Dual-comb microscopy (DCM), an interesting imaging modality based on the optical-frequency-comb (OFC) mode and image pixel one-to-one correspondence, benefits from scan-less full-field imaging and simultaneous confocal amplitude and phase imaging. However, the two fully frequency-stabilized OFC sources requirement hampers DCM practicality due to the complexity and costs. Here, a bidirectional single-cavity dual-comb fiber laser (SCDCFL) is adopted as a DCM low-complexity OFC source. Although the residual timing jitter in the SCDCFL blurs the image of a static object acquired by DCM, computational image correction significantly suppresses the image blur. Nanometer-order step surface profilometry with a 14.0 nm uncertainty highlights the computationally image-corrected DCM effectiveness. We further discuss a possibility to expand the computational image correction to a dynamic object and demonstrate its preliminary experiment. The proposed method enhances the DCM generality and practicality due to low-complexity OFC source.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Optical microscopy is an important imaging modality in fields of industrial inspection and life science research. In particular, confocal laser microscopy (CLM) [1–3] has attracted attentions for optical-sectioning two-dimensional (2D) imaging or three-dimensional (3D) imaging with depth selectivity of µm order. The confocality is achieved by a conjugate relation among a light-source pinhole, a focal point, and a detection pinhole; it enables us to extract a small volume fraction of a sample in the vicinity of a focal point. One drawback of existing CLMs is the requirement for the mechanical scanning of the focal spot to obtain the 2D or 3D image. While CLM has found many applications by use of optical-intensity-based image contrast related with absorption, scattering, reflection, or fluorescence, its application field will be further expanded if new image contrast can be further given CLM. For example, optical-phase-based image contrast enables the surface topography of nanometer-order unevenness or imaging of non-fluorescent transparent samples. Therefore, there is considerable need for CLM featuring the scan-less full-field imaging and multiple image contrasts.
Optical frequency comb (OFC) [4–6] has appeared as state-of-the-art light source having optical characteristics that are different from existing lasers. The ability to act as an optical carrier of amplitude and phase with a vast number of discrete, regularly spaced frequency channels is an interesting aspect of OFC. While this aspect has been effectively applied for optical frequency rulers in optical frequency metrology and spectroscopy with the help of laser control, the combination of this aspect with space-to-wavelength conversion opens a new door to imaging applications for OFCs, namely, dual-comb imaging (DCI) [7–15]. In DCI, the image pixels to be measured are spectrally encoded into OFC modes by space-to-wavelength conversion or spectral encoding (SE) [16–20]. Then, the entire image is decoded at the same time from the mode-resolved spectrum of the image-encoded OFC acquired by dual-comb spectroscopy (DCS) [21–24] based on the one-to-one correspondence between image pixels and OFC modes. Due to the scan-less imaging capability in SE and the capability for simultaneous acquisition of amplitude and phase spectra in DCS, the combination of DCI with CLM, namely, dual-comb microscopy (DCM) [7,8,11,13,14], enables scan-less confocal one-dimensional (1D) or two-dimensional (2D) imaging of amplitude and/or phase. For example, DCM has been effectively applied for surface topography of a nanometer-scale step-structured sample and nonstaining imaging of transparent, non-fluorescent cells . Furthermore, DCM has been further expanded to fluorescence microscopy featuring the scan-less fluorescence lifetime imaging , which is an important imaging modality in life science research. However, the need for two fully frequency-stabilized OFC sources hampers the practical use of DCI and DCM due to their costs and complexity.
Recently, low-complexity OFC sources have been extensively developed for practical DCS. A quantum cascade laser (QCL)  is a chip-scale, high-power OFC source. While a pair of QCLs has been applied for DCS , this approach often suffers from poor mutual coherence between them. The microresonator soliton comb (microcomb)  is another chip-scale OFC source with better mutual coherence between the microcombs. A pair of microcombs has been used for DCS  and even DCI . However, the relatively large repetition rate frep corresponding to the frequency spacing significantly reduces the number of sampling points in the spectrum or the image. For example, the total number of image pixels was only several hundred in 2D images .
