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Abstract
Balanced dispersion between reference and sample arms is critical in frequency-domain optical coherence tomography (FD-OCT) to perform imaging with the optimal axial resolution, and the spectroscopic analysis of each voxel in FD-OCT can provide the metric of the spectrogram. Here we revisited dispersion mismatch in the spectrogram view using the spectroscopic analysis of voxels in FD-OCT and uncovered that the dispersion mismatch disturbs the A-scan’s spectrogram and reshapes the depth-resolved spectra in the spectrogram. Based on this spectroscopic effect of dispersion mismatch on A-scan’s spectrogram, we proposed a numerical method to detect dispersion mismatch and perform dispersion compensation for FD-OCT. The proposed method can visually and quantitatively detect and compensate for dispersion mismatch in FD-OCT, with visualization, high sensitivity, and independence from sample structures. Experimental results of tape and mouse eye suggest that this technique can be an effective method for the detection and compensation of dispersion mismatch in FD-OCT.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical coherence tomography (OCT) is a powerful noninvasive imaging technology that enables high-resolution, three-dimensional imaging of biological tissues and materials [1]. By measuring the magnitude and echo time delay of backscattered light using a low coherence light source, OCT can provide high-resolution images of the microstructure of biological tissues [2,3]. Therefore, it has become one of the most widely used imaging tools for disease diagnoses. Recently, with ultra-broadband light sources, micro-resolution OCT has achieved an increasingly higher axial resolution, which has enlarged the OCT application field [4,5]. However, one difficulty that arises from using ultra-broadband light sources in the frequency-domain OCT (FD-OCT) setup is chromatic dispersion, and when the sample and reference arms contain different lengths of optical dispersive media, dispersion mismatch occurs. Dispersion mismatch between the sample and reference arms of FD-OCT is described as a wavelength-dependent phase error that causes chirping and broadening of the axial point spread function [6]. Achieving a balanced reference-sample arm dispersion is critical in high-resolution FD-OCT to attain images with the highest axial resolution.
Many works have been dedicated to improving the high-resolution OCT imaging performance by dispersion compensation using hardware-based or software-based methods. Traditional hardware-based methods rely on inserting the right amount of dispersion compensation material into one interferometer arm of the OCT setup [7]. Other hardware-based methods, such as grating-based phase delay scanners [8], dual optical fiber stretchers [9], and acousto-optic modulators [10], can also be used for dispersion compensation and present some degree of tunability. However, these hardware-based methods confer higher hardware costs, are inconvenient to operate, and have poor applicability. More software-based methods have been proposed for dispersion compensation in high-resolution OCT, which offer continuous adjustment capabilities and can be optimized for any amount of dispersion. Cense et al. [11] proposed a method for performing dispersion compensation by multiplying the dispersed cross-spectral density function with a phase term. This method requires a coherence function obtained from a well-reflecting reference point to determine this phase term for dispersion compensation. However, this method cannot be used in most OCT images because isolated reflections are often not available. Wojtkowski et al. [12] further proposed compensating for 2nd-order and higher-order dispersion by adding an optimized phase term that is found using a sharpness function that searches for the maximum signal magnitude in a given depth range. Hofer et al. [13] further proposed using the information entropy of the spatial domain signal as the sharpness metric to compensate for 2nd-order and higher-order dispersion. Although these works have made contributions to dispersion compensation in FD-OCT, these methods based on the sharpness metric of OCT images are easily affected by imaging noise, especially speckle noise, and they cannot work well when the sensitivity of the FD-OCT system is not high enough. Lippok et al. [14] proposed using the fractional Fourier transform to perform dispersion compensation in FD-OCT. However, the performance of the method is quite sensitive to the order parameter of the fractional Fourier transform and it requires obtaining an extremely accurate value of the order parameter, which is a major challenge.
