Optical coherence tomography (OCT) is a well-established tool in corneal imaging that achieves high axial resolution in a non-contact manner. Fourier-domain full-field optical coherence tomography (FD-FF-OCT) is one of the fastest volumetric OCT imaging techniques that can acquire 10 billion voxels per second due to the combination of FD signal acquisition and its parallelization with an ultrahigh-speed camera [1]. A spatially and temporally coherent laser, tunable across tens of nanometers, is used to acquire multispectral interference images that are then Fourier-transformed to generate a 3D volume of a sample. However, when imaging cornea in vivo with FD-FF-OCT, a highly coherent collimated laser beam is sent onto the cornea, where it gets focused on the retina by the natural eye optics; consequently, all of it can get focused to a 25 µm spot on the retina [2], with the intensity far exceeding the maximum permissible exposure (MPE). In time-domain (TD) FF-OCT corneal imaging [3], such a problem does not exist since a spatially incoherent light source is used, such as a LED, which cannot be focused to a small spot due to its large étendue. It also produces cross-talk-free images. However, TD-FF-OCT is a much slower volumetric imaging technique than FD-FF-OCT and requires moving elements for scanning. While other illumination schemes might be implemented in FF-OCT settings to avoid sharp focus on the retina, such as sending a highly convergent laser beam on the cornea, it, however, requires a more careful design to ensure eye safety. Here we resort on the most commonly used configuration of FF-OCT that is based on 4-f design principles. Recently we have shown that spatial coherence of the tunable (swept-source) laser can be reduced with an ultrafast-speed deformable membrane, which enabled in vivo imaging of the human cornea with FD-FF-OCT for the first time [4]. We have used this membrane previously for reducing cross talk in OCT in vivo images of skin [5] and the retina [6]. We do not expect substantial cross talk reduction in corneal images, due to the cornea’s relatively high transparency. However, the deformable membrane did produce some imaging caustic-like artefacts [4,5] because there was an additional amplitude modulation present. There is currently no other known method capable of reducing the coherence within the integration time (15 µs) of a single frame in the FD-FF-OCT.

Multimode fiber has also been used passively, without any moving elements, to reduce the cross talk and speckle contrast in TD-FF-OCT, as demonstrated on an aluminum plate [7] and a fruit fly [8]. The difficulty with using multimode fiber for spatial coherence reduction in FD-FF-OCT is that the (instantaneous) bandwidth of the swept-source laser is typically ${\sim}{0.1}\;{\rm{nm}}$, which is 2–3 orders of magnitude narrower compared to that used in TD-FF-OCT (10–100 nm). This narrow bandwidth can produce a high-contrast speckle pattern at the distal end of the fiber. Moreover, each generated spatial mode in the multimode fiber will acquire a different phase upon propagating the entire length of the fiber. Addition of all the modes will result in a complicated phase pattern and speckle realization that will change as a function of wavelength. In a proof-of-principle FD-FF-OCT setup [9], the spatial coherence was reduced with a system consisting of a multimode fiber (without given specifications), an acoustic mode mixer, and a holographic diffuser. However, the presented images seemed to suffer from shallow imaging depth and remaining cross talk.

In this Letter, we demonstrate in vivo corneal imaging with FD-FF-OCT by using a multimode fiber for spatial coherence reduction, which decreases the intensity on the retina to safe levels. The fiber was used passively—without any moving elements. On the one hand, the diameter of the fiber core was chosen to be large enough (50 µm) so that it produces low-intensity illumination (${{80}}\;{\rm{mW/m}}{{\rm{m}}^2}$) on the retina when the illumination is focused down by the eye. On the other hand, the core was still small enough to form a long depth-of-focus (DOF) of  ${\gt}1\;{\rm{mm}}$ on the cornea, which is essential in any in vivo FD-OCT imaging system. Finally, the length of the fiber was chosen so that the contrast of a speckle pattern would be minimal to provide uniform illumination. The spatial coherence reduction of a laser in the multimode fiber relies on the fact that the coupled-in single spatial mode breaks down into $N$ different modes. The following formula can be derived using $V = 2\pi {\rm{NA}}a/{{\lambda}}$ and $N \approx {V^2}/2$ [10] relations, where $V$ is the normalized frequency and $a$ is the core radius; NA is the numerical aperture of the fiber and $\lambda$–wavelength:

 

Fig. 1. Schematic diagram of Fourier-domain full-field OCT system with a multimode fiber for human corneal imaging in vivo. A swept laser source is coupled into the multimode fiber. Such illumination (red) will be focused to a broad spot on the retina. If a single-mode fiber is used, it would focus down to a tiny spot (white rays), causing a safety hazard. BS, beam splitter; ND, neutral density filter; obj., microscope objective ($\times {{10}}$, ${\rm{NA}} = {0.3}$). Inset shows that scattered light fills the whole cross section of a pupil plane in the sample objective, whereas illumination—only a small portion.