The ideal OFC source for practical DCI and DCM has high mutual coherence to suppress image blur and moderate frep to enable a sufficient number of 2D image pixels without the need for any frequency stabilization. Such OFC source has been investigated by multiplexing mode-locking oscillation in bidirectional Ti:Sapphire lasers , polarization-multiplexed SESAM solid-state lasers , and semiconductor disk lasers . In addition to these lasers, a single-cavity dual-comb fiber laser (SCDCFL) [32–40] benefits from compactness, robustness, and low cost together with multiplexed mode-locking oscillation. In an SCDCFL, a pair of OFCs with slightly different repetition frequencies (frep1, frep2 = frep1 + Δfrep) is generated from a single fiber cavity by multiplexing mode-locking oscillation in wavelength [32–34], polarization [35–37], or propagation direction [38–40]. Since the dual OFCs propagate through the same cavity, they experience almost the same cavity disturbances, and the resulting common-mode fluctuations prevent the decline in the mutual coherence between them under no active frequency stabilization. Furthermore, an frep of approximately 100 MHz leads to tens-to-hundreds of thousands of OFC modes within the range of the optical spectrum, which is sufficient for the number of 2D image pixels. Although these SCDCFLs have been extensively applied for DCS, no attempts to apply them for DCI and DCM have been made.
In this article, we adopted a bidirectional SCDCFL  for practical DCM. This bidirectional SCDCFL benefits from good spectral overlap over a wide spectral range, high stability and wide tunability of Δfrep, and passive cancelation of common-mode noise. The image blur resulting from the residual timing jitter between the dual OFCs in the SCDCFL was computationally corrected by use of a reference image.
2. Materials and methods
2.1 Experimental setup
Figure 1 illustrate a schematic drawing of the experimental setup for the computationally image-corrected DCM, which is composed of a light source, 2D-SE optical system, and DCS optical system. A bidirectional SCDCFL was used as a DCM light source. As the details of the bidirectional SCDCFL are given elsewhere , we briefly describe the laser here. Two independent mode-locking oscillations were achieved in clockwise-circulating light and counterclockwise-circulating light in a fiber ring cavity by nonlinear polarization rotation and two saturable absorber mirrors. Part of the noncommon optical path in the cavity suppresses the competition of the two mode-locking oscillations and enables independent tunability of frep1, frep2, and Δfrep. The temperature of the fiber cavity was actively controlled by a combination of a thermistor and a Peltier heater. After optical amplification with a pair of erbium-doped fiber amplifiers (EDFAs), two counterpropagating output light beams from the SCDCFL, namely, CCW-OFC (center wavelength = 1550 nm, mean power = 190 mW, frep_CCW = 43,037,370 Hz) and CW-OFC (center wavelength = 1550 nm, mean power = 7 mW, frep_CW = 43,038,493 Hz, Δfrep = frep_CCW - frep_CW = 1,123 Hz), were used as a signal OFC and a local OFC, respectively.
In the 2D-SE optical system, the CCW-OFC beam passed through an erbium-doped fiber amplifier (EDFA) and a beam splitter (BS), and then was fed into a 2D-SE optical system [8,17–19] including a virtually imaged phased array  (VIPA, free spectral range = 15.1 GHz, finesse = 110) and a diffraction grating (G, groove density = 1200 grooves/mm, efficiency = 90%). Then, it was irradiated as a 2D spectrograph of CCW-OFC modes on a sample after passing through a pair of lenses (L1 and L2, focal length = 150 mm) and a dry-type objective lens (OL, NA = 0.25, working distance = 5.5 mm, focal length = 16 mm). A 1951 USAF resolution test chart with a positive pattern (Edmond Optics, Barrington, NJ, USA, #38–257, spatial frequency: 1.00 lp/mm ∼ 228 lp/mm) was used as a sample. The reflection, absorption, scattering, and/or phase change of the CCW-OFC beam in the sample encode the image contrast into the amplitude and phase spectra of the 2D spectrograph. As the CCW-OFC beam from the sample passed through the same optical system in the opposite direction, each wavelength component of the spectrograph spatially overlapped as the signal-image-encoded CCW-OFC.
