1. Introduction

Optical coherence tomography (OCT) is a non-invasive imaging technology that uses the interference of backscattered broadband light to reconstruct high-resolution, three-dimensional images of biological tissues [1]. OCT is routinely used in ophthalmology for the diagnosis and monitoring of retinal diseases, including diabetic retinopathy [2], age-related macular degeneration (AMD) [3], and glaucoma [4,5]. OCT systems achieve broadband illumination using super luminescent diodes (SLDs) or supercontinuum (SC) lasers. Wavelength-dependent intrinsic power fluctuations within these light sources produce relative intensity noise (RIN), which is especially high in SC lasers [6]. In OCT images, RIN manifests as high background intensity at the zero-delay position that falls off gradually as depth increases. When using SC lasers as the light source, the effects of RIN can be mitigated by increasing detector exposure time, which reduces scanning rate, or using a low RIN light source, which can be cost-prohibitive [7]. Such drawbacks hinder the clinical adoption of OCT techniques that use ultrawide bandwidths or low central wavelengths, such as visible-light OCT (vis-OCT), where SC lasers are required.

Balanced detection OCT (BD-OCT) provides a means to suppress RIN by adding a second spectrometer to simultaneously measure the interferogram with a π phase shift [8]. Subtracting two simultaneously detected interferograms sums the π-shifted interference signals while suppressing RIN. Balanced detection is straightforward for swept-source OCT (SS-OCT) using only single-element detectors, which automatically temporally and spectrally correlate RIN before subtraction. Although balanced detection for spectrometer-based spectral-domain OCT (SD-OCT) was proposed previously [9–15], the full benefits of BD-OCT were not fully realized due to poor temporal and spectral RIN correlation. Recently, we [16] and others [17,18] substantially improved BD performance in SD-OCT through precise temporal and spectral matching of RIN components.

In SD-OCT, temporal correlation can be achieved using a common trigger to synchronize spectrometer acquisitions. Spectral correlation requires spectral co-registration with picometer-scale spectral precision to fully remove RIN. Previously, we demonstrated a three-fold reduction in RIN suppression after introducing a 1-pixel shift (50 pm spectral shift) between the spectrometer pair [16]. Subpixel matching can be performed in both hardware and software. Hardware matching is achieved by aligning the spectrometer pair with guidance from a correlation map generated from a RIN- or signal-dominated dataset [17,19]. However, the mechanical subpixel alignment of the spectrometers can be challenging. Moreover, environmental vibrations and fiber re-insertion can induce spectral shifts exceeding 50 pm, reducing RIN suppression. In comparison, software-based spectrometer matching uses an interpolation vector or transformation matrix to co-register one spectrometer to another [16–20]. Selecting the optimal interpolation vector or transformation matrix is critical for maximizing RIN suppression.

Interpolation vector selection can use a RIN- or signal-dominated dataset. A RIN-dominated dataset is synchronously acquired by spectrometers using minimized camera gain and exposure time with maximally allowable SC power, which maximizes RIN amplitude compared to other noise sources. The wavelength-dependent temporal noise fluctuations are used to identify correlated, wavelength-matched pixels between the spectrometers to produce an interpolation vector or matrix for subpixel matching [16,17,20]. Although robust, these methods require pre-calibrated measurements, many sample spectra, and light sources with a high RIN level. A signal-dominated dataset consists of many randomly phase-shifted A-lines containing interference signals that are synchronously acquired. The temporal signal fluctuations can then be used to produce an interpolation vector from the correlation matrix [19]. However, this technique requires additional finely tuned post-processing steps to filter residual coherence correlation, maximized SNR, and manual selection of the correlation matrix contour points to generate an interpolation vector. Furthermore, as mentioned previously, interpolation vector selection methods rely on the long-term stability of the spectrometer pair. Such instabilities require routine recalibration to ensure optimal RIN suppression over time. Thus, there is a need for an interpolation vector selection method that can be performed on any BD-SD-OCT dataset, regardless of RIN or signal level.

