1. Introduction

Optical coherence tomography (OCT) is a cross-section imaging technique based on low-coherence interference and has proven to be able to image the three-dimension (3D) scattering structure of biological tissues. This imaging technique has been undergoing a rapid development since 1990s when it was firstly demonstrated for measuring the thickness of retinal layers [1]. In particular, based on extensive successful demonstrations in laboratory-based research [2,3], OCT has been successfully translated into an essential tool for daily clinical practice in ophthalmology. Currently, it is also showing great potential in dermatology, cardiology, gastroenterology and pulmonology [4–7].

OCT is commonly configured as a confocal system with single mode fibers for light delivery and collection. The detection fiber core serves as the pin hole of normal confocal microscopy. However, the 3D point spread function (PSF) of OCT is not identical to that of confocal microscopy. In particular, the transverse PSF and the axial PSF are decoupled in OCT imaging; the former is determined by the objective’s numerical aperture and wavelength as in confocal microscopy while the latter is exclusively determined by the laser source as illustrated by the equation: $\delta L=2\ln \left(2\right){\lambda }_c^2/\left(\pi \Delta \lambda \right)$ where $\delta L$is the full-width at half maximum of the axial PSF and ${\lambda }_c$ and $\Delta \lambda$ are the central wavelength and the optical bandwidth of the laser source [8]. Consequently, the axial resolution of OCT imaging remains constant over the full imaging depth, while the transverse resolution is approximately maintained within the Rayleigh range. The Rayleigh range is defined as the range over which the width of the transverse PSF increases by a factor of $\sqrt{2}$. The depth-of-focus (DOF) of OCT imaging is given by twice the Rayleigh range. The Rayleigh range is proportional to the square of the lateral resolution. As a consequence, there is a trade-off between the lateral resolution and the DOF, where a high lateral resolution results in a short DOF.

It is widely accepted that the current gold standard for tissue diagnostics is still histopathology, inspecting biopsied tissue under a microscope to gain insights into cellular changes associated with diseases. This requires the transverse resolution to reach the cellular level (several micrometers), resulting in a reduction of the DOF to tens of micrometers. Consequently, OCT imaging with cellular lateral resolution can only be used for thin tissues. This limits the application of OCT as optical biopsy for in vivo diagnosis. Therefore, various methods have been reported to address the issue of limited DOF in OCT imaging, especially when high transverse resolution is required [9–17]. Among those reported methods, digital refocusing methods, such as the interferometric synthetic aperture method, deconvolution and a scalar diffraction model, have recently been demonstrated with the advantage that no system modification was needed [15–17]. However, these methods require phase-stable sequential OCT A-scans. Phase-apodization is another often reported method. For example, micro-OCT with a broad band light source and an annularly apodized light beam was demonstrated to be capable of imaging the subcellular structure with an extended focal-depth of 200 µm [18]. However, phase-apodization approaches suffer from low illumination and collection efficiency over the extended DOF [14].

In a previous study, we proposed a novel digital refocusing method based on a synthetic aperture technique that is not affected by inter A-scan phase instability [19]. This method can also be considered as a numerical adaptive optics (AO)/wavefront shaping method. Adaptive optics was initially investigated to correct the atmospheric distortion to improve astronomical imaging. It has been recently incorporated into ophthalmic OCT to correct the ocular aberration in order to improve the image transverse resolution and obtain retinal imaging at cellular level albeit at a very limited DOF [20,21]. More relevant to DOF extension, Sasaki et al reported to use AO to generate 3rd order spherical aberration so as to create long focal-depth in spectral domain OCT [22]. Our method requires only a small modification to a standard OCT system, which is pupil segmentation by an annular phase plate (APP). Pupil-segmentation based adaptive optics was proven to be able to recover near-diffraction-limited image performance in two-photon fluorescence microscopic imaging by correcting sample-induced optical aberrations [23]. This method is dedicated to the image at the actual focal plane; however it is not ideal for extending the DOF of OCT imaging. For our method, the phase plate segments the pupil into two parts, which, because of the double-pass through the sample arm, leads to three distinct optical apertures as illustrated in three inserts of Fig. 1: (i) optical aperture 1, the first light path passes through the center of the phase plate both on the way to the scattering object and back; (ii) optical aperture 2, the second path passes through the center on the way to the scattering object and travels back through the edge, or, equivalently, passes through the edge on the way to the scattering object and travels back through the center; (iii) optical aperture 3, the third light path passes through the edge of the phase plate both on the way to the scattering object and back [19]. The images formed by the three optical apertures are encoded to different depths in a single OCT B-scan. This makes it possible to correct the defocus-induced wave front curvature at the pupil by manipulation of the phase of the three images and coherent summation of the complex amplitudes to reconstruct a new image with improved focus. The beauty of our method is that the digital refocusing can be performed repeatedly at all image depths in post processing in order to obtain a new image with an extended DOF. Using this method we demonstrated a DOF extension by a factor of 5 [19].

