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Spectrally encoded dual-mode interferometry with orthogonal scanning

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Abstract

Spectrally encoded confocal microscopy (SECM) is a high-speed reflectance confocal microscopy technique. Here, we present a method to integrate optical coherence tomography (OCT) and SECM for complementary imaging by adding orthogonal scanning to the SECM configuration. The co-registration of SECM and OCT is automatic, as all system components are shared in the same order, eliminating the need for additional optical alignment. The proposed multimode imaging system is compact and cost-effective while providing the benefits of imaging aiming and guidance. Furthermore, speckle noise can be suppressed by averaging the speckles generated by shifting the spectral-encoded field in the direction of dispersion. Using a near infrared (NIR) card and a biological sample, we demonstrated the capability of the proposed system by showing SECM imaging at depths of interest guided by the OCT in real time and speckle noise reduction. Interfaced multimodal imaging of SECM and OCT was implemented at a speed of approximately 7 frames/s using fast-switching technology and GPU processing.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Spectrally encoded confocal microscopy (SECM) is a reflectance confocal microscopy technique that can significantly accelerate imaging. Unlike conventional spot scanning confocal microscopes, SECM can simultaneously capture a line view of a sample with spectrally dispersed line illumination and transmit it as a spectral signal through an optical fiber, enabling high-speed confocal imaging [1]. SECM has been applied to image large areas of esophageal tissue at high linear imaging rates [2,3]. Subsequently, in-vivo imaging of the human esophagus was performed using an SECM-based endoscope [4]. A spectrally encoded confocal scanning laser ophthalmoscope was used for in-vivo human fundus imaging [5]. Imaging of human skin has been performed using SECM, allowing visualization of cellular and subcellular details [6,7]. The potential of SECM for label-free imaging of the model organism Caenorhabditis elegans (C. elegans), has been reported [8]. Using spectral-domain interferometry, SECM is also capable of three-dimensional video-rate topographic [911] and flow imaging of blood cells by measuring spectral phases [12,13]. Spectral-encoded interferometric microscopy has also been used to measure the oscillation frequency of tissue motion of the tympanic membrane and tubal ciliary body [14,15].

Nevertheless, the SECM has some limitations. As with other high-resolution confocal microscopes, it is difficult to accurately predict the depth at which an en-face image is acquired below the sample surface. It is necessary to scan the depth of the focal point within the sample for cross-sectional images because of the narrow depth of focus generated by the high numerical aperture objective, which makes fast cross-sectional imaging difficult. There are approaches that can be integrated with optical coherence tomography (OCT), which enables fast cross-sectional imaging. The benefits of image aiming, guidance, and motion tracking can be obtained when two orthogonal images, SECM and OCT, are co-registered at the same target location. The reported multimodal systems share some of the illumination source, detection system objective lens, dispersive element, and scanning optics between SECM and OCT in a way that provides a simple multimodal system [1620]. However, because all components constituting the system cannot be shared, additional sophisticated optical alignments are required for accurate co-registration of SECM and OCT.

Additional consideration occurs when performing SECM below the surface of multi-scatter samples, such as living tissues. It is speckle noise caused by high temporal coherence owing to the multiple narrowband detections of spectrally divided illumination like imaging with coherent light. Speckle noise can be reduced by decreasing the spatial coherence using a multimode fiber in the detection path [3] or by using a light-emitting diode (LED) as a light source [6,7]. However, these two methods cannot be used in spectrometer-based or fiber-based SECM respectively. In fact, SECM using spectrometer detection and fiber optic illumination enables optical cross-sectional 3D imaging with low speckle noise only for low-scattering samples, such as Xenopus laevis, zebrafish embryos, and C. elegans [8].