In this study, we demonstrate an adaptive approach for subpixel matching that can be applied to any BD-SD-OCT dataset regardless of its RIN or signal level, referred to as adaptive balance. Next, we compare the performance of adaptive balance against three reported subpixel-matching methods using test cases designed to vary the level of RIN and signal strength of the vis-OCT image. These test cases include (1) spectrometer camera gain, (2) exposure time, and (3) SC laser repetition rate. Lastly, we demonstrate the performance of adaptive balance in the human retina.

2. Materials and methods

2.1 Visible-light optical coherence tomography

We constructed a fiber-based BD-vis-OCT system for small animal retinal imaging. The system is based on a modified Mach-Zehnder interferometer configuration, as shown in Fig. 1(a). Light from an SC laser (SCL; 30 MHz or 300 MHz, SuperK, NKT Photonics, Denmark) was filtered by a short-pass dichroic mirror (DM; DMSP650; Thorlabs, NJ), bandpass filter (BPF; FF01-560/94-25, Semrock, NY), and spectral shaping filter (SSF, Hoya B-460, Edmund Optics, NJ). After filtering, the light that enters the system has a full width at half maximum (FWHM) bandwidth of 91 nm (wavelength range from 513 nm to 604 nm) as detected by spectrometer 1 [16,20]. The SC laser power entering the interferometer was controlled using a variable neutral density filter wheel (NDF; NDC-25C-2 M, Thorlabs). We coupled the filtered SC laser light into a 10:90 single-mode fiber coupler (FC1; TW560R2A2, Thorlabs), where we connected the 10% output to the sample arm. A collimating lens (CL) collimated a 1.5 mm diameter beam onto a 2-axis, 5-mm galvanometric scanner (GM; 6210 h, Novanta, MA). A two-lens Keplerian telescopic system (KT) with a 3:1 magnification ratio delivered the illumination light to the sample. We connected the 90% output of FC1 to a transmission-mode reference arm consisting of a polarization controller (PC), variable neutral density filter (NDF), and dispersion compensation glass (DCG). The pathlength of the reference arm was adjusted using a translation stage (TS) to vary the position of the outcoupling collimating lens with respect to the other reference arm components. The backscattered light from the sample arm was input to the first port, and transmitted light from the reference arm was input to the second port of a 50:50 fiber coupler (FC2; TW560R5A2, Thorlabs). The output ports of FC2 were connected to two randomly selected commercial spectrometers (SR₁: spectrometer 1; SR₂: spectrometer 2; Blizzard SR, Opticent Health, IL) for interferogram detection. SR₁ had a wavelength detection range of 509 nm to 614 nm, and SR₂ had a detection range of 506 nm to 612 nm, as shown in Fig. 1(b). SR₁ and SR₂ had differences in optical alignment, as demonstrated by the k-spacing plots in Fig. 1(c). We performed subpixel matching using a method introduced previously [16,20], which is described in more detail in Section 2.3.5. The mapping from SR₂ to SR₁ is shown in Fig. 1(d). The plot in Fig. 1(e) indicates the pixel index separation, or offset, between matched pixels. This plot helps further visualize how well the two spectrometers are mechanically matched. Mathematically, the pixel index offset can be generated by $f[n] = n - L[n ]$, where n is the pixel index, $f[n ]$ indicates the pixel index offset, and $L[n ]$ is the interpolation vector. The spectrometer pair used for this study had a maximum pixel index offset of ∼54 pixels, corresponding to a 2.8-nm spectral shift.

 

Fig. 1. (a) Schematic of BD-vis-OCT system. BB: beam blocker; BPF: bandpass filter; CL: collimating lens; DCG: dispersion compensation glass; DP: data processing; DM: dichroic mirror; FC1,2: single-mode fiber couplers; GM: galvanometric scanning mirror; KT: Keplerian telescope; NDF: neutral density filter; PC: polarization controller; SCL: SC laser; SR: spectrometer; SSF: spectral shaping filter; TP: tape phantom; TS: translation stage; (b) reference arm spectra of the two spectrometers; (c) spectrometers k-spacing of the two spectrometers; (d) pixel map between the two spectrometers; (e) SR₂ pixel offset with respect to SR₁ pixel number after calibration.