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Illumination coming from the swept-source laser (Broadsweeper BS-840-2-HP, Superlum) with the tuning range of 800–878 nm was coupled into the multimode fiber and delivered to the system that was essentially a Linnik interferometer composed of a 50:50 non-polarizing beam splitter and two identical microscope objectives. The reference arm in the interferometer contained a tilted neutral density (ND) filter that attenuated the reference beam to ${\sim}{{10}}\%$ in the double-pass. The cornea and reference arm were illuminated with 5 mW of power. The backscattered light from the cornea and reflected light from the reference mirror were recombined by the same beam splitter and imaged onto the ultrahigh-speed camera (Fastcam SA-Z, Photron) by a tube lens, with an overall magnification of 16.7 times. The multimode fiber did not reduce the contrast of the interference detected on the camera since the phase relation between the two interferometer arms is preserved even when an incoherent source is used [12]. When a single-mode fiber is used to deliver the laser light, the optics in the system focuses the laser to a diffraction-limited spot in the objective’s pupil plane (${\sim}{{25}}\;{\rm{\unicode{x00B5}{\rm m}}}$), as well as on the retina (as illustrated in Fig. 1), because the light is fully spatially coherent. When the single-mode fiber is replaced with the multimode fiber, the illumination spot is expanded to ${\sim}{{250}}\;{\rm{\unicode{x00B5}{\rm m}}}$. In this case, the filling of the pupil plane is still small and creates a large DOF spanning the entire corneal thickness. Since the dominant source of the risk is thermal retinal damage, the safety regulations ${\rm{permit}}\;\sim{0.6}\;{\rm{mW}}$ of accessible emission limit (AEL) for CW laser continuous radiation of the retina at 800 nm. Assuming the smallest achievable spot size on the retina to be 25 µm [2], the expansion of the focal area is $\;{({250\;\unicode{x00B5}{\rm m}/25{\rm{\;\unicode{x00B5}{\rm m}}}})^2} = 100$ times. Such an increase in area will also increase the total permissible power for our system to 60 mW. In determining the total permissible power, we relied on ANSI standards, which by international agreement (WHO, 1982, No. 32) are equivalent and identical to European standards (60825-1-2014, CLC/TC 76), as well as Polish standards (60825-1: 2005/A2). Our system performed similar to the one in Ref. [4] in terms of optical parameters: it had an estimated lateral resolution of 2.4 µm and a measured axial resolution of 5.6 µm (estimated as 4.2 µm in the tissue). The field of view (FOV) was ${{615}}\;{\rm{\unicode{x00B5}{\rm m}}} \times {{615}}\;{\rm{\unicode{x00B5}{\rm m}}}$. The camera was operated at a maximum speed of 60 kHz when acquiring images of ${{512}} \times {{512}}$ pixels in size.

 

Fig. 2. Speckle noise generation by the multimode fiber (in the FD-FF-OCT system with blocked sample arm). (a), (b) Speckle patterns generated by the fiber at a single wavelength: (a) $\lambda$ and (b) $\lambda + {0.15}\;{\rm{nm}}$. The contrast of the speckles is ${\rm{C}}\; \approx \;{0.05}$. (c) A line profile along $x$ in image (a) as a function of wavelength. The inset shows a zoomed-in area with an enhanced contrast. (d), (e) Speckle noise in Fourier-transformed images at axial positions, (d) $z$ and (e) $z + 4.4 \;{\rm{\unicode{x00B5}{\rm m}}}$. (f) Axial ($xz$) image obtained by Fourier-transforming (c).

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Figures 2(a) and 2(b) show raw images acquired by the camera in the FD-FF-OCT system, where the sample arm was blocked. The speckle patterns appear to have low spatial frequency components essentially due to the relatively small core size of the fiber. This is because the fiber generates a certain number of coherence areas across the end face that is almost equal to the number of spatial modes, $N$, defined by Eq. (1). The number will remain the same after transformation by a lens, but the area will depend on the optics used. The diameter of the coherence area on the cornea can then be simply estimated as ${\rm{FOV}}/\sqrt {\rm{N}} \approx 21 \; {\rm{\unicode{x00B5}{\rm m}}}$, which effectively is also the size of the speckle. The speckle contrast $C$ in the image was calculated to be ${\sim}{{5}}\%$ from $C = \sigma / \langle I \rangle$, where $\sigma$ is the standard deviation and $\langle I \rangle$ is the average intensity of the speckle pattern. The slight discrepancy between the theoretical estimate [Eq. (4)] and the actual measurement could be explained by, for example, incomplete excitation of the fiber modes. The images in Figs. 2(a) and 2(b) also show that the fiber-produced speckle pattern changes when the laser is being tuned. The change will result in variation of the illumination intensity at a specific location on a sample and at a specific pixel on the camera, as illustrated in the $x\lambda$ image in Fig. 2(c). The image there was derived by stacking together line profiles taken along the $x$ direction in the raw images that were recorded at different wavelengths. Such change in speckle pattern as a function of wavelength will result in artefacts in OCT images because intensity variations are expected to occur only due to the variations in sample structure, and not illumination. To illustrate this conclusion, a Fourier-transform of the $x\lambda$ image along $\lambda$ direction results in a speckle-corrupted image, shown in Fig. 2(f). The en face images, shown in Figs. 2(d) and 2(e), were derived by first Fourier-transforming the whole $xy\lambda$ volume point-by-point along the $\lambda$ direction, and then extracting the two $xy$ images from the resulting volume. The en face images show clear speckle artefacts (with low spatial frequencies) that would also appear in real OCT images. Fortunately, the speckles can be efficiently filtered out because of their large size by Fourier-transforming en face ($xy$) OCT images and selectively blocking low spatial frequencies. Figure 3 shows a cross-sectional image of the cornea where fiber-induced speckles are removed without significant loss of signal. The differences seen in the filtered and unfiltered OCT images are due to the fiber-induced speckle removal, but not because of the removal of low spatial frequencies of the cornea. The higher the speckle contrast, the more OCT signal coming from the cornea will be lost to the filtering, making it essential to use a sufficiently long multimode fiber. The measured values of the signal-to-noise ratio (SNR) improvement were estimated to be 3.5 dB for random noise and 13 dB for parasitic noise. Filtering does not affect the OCT images visually, as can be seen by comparing endothelial cells in Fig. 4 and in Ref. [4].

