Speckle contrast reduction through the use of a modally-specific photonic lantern for optical coherence tomography

A few-mode optical coherence tomography (FM-OCT) system was developed around a 2 × 1 modally-specific photonic lantern (MSPL) centered at 1310 nm. The MSPL allowed FM-OCT to acquire two coregistered images with uncorrelated speckle patterns generated by their specific coherent spread function. Here, we showed that averaging such images in vitro and in vivo reduced the speckle contrast by up to 28% and increased signal-to-noise ratio (SNR) by up to 48% with negligible impact on image spatial resolution. This method is compatible with other speckle reduction techniques to further improve OCT image quality.

Few-mode OCT (FM-OCT) is an all-fibered version of bright and dark field (BRAD) OCT [37].In FM-OCT, the few-mode tip of a modally-specific photonic lantern (MSPL) [38][39][40] is coupled to an OCT imaging head allowing the collection of both the fiber fundamental mode (i.e., the linearly polarized (LP) mode LP01) and the first higher-order mode LP11.The MSPL then demultiplexes the two modes into two single-mode fibers connected to independent OCT systems [40].Illumination is otherwise performed through the fundamental mode.This approach allows FM-OCT to create two OCT images (or a composite one) from the backscattered light coupled into LP01 and LP11, respectively.
Here, we demonstrate how the two distinct OCT images create specific speckle patterns that can further be averaged to reduce the speckle contrast while increasing the signal-to-noise ratio (SNR) with minimal impact on the image's lateral resolution.

Instrumentation
The FM-OCT system used for data acquisition is illustrated in Fig. 1(a) and is similar to the one used in our previous work [40].The custom-built MSPL used to separate the modes was centered at 1310 nm.A wavelength-swept laser (Thorlabs SL1310V1, USA) and two balanced detectors (Thorlabs PDB430C, USA) were used for illumination and detection, respectively.The system allowed for simultaneous measurement of both MSPL channels (i.e., LP01 and LP11 modes).The MSPL was further replaced by a single-mode fiber (SMF) for comparing the performance of the FM-OCT with a conventional OCT setup.The collimator was changed to compensate for the difference in numerical aperture (NA) between MSPL and SMF and to obtain the same collimated beam diameter, resulting in a system NA of ∼0.05 after the imaging lens (Thorlabs LSM02, USA).The resulting theoretical coherent spread functions (CSF) [41,42] in each channel are illustrated in Fig. 1(b) and (c).For the CSF in the LP11 mode, the negative response (in blue) was due to a π rotation of the detected phase signals.The symmetry and anti-symmetry between Channel 1 (LP01) and Channel 2 (LP11) allow to generate uncorrelated speckle patterns.This characteristic is key to reducing speckle contrast after averaging.