In recent years, there are several high-resolution OCT-based methods that achieve both en-face and cross-sectional imaging. To enable tracking of the eye position and matching the arms of the full-field time-domain (FF-TD) OCT interferometer in real-time, SDOCT was integrated into FF-TD OCT. En-face images of corneal cellular structures were achieved at the rate of 275 frames per sec using a high speed camera [21]. A dual-mode line-field confocal (LC) OCT system was also introduced to produce both B-scans and C-scans in real time with a spatial resolution of ∼ 1 µm for skin imaging. The images were acquired in both modes at a rate of 10 frames per second [22]. Nonetheless, such OCT imaging using full and line field illumination has limitations for endoscopic implementation for flexible endoscopy. Spectrally encoded endoscopy, on the other hand, can be implemented using single-mode fiber as an endoscope guide into the body [23]. In spot scanning OCT, using a novel CMOS camera fast 3D OCT imaging with 600,000 A-scans/s was demonstrated at 1.8 µm axial and 1.1 µm lateral resolution [24]. However, the frame rate of en-face imaging, which is calculated as 2.4 frames/s when a frame is 500 × 500 pixels, is not sufficient to avoid sample-motion artifacts during X-Y beam scanning. On the other hand, SECM can perform fast lateral scanning at a rate of a few hundred frames unlike such Fourier domain OCT.

In this study, we present a method for integrating OCT with SECM by adding orthogonal scanning to an SECM configuration with single lateral scanning. The co-registration of SECM and OCT is automatic, as all components of the system including a diffraction grating are shared in the same order, eliminating the need for additional optical path and alignment, which is critical to make a miniaturized endoscopic probe. In addition, by shifting the spectral-encoded lines in the direction of dispersion, different wavelengths can be applied to the sample to generate speckles with different spatial structures, and speckle noise can be suppressed by averaging these speckles over time. Furthermore, an additional speckle noise reduction effect can be obtained when used in parallel with the aforementioned methods. We demonstrate the capability of the integrated multimodal system by showing SECM at depths of interest aimed at OCT and speckle noise reduction using a NIR card and a thick biological sample.

2. Methods

2.1 System setup

The layout of the proposed spectrally encoded dual-mode interferometric microscopy (SEDIM) is shown in Fig. 1. It is a fiber-based Michelson interferometer that uses a fiber coupler (75/25). A superluminescent diode (SLD, D-840-HP-I, Superlum Inc.) with a central wavelength of approximately 840 nm and bandwidth of 50 nm was used to generate a spectrally dispersed line. The 75% of the light from a fiber coupler (TW850R5A2, Thorlabs Inc.) was collimated and then diffracted by passing it through a transmission grating (1200 line/mm, Wasatch Photonics Inc.) in the Littrow configuration. The beams spectrally dispersed in the grating plane were recombined on the x-axis mirror of the galvanometer scanner using relay optics (2xAC254-050-B, Thorlabs Inc.) and then reflected by the other mirror for y-axis scanning. A combination of a scan (LSM03-BB, Thorlabs Inc.), tube (LSM03-BB, Thorlabs Inc.), and objective (NIR LCD Plan APO 20x, Mitutoyo Inc.) lens was used to create a high-resolution focal plane on the sample with an effective numerical aperture of 0.2. Theoretically, the lateral resolution was estimated to be 2 µm. The full width at half maximum of the spectrally dispersed line field on the sample was 210 µm. The backscattered light from the sample was passed to a custom spectrometer through the optics and fiber coupler. A reference beam reflected by a mirror in the reference arm was used to produce an interferometric signal with the backscattered light from the spectrally encoded line field of the sample. The reference arm included an optical delay line to compensate for the dispersion between the two arms.

 figure: Fig. 1.

Fig. 1. Schematic of the proposed spectrally encoded dual-mode interferometric microscopy

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A custom spectrometer equipped with a high-speed commercial CMOS line camera (maximum 70 k spectra/s for full pixels, 4096 pixels for full line, 10 µm × 10 µm per pixel; Basler Inc.) was used to measure the interference signals. The spectrally encoded line field can be decoded as a reflectance function of the sample position along the line field using a spectrometer. For imaging at a high acquisition rate of 200 k spectra/s, 1024 pixels of the line camera were used to digitize and record the spectral signal, spanning a bandwidth of 50 nm. Each pixel intensity was digitized to a 12-bit depth and then sent to the host computer using a camera-link frame grabber (PCIe-1473R, NI Inc.). The timing signal of the TTL pulse was generated with an FPGA in the frame grabber at an acquisition speed of 200 k spectra/s and used to synchronize with the galvanometer-based x-y scanning. The exposure time was set to 3.6 µs.

