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Abstract
Fast 3D volumetric imaging has been essential for biology, medicine and industrial inspections, and various optical coherence tomography (OCT) methods have been developed to meet such needs. Point-scanning based approaches, such as swept-source OCT and spectral domain OCT, can obtain a depth information at once, but they require lateral scan for full 3D imaging. On the contrary, full-field OCT needs the scanning of imaging depth while it records a full lateral information at once. Here, we present a full-field OCT system that can obtain multi-depth information at once by a single-shot recording. We combine a 2D diffraction grating and a custom-made echelon to prepare multiple reference beams having different pathlengths and propagating angles. By recording a single interference image between the reflected wave from a sample and these multiple reference beams, we reconstruct full-field images at multiple depths associated with the pathlengths of the individual reference beams. We demonstrated the single-shot recording of 7 different depth images at 10 µm for biological tissues. Our method can potentially be useful for applications where high-speed recording of multiple en-face images is crucial.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
3D optical microscopy has played an essential role in investigating the physiological states of various biological systems and noninvasive diagnosis in medicine. To get a 3D volumetric image, various approaches have been developed so far. For example, optical coherence microscopy (OCT) provides depth selectivity by using low temporal coherence of a broadband source [1]. Multi-photon microscopy and light sheet microscopy [2–5] provides volumetric fluorescence imaging by maximizing axial resolution using nonlinearity of multiphoton excitation and in-plane excitation, respectively. Unique methods have also been developed for obtaining multiple depth images at a time. For instance, several beams of different focus with time intervals illuminate a sample of interest, and they are distinguished by a detector to acquire multiple depth images without axial scan [6,7]. The light field microscopy [8] uses a lens array to record intensity information for each angle of light reflected from a sample, which are later used in a post-processing to simultaneously acquire images of multiple depths.
Optical coherence tomography has been one of the most widely used 3D imaging modalities in biology and medicine. Since its first invention [1], various forms of image acquisition modalities have been developed; time-domain OCT and spectral domain OCT [9] swept-source OCT [10], full-field OCT (FF-OCT) [11–17] Among them, time-domain OCT, spectral domain OCT and swept-source OCT can acquire information along the depth at a single shot, but it requires scanning in the lateral direction for volumetric imaging. On the contrary, FF-OCT records an image in the lateral at once through a 2D detector such as CCD or CMOS camera. However, it requires scanning in the depth direction. All of the above OCT-based interferometric studies required the scanning of laser beam, sample stages, mirrors, laser wavelengths and so on to obtain volume images.
Many studies have been carried out based on OCT to obtain a volume image without a scanning process [18–20]. In particular, diverse approaches have been proposed in the context of a multiplexing, and they can largely be divided into space division multiplexing (SDM) and spatial frequency division multiplexing (SFDM). SDM-based OCT simultaneously illuminates multiple beams with different time delays in different areas of the sample based on swept source OCT such that beams in different areas have different frequency ranges [21,22]. The SFDM-based OCT is a technique for obtaining multi-depth images at once by making multiple reference beams with different time delays and different spatial frequencies. Therefore, SFDM-based OCT uses single sample beam and multiple reference beams, while SDM uses multiple sample beam with single reference beam. SFDM was used to increase the axial scan range by obtaining multiple volumes at once by making multiple references in the swept-source OCT [23–26]. SFDM was also used to expand the image field of view and aperture synthesis [27–29]. They also used SFDM in FF-OCT to simultaneously acquire multiple depths [30]. In an optical system composed of several beam splitters and mirrors, multiple reference beams were configured to have different time intervals and angles to obtain images of different depths at once. In addition, it was shown that six holograms can be multiplexed without the camera's spatial bandwidth loss [29,31].