Imaging metrics
Following previous studies [5,43], speckle contrast (C s ) was defined as: where σ s and ⟨I s ⟩ are, respectively, the standard deviation and the average of the OCT speckle signal intensity in the absence of noise.More specifically, the OCT signal intensity is defined as the absolute values of the square of the complex signal of the field obtained by applying the Fourier transform [44].Here, we define noise as the signal measured in the absence of a sample and is thus dominated by shot noise.Since noise is also uncorrelated between the two channels, it does not affect C s .It was previously shown that for a fully developed OCT speckle contrast, C s = 1 [43,45].For FM-OCT, theory informs that averaging two uncorrelated speckle intensity patterns allows to reduce speckle contrast such that [43]: where ⟨I 1 ⟩ and ⟨I 2 ⟩ are the average OCT speckle intensities of Channels 1 and 2, respectively and C r is the expected reduced speckle contrast.When considering r = 1, C r is minimum and equals 1/ √ 2. In our work, the signal (I a ) averaged from signals measured in the two channels was calculated in linear scale as follows: Intensity averaging instead of complex field averaging is necessary to have a reduction in speckle contrast.When considering an FM-OCT system of N uncorrelated channels, the expected speckle contrast is given by C r = 1/ √ N [43].To ensure that two speckle patterns are uncorrelated, their cross-correlation was calculated using the second-order correlation function [45][46][47]: where ⟨I 1 ⊗ I 2 ⟩ is the ensemble average of the Hadamard product between I 1 and I 2 .
Combining signals I 1 and I 2 also affects the SNR, which can be assessed with different approaches [5,44,[48][49][50].In this work, an approach considering the OCT signal intensity [49] was selected: where I OCT is the OCT signal intensity measured from the sample while σ BN is the standard deviation of the OCT signal intensity measured in the absence of a sample, i.e., the background noise.With this approach, σ BN was dominated by shot noise, and not by speckle.
The maximum SNR of the system (SNR max ) was also assessed [48] for both the SMF and MSPL configurations.A mirror was used as a sample and placed at the focal plane to maximize the OCT signal.A tilted attenuator (Thorlabs NE40A, USA) was added to avoid saturating the balanced detector.One A-line was acquired to calculate SNR max using a modified version of Eq. ( 5) to account for the presence of an attenuator: where T is the attenuation transmission that was measured experimentally using a power meter (Thorlabs S145C, USA) and R m is the mirror power reflection coefficient, approximated as 1.Furthermore, the retro-reflection power was measured using the same power meter by adding an extra circulator between the MSPL and circulator C1.To confirm the origin of the retro-reflection power, the reference arm length was adjusted to permit OCT imaging at the MSPL tip and determine where the retro-reflection occurred.
An A-line was acquired from the reflection of a mirror to assess the system axial resolution of all system configurations.The full width at half maximum (FWHM) was evaluated by fitting a Gaussian curve on the linear intensity signal of the mirror.The mirror was tilted to avoid the saturation of the balanced detectors.Dispersion was measured using an approach described previously [51].
To evaluate the lateral resolution, a C-scan of 840 by 920 A-lines (field-of-view of 1093 µm by 954 µm) of a negative reflective USAF-1951 resolution test chart was acquired.The resolution target was placed at the focal plane of the imaging lens by maximizing the OCT signal originating from the test chart layer.The resulting en face image (1 pixel thick) was displayed in dB scale.The edge response was also extracted from this image in dB scale and displayed on a normalized scale to facilitate the comparison between the different MSPL channels.The 10-90% edge response distances were calculated using the resolution chart measurement in the horizontal and vertical axes.Cubic spline interpolation was used to measure the signal transition more precisely.The edge response was not calculated for Channel 2 since its CSF does not have a Gaussian response [40].The image spatial resolution was also assessed by measuring the smallest distinguishable USAF-1951 groups of elements (bars) in the vertical and horizontal directions.Measurements were performed for both SMF and MSPL configurations.

In vitro and in vivo imaging
The definition of speckle contrast from Eq. ( 1) considers that signal variability is explained only by the speckle effect.Experimentally, signal variation is caused by other processes, including, but not limited to, signal attenuation and sample heterogeneity.Because of this consideration, speckle contrast values are calculated locally, where speckle dominates signal variability.For both in vitro and in vivo experiments, the region of interest (ROI) was subdivided in homogeneous subregion blocs of 4 by 4 pixels.C s and SNR were calculated for each such subregion and then averaged.The metrics were calculated for the combined MSPL channel (I a ) as well as for individual MSPL Channels 1 (I 1 ) and 2 (I 2 ).
In vitro imaging was performed on a plastic cap engraved with the number "8" (Thorlabs, NJ, USA) and consisted of a C-scan composed of 840 by 920 A-lines (field-of-view of 8912 µm by 8137 µm).Speckle contrast and SNR were measured in an en face section within the cap (1 pixel thick) displayed in dB scale.The ROI for C s and SNR calculations included the entire 840 by 920 en face image.The normalized second-order cross-correlation between Channel 1 and Channel 2 was evaluated to assess their intensity-intensity correlation.
In vivo imaging was further performed near the free edge of an index fingernail.It consisted in a single B-scan comprising 1000 A-lines.C s and SNR were measured on a rectangular ROI of 40 pixels per 62 pixels.