Many works have shown that the spectroscopic analysis of each voxel in FD-OCT can provide new metrics [15,16], even for phase error detection of dispersion [17] and sub-aperture correlation [18]. Here we revisit the problem of dispersion mismatch in the spectrogram view using the spectroscopic analysis of voxels in FD-OCT. We uncovered that the dispersion mismatch disturbs the A-scan’s spectrogram and reshapes the depth-resolved spectra in the spectrogram. Based on this spectroscopic effect of dispersion mismatch, we proposed a numerical method to detect dispersion mismatch and perform dispersion compensation. The proposed method can visually and quantitatively detect and compensate for dispersion mismatches in FD-OCT, with visualization, high sensitivity, and independence from the sample structures. We conducted experiments on Scotch tape and mouse eye to demonstrate the improvement in dispersion mismatch detection and compensation.
2. Methods
2.1. Spectrogram and depth-resolved spectra in frequency-domain OCT
In FD-OCT, cross-sectional images are generated by measuring the echo time delay and magnitude of backscattered light. Backscattered light signals from different depths that correspond to different delays are brought to interfere with light from a reference path with a known delay. The interference produces fringes, which are detected by a spectrometer using a high-speed multielement CCD or photodiode array detector. For the example of discrete reflectors, the FD-OCT balanced fringe signal can be given by Eq. (1) after further removing the DC part in the fringes.
Because the light source used is necessarily broadband in FD-OCT, performing spectral/spatial analysis of each voxel in the OCT raw data can help us obtain the spectroscopic and depth information simultaneously [16]. In detail, spectral-spatial analysis can obtain the A-scan’ spectrogram, and enable the recovery of depth-resolved spectra at different depths in the spectrogram, and allow for the quantification of depth-resolved spectroscopic information by measurement of the full interference signal and the use of appropriate digital signal processing [15]. Bosschaart et al. [19] quantitatively compared the available methods to perform spectral-spatial analysis of Asan in FD-OCT, i.e. the short-frequency Fourier transform (SFFT), wavelet transforms, the Wigner-Ville distribution and the dual window method through simulations in tissue-like media. Here we use the SFFT method to obtain the A-scan’s spectrogram $S(\omega ,\tau )$ and the normalized depth-resolved spectra $\tilde{S}(\omega ,{\tau _n})$ at each imaging depth ${\tau _n}$, given by Eqs. (2) and (3), and its spectral centroid $C({\tau _n})$ at depth ${\tau _n}$ in the A-scan be given by Eq. (4).
If there is no dispersion mismatch in FD-OCT, the depth-resolved spectra at two different depths ${\tau _n}$ and ${\tau _m}$ have the following relation, given by Eq. (5) [20], where ${r_n}$ and ${r_m}$ are the field reflectivities, ${h_n}$ and ${h_m}$ are the chromatic transfer functions, $\mu$ is the absorption coefficient. Our previous work [21] has numerically predicted and experimentally proved that only transversely oriented and regularly arranged nano-cylindrical and nano-spherical structures selectively backscatter light and perceptibly change the spectral centroid of the backscatters light in OCT. In cases that scanning structures in a spatial-resolution-size voxel of OCT are chaotic, the recovered depth-resolved spectra of different imaging depths in the spectrogram have the very similar spectral centroids; under this condition, here ${r_m}, {r_n}, {h_m}$, and ${h_n}$ are approximately independent of frequency $\omega$, and their spectral centroids $C({\tau _n})$ and $C({\tau _m})$ have the very similar value, given by Eq. (6).
2.2. Reshaping of depth-resolved spectra caused by dispersion mismatch in the spectrogram
If there are dispersions in the reference and sample arms in FD-OCT, the field incident on the beam splitter after returning from the reference and sample arms will be time-stretched. Because the thickness of the optical dispersive media is in the meter range, we can assume that no gain or loss of light occurs in the optical dispersive media; thus, the dispersion-mismatch fringe signal can be given by Eq. (7) [13], where $\Phi (\omega ,{\tau _n})$ is a general frequency and delay-dependent phase shift that includes higher-order dispersive terms. Because the frequency-dependent phase distortion is the same for all depths in one axial scan, the dispersion is not depth-dependent. In this case, the phase shift $\Phi (\omega ,{\tau _n})$ becomes independent of the delay or axial position $\Phi (\omega ,{\tau _n}) = \Phi (\omega )$ which can be given by Eq. (8) [13,20,22].