2.2 Scanning control strategy

2.2.1 Fast switching between the SECM and OCT

We sequentially acquired 2000 spectra with a sampling period of 5 µs to form an image frame of the SECM or OCT while the spectrally spread line field was scanned. SECM images were acquired when the spectrally dispersed line field was laterally scanned perpendicular to the line direction, as shown in Fig. 2(a). In contrast, we obtained OCT images when the line field was scanned along the dispersed direction, as shown in Fig. 2(b). In Fig. 2(c), SECM generates en-face images in the x-y plane, and OCT generates cross-sectional images in the y-z plane. For SECM, a length of 210 µm was scanned with 2000 samples. In the OCT imaging mode, we scanned the line illumination by a length of 1.37 mm with a stair function of 2000 voltage steps for a frame, yielding a 0.7 µm sampling interval, which is three times less than the optical lateral resolution of 2 µm. The details of the signal processing used to generate the SECM and OCT images with the acquired 2000 spectra are explained in Section 2.3.

 figure: Fig. 2.

Fig. 2. Scanning direction for (a) SECM and (b) OCT. (c) SECM and OCT give a horizontal and vertical image, respectively. Both images have the same center position. (d) Voltage waveform pairs required for X- and Y-scans for the SECM and OCT were selected from the analog outputs of an ADC card and fed to the x and y galvanometer scanner using an analog multiplexer.

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Using a monolithic CMOS analog multiplexer (ADG609, Analog Devices Inc.), a pair of voltage waveforms required for X- and Y-scans for each SECM and OCT were selected and fed to the x and y galvanometer scanners. The two voltage waveforms for SECM X-Y scanning supplied from the analog outputs AO1 and AO2 of the analog digital converter (ADC, PCIe-6353, NI) were transferred to one of the four input channels of the multiplexer chip, and the outputs of AO3 and AO4 for the OCT were input to another channel, as shown in Fig. 2(d). The total switching time between the SECM and OCT was estimated to be at most 130 ns from the multiplexer chip specification.

2.2.2 Speckle reduction in SECM with an orthogonal scanning

Changes in the wavelength have a fundamental effect on the spatial structure of the speckle. A sufficient change in light wavelength results in uncorrelated speckle pattern intensities, and adding these decorrelated speckle intensities can reduce the speckle contrast. The cross-correlation between two speckle patterns (µs) of different wavelengths (λ1, λ2) can be expressed as a factor that governs the wavelength sensitivity of speckles. It is a characteristic function (Ml) of the path length change or equivalently expressed as an inverse Fourier transform of the path length probability density function (pl).

$${\mu _s} \approx {M_l}({\Delta q} )= \; \mathop \smallint \limits_0^\infty {p_l}(l ){e^{j\Delta ql}}dl, $$
where $\Delta q = 2\pi |{1/{\lambda_1} - 1/{\lambda_2}} |$ for normal incidence and observation. If volumetric scattering is the mechanism by which speckles are generated, the path delay can be much longer than that resulting from the surface scattering [25]. For high multiple scattering, such as in biological specimens, the width of the diversity of the path length increases, which corresponds to a small change in the wavelength domain. We could then produce fully decorrelated speckles by shifting a small wavelength shift with the Y-scanning orthogonal to the scanning direction of SECM (X-scanning) as shown in Figs. 2(a) and (b). After one scan in the x-axis direction to obtain the SECM image, a small wavelength was altered using the Y-scanner to generate an uncorrelated speckle pattern. By repeating this procedure, multiple images with uncorrelated speckles were obtained for averaging to reduce speckle noise.

2.3 Signal processing

Figure 3 shows a flowchart of data processing using a hybrid CPU–GPU processing method in the developed imaging software. The GPU was programmed using the LabVIEW GPU Toolkit, which provides NVIDIA libraries. An interferogram was obtained by sequentially acquiring 2000 spectra consisting of 2048 samples per spectrum. First, in the OCT imaging mode, 2000 consecutive measured spectra were rearranged to 1457 spectra, corresponding to the respective interference signals of the 1457 lateral positions over a lateral distance of approximately 1 mm across the sample [26,27]. Rearrangement signal processing was performed using a CPU. The 1457 spectra were transferred to the GPU, where the average was computed and then subtracted from every spectrum to suppress fixed noise. The 1457 spectra with removed fixed noise were resampled for wavelength-to-wavenumber resampling and then numerically corrected for dispersion mismatch between the sample and reference arm. Two signal processing steps, resampling and compensation, were performed using the respective conversion files precomputed on the CPU and prepared in the GPU memory before the imaging operation. The fast Fourier transform (FFT) operation was then implemented using the Compute Unified Device Architecture (CUDA)-based FFT. The intensity output of the FFT was displayed on a logarithmic scale using a CPU.

 figure: Fig. 3.