Results and discussion
Table 1 presents SNR max and retro-reflection optical power measured for the SMF and MSPL optical configurations, respectively.Table 1 also shows the FWHM of the Gaussian fit of an OCT A-line of a mirror in intensity in linear scale.Compared to the SMF configuration, a 10-20 dB decrease in SNR max is observed for the MSPL system.This decrease is due to increased retro-reflection power at the air-MSPL interface.Typically, fiber connectors for angled physical contact (FC/APC) are used in OCT as their tip is polished at an angle to minimize retro-reflections at the air-fiber interface.In its current configuration, the MSPL tip, however, has a minute diameter of 8 µm, which is too fragile for polishing.Cleaving the tip at a controlled angle is also challenging.An elegant solution involves splicing the MSPL tip to a few-mode fiber large enough to sustain polishing.It was successfully achieved by another group [52], albeit using equipment not currently available to our research group.
The SNR max for Channel 2 is also significantly lower than that of Channel 1.This difference may be explained by the coupling model previously suggested by our group [40] where light reflected off a mirror was coupled back into LP11 with reduced efficiency.Indeed, if illumination was performed with LP11 instead of LP01, we expect a larger SNR max for Channel 2. However, as the speckle reduction demonstration was performed under LP01 illumination, we present SNR data under the same experimental conditions.SNR max was not measured when considering the combination of Channel 1 and Channel 2 since they reached a maximum SNR for their specific alignments [40].Additionally, the power transmission of each optical component from one channel to the other can vary, which affects SNR. Figure 2(a) shows A-lines of a mirror comparing axial resolutions for the SMF and MSPL optical configurations.The normalized intensity is displayed in linear scale.The peaks were aligned and normalized for ease of comparison.In terms of FWHM (Table 1), Channel 1 shows a slightly higher resolution than the SMF configuration and Channel 2. This observation is likely due to the combined channels having a slightly better resolution than the SMF configuration but slightly worse than that of Channel 1.We believe these variations are due to physical compensations of the respective dispersion profiles.Figure 2(b) indeed shows that Channel 1 exhibits less dispersion than Channel 2. Combining the two channels resulted in an average of the resolutions of Channel 1 and 2. The MSPL did not induce significant dispersion, nor did combining the channels deteriorate the axial resolution significantly.Figure 3 shows en-face OCT images of a negative reflective USAF-1951 test chart (first row), zooms of the smaller groups (second row), and normalized intensity signals (third row) measured in ROIs (blue and green regions located in the squared element of the first row).Images are displayed in dB scales.The characterization of the system's lateral resolution was performed for the following optical configurations (Fig. 3): SMF (a), (e), (i), combined MSPL channels (b), (f), (j), MSPL Channel 1 (c), (g), (k), and MSPL Channel 2 (d), (h), (l).MSPL Channel 1, combined MSPL channels, and SMF configurations generated similar images in terms of spatial resolution.For the SMF configuration, the smallest distinguishable elements in the vertical and horizontal directions were Group 7, Element 1 (with a bar thickness of 3.91 µm) and Group 6, Element 6 (with a bar thickness of 4.38 µm), respectively.Both the combined channels and Channel 1 resolved Group 6, Element 6 (with a bar thickness of 4.38 µm) in both the vertical and horizontal directions.The difference in bar thicknesses measured for Group 6, Element 6 by the SMF and MSPL configurations might be explained by variations in the system NA as described in Sec.2.1.More interestingly, the combined channels and Channel 1 could resolve the same element, suggesting that averaging the speckle with our method did not affect the image spatial resolution.Figure 3(j)-(l) displays the 10-90% edge response distances horizontally and vertically.The horizontal and vertical SMF edge response distances were 5.3 µm and 5.9 µm, respectively.For the combined MSPL channels, the horizontal and vertical distances were 3.0 µm and 4.0 µm, respectively, while for Channel 1, the distances were 3.0 µm and 3.6 µm, respectively.The SMF spatial resolution assessed by the quantitative method was lower than for the MSPL system, while it was the opposite observation for qualitative measurements of the smallest distinguishable elements.This inconsistency is likely due to the limitation to obtaining a perfect Gaussian response in the MSPL configuration (Fig. 3(i)-(l)).Both the quantitative and qualitative methods to assess the MSPL spatial resolution suggest that combining the channels had limited impact on it.Figure 2(l) suggests that the MSPL Channel 2 acts as an edge detector in the vertical axis of the image.This is likely due to the CSF shape mimicking the application of a Sobel filter used for image edge detection [53].In Fig. 2(i), a dip in the signal was observed, which is not occurring in Fig. 2(j)-(l).It is probably due to a speck of dust on the test chart that was not present in the other images since the alignment was slightly changed when changing from the SMF to the MSPL configurations.second-order cross-correlation measured between MSPL channels was 1.04, suggesting that the two speckle patterns are uncorrelated.The engraved shape (number 8) of the cap becomes more visible when the speckle contrast is reduced, i.e., for the combined MSPL channels (C s = 0.713) compared to separate channels (C s = 0.979 and C s = 0.984 for MSPL Channel 1 and 2, respectively).This represents a reduction of 27% and 28%, respectively.This improvement corresponds to what was predicted by Eq. ( 2).SNR also improves when combining MSPL channels (SNR = 16.9)compared to MSPL Channel 1 (SNR = 14.5) and Channel 2 (SNR = 11.4),respectively.This represents an SNR improvement of 17% and 48%, respectively.In the zoom-in images, the averaged speckle pattern becomes smoother for the MSPL combined channels configuration, which indicates a lower speckle contrast.This observation also applies to the in vivo images of the fingernail, where the MSPL combined speckle contrast patterns (C s = 0.722) is reduced compared to that of individual channels (C s = 0.976 and C s = 0.991 for MSPL Channel 1 and Channel 2, respectively).This represents a reduction of speckle noise of 26% and 27% and an increase in SNR of 40% and 16%, for Channel 1 and Channel 2, respectively.A higher SNR was observed for in vivo images with respect to in vitro images.This difference is likely due to the depth of the ROI, which was higher for in vitro images.Furthermore, a higher SNR was observed in Channel 2 compared to Channel 1 in in vivo images compared to in vitro images.This is consistent with biological tissues containing a wide variety of scatterer geometries which were shown by our group to have a strong effect on modal coupling efficiencies [40].These results show a reduction of speckle noise in both in vitro and in vivo experiments when using an MSPL optical configuration for OCT imaging.The results also suggest that adding additional higher modes would further decrease speckle noise as long as additional CSFs are orthogonal.In addition, the MSPL could be combined with other speckle-reduction techniques for more effectiveness.These capacities have to be demonstrated in a future study.