According to Eqs. (2) and (9), we can see that if the dispersions between the sample and reference arms match well (${l_R} = {l_S}$), the frequency-based phase shift $\Phi (\omega )$ will disappear. After performing the Fourier transform, we obtain the result of the interferometric measurement of the apparent displacements (depths) of each sample reflector from the reference position as $2({\tau _R} - {\tau _{Sn}})$ with the full width at half maximum (FWHM) of the inverse Fourier transform $\gamma (z)$ of the light source spectra [3]. However, if the dispersions between the sample and reference arms are mismatched (${l_R} \ne {l_S}$), there will be a nonzero frequency-based phase shift $\Phi (\omega )$ which will cause the interferences of different-frequency light to locate at different locations in the Ascan’s spectrogram. Because the added phase shift $\Phi (\omega )$ has a positive correlation relation with $\omega - {\omega _0}$ when the thickness l is in the kilometer range, so there is a larger offset between the frequency $\omega$ and the center frequency ${\omega _0}$, and there is a larger frequency-based displacement shift in the spectrogram. Meanwhile, where there is a larger difference between the optical dispersive thicknesses ${l_R}$ and ${l_S}$ in the reference and sample arms, respectively, there is also a larger frequency-based displacement shift in the spectrogram.
2.3. Dispersion compensation using rebalancing of spectra centroids of recovered depth-resolved spectra
Many works have indicated that dispersion mismatch can be removed by multiplying the dispersed cross-spectral density function $I(\omega )$ with a phase term $\exp [i\bar{\Phi }(\omega )]$ in OCT imaging [6,13,25]. The compensated phase $\bar{\Phi }(\omega )$ can be expressed by Eq. (10) [13,25],
where the coefficient $- {a_2}$ is adjusted to cancel the group velocity dispersion imbalance (second-order term) and $- {a_3}$ is adjusted to cancel the third-order dispersion imbalance (third-order term). This method may be generalized to higher orders; however, compensation to the third-order is usually sufficient, assuming that the interferometer arms are approximately dispersion-matched initially [6].If the appropriate phase correction has been applied, this new axial depth scan is compensated for dispersion mismatch between the interferometer arms and has an optimum axial resolution. Conventional methods use the sharpness metrics of OCT images to choose the proper coefficients $- {a_2}$ and $- {a_3}$, such as that of Hofer et al. [13], who proposed estimating the frequency-dependent dispersive phase shift $\Phi (\omega )$ using the information entropy of the spatial domain signal as the sharpness metric. However, those methods based on the use of the sharpness function of OCT images may be affected by electronic noise and speckle noise, especially when the sensitivity of the OCT setup is not high enough. At the same time, the sample structures may also affect the sharpness function value when the sensitivity of the OCT setup is not high enough.
Here we propose using the recovered normalized depth-resolved spectra and its centroid in the spectrogram of an A-scan to detect the dispersion mismatch and further perform dispersion compensation, as shown in Fig. 1. Because only transversely oriented and regularly arranged nano-cylindrical and nano-spherical structures selectively backscatter light and perceptibly change the spectral centroid of the backscatters light in OCT, and the impact of multiple backscattering and multiple forward scattering on the spectra centroids of the light has been limited because of average effect in the spatial and spectral domains when calculating the spectral centroid. So the depth-resolved spectra of different imaging depths in the spectrogram have very similar spectral centroids if there is no dispersion mismatch, and the spectral centroid image should be smooth. From Section 2.1, we can see that if the dispersions are matched well, the normalized depth-resolved spectra at different depths approximately have the very similar shape and spectral centroid, which is approximately the spectra of the light source; thus, normalized depth-resolved spectra at different depths have the very similar spectral centroid. While if there is a dispersion mismatch between the sample and reference arms, it disturbs the A-scan’s spectrogram and affects the shapes and centroids of the normalized depth-resolved spectra.
Fig. 1. Schematic of the method proposed here, in which spectral/spatial analysis of each A-scan raw data point is performed to obtain the A-scan’ spectrogram, the normalized depth-resolved spectra at each depth of A-scan and its centroid.
