2.1.

OCT System Description

Figure 1 shows the schematic of the $1.2\mu \mathrm{m}$ swept laser source OCT system. The system used a swept laser source (Axsun Technologies Inc.) of 100 kHz sweep rate with a duty cycle of 41.9%. The laser had a spectral bandwidth of 101 nm at a center wavelength of 1220 nm and it delivers an average output power of 30 mW. In the OCT system, we used standard fiber optic components with a center wavelength of 1310 nm since commercial fiber optic components are not available specifically for the 1200 nm window. The output from the laser source was fed through a 90:10 fiber coupler (Thorlabs, TW1300R2A2) guides 90% of light toward the circulator (Thorlabs, CIR1310-50-APC) in the sample arm and 10% of light toward the circulator in the reference arm of the interferometer. The light from the fiber circulators is collimated through a fiber collimator (Thorlabs, F280APC-C). Achromatic doublets (Thorlabs, AC254-050-C) with a focal length of 50 mm are used on both arms, resulting in a lateral resolution of $25\mu \mathrm{m}$ at the focal plane. The system achieves an average optical power of 16.5 mW in the sample arm. The reflected light from the sample and reference mirror travels back to the respective circulators, where it is guided toward a wideband 50:50 coupler (Thorlabs, TW1300R5A2). The interference signal from the 50:50 coupler is detected by a dual-balanced photodetector (Thorlabs, PDB481C-AC). The signal from the photodetector, and the sampling clock signal generated from the laser, were digitized with a $2.5\mathrm{GS}/\mathrm{s}$, 12-bit digitizer (Teledyne SP Devices, ADQ32). Data acquisition was controlled using custom Python software, and the acquisition was triggered with the sweep trigger from the laser source.

Fig. 1

Schematic of OCT system. OC, optical coupler; CIR, circulator; CL, collimator; L, focusing lenses; PC, polarization controller; and BPD, balanced photodetector.

2.2.

Weakly Scattering Phantom Preparation

The absorption spectra of mineral oil, which contains lipids and pure water obtained from literature, are shown in Fig. 2.^25,26 As shown in Fig. 2, within the spectral bandwidth of the OCT system, lipid has a sharp absorption peak at 1210 nm, whereas the water has an almost flat absorption spectrum with a smaller absorption coefficient.

Fig. 2

Absorption spectra of lipid-containing mineral oil and water within the spectral bandwidth of the OCT system.

To validate our method, we fabricated two types of weakly scattering optical phantoms, which differ in their absorption features at the wavelength range of our OCT system. The first set of phantoms was intended to mimic lipid-rich tissues. We chose gel wax as the matrix material typically composed of mineral oil and polymer resin. These phantoms were prepared following a previously published recipe.²⁷ The gel wax itself is optically clear. We added titanium dioxide (${\mathrm{TiO}}_2$) powder (Dupont™ Ti-Pure^® CAS No: 13463-67-7) as optical scatterers in the native gel wax (Mindsets online, FF1003). In this study, phantoms with various scattering coefficients were prepared by varying the concentrations of ${\mathrm{TiO}}_2$ particles from 0.05% to 0.2% w/w.

The second set of phantoms was designed with agar as a matrix material. The absorption of this material is mainly due to water in the wavelength range of our OCT system. We employed the same concentrations of ${\mathrm{TiO}}_2$ powder in the agar matrix, to approximate the scattering coefficients of the gel wax phantoms. The background scattering of the agar is assumed to be smaller than that of the added ${\mathrm{TiO}}_2$. The samples were prepared by dissolving 2% agar (Sigma-Aldrich, A6549) and varying concentrations of ${\mathrm{TiO}}_2$ powder in 100 ml of deionized water. The solution was heated to 94°C and continuously stirred until the agar and ${\mathrm{TiO}}_2$ particles were wholly dissolved in water. The prepared solution was then allowed to cool down to room temperature and stored in a refrigerator for 24 h. In our phantom study, the samples described above were prepared in rectangular shapes, and two-dimensional B-scan imaging was performed with 1000 A-scans in a frame.