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2.2 BD-Vis-OCT processing

After data acquisition, we performed BD-vis-OCT processing on the interferograms simultaneously captured by SR₁ and SR₂. The interferogram fringes from SR₁ were digitally scaled by dividing by the mean spectrum from SR₁ and multiplying by the mean spectrum of SR₂. Interferograms from SR₁ were resampled using an interpolation vector (described in the following sections) to co-register the interferograms of SR₁ to SR₂ with subpixel precision. The interferograms from SR₂ were then subtracted from the resampled interferograms of SR₁. Portions of the balanced interferograms outside the region of spectral overlap were set to zero. Lastly, we performed traditional SD-OCT image reconstruction using k-space interpolation, automated dispersion compensation, and fast Fourier transformation (FFT).

2.3 Interpolation vector selection

Consider a pair of spectrometers (SR₁ and SR₂) with identical cameras consisting of a 1D array of N pixel elements (N = 2048 in this study). Although mostly overlapped through careful mechanical alignment, the wavelength distribution detected on the corresponding pixel elements of SR₁ and SR₂ are unique. Therefore, direct subtraction of simultaneously detected fringes in a BD-OCT system results in images with poor RIN suppression. This wavelength mismatch can be corrected by interpolating the spectra from SR₁ to co-align with the spectra from SR₂ before subtraction. Thus, proper interpolation vector selection is critical for achieving optimal RIN suppression.

Several approaches for generating interpolation vectors have been previously reported. In two reported methods, RIN-dominated images were acquired, and the temporal correlation of the wavelength-dependent RIN was used to identify matching pixels between the two spectrometers [17,20]. In another method, OCT images were used to match pixels that share the highest correlation of the temporal signal intensity [19].

In this work, our adaptive balance uses an optimization approach to iteratively update the interpolation vector until the RIN components concentrated near the DC term of the reconstructed OCT image are minimized. We compare the performance of adaptive balance against three interpolation vector selection methods detailed in Sections 2.3.1 to 2.3.3 under different RIN levels and vis-OCT signal strengths.

2.3.1 Linear minimum mean squared error

In this method, linear minimum mean squared error (LMMSE) estimation is used to obtain a transformation matrix, H, from a RIN-dominated dataset [17]. The signal from SR₁ and SR₂ are defined as ${S_1}$ and ${S_2}$, respectively. The calibration datasets from SR₁ and SR₂ are defined as ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} _1}$ and ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} _2}$, respectively, with cross correlation matrix ${R_{21}} = {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over \langle n} _2}{\left( {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} }_1}} \right)^T}\rangle$ and autocorrelation matrices ${R_{11}} = {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over \langle n} _1}{\left( {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} }_1}} \right)^T}\rangle$ and ${R_{22}} = {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over \langle n} _2}{\left( {{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over n} }_2}} \right)^T}\rangle$, where $\langle \ldots \rangle $ denotes expected value. The LMMSE estimate is given by $H = {R_{21}}{({{R_{11}}} )^{ - 1}}$. Finally, the balanced signal is given by ${S_{2 - 1}} = {S_2} - H{S_1}$, where ${S_{2 - 1}}$ is the balanced interference signal.

2.3.2 Noise-based cross-correlation

Noise-based cross-correlation (NCC) uses a RIN-dominated dataset to identify pixel pairs that share the highest temporal correlation [16,20]. First, a cross-correlation matrix is generated consisting of Pearson’s linear correlation coefficient for each pixel pair’s temporal RIN profile. Next, the matrix indices corresponding to the row-wise maximum correlation values are extracted. This produces a one-dimensional array consisting of integer values that map the temporally correlated pixels of one spectrometer to the other. To achieve subpixel mapping between the spectrometer pair, a third-order polynomial fit is applied to the pixel map vector to produce the final interpolation vector ($L[n ]$). This vector is defined by