Metrics
Aside from managing the retro-reflection from the tip of the MSPL, described earlier, limitations in this study included the SMF and MSPL having different NAs which required adapting the imaging head, namely the collimating lens, to compare the lateral resolution for each configuration properly.An additional challenge came from properly choosing the subregion size for speckle contrast measurement.The subregion size was chosen by simulating a range of phasors until speckle contrast yielded values consistent with that of a fully developed speckle pattern.

Conclusion
We have demonstrated how an MSPL can be used in an OCT system to reduce the speckle contrast and increase SNR with negligible impact on image spatial resolution.We have measured a significant decrease in speckle contrast in both in vitro (27-28%) and in vivo (26-27%) experiments.Combining the two channels into a composite image increased the SNR over Channel 1 and Channel 2 by 17% and 48%, respectively in vitro, and by 40% and 16%, respectively, in vivo.Further improvement is expected in speckle reduction by adding modes through a 3 × 1 or 4 × 1 MSPL, and by integrating common speckle reduction techniques to the resulting OCT image.However, as several reference arms are necessary to account for different modal propagation constants, photon budgeting must be adjusted accordingly with a more powerful laser.

Fig. 1 .
Fig. 1.(a) Schematic of the few-mode optical coherence tomography (FM-OCT) system including the modally-specific photonic lantern, the illumination and detection components, and two reference arms; one for each mode.(b), (c) Coherent spread functions of the LP01 and LP11 modes, respectively.

Fig. 3 .
Fig. 3. En-face OCT images of a negative reflective USAF-1951 resolution test chart (a)-(d) with a zoom-in of the region delimited by the red square (e)-(h) for the specific modes of collections: single-mode fiber (SFM), combined modally-specific photonic lanthern (MSPL) channels, MSPL Channel 1, and MSPL Channel 2. The system's edge responses in dB (i)-(l) for the vertical (corresponding to signals normalized from the green region, first row) and horizontal (corresponding to signals normalized from the blue region, first row) axes.The fields of view of the first and second rows are 1093 µm by 954 µm and 283 µm by 247 µm, respectively.

Figure 4 Fig. 4 .
Fig. 4. En-face OCT images of within a plastic cap engraved with the number 8 acquired with (a) the combined MSPL channels, (b) Channel 1, and (c) Channel 2. Speckle contrast (C s ) and SNR values are provided for each case.(d)-(f) Corresponding zoom-in images of the speckle pattern for each optical configuration.(g)-(i) In vivo B-scans of a fingernail and corresponding speckle contrast and SNR for each case.All images are displayed in dB scale.