In our proposed method for detecting the dispersion mismatch and compensation, as Fig. 1 shows, for each A-scan data point, we first obtain the spectrogram and recovered depth-resolved spectra at different depths using spectral/spatial analysis and normalize all of these recovered depth-resolved spectra at different depths. Then we calculate the spectral centroids of these normalized depth-resolved spectra. Finally, we obtain the spectral centroid image, with which we detect the dispersion and perform the dispersion compensation by estimating the frequency-dependent dispersive phase using the information entropy [26] of the spectral centroid image as the sharpness metric.
To generate the image of spectral centroids, we first did spectral/spatial analysis (short-frequency Fourier transform [15]) for each voxel raw data of OCT B-scan. After doing spectral/spatial analysis, we obtained the spectrogram of each voxel in OCT B-scan. Then we calculated the spectral centroid of the recovered depth-resolved spectra in the spectrogram following Eq. (4), and further generated the spectral-centroid images by mapping the spectral centroid values to gray values. As the above mentioned, the depth-resolved spectra of different imaging depths in the spectrogram have very similar spectral centroids if there is no dispersion mismatch, so the spectral centroid image should be smooth if the dispersion mismatch is compensated well. Here the optimization of the spectral centroid image was performed by searching for the minimum.
2.4. Experimental method
To show how dispersion mismatch detection and compensation are performed, we rebuild the SD-OCT setup. The schematic of SD-OCT is shown in Fig. 2. A low-coherence light source is guided through the single-mode fibers (SMFs). A fiber coupler (FC) is used to couple and split the light rays. Lenses L2 and L3 are used to focus the light rays, and lenses L1, L3, and L5 are used to collimate the light rays. A polarization controller (PC) is used to control the intensity of the coherence. A galvo scanner (GS) is used to control the scanned area. The spectrometer is composed of a transmission grating (G) and a line scan camera connected to a computer workstation that is responsible for the data processing and controls the line scan camera for imaging and the GS for scanning the entire tissue region. The sample arm and reference arm are dispersion-matched well. To obtain different dispersion mismatches, we further add different-thickness glass to the reference arm and sample arm, as shown in Fig. 2.
Fig. 2. Schematic of SD-OCT, FC: fiber coupler, PC: polarization controller, L1, L3, L5: collimator, L2, L4: lens, GS: galvo scanner; G: grating.
To show our proposed method can visually and quantitatively detect dispersion mismatches and perform dispersion compensation, we first used a mirror as the sample in the sample arm and added different-thickness dispersion glass into the sample and reference arms to obtain different kinds of dispersion mismatches. One group of dispersion mismatches is that in which the sample arm has thicker added glass than does the reference arm, while another group is that in which the reference arm has thicker added glass than does the sample arm. We also imaged Scotch tape and processed the OCT raw dataset using different methods to show the better performance of our proposed methods than other methods.
Meanwhile, in-vivo OCT imaging of eye retina has become the gold standard for eye disease research and diagnosis, and dispersion compensation is very critical in eye retina in-vivo imaging using FD-OCT because it has to use the eye lens as the objective to achieve the light focusing. Here we also imaged mouse eye retina in vivo using used a Bioptigen OCT setup (ENvisu R2210, Bioptigen) and processed the OCT raw dataset using different methods, to demonstrate the advantage of our method proposed.
3. Results
3.1. Depth-resolved spectra and their reshaping caused by dispersion mismatch
Figure 3 shows the Fourier transform (FT) results, the spectrograms, and the depth-resolved spectra of A-scans when imaging mirror when the OCT setup was under different conditions of dispersion mismatch. Figure 3(a) shows the FT result of an A-scan when the reference arm has a thicker glass than does the sample arm; Fig. 3(b) shows the FT result of an A-scan when the reference arm has a glass of the same thickness as that of the sample arm; Fig. 3(c) shows the FT result of an A-scan when the reference arm has a glass thinner than that of the sample arm. Figures 3(d), 3(e), and 3(f) are the corresponding spectrograms of A-scans in Figs. 3(a), 3(b) and 3(c) using the spectral-spatial analysis, respectively. Figures 3(g), 3(h) and 3(i) are the corresponding recovered depth-resolved spectra at depths 1(z=80), 2 (z=65) and 3 (z=50) of A-scans in Figs. 3(a), 3(b) and 3(c), respectively.