2.3.3 Image-based cross-correlation

Image-based cross-correlation (ICC) is similar to NCC, but uses a scanned OCT image to identify wavelength-matched pixels [19]. First, the DC terms from the signals detected by both spectrometers are removed, and a cross-correlation matrix consisting of Pearson’s linear correlation coefficient for each pixel pair’s temporal signal profile is generated. The correlation matrix is then filtered by performing 2D FFT and applying a crossline mask to suppress artifacts from residual DC components. After inverse FFT, two points along the diagonal contour of the correlation matrix are manually selected and used to fit a first-order polynomial, which serves as the interpolation vector.

2.3.4 Adaptive balance algorithm

RIN is a frequency-dependent noise that dominates at lower frequencies and falls off at higher frequencies [21,22]. Thus, in OCT images, RIN manifests as a high background signal near the zero-delay position (${z_0}$) that decays with depth. A single detection A-line extracted from a sample-free (background noise) image is depicted by the dashed black line in Fig. 2(a). The amplitude of the single detection A-line is highest near the zero-delay and gradually decays as depth increases due to the RIN.

 

Fig. 2. (a) Comparison of single detection A-line (dashed line), mismatched balanced A-line (red line), and matched balanced A-line (green line) from a background noise image. (b) Comparison of mismatched and matched balanced spectra.

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When the subtracted signals have low spectral correlation (mismatched spectra), the noise floor of the mismatched balanced A-line (${I_{bal}}(z ))$ increases in amplitude beyond the single detection A-line, as demonstrated by the red line in Fig. 2(a). When the subtracted signals have high spectral correlation (matched spectra), the noise floor of the matched balanced A-line reduces in amplitude; it becomes nearly constant, as demonstrated by the green line in Fig. 2(a). The mismatched balanced A-line shows a higher mean amplitude and variance than the single detection A-line up to a depth ${z_f}$, indicated by the dashed blue line in Fig. 2(a). This same phenomenon is observed in the balanced interferograms (${I_{bal}}(k ))$ depicted in Fig. 2(b). When the subtracted spectra are mismatched, the mean amplitude and variance of the balanced interferogram increase; after matching the spectra using an interpolation vector, the mean amplitude and variance of ${I_{bal}}(k )$ reduces.

In the adaptive balance algorithm, we seek to minimize the mean amplitude and variance of the balanced A-line by selecting the coefficients of an interpolation vector using the Nelder-Mead simplex search algorithm [23]. The flowchart in Fig. 3 depicts the adaptive balance algorithm. We start by modeling the interpolation vector as a first-order polynomial

The penalty term prevents the simplex search from converging at local minima and from producing unlikely interpolation vector coefficients, such as $[{{c_1},\; {c_0}} ]= [{\; 0,\; 0} ].$ The penalty term scaling factor, α, scales the penalty term to prevent it from reaching a direct match result ($[{{c_1},{c_0}} ]= [{1,0} ]$) when there is a large pixel offset between the spectrometers. We empirically selected α by finding the value that consistently produces interpolation vectors that maximize image quality.

 

Fig. 3. Flowchart for adaptive balance interpolation vector optimization procedure.

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 After the first round of optimization is complete, the interpolation vector is updated to a second-order polynomial

2.3.5 Pre-calibrated control

Throughout this study, a pre-calibrated control interpolation vector was generated from a RIN-dominated dataset without a sample present (background noise only), where the spectrometer camera gain and exposure time were minimized. The interpolation vector was generated from the sample-free, RIN-dominated dataset using the NCC method. This control method served as a benchmark for evaluating the image quality for each interpolation vector selection method.

2.3.6 Direct spectrometer matching

To demonstrate the effects of not performing subpixel matching between the spectrometer pair, we compared images generated by direct pixel matching. In this method, pixels from both spectrometers were paired 1:1 by applying the interpolation vector $L[n ]= n$.