 

Fig. 1 System schematic of optical coherence tomography imaging with an annular phase plate. L: Lens; PP: annular phase plate; CL: Collimator; M: reflection mirror; FC: fiber coupler; CIR: fiber circulator; PR: photon receiver; FBG: fiber bragg grating; BD: balanced detector. Three inserts labeled with (i)-(iii) describe the possible light propagation paths, which are defined as three different optical apertures.

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However, in our previous work the method was validated using a light source with a relatively short coherence length (5 mm in air). As described above, three copies of the image have to be separated axially, resulting in a significant sacrifice of imaging depth. For this reason we were able to measure only thin samples. With the advances in long coherence-length OCT laser sources [24], we are now able to demonstrate the full potential of our method on real thick biological tissues including an in vivo demonstration.

2. Materials and methods

2.1 Optical coherence tomography imaging setup

The optical coherence tomography imaging system is described in Fig. 1 (see details elsewhere [19]). The wavelength-swept laser source used in this study is a 1310 nm vertical cavity surface emission laser (VCSEL) with 3dB bandwidth of 75 nm, 12 mm coherence length and 200 kHz sweep rate (SL1310V1, Thorlabs, Newton, NJ, USA). To avoid polarization-mode dispersion, the system was built without fiber circulators in the interferometer part. In brief, the light from the swept source is split into two parts. One part (10%) is sent to a fiber Bragg grating (FBG) used to create an optical trigger signal. The other part (90%) is fed into the interferometer. In the sample arm, the light is collimated to a 3.4 mm (diameter) beam by a fiber collimator (F280SMA-C, Thorlabs, Newton, NJ, USA). With this collimated beam, the objective (LSM02, Thorlabs, Newton, NJ, USA) creates a 10.1 µm focal spot and a Rayleigh range of about 83.7 µm in air. The back focal plane of the objective is relayed to the galvo scanning mirror by a pair of achromatic lenses (focal length: 45 mm) and further relayed to the annular phase plate (8-mm thick polycarbonate disc, refractive index n = 1.56, with a 1.8 mm hole in the center) by another pair of achromatic lenses (focal length: 60 mm).

For raster scanning, the galvo mirror scanning system is driven with a saw-tooth waveform generated by a 16-bit DAQ board (PCIe-6259, National Instruments, Austin, TX, USA). The OCT signal detected by the balanced detector (PDB480C, Thorlabs, Newton, NJ, USA) is digitized by a 12-bit PCI express digitizer (ATS9360, Alazar Technologies Inc., Pointe Claire, QC, CA). The digitizer is driven by an external k-clock provided by the laser source. This ensures the spectrum is linearly sampled in k-space which allows for direct Fourier transformation of the measured spectrum. Each A-scan is triggered by an optical trigger instead of the sweep trigger provided by the laser source. This reduces phase-errors resulting from jitter of the sweep trigger relative to the k-clock. Data acquisition, galvo scanning control and real-time display was implemented in LabVIEW (National Instruments, Austin, TX, USA) [19].