Finally, independent lipid and non-lipid phantoms were used for validation. A gel wax phantom and a weakly scattering polyvinyl alcohol (PVA) phantom, both with 0.1% ${\mathrm{TiO}}_2$ scatterer concentration were used. PVA (5% w/w) and ${\mathrm{TiO}}_2$ were mixed in water and heated to 70°C and left to cool. The solution underwent three freeze-thaw cycles, creating an aqueous scattering gel.

2.3.

OCT Signal Processing and Image Reconstruction

Figure 3 shows the block diagram of signal processing steps to reconstruct the OCT intensity image. First, the background signal is measured by blocking the OCT system’s sample arm and subtracting it from the acquired interferogram. The dual-balanced photodetection in the system is not perfect, particularly due to imperfect power balancing over the whole spectral range. Therefore, residual excess noise remains in the system. Moreover, any imperfection in background subtraction results in a DC component in the signal. Therefore, the background subtracted interference signal is further filtered using a digital bandpass filter. The smaller and larger frequency components of the acquired interferogram that corresponds to the signals from the surface and highest imaging depth of the sample are used as the cut-off frequencies of the filter. These frequency components are determined by the Fourier transform of the acquired interferogram. The swept laser source used in our OCT system has nonlinear sweep characteristics in the wave number (k) domain, requiring $k$-linear resampling of the acquired interference signals. We employed a numerical resampling method that involves linearizing the unwrapped phase of the sampling clock signal to generate the calibration vector for interpolation as presented by Wu et al.²⁸

Fig. 3

Block diagram of the signal processing algorithm to generate OCT intensity image.

Once $k$-linearized, the interference signals were processed for dispersion compensation. We adopted a method²⁹ to numerically compensate the dispersion mismatch between the interferometer’s sample and reference arm optics. To determine the system dispersion mismatch, 200 A-scan measurements of a mirror at a fixed location on the sample arm were carried out. After background subtraction and $k$-linearization, the interferograms were averaged, and the Hilbert transform was applied to determine the spectral phase. A linear fit on the unwrapped Hilbert phase was computed. Then, the nonlinear phase $[{\varphi }_{\mathrm{disp}}(k)]$ due to system dispersion mismatch was estimated by subtracting the spectral phase and the linear fit. The estimated nonlinear phase $[{\varphi }_{\mathrm{disp}}(k)]$ was stored as a calibration vector in computer memory and it was employed to compensate the dispersion mismatch by multiplying the $k$-linearized interference signals with exp $[-\mathrm{i}{\varphi }_{\mathrm{disp}}(k)]$.

In our OCT system, the optical spectrum at the interferometer’s output significantly deviates from the original laser spectrum since fiber optic components used in the system are not optimized for the 1200 nm wavelength window. This could effectively reduce the theoretically attainable OCT axial resolution. Therefore, in the signal processing chain, we implemented an additional signal processing technique of spectral flattening.³⁰ This signal processing step compensates for the spectrum shape change due to wavelength-dependent attenuation of fiber optic components in the system. Moreover, we implemented a multiwindow signal processing using a series of Kaiser–Bessel windows on the spectral flattened interference signal.³⁰ This effectively reduces the axial side lobe level and achieves a better axial resolution than convention signal processing windows. The interference signals were zero-padded to four times their original length before the Fourier transform. The logarithmic compressed OCT intensity image was generated using the magnitude of the complex signal in the spatial domain.

2.4.

Spectroscopic OCT Data Processing

2.4.1.

Attenuation spectral analysis

The OCT backscattered intensity signal $[I(z)]$ from depth $z$ of the sample can be modeled using the single scattering model that obeys Beer-Lambert law as

Eq. (1)

$$⟨I(z)⟩=I_{0}T(z)\hat{S}(z)e^{-{\mu }_{t}z},$$

where $T(z)$ is the longitudinal point spread function of single mode fiber-based OCT system, $\widehat{S}(z)$ represents the signal-roll off of the system, and ${\mu }_t$ is the total attenuation coefficient of the sample. The attenuation coefficient ${\mu }_t$ of a sample has both absorption ${\mu }_a$ and scattering (${\mu }_s$) contributions (${\mu }_t={\mu }_a+{\mu }_s$).

Since the scattering and absorption coefficients of a material are wavelength-dependent parameters, the measurement of spectral-dependent OCT intensity profiles $[I(\lambda ,z)]$ can offer material classification based on either scattering or absorption features.^23,31,32 In this study, we exploited the distinct absorption features of water and lipid containing samples for the classification of materials.