2.4 Tape phantom preparation and imaging parameters

To demonstrate BD-vis-OCT in a controlled sample, we imaged a phantom retina constructed using a 3 mm diameter borosilicate bead (P000464739, Winsted Precision Ball Co., Winsted, CT) fixed to a roll of tape (Scotch Magic Tape, 3 M) using optical adhesive (Norland Optical Adhesive 81, Cranbury, NJ). We acquired tape phantom image volumes consisting of 4096 A-lines × 128 B-scans over a scan range of 1000 µm × 40 µm.

2.5 Image quality assessment

We adopted three commonly used image quality metrics to compare BD-vis-OCT images. The standard deviation of the noise floor, ${\sigma _{floor}}$, was calculated to quantify the remaining pixel uncertainty after RIN suppression. Noise floor standard deviation was recorded between the zero-delay position and the surface of the tape phantom. The peak signal-to-noise ratio (PSNR) was calculated to quantify the pixel uncertainty with respect to the maximum signal value. We defined PSNR as

We measured the contrast-to-noise ratio (CNR) to quantify image contrast with respect to pixel uncertainty. CNR is defined as

2.6 Statistical analysis

A one-way analysis of variance (ANOVA) test was used to compare the image quality metrics for each case. A significance level of 0.05 was used for all statistical comparisons. All results were reported as mean ± standard error.

3. Results

3.1 Influence of spectrometer camera gain

We acquired tape phantom images before and after increasing the camera gain by 16. The images were then used as input datasets to generate interpolation vectors using the five methods described above. For each pixel-matching method, 4096 spectra were used as input throughout this study. Figure 4(a) shows balanced tape phantom B-scan images with low camera gain after subpixel matching using (from left to right in Fig. 4(a)) direct (1:1) matching, LMMSE, NCC, ICC, adaptive balance, and the pre-calibrated control method. The white arrow in Fig. 4(a) indicates the edge of the bead in the low gain control image. Qualitatively, we observed lower SNR for direct, LMMSE, and ICC methods compared to the NCC, adaptive balance, and control methods. In contrast, Fig. 4(b) shows tape phantom images with high camera gain after pixel matching using (from left to right in Fig. 4(b)) direct matching, LMMSE, NCC, ICC, adaptive balance, and the pre-calibrated control method. Comparatively, the direct, LMMSE, and ICC methods show lower SNR than the NCC, adaptive, and control matching methods with high camera gain.

 

Fig. 4. Tape phantom B-scan images with (a) low and (b) high camera gain reconstructed using (right to left) direct mapping, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control. White arrow indicates the edge of the glass bead; (c) σ_floor, (d) PSNR, (e) L₁ CNR, and (f) L₅ CNR for low and high camera amplification. Bars: 250 µm.

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Next, we compared the image quality metrics for each pixel-matching method and camera gain level. Figures 4(c)–4(f) respectively depict the σ_floor, PSNR, layer 1 (L₁) CNR, and layer 5 (L₅) CNR for each mapping method and camera gain level. The (*) in Figs. 4(c)–4(f) indicates no significant difference with respect to the control results. All the values are listed in Table 1. For low camera gain, the adaptive balance performed similarly to the control method in terms of PSNR and CNR for L₁ and L₅. The LMMSE and NCC methods produced similar CNR values for L₁ and L₅ compared to the control method but performed worse across all other metrics. Conversely, direct mapping and ICC methods performed consistently worse than the control method with low camera gain. For high camera gain, only the adaptive balance method showed comparable image quality to the pre-calibrated control method for PSNR, L₁ CNR, and L₅ CNR. The NCC method achieved comparable CNR values for increased camera gain.

Table 1. Spectrometer Camera Gain Image Quality Metrics^a

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3.2 Influence of spectrometer camera exposure time

We compared each pixel-matching method with short (8 µs) and long (40 µs) spectrometer camera exposures. Figure 5(a) shows the resulting tape phantom B-scan images for shorter exposure time after applying (from left to right in Fig. 5(a)) direct matching, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control matching methods. Qualitatively, we observed reduced SNR from the direct and LMMSE methods compared to the control image. SNR appeared to be comparable to the control for the NCC, ICC, and adaptive methods; however, the sharpness of the tape layers reduces with depth for the ICC matching method. Figure 5(b) shows the tape phantom B-scan images for longer exposure time after applying (from left to right in Fig. 5(b)) direct matching, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control methods. SNR appeared to be lower for the LMMSE method and more comparable to the control for the direct, NCC, ICC, and adaptive balance methods.