In the DCS optical system, the optical bandwidth of CW-OFC for use as the local OFC in DCS was reduced by an optical bandpass filter (OBPF, center wavelength = 1556 nm, transmission passband = 6 nm) to avoid the aliasing effect in DCS. Then, the image-encoded CCW-OFC beam was spatially overlapped with the CW-OFC beam in a 90:10 single-mode fiber coupler (FC). The optical power ratio of the CCW-OFC beam to the CW-OFC beam was set to 1:1 to obtain good contrast for the interferogram in the time domain. A polarization controller (PC) was used for good polarization overlap between CCW-OFC and CW-OFC. The interferogram signal was detected by a fast photodetector (PD1, Thorlabs, Inc., Newton, NJ, USA, PDA015C, bandwidth = DC to 380 MHz) connected to an electric low-pass filter (LPF, cutoff frequency = 21.4 MHz) and was acquired with a time window size equal to 1/Δfrep by a digitizer (National Instruments Corp., NI PCI-5122, sampling rate = 100,389,194 samples/s, number of sampling points = 81,353, resolution = 14 bit). A portion of the CW-OFC beam was detected by another fast photodetector (PD2, Thorlabs, Inc., Newton, NJ, USA, PDA015C, bandwidth = DC to 380 MHz) to obtain the RF comb of CW-OFC (freq. = frep_CW, 2frep_CW, 3frep_CW, •••••, nfrep_CW). Then, we extracted the second harmonic component of frep_CW by an electric bandpass filter (BPF, center passband frequency = 87 MHz) and used it as a sampling clock in the digitizer. Although the repetition rate of the interferogram is equal to Δfrep ( = 1,123 Hz), each interferogram was discretely acquired at 15 Hz in practice to reduce the data size of consecutive interferograms.
We obtained the mode-resolved CW-OFC spectrum of amplitude and phase by calculating Fourier transform of the acquired interferogram and rescaling its frequency scale by frep1/Δfrep. As each CW-OFC mode of amplitude and phase is respectively corresponding to each pixel of 2D confocal amplitude and phase images, we reconstructed their images based on one-to-one correspondence between them .
2.2 Computational image correction
The residual timing jitter between the dual OFCs in the SCDCFL fluctuates the 2D spectrograph of OFC modes, leading to a blurred image in DCM. To compensate for this image blur, we proposed an image correction based on an image autocorrelation analysis , namely self-reference image correction. Before performing the computational image correction, we calculated an autocorrelation function of a single confocal amplitude image and extracted the center of the function as a reference signal for the self-reference image correction. Then, we corrected the position of each acquired image by comparing the center of the autocorrelation function in the acquired image with that in the beforehand-acquired reference image and compensating for the difference between them. This method benefits from high robustness to external disturbance due to the use of the common optical path and is effective for imaging static objects with high image contrast.
3.1 Basic performance of the bidirectional SCDCFL
We first evaluated the basic performance of the bidirectional SCDCFL. Figure 2(a) shows optical spectra of CCW-OFC and CW-OFC at the oscillator output, measured by an optical spectrum analyzer (Yokogawa Electric Corp., AQ6315A). The dual OFCs have similar spectral shapes and spectral bandwidths while maintaining good spectral overlap. These spectral characteristics are attractive for DCM. We next evaluated the frequency fluctuation of frep_CCW, frep_CW, and Δfrep. The temporal fluctuation of frep_CCW and frep_CW was continuously measured at a gate time of 1 s with a time window size of 1000 s by an RF frequency counter (Keysight Technologies, Inc., Santa Rosa, CA, USA, 53230A), as shown by red and blue plots in Fig. 2(b). Also, using a statistical analysis function in the same frequency counter, we evaluated an Allan deviation of frep_CCW and frep_CW at a gate time of 0.01 s (data number = 10000), 0.1 s (data number = 1000), 1 s (data number = 1000), 10 s (data number = 100), and 100 s (data number = 10), as shown by red and blue plots in Fig. 2(c). In Fig. 2(b), while frep_CCW and frep_CW have slow drifts, their drifts are common to each other with a constant frequency spacing. Such behavior is also well reflected in Fig. 2(c) as overlapping profiles of the Allan deviation. In the same manner as the evaluation of frep_CCW and frep_CW, we evaluated the temporal fluctuation and an Allan deviation of Δfrep. Figure 2(d) shows the temporal fluctuation of Δfrep (gate time = 1 s). We obtained an Allan deviation of 0.0076 Hz at a gate time of 1 s (data number = 1000, corresponding to 1000 sec). Regardless of the slow drifts in frep_CCW and frep_CW, Δfrep was passively stabilized in this drift measurement. To investigate the fluctuation of Δfrep in different time ranges, we obtained the Allan deviation of Δfrep with respect to different gate times as shown in Fig. 2(e). Similar behavior was confirmed in Figs. 2(c) and 2(e). Although the laser cavity includes a small noncommon optical path portion, its noncommon-mode influence is negligible.