Here, we introduce the FF-OCT system using SFDM for acquiring 3D volumetric image at 10 µm depth interval by a single-shot camera recording. We propose a simple and scalable design of multiplexing multiple spatial frequency divisions in comparison with the previous methods. In an off-axis digital holographic microscopy, we installed a spatial light modulator (SLM) in the reference beam path to display a 2D diffraction grating pattern for generating multiple reference beams whose propagation angles are different from one another. By introducing a set of echelons, we control the pathlength of each reference beam. In this configuration, the number of reference beams can be controlled by changing the pitch of the diffraction grating pattern written on the SLM. And the pathlength among reference beams can be adjustable by controlling the immersion medium where the echelon is embedded. The interference of the sample wave with these reference beams contains multi-depth information over the full field of view. In other words, the multi-depth information is multiplexed in the spatial-frequency domain. By applying a 2D bandpass filter selecting the respective cross-correlation term associated with each reference beam in the spatial-frequency domain, we reconstructed multiple depth images whose interval is set by the pathlengths of the reference beams.
2. Setup and methods
The experimental setup for the multi-depth imaging system is shown in Fig. 1(a). A Ti:sapphire laser system (Coherent Vitara, center wavelength: 800 nm, repetition rate: 80 MHz, and wavelength bandwidth 70 nm) was used as a light source. Laser beam was separated by a polarizing beam splitter (PBS1) and traveled to the sample and reference arms. In the sample arm, a motorized scanning mirror (SM) was installed to match the overall sample and reference beam paths. The sample beam reflected by a target object was captured by an objective lens (OL; Olympus RMS 4X, 0.1 NA) and delivered to the camera (PCO.Edge 4.2) by a set of lenses. The magnification from the sample to the camera was 13.9, and field of view (FOV) was $325 \times 325\;\mathrm{\mu}{\textrm{m}^2}$ with the diffraction-limited resolution of 8 $\mathrm{\mu}\textrm{m}$. In the reference arm, the laser beam was illuminated to a 2D grating pattern written on the spatial light modulator (SLM, fourth dimension display, QXGA-R9) to generate a few diffracted beams with different propagation angles. The 2D grating pattern consists of 7 µm squares at 49 µm interval. Each diffracted beam was focused by a lens L1 with the focal length of 250 mm.
Fig. 1. Experimental setup for multi-depth OCT imaging. (a) Schematic diagram of the imaging setup. BP, bandpass filter: BS1-2, beam splitters; SLM, spatial light modulator; BB, beam block; L1-6, lenses; PBS1-3, polarizing beam splitter; HWP, Half wave plate; QWP, Quarter wave plate; SM, scanning mirror; OL, objective lens. For simplicity, only three echelons are shown. (b) The photo of echelon. Each number (minus 1) indicates the number of stacked cover glasses. Yellow line indicates border of each coverglass.
Spacing between neighboring diffracted beams was 4 mm. We placed an echelon at the focal plane so that each beam experiences a different optical pathlength delay. Echelon was manufactured using a No. 0 cover glass, whose thickness was 100 $\mathrm{\mu}\textrm{m}$ and refractive index was 1.508. The echelon was placed as shown in Fig. 1(b) to control the pathlength of 7 different diffracted beams. Therefore, the pathlength difference between neighboring beams was about 50 µm when the echelon was placed in air. One way to control the temporal delays of the reference beam is to manufacture the echelon using thin glasses of the controlled thickness. The other more controllable way that we employed here was to place the echelon in a cuvette as shown in the Fig. 1(b). By filling the cuvette with a liquid medium having a specific refractive index, we can control the pathlength spacing between the neighboring diffraction orders. In our experiment, the pathlength spacing was reduced by filling the cuvette with water having a refractive index of 1.329 at the wavelength of 800 nm. We experimentally determined the pathlength spacing of the reference pulses by measuring interference intensity while moving the SM. As shown in Figs. 2(a) and 2(b), the pathlength spacing was measured to be 50 µm in air and 20 µm in water. Since the beam reflected from the sample takes double pass, the depth interval in the sample is half of the reference pass length spacing. In case of the cuvette is filled with water, the depth interval is 10 µm. The width of each reference pulse was measured to be 10 µm in air, slightly larger than the expected value 7 µm due to the dispersion in the optics. It is necessary to correct dispersion mismatch between the sample and reference arms for achieving the maximum axial resolution afforded by the full bandwidth of 70 nm. In the present study, the output beam bandwidth was reduced to 40 nm using a bandpass filter to reduce the dispersion mismatch effects, resulting in an axial resolution of ∼10 µm. It is noted, however, that the fundamental limit of the axial resolution of our single-shot multiple-depth OCT imaging technique is solely determined by the bandwidth of the light source and independent of the number of depth images obtained by a single-shot recording. Essentially, our method allowed us to prepare multiple reference beams by using adjustable grating on SLM and echelon, and the pathlength spacing of the reference beam can be adjusted by changing the medium in echelon cuvette.