2.2 Digital refocusing algorithm

As derived in our previous paper [19], the OCT signal associated with optical aperture 2 can be expressed as the equation below:

2.3 Phantom preparation

The artificial phantom was constructed by mixing 1.5 mg melamine spheres with 5-μm diameter (PMa-5.0,, Kisker Biotech GmbH & Co. KG) with 2 grams of curing agent from a transparent silicone elastomer kit (Sylgard 184, Dow Corning). To remove residual clusters, this mixture stored in a vial was put in an ultrasonic bath for 15 minutes. The contents of this vial was stirred for 5 minutes with 20 grams of the elastomer kit base part and then degassed at 8 mbar in a vacuum chamber until all the air was removed. Subsequently, a small droplet was sandwiched between two glass plates, which were separated by two 300 μm thick spacers. The sample was retrieved from the glass plates after 48 hours of curing and then was cut into four parts. These four parts were mounted onto each other to reach a sample thickness of 1.2 mm. A small drop of silicone oil (Xiameter PMX-200 silicone fluid, 50 cs, Dow Corning) was applied to the interfaces between layers in order to minimize the reflection from the interfaces.

3. Results and discussion

Prior to validation on biological scattering samples, we first investigated the efficacy of our method on an artificial weak-scattering phantom with a thickness of 1.2 mm, which is four times thicker than the phantom used in previous work [19]. The manufacturing protocol of this phantom is described in detail in Section 2.3 Phantom preparation. The phantom is a silicon block with sparsely embedded spheres with a diameter of 5 µm, which is below the diffraction limit of the system. Using these spheres of known size enabled us to quantitatively evaluate the method. Figure 2 compares the resolution as a function of image depth between a conventional full Gaussian beam image and a digitally refocused image with a phase plate inserted in the beam path. It is clear that, in the full beam image (Fig. 2(a)), the out-of-focus spheres (en-face slices 1 and 3) appear to be much bigger than the in-focus spheres (en-face slice 2). At higher magnification we see that the spheres in Fig. 2(b) are approximately 2.5 times larger than those in Fig. 2(c), which can be accounted for by the 329 µm (~1.9 Rayleigh ranges) defocus towards the objective. When the spheres are further defocused by 707 µm (~4.1 Rayleigh ranges) away from the objective as shown in Fig. 2(d), they appear completely blurred and indistinguishable. In comparison, in the digitally refocused image in Figs. 2(e)-2(h), the resolution is significantly improved in the two defocused en-face planes. At the in-focus depth (Fig. 2(g)), the resolution of the digitally refocused image is equal to that of the full beam image (Fig. 2(c)). The signal intensity in the digitally refocused image is approximately 2 to 4 times lower than the full beam image, which is in reasonable agreement to the predicted value of two [19]. For the image defocused towards to the objective (Fig. 2(f)), a substantial improvement in the resolution makes each individual sphere well separated from its neighboring spheres while overlap between different spheres often occurs in the full beam image. For the 707 µm defocussed plane (Fig. 2(h)), improving the resolution is even more important. The spheres are barely identifiable in the full beam image (Fig. 2(d)) but they can be easily distinguished in the digitally refocused image. The results above demonstrate that our synthetic aperture digital refocusing method is capable of improving the resolution at significantly defocused depths. A new volume image with extended depth-of-focus can be reconstructed by fusing all refocused en-face images from all depths.

 

Fig. 2 Orthoslice view of a 3D volume of the silicon phantom (logarithmic greyscale): (a) The images acquired without phase plate; (e) The corresponding digitally refocused images. Three en-face images are selected to be visualized. The middle image is located around the actual focal plane. The top image is about 329 µm (~1.9 Rayleigh ranges) from the middle image towards the phantom surface. The bottom image is about 707 µm (~4.1 Rayleigh ranges) away from the middle image on the other side. For better comparison between the images with and without digital refocusing, a small en-face plane is selected from each image and shown in separate magnified windows: (b)-(d) The images acquired without phase plate; (e)-(h) The corresponding digitally refocused images. The diameter of the spheres is 5 µm, which is below the diffraction limit of the current setup. The en-face image is 980 µm by 980 µm.

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To gain a better understanding of the digital refocusing process, we analyzed the intermediate results produced during the refocusing process. As described in Section 2.2 Digital refocusing algorithm, after depth-decoding the OCT signals through optical apertures 2 and 3, the OCT signals were then Fourier-transformed to generate the complex cross-sectional images (B-scans). To reduce the specular reflection of the sample surface, the sample was tilted a bit with respect to the plane normal to the optical axis. This caused the focal plane to be tilted with respect to the sample surface and resulted in the actual focal plane being located at different optical delays in subsequent B-scans. Therefore, prior to coherently synthesizing the three different optical apertures, the actual focal planes in all B-scans were shifted to the same optical delay. The amount of shift to be applied was given by $\Delta d\left(n^2-1\right)$ where $\Delta d$ is the axial displacement of each B-scan relative to the first B-scan and n is the refractive index of sample.