A schematic overview of SOCT data processing is shown in Fig. 4. First, the $k$-linearized and dispersion compensated interference signal of the sample were analyzed with time-frequency distributions. In our study, we used the short time Fourier transform with Hanning windows for the time-frequency analysis, which resulted in a spectral and spatial resolution of 8.4 nm and $101\mu \mathrm{m}$, respectively. To reduce the speckle noise in the spectral-dependent OCT intensity profiles, we averaged the spectrograms obtained from 200 A-scans, which were sampled by 100 lateral speckles over the scanning range of 2.5 mm. The scanning range in one B scan was 35 mm, limited by the length of the phantom samples. Subsequently, the averaged spectral-dependent intensity profiles were divided by the longitudinal point spread function of the OCT system and then linearized by logarithmic compression.³³ We also included the correction for sensitivity roll-off of the OCT system. Then, we extracted the wavelength-dependent attenuation coefficients $[{\mu }_t(\lambda )]$ by fitting straight lines on the logarithmic compressed spectral-dependent intensity profiles. The resulting attenuation coefficients ${\mu }_t(\lambda )$ from different lateral positions on the sample were further processed for material classification.

Fig. 4

Block diagram of signal processing algorithm to generate attenuation spectrum.

3.1.

Swept-Source OCT System Performance

To assess the performance of the OCT system over the entire imaging range, a series of measurements were performed by positioning a silver coated mirror at the focal plane of the sample arm along with a Neutral Density filter of $-32\mathrm{dB}$ attenuation. The sensitivity was measured as a function of depth by varying optical path length in the reference arm of the interferometer. The maximum sensitivity of the system was experimentally determined as 95 dB. The measured maximum sensitivity is $\sim 20\mathrm{dB}$ lower than the shot noise limited value. This larger deviation of sensitivity from shot noise limited value could be attributed to two reasons. One is the excess noise of swept laser source used in the system, and the additional losses and noise due to guidance of multiple spatial modes in standard optical fiber components as the laser used in the system operates below the cut-off wavelength of SMF-28. Therefore, the sensitivity of the system can be improved in future using components made from optical fibers with lower cut-off wavelength than the minimum wavelength of the laser source used in the system. Figures 5(a) and 5(b) display sensitivity roll-off performance as a function of the imaging depth and dynamic range of our OCT system. The system has a 6 dB sensitivity roll-off at 4.2 mm in air and the dynamic range of 46 dB. The axial resolution of the OCT system was measured as the full-width half maximum of the OCT A-scan profile of a perfect reflector. Figure 5(c) shows the measured axial point spread function and the Gaussian fit at the axial distance of 0.81 mm. The measured axial resolution was $7.2\mu \mathrm{m}$ in air, close to the theoretical axial resolution of $6.5\mu \mathrm{m}$. The achieved axial resolution is 1.38 times narrower than the commercially available 1310 nm OCT system.³⁶ The depth dependence of the axial resolution is shown in Fig. 5(d). The axial resolution preserves the value around $7.2\mu \mathrm{m}$ up to a depth of 3.3 mm, and it slowly increases to $8.6\mu \mathrm{m}$ at a higher imaging depth. This slight variation in axial resolution at higher imaging depth could be due to the calibration error in the $k$-linearization algorithm and mismatch in dispersion at higher imaging depth.

Fig. 5

(a) Sensitivity roll-off performance of OCT system. (b) Dynamic range of OCT system. (c) Point spread function of OCT system. (d) Axial resolution of the OCT system at different imaging depths.

3.2.

OCT Intensity Imaging and Spectroscopic Analysis

The OCT B-scan intensity images were generated for each phantom with different scatterer concentrations, as shown in Fig. 6.

Fig. 6

OCT images of phantoms. (a)–(c) Gel wax with 0.05% TiO2, 0.1% TiO2, and 0.2%, respectively. (d)–(f) Agar phantoms with 0.05%, 0.1%, and 0.2% TiO2 scatterers.