Fig. 2. Operation principle of multi-depth imaging process. (a) Interference intensity of each reference beam with respect to a sample beam while scanning the pathlength of the sample beam using the scanning mirror (SM). This interference intensity shows the spacing between multiple reference beams. Reference beam pathlength interval is determined by the echelon thickness and refractive index difference between the echelon glass and the air. (b) Interference intensity of multiple reference beams when the cuvette was filled with water. This made the refractive index difference between the echelon and host medium small. All intensity profiles were normalized by their maximum intensity. (c) Multi-depth imaging process. In the case of a sample having structures expanding over multiple depths, different interference patterns can be seen in raw interference image depending on sample depths. These interference patterns can be separated into three different frequency spectra in this illustration after 2D fast Fourier transform (FFT) associated with different $\textbf{k}_{\textrm{R}}^{\textrm{j}}$. Selecting each spectrum and carrying out its inverse Fourier transform leads to the reconstruction of each depth information.
The acquisition time of the single-shot multi-depth imaging was 100 µs, which is limited by the minimum exposure time of the camera used in this demonstration. Post-processing time for image reconstruction was about 40 ms. In total, our single-shot multi-depth imaging system can achieve volumetric imaging with a frame rate up to 25 Hz, which allows for real-time video-rate volumetric imaging of live biological samples. One of the advantages is that our proposed method is scanning-free, thus it is less susceptible to motional artifacts compared to other multi-depth imaging methods (based on either A-scan or B-scan). For imaging fast dynamic processes in a sample, the image acquisition time could be further reduced by introducing an ultra-high-speed camera so long as the photon budget is allowed. Also, there is ample room for improving the frame rate by optimizing the post-processing algorithm.
The electric field of the multiple reference beams with different time delays and propagation angles can be described by ${\textrm{E}_\textrm{R}}(t )= \mathop \sum \nolimits_{\textrm{j} = 1}^n \textrm{E}_\textrm{R}^{\textrm{j}}(t )= \mathop \sum \nolimits_{\textrm{j} = 1}^n \textrm{a}({\textrm{t} - {\mathrm{\tau }_{\textrm{j}}}} ){\textrm{e}^{ - \textrm{i}\textbf{k}_\textrm{R}^{\textrm{j}} {\cdot} \textbf{r}}}$. Here n is the number of reference beams, and ${\mathrm{\tau }_\textrm{j}}$ and $\textbf{k}_\textrm{R}^\textrm{j}$ are respectively the time delay and the transverse wavevector of each reference beam $\textrm{E}_\textrm{R}^{\textrm{j}}(t )$. $\textrm{a}({\textrm{t} - {\mathrm{\tau }_\textrm{j}}} )$ represents the temporal envelope of each reference beam whose width $\mathrm{\Delta }t$ is set by the laser output pulse width. The electric field ${\textrm{E}_\textrm{S}}({\textbf{r},t} )$ of the reflected waves from the sample is recorded at the detector plane $\textbf{r} = ({x,y} )$. Its temporal distribution is associated with the 3D structural information of a target object. In the camera, the interference of the sample and reference beams are recorded during the exposure time $\tau $ much longer than the temporal span of ${\textrm{E}_\textrm{S}}({\textbf{r},t} )$, i.e. ${I_{\textrm{tot}}}(\textbf{r} )= \mathop \smallint \nolimits_0^\tau {|{{\textrm{E}_\textrm{S}}({\textbf{r},\; t} ) + {\textrm{E}_\textrm{R}}(t )} |^2}dt$. Interference between ${\textrm{E}_\textrm{S}}$ and each reference beam $\textrm{E}_\textrm{R}^j$ is approximately written as
Assuming that ${\textrm{E}_\textrm{S}}(t )$ is slowly varying with respect to the pulse width $\mathrm{\Delta }t$. From $I_{AC}^j({\textbf{r},{\tau_j}} )$, we can obtain ${\textrm{E}_\textrm{S}}({\textbf{r},{\tau_j}} )$, from which the depth-dependent image ${\textrm{E}_\textrm{S}}({\textbf{r},{z_j}} )$ is acquired by the simple relation, ${z_j} = c{\tau _j}/2$, where c is the average speed of light in the sample. The depth resolution is set by $\mathrm{\Delta }z = c\mathrm{\Delta }t/2$, which was measured to be 10 µm in air in the experiment.