3.2 Confocal amplitude and phase imaging
A temporal waveform of a single interferogram was acquired with a time window size equal to 1/frep1. Spectral plots obtained by Fourier transform of the interferogram are respectively corresponding to spectral peaks of all CCW-OFC modes. The number of CCW-OFC modes ( = 17,400) determines the number of 2D image pixels. The confocal 2D images of amplitude and phase were reconstructed from CCW-OFC spectral plots of amplitude and phase based on the one-to-one correspondence between OFC modes and 2D image pixels. Before performing the computational image correction, we first acquired the reference amplitude image from CCW-OFC, as shown in Fig. 3(a) (image size = 252 µm by 294 µm, pixel size = 50 pixels by 348 pixels, no image accumulation, no image correction). A confocal amplitude image of a test chart, corresponding to the 2D reflection distribution, was obtained with moderate contrast even in single-shot image acquisition (image acquisition time = 890 µs). Then, we calculated its image autocorrelation function, as shown in Fig. 3(b). The right graph of Fig. 3(b) shows the amplitude profile of the functional center along the vertical white lines in Fig. 3(b). Although one can obtain the amplitude profile along the horizontal direction in addition to it, image fluctuation mainly occurs along the vertical direction as shown later, due to difference of dispersion power in 2D spectral encoding. Therefore, we extracted only the amplitude profile along the vertical direction. From this profile, we extracted the center position of the function. After we acquired the signal image, we corrected its position by comparing the center of its autocorrelation function with that in the beforehand-acquired reference image and compensating for the difference between them. We achieve the computational correction of amplitude image by repeating this procedure. The computational correction of phase image is achieved by moving the position of phase image as much as the computationally corrected amplitude image.
Figure 4(a) compares snapshots of confocal amplitude and phase images (image size = 252 µm by 294 µm, pixel size = 50 pixels by 348 pixels, image acquisition time = 890 µs) for a test chart at the beginning and end of measurement between no image correction and self-reference image correction. Their corresponding movie is shown in Visualization 1. When comparing these images at the beginning and end of the measurement, the image position moved in the no image correction result of Fig. 4(a) despite the static sample due to the residual timing jitter in the SCDCFL. However, little change was observed in the image position in the self-reference image correction result of Fig. 4(a). This effect of the image correction was more clearly confirmed in Visualization 1. In the no image correction, the position of the confocal amplitude and phase images quickly fluctuated along the vertical direction; additionally, its slow drift along the same direction was confirmed (for example, see the moving horizontal black stripe in Visualization 1, indicating the image edge). However, no fluctuation or drift of the image occurred along the horizontal direction. In the present 2D-SE setup, the dispersion directions of the VIPA and the grating are vertical and horizontal in the image, respectively, and the dispersion power of the VIPA is much larger than that of the grating. The resulting 2D spectrograph spatially develops as a vertical zigzag line in the focal plane . Therefore, the image fluctuation and drift in the vertical direction are more sensitive than those in the horizontal direction. Notably, a vertical image shift by a single pixel corresponds to a frequency shift by frep in the optical spectral region; hence, DCM is more sensitive to the residual timing jitter than Doppler-broadening or pressure-broadening gas DCS with GHz spectral features. In the self-reference image correction, the image blur was perfectly suppressed, indicating a high image correction capability for static objects. For quantitative analysis of the image correction, we calculated the temporal fluctuation of the center of the image autocorrelation function along the vertical direction from confocal amplitude images of Visualization 1, as shown in Fig. 4(b). The contribution of image correction was clearly confirmed: combined fast fluctuation and slow drift in no image correction were completely suppressed in the self-reference image correction.