 

Fig. 3. Filtering out fiber-induced speckles in corneal images. Filtered B-scan image, shown in the linear scale on the bottom right, reveals the corneal structure in its entire thickness that was masked by the speckle pattern shown in the top right image. The OCT image was derived from a single volume acquired in 8.6 ms.

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Fig. 4. Cross-sectional (B-scan) and en face images of the human cornea acquired in vivo with spatially partially coherent FD-FF-OCT (30 volumes averaged). The images were corrected for chromatic dispersion and motion. OCT images were Fourier-filtered to remove fiber-induced speckle pattern followed by a layer flattening to segment the layers of interest. The white arrow indicates the location of the endothelial layer segmented and displayed as a separate panel. Projections of Descemet’s membrane and the posterior stroma come from 10 µm thick layers located 10 µm and 100 µm above the endothelium, respectively. The yellow arrow indicates the extension of the blurred area. The dark circle located at the left down corner is an artefact related to opacities present in the front part of the cornea.

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The corneal images were acquired in vivo with the FD-FF-OCT system from a healthy 45-year-old volunteer. The system acquired 512 images while tuning the laser with a speed of 8700 nm/s, resulting in the acquisition of 116 volumes per second (8.6 ms per volume). We acquired 30 such volumes, corresponding to a total acquisition time of 250 ms. A chromatic dispersion mismatch correction was performed, as well as a correction for the eye axial motion that happens during the laser sweep in each volume [13]. We corrected numerically each volume for defocus aberration, which is possible despite the use of spatially incoherent illumination [12], such as provided by multimode fiber. For selected depth range, we employed the split aperture approach [14], which provided the depth-resolved defocus parameter, $d(z)$. After rejecting outliers, we fit $d(z)$ to a line, $D(z) = az + b$. Given the parameters $a,b$, we then constructed the phase corrector, $P(z) = \exp [{- iD(z)Z_2^0}],$ where $Z_2^0$ denotes the defocus Zernike polynomial. Subsequently, the phase corrector was applied to the entire volume. The volumes were then registered and integrated incoherently. Figure 4 shows cross-sectional and en face images of the human cornea acquired in vivo; various corneal layers are clearly visualized, such as the endothelium, stroma, and Descemet’s membrane. One can see that the cross-sectional image of the cornea spans its entire thickness, which is an improvement from our previous work [4]. However, certain parts of the cornea are not in focus (blurred), as indicated by the yellow arrow in Fig. 4. Indeed, as previously, we could not extract all the corneal layers in one measurement [4]. This limitation could be explained by the fact that even though the illumination NA is restricted to give a large illumination DOF, the detection NA was not. Since the signal from the cornea filled the whole pupil plane of the objective, it resulted in a smaller detection DOF, so only a part of the cornea was actually in focus on the camera. Computational defocus correction was not able to fully correct for that most likely due to extrapolation failure, and also due to numerical errors that appear for layers, lacking enough sample features to enable sufficient correlation between digitally applied apertures. To extend the DOF, additional phase manipulation could be attempted either computationally or physically. We could not acquire images using single-mode fiber for comparison purposes since that required lowering the power 8.3 times—to 0.6 mW, which made it hard to detect any OCT signal coming from the cornea. In conclusion, we have demonstrated in vivo corneal imaging with FD-FF-OCT by using a multimode fiber with carefully chosen parameters to produce an optimal light source for in vivo corneal imaging. The source enabled volumetric imaging without causing laser safety risk to the retina. Compared to the deformable membrane employed before [4], use of multimode fiber was cheaper and also safer. For example, in the case of malfunction, the deformable membrane would act as a mirror, and light would focus down to a spot on the retina, risking damage. Use of a more powerful laser is expected to increase SNR, especially if specular reflections from the cornea are minimized.