Fig. 3. Fourier transform results, spectrograms, and recovered depth-resolved spectra of A-scans under different conditions of dispersion mismatches. (a)-(c), Fourier transform results of A-scans under the following conditions: ${l_R} < {l_S}$, ${l_R} = {l_S}$ and ${l_R} > {l_S}$, respectively. (d)-(f) Sptectrograms of A-scans under the following conditions: ${l_R} < {l_S}$, ${l_R} = {l_S}$ and ${l_R} > {l_S}$, respectively. (g)-(i) Recovered depth-resolved spectra of A-scans at depths 1(z=80), 2 (z=65), and 3 (z=50) under the following conditions: ${l_R} < {l_S}$, ${l_R} = {l_S}$ and ${l_R} > {l_S}$, respectively.
From Figs. 3(a)–3(c), we can see that FT cannot distinguish different kinds of dispersion mismatches. From Figs. 3(d)–3(i), we can see that the dispersion mismatch between the sample and reference arms can cause spectroscopic effects on the A-scan’s spectrogram and its depth-resolved spectra. In detail, if there is no dispersion mismatch, after performing the Fourier transform, we obtain the result of the interferometric measurement of the apparent displacements (depths) of each sample reflector from the reference position as $2({z_R} - {z_{Sn}})$ with the FWHM of $\gamma (z)$, as shown in Figs. 3(b), 3(e) and 3(h). However, if the dispersions between the sample and reference arms are mismatched (${l_R} \ne {l_S}$), there will be a nonzero frequency-based phase shift $\Phi (\omega )$ that will cause the interferences of different-frequency light to locate at different locations, and the difference between the optical dispersion thicknesses ${l_R}$ and ${l_S}$ affects the locations of the interferences of different-frequency light, as shown in Figs. 3(d) and 3(f). These spectroscopic effects of dispersion mismatch on the spectrogram can be seen in the normalized depth-resolved spectra, as shown in Figs. 3(g)–3(i). From Figs. 3(g)–3(i), we can see that if the dispersion is matched well, the depth-resolved spectra of backscattered light are approximately the spectra of the light source, and different conditions of dispersion mismatch reshape the depth-resolved spectra in the spectrogram differently.
3.2. Detection and compensation of dispersion mismatch
From Fig. 3(a) and Fig. 3(c), we can see that the Fourier transform can show only the change in the resolution and cannot detect different conditions of dispersion mismatches. Here the results show that the proposed method can visually and quantitatively detect different conditions of dispersion mismatches and perform dispersion compensation well. Figure 4 shows the A-scan’s spectrograms of the mirror surface under different conditions of dispersion mismatch before and after doing dispersion compensation.
Fig. 4. Spectrograms of A-scans from the mirror under different kinds of dispersion mismatches. (a)-(c) Spectrograms of A-scans under $l_R^a < l_R^b < l_R^c = {l_S}$. (d)-(e) Spectrograms of A-scans under $l_R^d > l_R^e > {l_S}$. (f)-(i) Spectrograms of A-scans in (a)-(b) and (d)-(e), respectively, after performing dispersion compensation using the method proposed here.
Figures 4(a)–4(b) are the A-scan’s spectrograms when the reference arm has different optical dispersive lengths ${l_R}$, both of which are smaller than the optical dispersive length ${l_S}$ of the sample arm ($l_R^a < l_R^b < {l_S}$). Figure 4(c) is the A-scan’s spectrogram when ${l_R} = {l_S}$. Figures 4(d)–4(f) are the A-scan’s spectrograms when the reference arm has different optical dispersive lengths ${l_R}$, both of which are larger than the optical dispersive length ${l_S}$ of the sample arm ($l_R^d > l_R^e > {l_S}$). Figures 4(f)–4(i) are the A-scan’s spectrograms of A-scans in Figs. 4(a)–4(b) and Figs. 4(d)–4(e) after performing dispersion compensation using the proposed method, respectively.