3.3 Evaluation of image accumulation
Image accumulation is often required to improve the signal-to-noise ratio (SNR) or contrast of the image in DCM. However, when the image position fluctuates or drifts due to the residual timing jitter of the SCDCFL, image accumulation will lead to decreased image SNR and/or contrast. To evaluate the effectiveness of the image correction from the viewpoint of image accumulation, we acquired a series of confocal amplitude and phase images of the same sample and accumulated them. Figure 5(a) compares single image acquisition, 10-image accumulation, and 100-image accumulation with no image correction and self-reference image correction for confocal amplitude and phase images. In the no image correction result of Fig. 5(a), the confocal amplitude and phase images became blurred along the vertical direction due to the residual timing jitter, making observation of the chart pattern difficult. In contrast, the image accumulation effectively improves the image quality in the self-reference image correction result of Fig. 5(a).
For quantitative analysis of the image accumulation contribution in confocal amplitude imaging, we calculated the image SNR from the confocal amplitude images of Fig. 5(a). Here, we defined the image SNR as the ratio of the mean to the standard deviation in the bright square region in the top right of each confocal amplitude image. Figure 5(b) shows the image SNR with respect to the number of accumulated images for no image correction and self-reference image correction. Although no accumulation effects were found for the no image correction, the image SNR was improved with increasing the number of accumulated images for the self-reference image correction.
We also calculated the image contrast of the confocal amplitude images when the image contrast was defined as the ratio of the difference to the sum of the maximum and minimum amplitudes across a chart pattern. Since no differences exist in the image contrast along the horizontal direction (not shown), we show here the image contrast along the vertical direction. Figure 5(c) shows a comparison of the image contrast with respect to the number of accumulated images for no image correction and self-reference image correction. We confirmed a similar effect as for the image SNR in Fig. 5(b): a declined contrast for the no image correction and a slight decline for the self-reference image correction.
For quantitative analysis of the image accumulation contribution in confocal phase imaging, we calculated the phase stability from the confocal phase images of Fig. 5(a). The phase stability was defined as the standard deviation of the temporal phase noise at a certain image pixel. Figure 5(d) shows the phase stability with respect to the number of accumulated images for no image correction and self-reference image correction. While the phase fluctuation was not suppressed in the no image correction, we confirmed an improved phase stability in the self-reference image correction. In this way, we confirmed the effectiveness of image accumulation with the proposed image correction of confocal amplitude and phase images.
3.4 Quantitativeness of confocal phase imaging
We next evaluated the quantitativeness of the confocal phase imaging with self-reference image correction. The test chart has surface unevenness corresponding to the presence or absence of reflective film, and its reflectivity depends on the presence or absence of the reflective film. To obtain a reflective sample with surface unevenness and constant reflectivity, we formed a thin gold coating on the test chart and used this chart as a confocal phase imaging sample. Figure 6(a) shows the image corresponding to accumulation of 1,000 confocal phase images, in which the phase measurement range was limited to ±π and the phase resolution was determined by the phase stability in Fig. 5(d). A confocal phase image of the test chart was clearly visualized with high contrast. Figure 6(b) shows a cross-sectional profile of the confocal phase image along the white vertical line in Fig. 6(a). The step profile was corresponding to a phase difference of 0.782 rad. Spatial distribution of step height, H(x, y), is calculated from that of phase difference, ϕ(x, y), by1), we added an axis of step height in a right axis in Fig. 6(b). The resulting step height was determined to be 97.1 nm. For comparison, we beforehand determined this step height to be 90 nm by atomic force microscopy (AFM, Hitachi High-Tech, AFM5500M, axial repeatability ≤ 1 nm). In Fig. 5(d), the phase stability of the self-reference image correction was 0.057 rad for 1000 consecutive images, corresponding to an uncertainty of 14.0 nm in the step height. The difference in the step height between DCM and AFM was within the range of this uncertainty. Importantly, axial precision to nanometer order was achieved with the help of the self-reference image correction even though the free-running SCDCFL was used for DCM.