 

Fig. 5. Tape phantom B-scan images with (a) 8 µs and (b) 40 µs spectrometer exposure time reconstructed using (right to left) direct mapping, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control methods; (c) σ_floor, (d) PSNR, (e) L₁ CNR, and (f) L₅ CNR for 8 µs and 40 µs exposure time. Scale bars: 250 µm.

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The quantitative image quality metrics are shown in Figs. 5(c)–5(f), including σ_floor, PSNR, L₁ CNR, and L₅ CNR. The values for each matching method and exposure time are given in Table 2. For short spectrometer camera exposure time, the adaptive balance performed as well as the pre-calibrated control method for all metrics other than σ_floor. NCC showed comparable performance for L₁ and L₅ CNR. For long spectrometer camera exposure time, the adaptive balance had comparable image quality to the control case for all metrics other than σ_floor. NCC and ICC methods had comparable image quality to the control method for L₁ and L₅ CNR.

Table 2. Spectrometer Camera Exposure Time Image Quality Metrics^a

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3.3 Influence of SC laser repetition rate

We compared the performance of each spectrometer matching method with low (30 MHz) and high (300 MHz) SC laser repetition rates. Figure 6(a) shows the tape phantom B-scan acquired using the low repletion rate with (from left to right in Fig. 6(a)) direct matching, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control methods. Qualitatively, we observed low SNR images after applying direct matching, LMMSE, and ICC methods. SNR was comparable to the control method for NCC and adaptive balance methods. Figure 6(b) shows the tape phantom B-scans acquired using the high repetition rate after applying (from left to right in Fig. 6(b)) direct matching, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control methods. SNR appeared to be reduced after applying direct matching, LMMSE, and ICC matching methods. SNR was comparable to the control method for ICC and adaptive balance methods.

 

Fig. 6. Tape phantom B-scan images with (a) 30 MHz and (b) 300 MHz SC laser repetition rate reconstructed using (right to left) direct mapping, LMMSE, NCC, ICC, adaptive balance, and pre-calibrated control methods; (c) σ_floor, (d) PSNR, (e) L₁ CNR, and (f) L₅ CNR for 30 MHz and 300 MHz repetition rate. Scale bars: 250 µm.

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Comparisons of the image quality metrics are shown in Figs. 6(c)–6(f) for σ_floor, PSNR, L₁ CNR, and L₅ CNR, respectively, where (*) indicates no statistically significant difference with respect to the control result. Values for each image quality metric are listed in Table 3. For low SC laser repetition rate, the adaptive balance showed comparable performance to the control method for all image quality metrics other than σ_floor. The NCC method achieved similar CNR values compared to the control. For a high repetition rate, the adaptive balance had comparable performance to the control method for all image quality metrics.

Table 3. SC Laser Repetition Rate Image Quality Metrics^a

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3.4 Human retinal imaging

To further demonstrate the performance of adaptive balance, we used a human retina image as input to determine the spectrometer interpolation vector. Human imaging was performed using an experimental BD-vis-OCT system described previously [16]. All imaging procedures were approved by Northwestern University IRB.

We acquired 5 mm × 5 mm volumes (16 B-scans × 8192 A-lines/B-scan) from a healthy 26-year-old male subject. Figures 7(a)–7(c) respectively show the test retinal B-scan image after applying direct matching, adaptive balance, and pre-calibrated control. Qualitatively, the adaptive and pre-calibrated control methods show the least background noise and higher SNR than direct matching. Further, the adaptive balance method shows better autocorrelation artifact removal, as indicated by the yellow boxes in Figs. 7(a)–7(c), compared to the direct matching and pre-calibrated control methods. The magnified images in Figs. 7(d)–7(f) further compare the level of RIN and autocorrelation artifact removal using direct matching, adaptive balance, and the control method, respectively.