From Fig. 4, we can see that different conditions of dispersion mismatches can cause different changes on the spectrogram. First, if there is a dispersion mismatch, the interferences of different-wavenumber light will be located at different depths in the A-scan’s spectrogram, which causes the shape-changing of the recovered depth-resolved spectra in the spectrogram. Second, if the reference arm has a smaller optical dispersive thickness than that of the sample arm, the interference of the small-wavenumber light will be located at a deeper depth than the centroid frequency, and the interference of the larger-wavenumber light will be located at a shallow depth, while if the sample arm has a smaller optical dispersive thickness than that of the reference arm, the situation will be reversed. Third, if the reference arm has a smallser optical dispersive thickness than that of the sample arm, then the more serious the dispersion mismatch is, the deeper the location of the interference of the small-wavenumber wave, while the shallower the location of the interference of the large-wavenumber wave. If the sample arm has a smaller optical dispersive thickness than that of the reference arm, then the more serious the dispersion mismatch is, the deeper the location of the interference of the larger-wavenumber wave, while the deeper the location of the interference of the large-wavenumber wave.
Here we first tested the proposed method on an ideal scenario, a mirror surface, to show how different methods performed, then we tested the complicated scenarios of Scotch tape and mouse eye. Figure 6 shows the OCT images and spectral centroid images of the mirror surface obtained using different methods and their corresponding spectral centroid images. Figures 6(a)–6(c) are the OCT images of the mirror surface obtained without dispersion compensation, by using the method in Ref. [13] and the method proposed here, respectively. Figures 6(d)–6(e) are the corresponding spectral centroid images of Figs. 6(a)–6(c), respectively.
Figure 5 shows the A-scan’s spectrograms of complicated structures, the mouse eye, obtained using different methods. The corresponding A-scan voxel used here was the central A-scan voxel of the B-scan in the following in-vivo mouse eye experiment. Figures 5(a)–5(c) are the spectrograms of the mouse eye obtained without dispersion compensation, with dispersion compensation using the method in Ref. [13], and the proposed method here, respectively. From Fig. 5(a), we can see the same phenomenons as that of Fig. 4(d), and after dispersion compensation, we can see that the proposed method can remove the effect of dispersion mismatch on the spectrograms better than the method in Ref. [13], and obtain better balanced depth-resolved spectra.
Fig. 5. Spectrograms of the mouse eye obtained using different methods. (a)-(c) Spectrograms of A-scans from the mouse eye obtained without dispersion compensation, with dispersion compensation using the method in Ref. [13], and the proposed method here, respectively.
Fig. 6. OCT images and the spectral centroid images of a mirror surface obtained using different methods. (a)-(c) OCT images obtained without dispersion compensation, with dispersion compensation using the method in Ref. [13], and the proposed method here, respectively. (d)-(f) are the corresponding spectral centroid images of (a)-(c), respectively.
Figure 7 shows the OCT images and spectral centroid images of Scotch tape obtained using different methods and their corresponding spectral centroid images. Figures 7(a)–7(c) are the OCT images of Scotch tape obtained without dispersion compensation, by using the method in Ref. [13] and the method proposed here, respectively. Figures 7(d)–7(e) are the corresponding spectral centroid images of Figs. 7(a)–7(c), respectively. Figure 8 shows the in-vivo OCT images of mouse eye obtained by using different methods and their corresponding spectral centroid images, using the Bioptigen OCT setup. Figures 8(a), 8(c), and 8(e) are the in-vivo OCT images of mouse eye obtained without dispersion compensation, by using the method in Ref. [13] and the method proposed here, respectively. Figures 8(b), 8(d), and 8(f) are the corresponding spectral centroid images of Figs. 8(a), 8(c) and 8(e), respectively. Contrast-to-noise ratio (CNR) [27] measures the contrast between the signal region and the background region of images, Table 1 shows the CNRs of the selected regions in Fig. 7 and Fig. 8.
Fig. 7. OCT images and spectra centroid images of Scotch tape. OCT images of Scotch tape without dispersion compensation (a), with dispersion compensation via the method in Ref. [13] (b) and our proposed method (c). (d)-(f) are the corresponding spectral centroid images of (a)-(c), respectively.
Fig. 8. OCT images and spectra centroid images of mouse eye in vivo. In-vivo OCT images of mouse eye without dispersion compensation (a), with dispersion compensation via the method in Ref. [13] (c), and our proposed method (e). (b), (d) and (f) are the corresponding spectral centroid images of (a), (c), and (e) respectively.