Fig. 3. Signal processing flow diagram of the acquisition, computation, and display using CPU and GPU for the SECM and OCT.

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In the SECM imaging mode, we acquired 2000 spectra, which are the reflected line fields modulated by a carrier frequency determined by the path-length difference between the interferometer arms. To increase the signal-to-noise ratio, 2000 consecutively obtained spectra were averaged every four spectra, thus obtaining 500 spectra. The reflectance envelope of each of the 500 interference line fields was extracted from the analytical signal calculated using discrete Hilbert transforms performed after filtering the DC part in the spectral domain. All signal processing, except for intensity image display, was performed on the GPU. It took an average of 20 ms for the SECM and 110 ms for the OCT to create an image from the acquired 2000 spectra. To image the alternation between SECM and OCT, we intentionally put a 90 ms delay in the SECM signal processing.

3. Experimental results

3.1 System performance

To measure the lateral resolution of the SECM, we performed a test with a U.S. Air Force negative test target (Negative 1951 USAF, Thorlabs Inc.). The non-uniform brightness of the background in Fig. 4(a) results from the bell shape of the spectral power density. The smallest pattern that can be resolved by SECM is element 6 in Group 7, as indicated by the red circle. This can be regarded as a measured lateral resolution of approximately 2.2 µm, which agrees well with the theoretical lateral resolution of 2 µm. A line grating of a resolution target (R1L3S6P, Thorlabs Inc.) was imaged with the spectrally encoded line field. A central edge profile was differentiated to yield the line-spread function. The lateral resolution in the spectrally dispersed direction was measured approximately 2.3 µm with full width at half maximum (FWHM) and shown in Fig. 4(b). We measured the depth of focus as the axial resolution of SECM by measuring the reflected intensities with translating a mirror every 10 µm along the optical axis of the objective lens. The measured axial resolution was approximately 60 µm with FWHM and shown in Fig. 4(c). The field of view (FOV) of the SECM was 360 × 210 µm2. A performance test in the OCT imaging mode for depth-range evaluation involves the measurement of its sensitivity roll-off characteristics. The OCT sensitivity measured at a depth of 0.5 mm was 98 dB (20x log scale). As shown in Fig. 4(d), a sensitivity of more than 80 dB was maintained over an imaging distance of approximately 2.5 mm. The axial resolution was measured as approximately 8 µm. We acquired line fields at a speed of 200 k spectra/s. It took approximately 20 ms for all signal processing to display an image from the acquired raw spectrum in the SECM, whereas the OCT signal processing took approximately 110 ms. The SECM and OCT images were alternately displayed at an average rate of approximately 7 Hz, imparting a deliberate 90 ms delay to the signal processing time of the SECM. As shown in Fig. 4(c) and (a) real-time recorded video (Visualization 1), the horizontal and vertical views of the SECM and OCT, respectively, were monitored simultaneously such that it was easy to examine the high-resolution en-face image at the desired depth position.

 figure: Fig. 4.

Fig. 4. (a) Resolution test of the SECM using a 1951 USAF negative test target. (b) Line spread function from edge-response measurement. (c) Depth of focus. (d) OCT sensitivity roll-off measurement according to imaging depth. (c) SECM en-face image and its OCT cross-sectional image of an NIR detection card. (Visualization 1) is included. Scale bars in OCT and SECM, 100 µm, and 35 µm respectively.

