] $I_{\rm r} (\lambda, \theta _{\it n})$ $I_{\mathrm{r}}(\lambda ,{\theta }_{\mathit{n}})$ is relatively stable, it is saved only once at the beginning of each data acquisition session. [TeX:] $I_{\rm s} (\lambda, \theta _{\it n})$ $I_{\mathrm{s}}(\lambda ,{\theta }_{\mathit{n}})$ , however, is measured immediately prior to every acquisition of the combined field to minimize field fluctuation in the subtraction. The highest acquisition rate of the system is 2.5 Hz, limited by the shutter speed, which can be improved by the use of fiber-optic switches.

After subtraction, the interferometric term is resampled into wavenumber domain, Fourier transformed, and normalized to yield a depth-resolved angular intensity distribution,³² which is subsequently analyzed at each depth using Mie theory model for size determination.

3.2.

Angular Range

We first measure the probe's angular range, an important parameter for accurate analysis of light-scattering data. Using a rotating mirror as shown in Fig. 3a, the scattering angle θ is found to be linearly dependent on the CCD pixel position N. The collimated illumination beam is reflected by the mirror and focused onto the fiber bundle while the mirror rotates. For convenience, we define θ as the compliment of the conventionally defined scattering angle (i.e., θ = 0 deg for backscattering instead of 180 deg).

Figure 3a shows superposed images of multiple focused spots that are observed as the mirror rotates in steps of 0.035 rad (2 deg) for a range of 0.56 rad (32 deg). The position of the focused spot relative to the optical axis h, which has a linear dependence on N, is related to θ by

We note that, because the mirror experiment is carried out in air, these angles differ from those in other samples, such as tissue and phantoms, due to Snell's law by a factor of 1/n with n being the sample's refractive index. In our fitting models, the angles are always scaled to the equivalents in air.

Fig. 3

Rotating mirror experiment: (a) Superposed images of fiber bundle and focused spots; (inset) schematics of the experiment: PMF-polarization maintaining fiber; FB-fiber bundle; M-mirror. (b) Position of the focused spots versus mirror angle.

3.3.

Depth Range

The achieved probing depth is a critical parameter for the clinical a/LCI probe. It is not only dependent on signal falloff, but more importantly related to its angular range. We examine the impact of sample depth on angular range and scattering intensity by repeating the mirror experiment at various offsets (depths) between the mirror and the optical window. Figure 4a shows the change of spot position for four angles as the mirror is progressively moved from 150 to 750 μm beyond the optical window. The spot position remains nearly the same with a standard deviation of 0.6 pixel (0.004 rad), or 0.7% full scale. We therefore conclude that the angular range remains constant over this range of depth.

In Fig. 4b, we also plot the signal intensity trend throughout the depth. At each angle, the intensity falls off as a function of depth due to beam divergence and lens aberration, which reduce back-coupling efficiency. Also, light intensity at higher angles experiences a faster decline as a consequence of the oblique incidence, as illustrated in Fig. 4b. For scattering location 1, the high angle reflection is well received. At a deeper location 2, however, the reflection at the same angle is shifted downward due to the oblique incident and therefore becomes uncollectable by the lens. Scattering from these deep sites is still detectable but with a reduced angular range. The depth dependence of the maximum detectable angular range, θ _max, can be mathematically written as

Again we note that, owing to the Snell's law description of the refraction at the sample surface, the sample site 1 at a physical depth of D produces an angular distribution comparable to a mirror measurement at depth D/ n (site 1^′) in air with n being the sample's refractive index. Hence, the range of angles received in the mirror experiment at a depth of 350 μm translates to the same range of angles that would be received at a depth of 470 μm in tissue (n = 1.35), enough to detect the full thickness of the epithelial layer of tissue (200–300 μm).

Fig. 4

The impact of sample depth on detected signal: (a) Angular range remains constant throughout the examined depth range for both high and low angles and (b) sample intensity declines with depth faster at high angles due to limited lens collection aperture.

3.4.

Dispersion Compensation

The fiber bundle has some unique optical properties that are important to its application in LCI and will be discussed in this and the following subsections. In this a/LCI system, dispersion is introduced by the variety of fibers involved, in particular, the fiber bundle. Various dispersion compensation techniques have been developed in the past, based on either hardware or numerical correction.^{34, 35, 36} We employ the latter approach with a second-order dispersion compensation. Let X (k, θ) denote the cross-correlation term in Eq. 1 in wavenumber domain. Dispersion compensation is performed as [TeX:] ${\rm HT}[X(k,\theta)]e^{j(ak^2 + bk)}$ $\mathrm{HT}\left[X(k,\theta )\right]e^{j(a{k}^2+bk)}$ , where HT(·) is Hilbert transform and a and b are the second- and first-order compensation parameters.