 

Fig. 7. Human retinal images reconstructed using (a) direct matching, (b) adaptive balance, and (c) pre-calibrated control interpolation vector. Yellow boxes indicate an autocorrelation artifact. (d)-(f) magnified views of regions highlighted in panels a-c, respectively. Bars: 250 µm.

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4. Discussion

We introduced an adaptive, calibration-free approach for matching the wavelength-dependent pixel elements of a spectrometer pair with subpixel accuracy, referred to as adaptive balance. We demonstrated the robustness of this method against other subpixel matching techniques by comparing each method’s ability to suppress RIN from tape phantom images acquired with varying spectrometer camera gain, exposure time, and SC laser repetition rate. Lastly, we compared adaptive balance with two other methods in humans.

RIN is a frequency-dependent noise that is strongest at lower frequencies and falls off rapidly at higher frequencies [21,22]. Thus, in traditional SD-OCT images, RIN manifests as a high-intensity background signal near the zero-delay position that falls off gradually as depth increases. The RIN bandwidth, or depth at which the background intensity reaches 6 dB of its zero-delay intensity, is inversely proportional to the spectrometer’s exposure time and SC laser’s repetition rate [24]. Thus, the RIN bandwidth reduces with increased spectrometer camera exposure time and SC laser repetition rate. However, prolonged spectrometer exposure time leads to a reduced A-line rate, which increases the probability of motion artifacts in human imaging. In addition, SC lasers with high repetition rates are significantly more expensive, which can be cost-prohibitive for users. Suppressing RIN with BD-OCT has increased the imaging speeds and allowed the use of less expensive, low repetition rate SC lasers, which makes techniques, such as vis-OCT, more practical for clinical adoption.

Adaptive balance uses the background intensity decay caused by RIN to generate the pixel-matching interpolation vector. Selecting pixels near the zero delay effectively serves as a low-pass filter to extract the balanced DC components. When the wavelengths of the subtracted interferograms are mismatched, the DC component of the balanced interferogram increases in amplitude and variance. Our adaptive balance method automatically selects interpolation vector coefficients that minimize the amplitude and variance of the DC term. Because adaptive balance selects interpolation vector coefficients based on the characteristics of the DC component, it can be applied to any SD-OCT dataset regardless of RIN or signal level. As demonstrated by each test case shown in Figs. 4–6, adaptive balance can achieve the same level of noise suppression as the control method that generated an interpolation vector from a RIN-dominated dataset. Such noise suppression was achieved in a spectrometer pair that had a maximum separation of ∼54 pixels, which corresponded to a 2.8 nm separation in wavelength. This separation had a negligible impact on the axial resolution before and after balancing.

The spectrometer camera gain level influences the intensity of the detected interferogram before reaching the saturation level of the camera’s digital-to-analog converter. Thus, with low camera gain, higher intensity can be recorded. At low camera gain, the reference arm power can be increased to its maximum level, as we did here. Because RIN scales by a power of two of the incident power [11], spectrometer matching methods requiring RIN-dominated input perform better with low camera gain. Indeed, we observed improved performance from the NCC method at low camera gain. However, when the camera gain was increased 16-fold, the reference arm power had to be reduced by 16 to avoid detector saturation, which reduced the RIN amplitude relative to other noises. We observed improved image quality from the ICC method when gain was increased. Notably, adaptive balance performed better than or comparable to the pre-calibrated control method regardless of amplification level, thus, providing a robust subpixel matching method without needing pre-calibration.

In traditional SD-OCT systems using only one spectrometer, the effects of RIN can also be mitigated by increasing camera exposure time. Longer exposure time integrates more SC pulses for each A-line, which effectively increases the signal and reduces the RIN [24,25]. Thus, for RIN-based spectrometer matching methods, the exposure time is reduced to a minimal value to capture the highest RIN amplitude possible. Although the NCC method showed better image quality for 8 µs than 40 µs, it did not perform as well as adaptive balance in either case. At 40 µs exposure time, ICC image quality improved but did not surpass adaptive balance quality. The integration time test case results suggest adaptive balance is the most robust spectrometer matching method when the exposure time is varied.