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3.2 Speckle reduction in SECM

The multiple scattering structures in the NIR detector were aimed at depth by OCT imaging, as shown in Fig. 5(a). The layer of the phosphore-located scatterer was imaged using SECM. To evaluate the speckle reduction, a region with relatively few inherent non-uniform distributions of the sample was selected, as indicated by the red box in Fig. 5(b). We compared the decreases in speckle contrast for different distances of lateral shifts with Y-scanning. The decreases were proportional to the average number of images with uncorrelated speckle noise. Speckle contrast was defined as the normalized standard deviation of the pixel intensities. The case of no shift exhibited a minimal reduction (4.2%) in speckle contrast even with an averaging of 30 frames, indicating that speckle noise was not affected by normal averaging. In comparison, the wavelength shifting method with equivalent averaging led to a significant reduction (68.1%) in speckle contrast as a result of the reduction in speckle noise. It should be noted that a lateral shift Δd greater than 0.56 um generated fully decorrelated speckles, and the decrease was inversely proportional to the square root of the averaging number with a constant proportionality. The inverse square root function was fitted and is shown by the dashed gray line in Fig. 5(c). When Δd is 0.34 um and the averaging number of frames is 30, the speckle contrast is similar to averaging approximately 10 frames with a shift of 1.13 um. Different cases of Δd at an averaging of 30 frames in the graph of speckle contrast versus average count were selected and marked with gold asterisks for comparison with the non-averaged original image. The corresponding images are shown in Figs. 5(d)–(h). Figure 5(i) shows the full field after speckle noise reduction with a Δd of 1.13 um. Intrinsic structures obscured by speckle noise were observed.

 figure: Fig. 5.

Fig. 5. Speckle noise suppression in the SECM by shifting the spectral-encoded frames in the direction of dispersion. (a) Cross-sectional image of NIR detection card indicating the depth position focused on the phosphore-coated scatterer layer. (b) Corresponding SECM image at the depth indicated in (a). (c) Change in the normalized standard deviation of pixel intensities in the red box with number of images used for averaging over different distances of lateral movement through Y-scanning. (d) Original SECM image without speckle suppression. SECM images in the respective cases marked with gold asterisks for (e) Δd = 0, (f) Δd = 0.11 µm, (g) Δd = 0.34 µm, and (h) Δd = 0.56 µm. (i) SECM image with speckle suppression from the image shown in (b). Scale bars in OCT and SECM, 100 µm, and 35 µm respectively.

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3.3 Spectrally encoded dual-mode imaging of a biological specimen

To evaluate the capabilities of SEDIM in biological samples, imaging tests were performed using an insect sample (female Ixodes dammini fixed on a microscope slide, Carolina Inc.) with dimensions of 4 mm wide, 4 mm long, and 1 mm thick, as shown in the small inset of Fig. 6(a). From Figs. 6(a) and (b), along with a video (Visualization 2), observing OCT and SECM images together in real time was useful for viewing high-resolution images at a desired position and depth while sequentially exploring the head, legs, and chest of the large sample insect. Figures 6(c) and (d) illustrate the SECM image of the insect chest before and after removing speckle noise by averaging 30 frames generated with a Δd of 1.13 µm, respectively. By comparing the images in the two red boxes in Figs. 6(c) and (d), microstructures such as small dots that were not visible due to speckle noise were revealed. We also used a 60x objective (RMS60X-PFC Olympus, Thorlabs Inc.), which generated the effective NA of 0.7, to image cellular structures in the chest region of the insect sample. Twenty frames were averaged with a Δd of 1.13. The SECM image and its corresponding OCT image are shown in Fig. 6(e) and (f) respectively.

 figure: Fig. 6.

Fig. 6. (a) SECM en-face image and (b) its OCT cross-sectional image of a fixed female Ixodes dammini that is shown in the embedded photograph. (Visualization 2) is included. (c) SECM image of the insect chest without removing speckle noise. (d) SECM image in which the speckle noise has been removed by averaging 30 frames generated with a Δd of 1.13 µm. Scale bar in SECM and OCT, 35 µm, and 100 µm respectively. (e) SECM image obtained with a 60x objective lens and by averaging 20 frames with a Δd of 1.13 µm. (f) Its corresponding OCT image. Red arrows indicate the cover glass surfaces. Scale bars in SECM and OCT with a 60x objective lens, 12 µm, and 34 µm respectively.