Figure 5 shows a mirror signal with a depth resolution of 26 μm in air after compensation. Compared to the theoretical value, [TeX:] $2\,\,\ln 2\lambda ^2 /(\pi \Delta \lambda) \approx 16\,{\rm \mu m}$ $2\ln 2{\lambda }^2/\left(\pi \Delta \lambda \right)\approx 16\mu \mathrm{m}$ , the discrepancy may come primarily from the high-order (≥3rd) dispersion of the fiber bundle with a possible minor contribution from aberrations in the drum lens. We note that further improvements in dispersion compensation are not crutial for the current a /LCI study for the following reasons: (i) quadratic compensation is able to correct most dispersion; (ii) dispersion is not the only factor governing depth resolution for a fiber-bundle-based probe, as discussed later; and (iii) with a /LCI, we intend to measure average nucleus size for a population of cells and, therefore, an adequately large volume or depth is preferred. In this study, it is sufficient to use the same quadratic compensation for all fiber bundle pixels.

Fig. 5

FWHM of a mirror reflection before (580 μm) and after (26 μm) dispersion compensation.

Figure 6 shows dispersion compensation results with the unprocessed depth-resolved angular scattering of a cover slip positioned in front of the probe tip [Fig. 6a] and the restored image after dispersion compensation where multiple surfaces can be identified [Fig. 6b]. The first surface seen is the sample-side surface of the lens, which strongly reflects the light to high angles due to the lack of an antireflection (AR) coating. If necessary, it could be reduced by the use of a properly AR-coated lens. The second surface is the inner surface of the optical window, which is almost invisible because the preassembling cleaning minimizes its scattering. Its signal is hence dominated by the adjacent lens surface. The other three visible surfaces—the outer surface of the optical window, the front and back surfaces of the sample coverslip—are intentionally made visible by slight finger touches to enhance scattering. The measured thicknesses of the two cover slips are consistent with the calculated value of 150×1.5 = 225 μm.

Fig. 6

Depth-resolved angular scattering from a cover slip: (a) Before and (b) after dispersion compensation, (c) field flattening by introducing extra phase shift to each angular channel.

The surfaces in Fig. 6b exhibit a curved field. The center of the fiber bundle appear ∼ 250 μm (optical pathlength) deeper than the edges. A possible cause of this variation is a refractive index gradient in the bundle arising during the manufacturing process. Another possibility could be the variation of the physical length of the individual fibers.

Nonetheless, the field curvature can be flattened by numerically shifting each horizontal line. The operation is implemented together with the dispersion-compensation process by adding an extra angle-dependent phase term, [TeX:] $e^{ - jL(\theta)k}$ $e^{-jL\left(\theta \right)k}$ , with L(θ) being the relative optical depth offset at angle θ. It results in [TeX:] ${\rm HT}[X(k,\theta)]e^{j[ak^2 + bk - L(\theta)]}$ $\mathrm{HT}\left[X(k,\theta )\right]e^{j[a{k}^2+bk-L\left(\theta \right)]}$ , the Fourier transform of which is then shifted by L(θ) to remove the curvature. To determine L(θ), solutions of small microspheres (e.g., 260 nm) are used to generate nearly uniform scattering across the entire angular range, which makes the interface of the sample clearly visible. L(θ) can then be determined by calculating the correlation between the sample fields at θ ₀ and θ and is plotted in Fig. 6b, with the corrected field shown in Fig. 6c.

The accuracy of the field curvature correction could be another factor affecting the depth resolution achieved with this probe if the correction is not carried out carefully. Figure 6c shows that, after the correction, the depth variation of each surface is insignificant compared to the peak width, indicating the correction is sufficiently accurate such as there is no influence on depth resolution.

3.5.

Interpixel Averaging

In the spectrograph, each CCD pixel can receive signals from multiple fiber pixels. If the multiple fibers differ in path length, then this effect would influence the achieved depth resolution. In our system, the bundle has ∼160 fiber pixels across its diameter, which are imaged onto 85 CCD rows. Therefore, each row, on average, represents the summed interference signal from two adjacent fiber pixels. Figure 7 shows a dispersion-compensated mirror signal from a single row. Two peaks are evident with a separation of ∼22 μm, causing an effective broadening of the apparent peak width. For applications requiring higher depth resolution, this effect can be avoided by increasing the magnification of the 4f imaging system to reduce the number of fiber pixels received per CCD row. The trade-off is that a higher number of CCD pixels is required to acquire scattering data from the full angular range.