We illustrated the way to extract each interference term $I_{AC}^j({\textbf{r},{\tau_j}} )$ in Fig. 2(c). For an object composed of three different depths, the recorded interferogram ${I_{\textrm{tot}}}(\textbf{r} )$ exhibits multiple different interference fringes set by $\textbf{k}_\textrm{R}^j$ associated with each reference beam. By taking the 2D Fourier transform of ${I_{\textrm{tot}}}(\textbf{r} )$, we can separate each spectrum of $I_{AC}^j({\textbf{r},{\tau_j}} )$ in the spatial frequency domain. We can extract each depth image for $I_{AC}^j({\textbf{r},{\tau_j}} )$ by applying a 2D bandpass filter selecting the respective spectrum, followed by an inverse Fourier transform [32,33].
3. Results and discussion
We performed multi-depth imaging for a sample composed of stacked coverglasses. As shown in Fig. 3(a), three coverglasses were stacked to generate reflections from the glass-air and glass-glass interfaces. No.1 coverglasses with the thickness of 150 µm were used for the sample. We first obtained single-depth FF-OCT image (Fig. 3(b)) by moving the scanning mirror (SM) at 10 µm interval over the depth range of 700 µm. Single-depth FF-OCT images are obtained by using only one reference beam while others are blocked in the multi-depth imaging system. Therefore, 70 different depth images were recorded to reconstruct volumetric images covering $325 \times 325 \times 700\;\mathrm{\mu}{\textrm{m}^3}$. To cover the same volume, we recorded only 10 multi-depth images by moving the SM at an interval of 70 µm (Fig. 3(c)). Since each multi-depth image simultaneously recorded 7 images at the interval of 10 µm, we could obtain the same volumetric image as the single-depth image by recording just 10 images rather than 70 images. Figure 3(d) compares the depth profile between the single-depth image and our multi-depth image and proves that their image qualities were almost identical.
Fig. 3. Multi-depth imaging with a phantom sample. (a) Schematic geometry of the stacked coverglasses. Four reflection signals from glass-air and glass-glass interfaces were captured by an objective lens. (b) single-depth FF-OCT image taken by moving the scanning mirror (SM) for 10 µm intervals over the depth range of 700 µm. (c) Multi-depth image by moving the SM at 70 µm intervals over the same range as (b). Scale bars, 100 µm. (d) Depth profiles along the white dashed lines in (b) and (c).
We also performed multi-depth FF-OCT imaging for biological tissues. We chose a slice of onion tissue as a sample as it has multiple stacked layers of cells. Figures 4(a) and (b) show raw interferograms recorded by the single-depth FF-OCT using a single reference beam and our multi-depth FF-OCT, respectively. Zoom-in image in Fig. 4(a) shows interference fringes with single carrier frequency. On the contrary, zoom-in image in Fig. 4(b) shows 2D interference patterns containing multiple carrier frequencies. This difference is made clear in the spatial frequency spectra of Figs. 4(a) and (b) shown in Figs. 4(c) and (d), respectively. While the single-depth FF-OCT shows only one passband (a dashed blue circle), multi-depth FF-OCT shows clearly distinct 7 passbands (dashed red circles). By taking the 7 individual passbands from the single-shot multi-depth recording, we could obtain multi-depth images as shown in Fig. 4(e) at an interval of 10 µm. We could observe different structures coming out from different depths. In particular, it can be seen that the boundaries of constituting cells are prominent. The corresponding single-depth FF-OCT images obtained from the sideband in Fig. 4(c) are shown in Fig. 4(f). To acquire images in Fig. 4(f), we moved the scanning mirror in the sample beam path at the pathlength interval of 10 µm and recorded 7 interference images.