We first discuss the reason for the fluctuating center of the image autocorrelation function in the absence of image correction [see the black plot in Fig. 4(b)]. The center fluctuated within a standard deviation of 10 pixels in the short term and a peak-to-peak of 200 pixels in the long term. This fluctuation occurs in the optical frequency range related with OFC and/or the RF region related with DCS. The fast fluctuation of 10 pixels corresponds to 10frep_CCW ( = 430 MHz) in the optical frequency region or 10Δfrep ( = 11.23 kHz) in the RF region, whereas the slow fluctuation of a peak-to-peak of 200 corresponds to 200frep_CCW ( = 8.60 GHz) in the optical frequency region or 200Δfrep ( = 224.6 kHz) in the RF region. We consider that such fluctuations result from the residual timing jitter in the SCDCFL as follows: (1) fluctuation of frep_CCW (δfrep_CCW) in the optical frequency region, (2) fluctuation of Δfceo (δΔfceo) in the RF region when Δfceo = fceo_CCW - fceo_CW, and (3) fluctuation of Δfrep (δΔfrep) in the RF region. From the center optical frequency of 193.4 THz and frep_CCW of 43.04 MH in the SCDCFL, we assume that the number of OFC modes m is 4,493,000. Regarding (1), the δfrep_CCW of 0.002 Hz at a gate time of 1 s [see Fig. 2(c)] is multiplied by m in the optical frequency region; namely, mδfrep_CCW = 8.986 kHz, which was much smaller than 10frep_CCW or 200frep_CCW. Therefore, contribution of (1) is negligible. Regarding (2), the δΔfceo of 30.5 kHz in the bidirectional SCDCFL  contributes to the fluctuation in the RF region. In other words, δΔfceo can change the center of the image autocorrelation function within a few tens of pixels. Regarding (3), mδΔfrep contributes to the fluctuation in the RF region. As δΔfrep is 0.0076 Hz at a gate time of 1 s [see Fig. 2(e)], mδΔfrep is estimated to be 34 kHz in the RF region, leading to fluctuations in the center of the image by a few tens of pixels. The contribution of δΔfceo and/or mδΔfrep is in reasonable agreement with the slow and fast fluctuations in the absence of image correction. In this way, we consider that the slow and fast fluctuations are mainly due to δΔfceo and/or mδΔfrep in the RF region. Although δΔfceo shifts the image position while mδΔfrep deforms the image similar to an accordion, observing such a difference in confocal amplitude and phase images is difficult due to the insufficient number of image pixels and/or the large m value. More importantly, the image blur resulting from those δΔfceo and/or mδΔfrep was effectively suppressed by the self-reference image correction. In other words, the image-based computational correction has a potential to strongly suppress the influence of residual timing jitter in DCS-based applications using a free-running single-cavity dual-comb laser.
We next discuss the possibility of further reducing the number of accumulation and/or increasing the image SNR in Fig. 5(b). The image SNR was mainly limited by the signal loss in the VIPA. A higher total power of OFC will efficiently contribute to improvement of the image SNR or reduction of the image acquisition time. The large signal loss in the VIPA is due to the use of zero-order dispersion mode with the highest spectral resolution. Use of higher-order dispersion mode will lead to the decreased signal loss at the expense of spectral resolution. From the viewpoint of signal detection, there is still space to increase the image SNR by use of an OL with higher numerical aperture.
The self-reference image correction was effective for a static object demonstrated above; however, it is not suitable for a dynamic object because consecutively acquired images of the dynamic object are corrected by always comparing with the beforehand-acquired reference image acquired before the beginning of the measurement. Instead of comparison with the beforehand-acquired reference image, one may use the former image for the correction of the latter image in two consecutively acquired images if an object slowly moves. However, if an object quickly moves, finite acquisition time of two consecutive images leads to the image blur. One potential method applicable for dynamic objects is a computational image correction based on an external reference image, namely external-reference image correction. In this case, we simultaneously acquire confocal amplitude images of a sample object and a reference object. Then, we calculate their autocorrelation functions and extracted their centers as an error signal of image blur. Finally, we correct the position of each acquired signal image by comparing the centers of the autocorrelation functions. For preliminary experiment of this external-reference image correction, we inserted a reference arm after the 2D-SE optics as shown in an inset of Fig. 1. A portion ( = 50%) of the CCW-OFC beam passing through L2 was separated by a combination of a half-wave plate (HWP) and a polarization beam splitter (PBS). Then, the separated CCW-OFC beam was irradiated as a 2D spectrograph of CCW-OFC modes on another test chart (negative type, Edmond Optics, Barrington, NJ, USA, #38–256, spatial frequency: 1.00 lp/mm ∼ 228 lp/mm) after passing through a lens (L3, focal length = 200 mm) to encode the reference image of the separated CCW-OFC, namely, the reference-image-encoded CCW-OFC. The reference-image-encoded CCW-OFC beam was combined with the signal-image-encoded CCW-OFC beam with a time separation of 2.67 ns by the PBS, and both were fed into the DCS experimental setup. A temporal waveform of two interferograms of the signal-image-encoded CCW-OFC and the reference-image-encoded CCW-OFC was acquired with a time window size equal to 1/frep1. We separated it into two temporal waveforms [time window size = 1/(2frep1)] including the signal-image-encoded CCW-OFC and the reference-image-encoded CCW-OFC, respectively. After adding null data to their temporal waveforms up to a time window size equal to 1/frep1, we calculated Fourier transform of them. We obtained the confocal 2D images of amplitude and phase for the signal-image-encoded CCW-OFC and the reference-image-encoded CCW-OFC based on the one-to-one correspondence between OFC modes and 2D image pixels, and then performed the external-reference image correction.