Fig. 7

Dispersion compensated mirror signal from a single CCD row showing signals from two neighboring fiber pixels. The 22 μm peak-to-peak separation indicates the path length difference between the two pixels.

3.6.

Intermodal Interference

Another property worth discussing is the multimode operation of the fiber bundle due to its large numerical aperture. We note that higher order modes travel at different velocity through the multimode fiber and hence can be path-length resolved by the LCI detection scheme. When the reference field is matched to the fundamental mode (i.e., the lowest-order mode in an optical fiber or the only mode allowed in a single-mode fiber), higher-order modes are offset by several millimeters, which is beyond the probing range of the system.^{32, 37} In addition to path-length concerns, the energy distribution among the modes plays an important part in suppressing intermodal crosstalk. As indicated in Fig. 1b, sample scattering is focused into the fibers with nearly normal incidence, which allows most energy to be coupled into the fundamental mode. Indeed, no high-order signal is experimentally observable within a 20-mm range around the matching position of the reference arm. This result confirms (i) the LCI system detects the fundamental mode traveling through the fibers in the bundle, and (ii) minimal energy has been coupled into higher-order modes. Hence, for the current a /LCI system, intermodal interference is not found to be a critical issue.

3.7.

Pathlength Stability

Another relevant property of the fiber probe is the stability of the path length due to various factors, such as bending and ambient temperature. In general, the path length of a fiber can be changed when subjected to strain or temperature variation. In laboratory experiments, we randomly place and bend the probe under normal operation conditions and record no observable change of its path length. This result can be attributed to the strain relief connector used to isolate the fiber bundle from bend-induced strain, shown in Fig. 2b. The PEEK sheathing sustains the strain while the fiber bundle is free to move inside. The probe sheathing is also responsible for the insensitivity to room-temperature variation. Indeed, experiments that immersed the gastroscope with the probe in its accessory channel in a warm bath (37°C), showed no observed changes in path length. In clinical testing, small pathlength variations of up to 100 μm are observed, possibly due to mechanical and temperature influences. These variations are small and can be automatically corrected for using the lens reflection as a marker.

To summarize the probe characterization, we have discussed the optical properties of the bundle and the factors that affect the depth resolution of the system. Methods for further improvements, if necessary, were also suggested. In our current system, rather than characterizing these factors individually, we determine the effective depth resolution from the measured scattering intensity. In Section 5, we show that the effective depth resolution for this system is 26 μm in tissue, which is sufficient for our purpose of measuring the average nucleus size in the epithelial layer.

4.1.

Single-Size Phantom

Phantom testing using single-sized microspheres is a standard procedure to assess the performance of a/LCI systems.³²Figure 8a shows a typical depth-resolved angular scattering distribution measured by immersing the probe tip into a solution of 7 μm (mean diameter: 6.982 ± 0.055 μm, NIST traceable) microspheres. By fitting the angular oscillations within the first 50 μm of the sample to Mie theory as shown in Fig. 8b, the scatterer size is determined to be 6.96±0.20 μm. The depth-dependent sizing results for the first 500-μm optical depth of the sample are also shown in Fig. 8c, demonstrating that subwavelength sizing accuracy is obtained across this range of depths. Figure 8d shows that the a/LCI sizing results are in good agreement with NIST traceable sizes for 6.98-, 7.98-, 10.00-, 12.01-, and 15.02-μm microspheres.

Fig. 8

Single-size microsphere phantom test: (a) Depth-resolved angular scattering distribution of 7 μm microspheres, (b) Mie theory fit of angular distribution, (c) depth dependence of sizing results, and (d) a /LCI sizing results of microspheres with NIST sizes.

4.2.

Double-Layer Phantom

A double-layer phantom was also prepared to demonstrate depth-resolved analysis of differently sized scatterers. The phantom consists of a chamber sandwiched by a coverslip and a microscope slide. When the microsphere-filled chamber is brought to the proximity of the probe tip, the space inbetween is filled with a second microsphere solution. Figure 9a shows the scattering distribution of a 100-μm-thick, 6-μm microsphere layer (mean diameter: 5.990 ± 0.045 μm, NIST traceable) followed by a 150 μm-thick 10-μm microsphere layer (mean diameter: 10.00 ± 0.05 μm, NIST traceable).

Fig. 9

Double-layer phantom testing: (a) Angular scattering distribution of 6- and 10-μm microspheres, (b) Fitting results of 6-μm microsphere using Mie theory, and (c) 10-μm microsphere results.