Fig. 4. Multi-depth OCT imaging of onion tissues. (a) Raw interference image of a single-depth FF-OCT. The inset shows the zoomed view of interference fringes. (b) Raw interference image of the multi-depth imaging. The inset shows the zoomed view of 2D interference patterns. Scale bar, 100 µm. The contrasts of the raw interference images in (a) and (b) were adjusted for better visualization of the interference patterns. (c) Spatial frequency spectrum of (a) after taking 2D FFT. Only a single diffraction order is visible. The dashed blue circle indicates the passband edge set by the objective lens’s NA of 0.1. (d) Spatial frequency spectrum of (b), showing multi-depth spectra for 7 different diffraction orders. The dashed red circles indicate corresponding passbands. The number on each circle in (c) and (d) indicates the relative imaging depth in microns. (e) Multi-depth OCT image reconstructed by the images in (b) and (d). (f) single-depth FF-OCT OCT image. Scale bar, 100 µm. Images in (e) and (f) are normalized by corresponding reference beam intensities. The ratios of reference beam intensities from left to right are 0.07, 0.24, 0.66, 1, 0.66, 0.22, and 0.07.
To quantitatively analyze the performance of our multi-depth FF-OCT, we calculated the structural similarity index (SSIM) values between the single-shot multi-depth FF-OCT images (Fig. 4(e)) and corresponding single-depth FF-OCT images (Fig. 4(f)). The obtained SSIM values from left to right are 0.29, 0.89, 0.77, 0.68, 0.94, 0.76, and 0.27. It can be seen that a high degree of similarity is shown at a depth with high reflectivity. However, the image quality of the first and last images was poorer than that of the single-depth FF-OCT. This is mainly due to the small diffraction efficiency of the high-order diffraction by the 2D grating pattern. Proper designing of the phase grating, instead of amplitude grating, will make it possible to solve this problem by making the diffraction efficiency of different diffraction orders uniform [34].
A spatial resolution is determined by the spectral bandwidth of each passband indicated by the dashed red circle in Fig. 4(d). For a given camera resolution, i.e. total number of camera pixels, and a field of view, there is a trade-off between the spatial resolution and the number of multiplexed images. Alternatively, by sacrificing a field of view, one can increase the number of images while maintaining the diffraction-limited resolution given by a numerical aperture (NA) of the objective lens. In this demonstration, a FOV of $325 \times 325$ µm2 was imaged by $650 \times 650$ camera pixels with a magnification factor of 13.9, resulting in a single pixel resolution Δx of 0.5 µm. The maximum special frequency fmax is then given by fmax = 1/ (2Δx) = 1 µm−1 as shown in Figs. 4(c) and (d). The diameter f2NA of each passband is set by the objective lens’s NA of 0.1: f2NA = 2NA/ λ0 = 0.25 µm−1 for the center wavelength λ0 = 800 nm. The maximum number NSFDM of passbands occupying the total special frequency domain of [-fmax, fmax] without overlapping each other in the fx direction is then given by NSFDM = 2fmax/ f2NA = 8. In this demonstration, only seven passbands were used to ensure sufficient separations between the passbands. In fact, there are ample unused spectral bands to support two more rows of passbands in the positive fy spectral region. Also, three more passbands can be located on the positive fx-axis. In total, our current setup can multiplex up to 24 depth images in a single shot. A geometry utilizing the spectral bandwidth in most efficient way [29] can also be introduced with an appropriate modification of the 2D grating pattern and echelon design.