To evaluate its effectiveness to dynamic objects, the test chart was laterally moved by a translation stage. Figure 7 compares snapshots of the confocal amplitude and phase images for the test chart (image size = 252 µm by 294 µm, pixel size = 50 pixels by 348 pixels, image acquisition time = 890 µs) between (a) no image correction and (b) external-reference image correction. In the external-reference image correction, one corrected image was reconstructed from two images: a signal image and a reference image of CCW-OFC beam. Although there are no significant differences of confocal amplitude image between Figs. 7(a) and 7(b), the comparison of confocal phase image indicated that the phase wrapping in no image correction of Fig. 7 was well suppressed in external-reference image correction of Fig. 7. Visualization 2 shows the corresponding movie of confocal amplitude and phase images when the test chart was laterally moved. In the no image correction, movement of the test chart was observed together with image blur resulting from the residual timing jitter in the SCDCFL. In the external-reference image correction, the slow image blur was reduced, and the resulting image visualized the movement of the test chart. However, the fast image blur still remained. One potential reason for the residual fast image blur is the noncommon optical path between the signal-image-encoded CCW-OFC and the reference-image-encoded CCW-OFC; however, a noncommon reference arm worked well in compensating for the phase fluctuation in previous research on DCM [9,14]. Another potential reason is the time separation of the interferogram ( = 2.67 ns in effective time corresponding to 0.102 ms in lab time) between the signal-image-encoded CCW-OFC and the reference-image-encoded CCW-OFC, suffering from the temporal noncommonness sensitive to the residual timing jitter in the SCDCFL. To achieve temporal commonness, the signal-image-encoded CCW-OFC and the reference-image-encoded CCW-OFC have to be multiplexed with no time separation. Polarization multiplexing is one possible method, although one has to consider the polarization dependence of the 2D-SE. Works is in progress to further reduce the fast image blur.
We introduced the SCDCFL into DCM to generalize DCM from the viewpoint of reduced complexity of the light source. To compensate for the image blur caused by the residual timing jitter in the SCDCFL, computational image correction was applied for confocal amplitude and phase imaging. The self-reference image correction completely suppressed both the slow and fast image blur in the static sample, and its high phase quantitativeness was highlighted by the surface profilometry of a nanometer-order step surface with an uncertainty of 14.0 nm. For the DCM option for dynamic objects, we preliminarily demonstrated confocal amplitude and phase imaging of the moving sample by use of the external-reference image correction and show the potential to suppress the slow image blur. We expect that further improvement in the performance of common-noise suppression in the SCDCFL will reduce the requirement in the image correction and improve the image quality especially for dynamic objects. This DCM featuring reduced complexity of the light source will expand the application field of DCM in life sciences and industry.
Exploratory Research for Advanced Technology (JPMJER1304); Japan Society for the Promotion of Science (18H01901, 18K13768, 19H00871); Cabinet Office, Government of Japan (Subsidy for Reg. Univ. and Reg. Ind. Creation); Nakatani Foundation for Advancement of Measuring Technologies in Biomedical Engineering; Research Clusters program of Tokushima University (1802003).
The authors declare no conflicts of interest.
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