Table 1. CNRs of images obtained using different methods.
From Fig. 7, Fig. 8, and Table 1, we can see that the proposed method has better performance in dispersion compensation. In Fig. 7(a) and Fig. 8(a), it is difficult to observe the detailed microstructure, such as different tape layer in Fig. 7(a) and different eye retina layers in Fig. 8(a), because of the serious dispersion mismatch. Figure 7(d) and Fig. 8(b) show the corresponding spectral centroid images of Fig. 7(a) and Fig. 8(a) are not smooth. Figure 7(b) and Fig. 8(c) show that the method in Ref. [13] can perform dispersion compensation for FD-OCT, however, its performance is limited by speckle noise, electronics noise, and setup sensitivity, et al., when using the sharpness function of OCT images, its spectra centroid images still have obvious bright and dark lines. From Fig. 7(c) and Fig. 8(e), we can see that our proposed method has a better performance of dispersion compensation, such as the tape edge is sharper, and more detailed microstructure of mouse eye can be observed. Corresponding, their spectral centroid images are the most smooth, as shown in Fig. 7(f) and Fig. 8(f). From Figs. 7(d)–7(f) and Figs. 8(b), 8(d), and 8(f), we can see that our proposed method is more sensitive to dispersion mismatch and can achieve a better dispersion mismatch detection and compensation.
4. Discussions and conclusion
In this work, we uncovered the spectroscopic effects of dispersion mismatch on the A-scan’s spectrogram and its recovered depth-resolved spectra in FD-OCT, which have not been fully addressed by previous works. We established a theoretical and experimental approach to understand and characterize the effects of dispersion mismatch on the A-scan’s spectrogram and its recovered depth-resolved spectra in FD-OCT. We showed how the A-scan’s spectrogram and its recovered depth-resolved spectra change under different kinds of dispersion mismatches, which further shows how the dispersion mismatch affects the axial resolution of OCT imaging. Based on the spectral centroid in the recovered depth-resolved spectra, which is caused by the dispersion mismatch between the sample and reference arms, we proposed a complementary method to detect the dispersion mismatch and perform dispersion compensation in FD-OCT. The results demonstrate a clear advantage in dispersion mismatch detection and compensation over the existing methods.
Because there is a spectral/spatial resolution trade-off in spectral/spatial resolution when doing the spectral/spatial analysis (short-frequency Fourier transform), and too low spectral or spatial resolution will affect the accuracy of the recovered depth-resolved spectra in the spectrogram, so we need to choose a proper window size to obtain a good trade-off in spectral/spatial resolution. Here a moving window of 0.43 µm−1(at 850 nm) is applied to the fast Fourier transforms (FFTs) of the interferometric data. The window is moved in 50 nm steps of 0.25 nm. After windowing, the air axial resolution is found to be 6 µm. The a2 and a3 values obtained by different methods were different, such as in the mouse eye imaging, the mouse eye imaging, the a2 and a3 values obtained by the proposed method here were −0.0962 and 1.2762e-06, respectively; while the a2 and a3 values obtained by the method in Ref. [13] were −0.0878 and 1.1655e-06, respectively. This is because the method in Ref. [13] uses the image domain of scanning voxels in B-scan, which is affected by the noise, especially the speckle, while the proposed method here uses a transform domain of scanning voxels in B-scan.
In our previous work [21], we numerically predicted and experimentally proved that transversely oriented and regularly arranged nanocylinders selectively backscatter light of long wavelengths and generate spectral centroid shifts toward long wavelengths within the spectral window of $700\; - \;950\;\textrm{nm}$. Therefore, when using the proposed method under these conditions, we need to choose a sample region that does not contain transversely oriented and regularly arranged nanocylinders.
In conclusion, we uncovered the spectroscopic effect of dispersion mismatch on the A-scan’s spectrogram and recovered depth-resolved spectra in FD-OCT and developed a digital method to detect the dispersion mismatch and perform dispersion compensation. We further noted that the proposed method can be very helpful to guide hardware dispersion compensation when building an FD-OCT setup.
Funding
National Natural Science Foundation of China (61905036, 61421002, 61575037, 61927821).
Disclosures
The authors declare no conflicts of interest.
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