To dramatically reduce the amount of computation work, the optimal phase shift that needed to be added to the complex images of optical apertures 2 and 3 before coherently summing the three images was determined in two steps (See details in Section 2.2 Digital refocusing algorithm). First, the optimal initial phases of the complex images of optical aperture 2 and 3 were determined by maximizing the speckle variance for each coherently summed B-scan over a single pre-defined depth range, which was approximately one Rayleigh range. It was found that the resulting optimal initial phase showed a continuous trend correlated with the position along the slow scanning axis of the 3D volume for both optical apertures 2 and 3 as depicted in Fig. 3(a). The initial phase curves were fitted with a 2nd order polynomial function to extract the systematic trend from the noise. The first and second order coefficients generated from the fitting for optical aperture 3 were about twice of that for optical aperture 2, which is consistent with the double pass of the photons through the solid edge part of the phase plate for optical aperture 3 compared with a single pass for optical aperture 2.

 

Fig. 3 The analysis of the phase produced during the digital refocusing process. (a) The initial phases of optical apertures 2 and 3 (Fig. 1) as a function of the slow scanning axis. The second order polynomial fitting yielded the first order coefficients of −0.002 and −0.004 for optical apertures 2 and 3, respectively. The corresponding second order coefficients were 2.6E-6 and 5.2E-6, respectively. (b) The k-independent phase needed to correct defocus for aperture 2 as a function of defocus extent (red). The blue curve represents the linear fit of the experimental results. The slope of the fit is 6.93 mrad/µm.

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After this first step the optimal phases for a single depth was found. Then, the determination of the optimal phase for refocus was repeated at all the depths based on the en-face image instead of individual B-scans. First, the fitted optimal initial phases were added to the complex images of optical apertures 2 and 3, respectively. Then, extra phases, called k-independent phase, were added to correct the defocus-induced phase difference among different optical apertures. In theory, the optimal k-independent phase for optical aperture 3 is twice of that for optical aperture 2 due to the double pass through the solid edge part of the phase plate for optical aperture 3. This has been confirmed experimentally in our previous work [19] and therefore was implemented in the current refocusing process, which significantly reduced the computation time. Figure 3(b) describes the k-independent phase needed for optical aperture 2 to optimize the focus at various depths. The experimental curve (red) contains a clear linear part from 100 to 900 µm. Fitting the experimental curve with a linear function yielded a slope of 6.93 mrad/µm, which is very close to the theoretically predicted value (7.25 mrad/µm) [19]. It is also consistent with our previous reported experimental result (6.81mrad/µm), indicating a good experimental reproducibility.

Following the successful demonstration of this refocusing algorithm on an artificial sample, we demonstrate the method on scattering biological tissues. Figures 4(a)-4(d) depict the full Gaussian beam en-face images of a zebrafish at four different depths. The light was approximately focused at the depth of Fig. 4(a). Figures 4(b)-4(d) are defocused from Fig. 4(a) by about 238, 500 and 725 µm (~1.6, 3.4, 4.9 Rayleigh ranges), respectively. The corresponding digitally refocused images are presented in Figs. 4(e)-4(h). The muscle fibers in the somite, labelled with the pink arrows, are sharply focused in both Figs. 4(a) and 4(e). This confirms that at the in-focus depth, the digitally refocused image is comparable to the full Gaussian beam image in terms of the resolution. When being 238 µm away from the focus the muscle fibers blur in the full beam image (Fig. 4(b)) while they are still fairly sharp in the refocused image (Fig. 4(f)). The digital refocusing method is also capable of improving the resolution at larger defocused depths as illustrated in Figs. 4(c)-4(d) and 4(g)-4(h).