Another solution for mitigating the effects of RIN in traditional SD-OCT systems is to use a high repetition rate SC laser. Increasing the repetition rate allows more SC pulses to be integrated for the same spectrometer camera exposure time [24,26]. In Fig. 6, we compared balanced image quality using a 30-MHz and a 300-MHz laser. Like other tests, adaptive balance performed as well as the pre-calibrated control and better than the other subpixel matching methods regardless of the repetition rate. Similarly, we saw improved performance from the NCC over the ICC method using the 30 MHz laser compared to the 300 MHz laser. These findings also suggest adaptive balance is the most robust spectrometer matching approach when the light source repetition rate is varied.

One of our goals was to generate the optimal pixel-matching interpolation vector from any input OCT image. For each test case, we used tape phantom images as input data for each pixel-matching method. We found that LMMSE yields significantly worse image quality when an OCT dataset containing an interference signal was used as input rather than a signal-free, RIN-dominated dataset. This is because LMMSE assumes the intensity values of the input vectors are normally distributed [27]. When a RIN-dominated dataset without sample interference is used, this assumption holds true because there is no signal to affect the pixel intensity distribution. However, when the input dataset is not RIN-dominated or contains sample interference, the input datasets are no longer normally distributed, leading to a biased LMMSE result. Thus, for cases where the RIN-dominated, sample-free condition cannot be satisfied, the LMMSE method should be avoided.

We tested the performance of adaptive balance using only ten spectra from the tape phantom as input. The results showed that even with very few spectra, the adaptive balance still achieved no significant difference in PSNR and CNR, whereas all the other methods showed significantly worse performance. This is because adaptive balance optimizes the shape of the balanced spectrum directly, while the other methods, such as LMMSE, NCC, and ICC require many samples to detect a strong enough temporal correlation from RIN or signal. This result also demonstrates the robustness of adaptive balance for identifying optimal interpolation vectors.

The computational time for each method to generate an interpolation vector from 4096 A-lines was as follows: LMMSE: 0.5 sec, NCC: 0.6 sec, ICC: 14.0 sec, and Adaptive Balance: 98.3 sec using a computer with an 8 core 3.6 GHz processor, NVIDIA RTX 3070 graphics processor, and 128 GB of memory, Despite having a longer computational time, we demonstrated that our adaptive pixel-matching approach is more robust than previously proposed methods that require RIN- or signal-dominated inputs. Further, we found that pixel maps for a commercial spectrometer pair can remain stable for months. Therefore, the optimization process does not need to be repeated for each patient, but rather every few months to ensure optimal noise suppression.

5. Conclusion

Previously, we demonstrated that balanced detection using the pre-calibrated control method for subpixel spectrometer matching enables shot-noise-limited imaging [16]. In SD-OCT, A-line intensity scales linearly with reference arm power [10,28]. For a shot-noise-limited system, A-line noise variance scales linearly with reference arm power, whereas for a RIN-dominated system, it scales with the square of the reference arm power [10]. Thus, image quality metrics, such as PSNR, in a shot-noise-limited system should remain the same when the reference arm power varies [10,11,24]. In the present study, reference arm power changed 93% between the low and high spectrometer camera gain images. However, the PSNR and CNR values showed no significant difference between the low and high gain cases for adaptive balance and the control methods. Further, there was no significant difference between adaptive balance and the control methods for low and high spectrometer camera gain. Moreover, for varied spectrometer camera exposure time and SC laser repetition rate, we found no significant difference between adaptive balance and the control method for PSNR and CNR. In conclusion, our adaptive balance method achieves shot-noise-limited imaging for SD-BD-OCT without the need for pre-calibration, which sets the stage for future clinical adoption.