The average angular distribution within a 50-μm layer in the middle of each sample is fit to Mie theory, and the diameters of these two samples are determined to be 6.32±0.20 and 9.84±0.70 μm, respectively. These results are in excellent agreement with the sample specification and demonstrate the a/LCI's ability to achieve good fitting with multilayer samples up to 700 μm of optical depth (∼500 μm of physical depth).

5.1.

Clinical Data Acquisition

In order to collect in vivo light-scattering information from esophageal epithelium, the a/LCI fiber probe is fed by the endoscopist through the accessory channel of the gastroscope once it has been deployed [Fig. 10a]. By manipulating the fiber probe and flexible tip of the gastroscope as one would do with a set of biopsy forceps, the clinician positions the probe tip in contact with the tissue of interest and applies gentle pressure in order to create a flat tissue surface from which to take measurements. The tissue becomes stretched across the probe face, resulting in consistent measurement geometry. While the clinician applies pressure, multiple acquisitions are taken of the same biopsy site by the clinical a/LCI device, after which the fiber probe is removed from the accessory channel. Following withdrawal of the a/LCI probe, a set of biopsy forceps are inserted into the accessory channel and a standard biopsy is taken at the same site of the optical biopsy, located by a transient depression in the tissue from the pressure of the probe tip. For each patient, this process is repeated at three to six clinically relevant biopsy sites selected by the clinician. Following extraction, the biopsies are fixed, stained, and analyzed by a pathologist to determine a diagnosis for the tissue in question. Figure 10b shows the image of one H&E stained biopsy from the squamocolumnar junction.

Fig. 10

In vivo data collection using the a/LCI fiber probe: (a) Endoscopic photograph of the a/LCI probe deployed in human esophagus, (b) light microscopy image of H&E stained biopsy from the squamocolumnar junction, and (c) depth profiles obtained by summing across all angular channels without (dashed line) and with (solid line) the presence of tissue. The gray lines indicate the depth bins for processing, and the gray bar estimates the basal layer.

5.2.

Clinical Data Processing

Once acquired, the data are processed with an automatic a /LCI processing script to determine the depth-resolved nuclear sizes and densities for each tissue layer,²⁹ corresponding to 50 μm in physical depth. The starting depth is determined by analyzing the depth profile, obtained by summing the data across all the angular channels of the a /LCI scan, as shown in Fig. 10c. With no sample present (dashed line), the depth profile reveals two peaks, one from the lens surface and the other from the outer surface of the optical window. Both have a FWHM of 26 μm, which is the actual physical depth resolution achieved with the probe after taking into account the effects of high-order dispersion, field-flattening error, and interpixel averaging. The 50-μm bin size has been chosen to average over a larger tissue volume.

The second surface of the optical window is used to determine the topmost surface of the sample and remains constant throughout the remaining scans. Analysis is executed for the first 500 μm of the tissue, which is consistent with the effective depth range of the probe. This range is sufficient to capture the entire epithelial layer of the tissue, including the diagnostically relevant basal layer, which appears 200–300 μm into the epithelium. Figure 10c also shows the depth profile obtained when probing a tissue in vivo (solid line). The signal from the outer surface of the optical window is not individually indentified due to the contact with the tissue but its position can be determined relative to the first surface.

5.3.

Clinical Sizing Results

Figure 11a shows the nuclear sizing information obtained from the clinical scan for the first 400 μm of tissue taken from the same site in Fig. 10b. The histopathological diagnosis for this particular tissue biopsy indicates that the tissue biopsy is from the squamocolumnar junction with no evidence of intestinal metaplasia (Barrett's esophagus) or dysplasia. Unique sizing information is obtained from each depth layer of the tissue, indicating the ability of the clinical a/LCI system to retrieve depth-resolved in vivo morphological and optical information from the tissue in question. We note that the pattern observed of a decreasing nuclear size across the epithelial layer is similar to that observed for squamous tissue in Ref. 29, with the reading at the basal layer (gray box), indicating a nuclear size and density measurement consistent with the histopathological diagnosis of a normal tissue type. For comparison, Fig. 11a also shows the results for a biopsy diagnosed with nondysplastic BE from the same patient, where the pattern of nuclear sizes reaches a maximum between the surface and basal layers of the epithelium, similar to that observed for gastric tissue in Ref. 29. These depth-resolved sizing patterns are closely associated with the pathological tissue conditions and can serve as a basis for using the a /LCI probe for potential assessment of tissue health. Further clinical studies will seek to better define the ability of a /LCI to discriminate between tissue types. Figure 11b shows the nuclear density information for these two biopsies.

Fig. 11

(a) Nuclear sizing and (b) density information for the clinical depth scan of normal squamocolumnar junction tissue (diamond) and BE tissue (square). Gray area estimates the basal layer.