Figures 7(a) and 7(b) show the measured attenuation spectra $[{\mu }_t(\lambda )]$ of the gel wax and agar phantoms from an averaged spectrogram over the scanning range of 2.5 mm. The error bars in attenuation spectra represents the variation of measured spectral dependent attenuation coefficients in terms of root mean square error (RMSE). The RMSE is calculated from the residuals of linear fit on the averaged spectral dependent intensity profiles over the scanning range of 2.5 mm. The measured attenuation spectra are analyzed with respect to the absorption feature of the phantom materials. The absorption signature of lipid in the gel-wax phantoms is correlated with a small peak around 1210 nm in the attenuation spectrum. On the other hand, the agar phantoms exhibit a flat attenuation spectrum, which is associated with the absorption spectrum of water in the phantoms. The absorption behavior of phantom materials in the attenuation spectra is discernable only at the lower concentration of scatterers, whereas the measured spectra significantly differed at higher scatterer concentrations. This significant deviation of spectral shape with increasing concentration of ${\mathrm{TiO}}_2$ is attributed to the dominant contribution of light scattering with minimal absorption to the overall attenuation coefficient. The measured values at the edges of the spectrum were considered erroneous due to the lower signal-to-noise ratio of the spectrum at the ends.

Fig. 7

Optical attenuation spectra of (a) gel wax phantoms and (b) agar phantoms with 0.05%, 0.1%, and 0.2% TiO2 scatterers.

The measured attenuation coefficient at each wavelength increases linearly with the concentration of ${\mathrm{TiO}}_2$ scatterers. This confirms that the wavelength-dependent absorption coefficients can be obtained by solving the linear equation system established for different scattering concentrations.

Figures 8(a) and 8(b) show the reference absorption spectra of mineral oil and water along with the absorption spectra of gel wax and agar phantoms that we derived by solving Eq. (2) using the measured attenuation spectra for different scattering concentrations. The estimated absorption spectrum of gel wax has a prominent absorption peak at 1210 nm with an absorption coefficient of $0.15{\mathrm{mm}}^{-1}$, which is close to those published in the previous studies. Error bars in Fig. 8 represent the variation of estimated absorption coefficients in terms of root means square error. On the other hand, the agar phantom demonstrates a broad absorption spectrum similar to that of water in the measured wavelength range with an estimated absorption coefficient of $0.12{\mathrm{mm}}^{-1}$ at 1200 nm. This result confirms the evidence of absorption features in the attenuation spectra, so a predictive model can be used to classify the lipid and non-lipid weakly scattering samples.

Fig. 8

(a) Retrieved absorption spectrum of gel wax phantom and reference spectrum of mineral oil. (b) Retrieved absorption spectrum of agar phantom and the reference spectrum of water.

Figure 9 shows the outcome of the predictive model. The open and solid symbols of circles, squares, and triangles represent the lipid-containing gel wax and the water-based agar phantoms at 0.05%, 0.1%, and 0.2% scatterer concentrations, respectively. This predictive model shows the significant quality of fit $[R^2(X)]$ of 0.653 with a predictive ability ($Q^2$) of 0.591. The sevenfold CV-ANOVA of model results in the $p=2.{158\mathrm{e}}^{-09}$, which is considerably smaller than the significance threshold.

Fig. 9

OPLS-DA score plot of gel wax phantoms (open symbols) and agar phantoms (solid symbols) as training set and gel wax phantoms (open stars) and PVA phantoms (solid stars) as validation set. The horizontal axis shows variation between groups, and the vertical axis shows variation within groups.

In Fig. 9, the star symbols represent the validation set of samples results from a fit to the entire training dataset. The open symbols of stars indicate the validation set of lipids containing gel wax samples, and the solid stars stay for water-based PVA samples. In the validation dataset, 95% of the datasets were correctly assigned to their respective classification.

Figure 10 shows the OPLS-DA model based on normal attenuation coefficients of gel wax and agar phantoms. The model based on attenuation coefficients shows quality of fit $[R^2(X)]$ of 0.468 with a predictive ability ($Q^2$) of 0.446. The value of $R^2<0.5$ indicates a poor quality of fit and hence the classification based on attenuation coefficients is insignificant. Consequently, the agar phantoms were misclassified as gel wax. This analysis further confirmed the significance of attenuation spectra-based classification of samples.

Fig. 10

OPLS-DA score plot based on normal attenuation coefficients of gel wax (open symbols) and agar phantoms (solid symbols). The horizontal axis shows variation between groups, and the vertical axis shows variation within groups.