In addition to the geometrical factor discussed above, the dynamic range of the camera and shot noise set another limitation to the maximum achievable number of multiplexed images. The interference intensity detected at the camera can be written as
The signal to background ratio (SBR) is given approximately as $SBR \cong I_{AC}^j/({{I_S} + N{I_R}} )\approx \sqrt {\delta z/({4LN} )} .$ To resolve the signal, the detector dynamic range D should be larger than the inverse of SBR, which leads to the condition that $\textrm{N} \le ({\delta z/4L} ){D^2}$. We roughly estimate the depth range L in which an objective lens can collect light to be on the order of a few hundred micrometers to ∼1 mm depending on NA values. Since the depth resolution was 10 µm and the camera has a dynamic range of 37500, dynamic range is not the major limiting factor to determine N.
The shot noise of the background also needs to be considered for the maximum number of multiplexed images. the signal to noise ratio is given by $\textrm{SNR} = I_{AC}^j/\sqrt {{I_S} + N{I_R}} = \sqrt {\delta z/({2LN} )} \sqrt {{I_S}} $. Considering that the full well capacity of our camera is C = 30,000 e−, the number of signal electrons in a pixel corresponding to the signal intensity of ${I_S} = D/2$ is C/2. From the condition that $\textrm{SNR} > 1$ with ${I_S} = C/2$, the maximum achievable number of multiplexed images is given by ${N_{max}} = ({\delta z/4L} )C$. For example, for $L = 500\; \mathrm{\mu}\textrm{m}$, ${N_{max}}$ is 150. However, the above estimation is limited to the case of photon-shot-noise limited detection, where the noise due to time-gated multiple-scattered light is relatively weaker than the photon shot noise. In the strong multiple scattering regime, the image SNR and imaging depth will be severely deteriorated and mainly governed by the single-to-multiple scattering ratio.
The FF-OCT systems based on spatially coherent illumination have drawbacks in signal to background ratio and spatial resolution due to a coherent crosstalk noise caused by multiple scattered light [35]. On the contrary, the use of spatially incoherent light source requires a highly symmetric interferometer such as a Linnik interferometer, which cannot be easily applicable to off-axis interferometry-based approaches. Incorporating such techniques minimizing the crosstalk noise [36] would be a potential direction to achieve a crosstalk-free single-shot multi-depth imaging in the future application.
4. Conclusion
We proposed the FF-OCT system that can acquire a 3D volumetric image from a single-shot camera recording. By using the 2D diffraction grating and custom-made echelon, we prepared multiple reference beams having a different propagation angle and pathlengths. Essentially, these reference beams allow us to perform spatial-frequency division multiplexing in their interference with the sample beam reflected from a target object. Since the angle of the reference beam separates signals from different depths, that is, signals from different times in spatial frequency space, image information from different depths can be separately extracted from a single interferogram. By preparing 7 reference beams, we demonstrated the acquisition of as many depth images by a single-shot recording. We presented a single-shot volumetric imaging of onion tissues over a depth range of 70 µm with a 10-µm interval.
Our setup employing the SLM-based diffraction grating and custom-made echelon embedded within a cuvette is highly flexible in generating a large number of reference beams and controlling their relative pathlength interval, or depth interval. In fact, the current setup can accommodate up to 24 reference beams, which is set by the geometric factors such as the numerical aperture, field of view and optics size. The depth interval was 10 µm in our demonstration, but it can easily be adjusted by controlling the immersion medium of the echelon and the thickness of the coverglasses constituting the echelon. However, the increase of the number of reference beams is accompanied by the reduction of the bandwidth of each depth image. Additional limitation may arise due to the degradation of signal to noise ratio (SNR) at each camera pixel due to the multiplexed spatial frequency spectra. SNR is determined by the camera's shot noise and dynamic range, and the effect of the shot noise is more dominant. Considering this, number of images limit will be about 150.
Our proposed method is less susceptible to motional artifacts compared to other multi-depth imaging methods since a 3D volumetric OCT image of a specimen is simultaneously obtained in a single camera exposure. Such compact, fast, and highly scalable single-shot volumetric imaging technique can find applications in biological research such as living human retinal imaging.
Funding
Institute for Basic Science (IBS-R023-D1).
Disclosures
The authors declare no conflicts of interest.
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