 

Fig. 4 En-face images of zebrafish at four different depths. (a)-(d): Full Gaussian beam images; Images (b)-(d) are defocused from image (a) by about 238, 500 and 725 µm (~1.6, 3.4, 4.9 Rayleigh ranges), respectively. (e)-(h): The corresponding images generated from digital refocus with synthetic aperture method. The scale bar of 400 µm applies to both lateral dimensions.

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We further tested our method in vivo on a human palm. Figure 5 shows four pairs of en-face images at different depths of a human palm. The full beam images in Figs. 5(b)-5(d) are 112, 242 and 355 µm (~0.7, 1.5, 2.3 Rayleigh ranges) deeper than Fig. 5(a), respectively. The corresponding refocused images are Figs. 5(e)-5(h). Selected features are pointed out by green arrows, for example, the blood vessels in the refocused images (Figs. 5(g) and 5(h)) are sharper and more narrow than in the full Gaussian beam images (Figs. 5(c) and 5(d)). The skin images analyzed here are only down to 355 µm deep, which is about half of the image depth analyzed for zebrafish because skin tissue exhibits more scattering, causing a faster attenuation of the incident light beam and consequently a lower signal-to-noise ratio at larger depths.

 

Fig. 5 En-face images of a human palm at different depths. (a)-(d): Full Gaussian beam images; Images (b)-(d) are defocused from image (a) by about 112, 242 and 355 µm (~0.7, 1.5, 2.3 Rayleigh ranges), respectively. (e)-(h): The corresponding images generated from the digital refocus with the synthetic aperture method. The scale bar of 400 µm applies to both lateral dimensions.

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To evaluate our method more quantitatively, an image sharpness criterion, anisotropy, was calculated for both the full beam and refocused en-face images of both zebrafish and skin. This criterion has been demonstrated to be an effective indicator of image sharpness. The anisotropy value decreases as the image becomes blur [25]. It has also been used to evaluate the performance of another digital refocusing method, interferometric synthetic aperture microscopy [26]. The anisotropy criterion is different from the maximum speckle variance criterion that was used to find the optimal phase shifts in the digital refocusing process. Therefore, the anisotropy provides an objective means to assess our digital refocusing method. The anisotropy ratio of the refocused image to the full beam image was calculated over the full image depth as described in Fig. 6. For zebrafish images, the anisotropy ratio was above one from 0 till 900 µm in depth, indicating a resolution improvement. The depth positions denoted by z1 to z4 correspond to the four pairs of en-face images in Fig. 4. The anisotropy ratio also appeared to fluctuate about 1.25 before the depth position of 450 µm, after which it started to show a clear decreasing trend. At around 870 µm the anisotropy ratio peaked, which was attributed to an artifact in the refocused image visible in Fig. 4(h) as a black spot which was not present in the full beam image (Fig. 4(d)). For the skin images, the anisotropy ratio above 1 was found from about 100 to 500 µm except a short band with a ratio of less 1 at round 200 µm. The depth positions denoted by p1 to p4 correspond to the four pair en-face images in Fig. 5. Overall the anisotropy ratio for skin is smaller than that for zebrafish. This is consistent with the findings in our images (Figs. 4 and 5) that the improvement of focus is less pronounced in skin than in zebrafish. It is also observed that the anisotropy ratio went down more quickly from about 500 µm for skin images. The two differences are very likely due to stronger scattering characteristic of skin tissue as we discussed above.

 

Fig. 6 Image anisotropy ratio of the digitally refocused image to the full Gaussian beam image: (a) zebrafish, (b) human palm. z1-z4 denote the depth positions of zebrafish images in Figs. 4(a)-4(d), respectively. p1-p4 denote the depth positions of palm images in Figs. 5(a)-5(d), respectively.

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Although the exact scattering properties of the biological samples were unknown, it is clear that the improvement in lateral resolution in biological samples is less pronounced than in the phantoms, which we attribute to scattering..Our digital refocusing method can correct the defocus effect, but not the scattering effect on optical resolution.

4. Summary

In summary, we demonstrated that this novel depth-encoded synthetic aperture digital refocusing method provides a sharp focus over a significantly larger depth range than conventional OCT imaging. The demonstration on human skin in vivo strongly encourages an endoscopic implementation. The method could also be integrated into ophthalmic OCT imaging systems and together with conventional adaptive optics, could lead to extended DOF high-resolution imaging.