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4. Conclusion

In conclusion, we implemented a multimodal imaging system that simultaneously displays depth-resolved lateral and vertical images by combining SECM and OCT as a means of complementary imaging. The integration of SECM and OCT was realized by simply adding orthogonal scanning to the SECM configuration. By sharing all components, SECM and OCT were automatically co-registered. In addition, the multimode imaging system is compact and cost-effective while providing the benefits of imaging aiming and guidance. The lateral resolution of the SECM and axial resolution of the OCT were measured to be approximately 2.2 µm and 8 µm, respectively. The line fields were acquired at a rate of 200 k spectra/s; however, we deliberately reduced the SECM rate to display the interlaced images of the SECM and OCT. The images of both modalities were displayed with an average of approximately 7 Hz. The en-face image of the SECM and cross-sectional image of the OCT could be observed seamlessly in real time as the samples were investigated. Furthermore, we presented a method to achieve speckle reduction in high multiple scattering, such as in biological samples, by averaging the decorrelated speckles generated by shifting the SECM image in the dispersed direction. An additional speckle noise reduction effect can be obtained when used in parallel with other methods such as a moving diffuser. The presented multimodal system will, in future work, be applied to in-vivo application such as cornea imaging. To implement it properly in the in-vivo application, we plan to acquire line averages with a high speed resonant scanner instead of frame averages.

Funding

Korea Basic Science Institute (D300300, C330210); Institute for Information and Communications Technology Promotion (No. 1711152793).

Acknowledgments

This work was supported by the Korea Basic Science Institute [grant numbers D210300 and C330210] and Institute of Information & Communications Technology Planning & Evaluation (IITP) funded by the Korean government (MSIT) [No. 1711152793, Development of Signal Processing and Image Display Device Technologies for Lightweight AR Device].

Disclosures

The authors declare no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Supplementary Material (2)

NameDescription
Visualization 1       En face and its cross-sectional imaging of a NIR detection card using spectrally encoded dual-mode interferometric microscopy
Visualization 2       En face and its cross-sectional imaging of an insect using spectrally encoded dual-mode interferometric microscopy

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Schematic of the proposed spectrally encoded dual-mode interferometric microscopy
Fig. 2.
Fig. 2. Scanning direction for (a) SECM and (b) OCT. (c) SECM and OCT give a horizontal and vertical image, respectively. Both images have the same center position. (d) Voltage waveform pairs required for X- and Y-scans for the SECM and OCT were selected from the analog outputs of an ADC card and fed to the x and y galvanometer scanner using an analog multiplexer.
Fig. 3.
Fig. 3. Signal processing flow diagram of the acquisition, computation, and display using CPU and GPU for the SECM and OCT.
Fig. 4.
Fig. 4. (a) Resolution test of the SECM using a 1951 USAF negative test target. (b) Line spread function from edge-response measurement. (c) Depth of focus. (d) OCT sensitivity roll-off measurement according to imaging depth. (c) SECM en-face image and its OCT cross-sectional image of an NIR detection card. (Visualization 1) is included. Scale bars in OCT and SECM, 100 µm, and 35 µm respectively.
Fig. 5.
Fig. 5. Speckle noise suppression in the SECM by shifting the spectral-encoded frames in the direction of dispersion. (a) Cross-sectional image of NIR detection card indicating the depth position focused on the phosphore-coated scatterer layer. (b) Corresponding SECM image at the depth indicated in (a). (c) Change in the normalized standard deviation of pixel intensities in the red box with number of images used for averaging over different distances of lateral movement through Y-scanning. (d) Original SECM image without speckle suppression. SECM images in the respective cases marked with gold asterisks for (e) Δd = 0, (f) Δd = 0.11 µm, (g) Δd = 0.34 µm, and (h) Δd = 0.56 µm. (i) SECM image with speckle suppression from the image shown in (b). Scale bars in OCT and SECM, 100 µm, and 35 µm respectively.
Fig. 6.
Fig. 6. (a) SECM en-face image and (b) its OCT cross-sectional image of a fixed female Ixodes dammini that is shown in the embedded photograph. (Visualization 2) is included. (c) SECM image of the insect chest without removing speckle noise. (d) SECM image in which the speckle noise has been removed by averaging 30 frames generated with a Δd of 1.13 µm. Scale bar in SECM and OCT, 35 µm, and 100 µm respectively. (e) SECM image obtained with a 60x objective lens and by averaging 20 frames with a Δd of 1.13 µm. (f) Its corresponding OCT image. Red arrows indicate the cover glass surfaces. Scale bars in SECM and OCT with a 60x objective lens, 12 µm, and 34 µm respectively.

Equations (1)

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μ s M l ( Δ q ) = 0 p l ( l ) e j Δ q l d l ,
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