## Abstract

A simple pixel shift technique is proposed to double the spectral sampling rate and enhance the signal to noise ratio of spectral-domain optical coherence tomography (SDOCT) in the 1.3um wavelength range. Both theoretical analysis and experimental comparison are presented. The results show that interpixel shifted SDOCT can not only double the depth of field of SDOCT image but also eliminate the artifacts induced by aliasing effect, thus improving image contrast in areas with large depths (e.g., Δz≥1.5mm). If combined with endoscopic OCT, this technique has the potential to enhance *in vivo* diagnosis of biological tissues that require a larger field of view in the axial direction, such as cartilage degeneration and bladder tumors with deep asperities or invaginations.

© 2006 Optical Society of America

## 1. Introduction

Optical coherence tomography (OCT) is an advanced optical imaging technique that permits noninvasive and high resolution cross-sectional visualization of biological tissue. Recent advances in the development of Fourier-domain OCT (FDOCT) or spectral-domain OCT (SDOCT) has dramatically improved the dynamic range and imaging rate of OCT techniques [1, 2], taking advantage of parallel detection and signal processing of spectral radar. Compared with conventional time-domain OCT (TDOCT), the need for high-speed mechanical axial scan in reference arm is circumvented, thus enabling up to 100-fold imaging speed enhancement and near real-time 3-D imaging [3–6] of living biological tissue. Recent interesting work include removal of “complex conjugate ambiguity” [7–10] to enhance signal to noise ratio and echo-free imaging range, Doppler FDOCT to image blood flow [11, 12] in real-time, ultrahigh-resolution SDOCT [13, 14] for 2D and 3D retinal imaging, polarization sensitive SDOCT[15, 16] and spectral second harmonic generation [17] OCT to provide more specific image contrast of biological tissue. In addition to technological advances, clinical applications of SDOCT have been performed on various types of tissue such as eye [3], esophagus [18] and urinary bladder [19], showing drastic improvement on image fidelity and imaging rate. Despite substantive technological advances in SDOCT, some technical issues remain to be addressed for future clinical uses. For instance, the degradation in signal to noise ratio (SNR) along the depth due to limited spectral resolution compromises the effective field of view in the axial direction and may induce artifacts (e.g., decay of OCT image contrast) to complicate diagnostic sensitivity and specificity. It was found in our *in vivo* clinical study of bladder cancer diagnosis that because of SNR degradation with depth, SDOCT diagnosis was more prone to distance change between scope and bladder surface or bladder surface asperities than TDOCT diagnosis. To tackle this problem, we propose to apply the pixel shift technique to increase the imaging depth and SNR of SDOCT. Pixel shift is widely used in advanced digital cameras to improve spatial resolution and image contrast. Because of limited pixel numbers (e.g., 512- or 1024- pixels) of current InGaAs diode arrays, this technique can be of great interest to enhance pixel resolution and image fidelity of SDOCT in the 1.3um wavelength range, in particular, ultrahigh-resolution SCOCT. We will describe the experimental setup for interpixel shifted SDOCT at 1320nm, and present results that demonstrate the potential of interpixel shifted SDOCT to enhance system SNR and to visualize image features beyond the depth of field of conventional SDOCT with no pixel shift.

## 2. Methods

#### 2.1 Experimental setup

Figure 1 depicts the schematic diagram of the SDOCT setup used in this study. The fiberoptic interferometer is illuminated by a high power broadband source (BBS) with pigtailed output power of 12mW, central wavelength at *λ*=1320nm and full-width-half-maximum spectral bandwidth Δ*λ*
_{FWHM}=78nm (yielding a coherence length of L_{c}≈10μm). The 1320nm light from BBS is equally divided in the fiberoptic interferometer, and the red light from a 670nm light from AL is coupled in the source fiber via a 95%:5% coupler for visual guidance. In the reference arm, instead of a grating-lens-based optical delay line for axial scanning in TDOCT, a stationary mirror is used to match the optical pathlengths between the sample and the reference arms of the fiberoptic interferometer. The sample arm is connected to a bench-top stereoscope in which light exiting the fiber is collimated to ϕ4.2mm, scanned laterally by a servo mirror, and focused by an f=40mm achromatic lens onto biological tissue under examination. The sample arm can also be connected to a MEMS-based endoscopic OCT catheter for *in vivo* imaging study. The light beams returning from the sample and reference arms are recombined in the detection fiber and connected to a spectral radar in which light is collimated by a fiberoptic achromatic lens CM (f=55mm), diffracted by a holographic grating G (d= 1200mm^{-1}) and focused by an achromatic lens AC (f=120mm) onto a line InGaAs photodiode array LSC (Sensors Unlimited, NJ) mounted on a small PZT-actuated stage for interpixel shift or stepping in the lateral direction. The detected spectral graph, including spectrally encoded interference fringes from different depth within the biological sample, is digitized and streamlined to hard disk of a PC (Precision 670, Dell) via a multi-channel 12bit A/D (DAQ6111E, NI) at 5MHz to permit 2D imaging at nearly 8fps. Simultaneous image processing and display is updated at 4 fps due to complex FFT computation. Stepping of line InGaAs array and the lateral servo mirror in the sample arm for 2D imaging is triggered following detection of each spectral graph (i.e., A-scan). Based on the above parameters used in our SDOCT setup, the axial resolution, i.e., L_{c}≈10μm, the lateral resolution is ~12μm, and the system dynamic range is ~111dB at 8fps. For pixel shifted SDOCT, stepping the bulky camera is currently limited to 10ms per step.

#### 2.2 Spectral calibration

As SDOCT is based on spectral radar, the depth-resolved backscattering profile (A-scan) is encoded on spectral interferograms at different modulation frequencies, inverse Fourier transform performed to reconstruct the image, during which spectral calibration, i.e., conversion of the measured spectrographs from *λ*-space to k-space (k=2*π*/*λ*) is required to be uniformly resampled in k-space [20]. Stringent spectral calibration for SDOCT is crucial to avoid severe deterioration of axial resolution and SNR. Several calibration methods have been reported, including parametric iteration [16] and phase linearization [5]. Here, we use a simple fringe mapping method similar to that used in swept-source OCT. To calibrate the system, a mirror is placed in the sample arm and moved axially (e.g., ΔL≈1mm) until high-density fringes are detected by SDOCT and a high-resolution fiberoptic optical spectrum analyzer (Ando 6245, Δ*λ*=0.05nm), as shown in Fig. 2. By fitting the peaks of these interference fringes the spectral values of SDOCT (i.e., line InGaAs array) can be calibrated accurately both locally and globally across the entire 110nm spectral range. As shown in Fig. 3, the measured axial resolution (Δz_{c}=10.2μm) of the reconstructed autocorrelation function or the axial point spread function (PSF) matches well with the theoretical result (L_{C}≈10μm).

#### 2.3 Pixel Shift

For SDOCT, 1-D spectrograph is detected per A-scan; therefore, pixel shift can be easily implemented by either stepping the line InGaAs camera in the lateral direction or rotating the diffraction grating. The pixel size of the line InGaAs camera used in this study is Δx (e.g., 50 or 25μm), an interpixel shift of Δx/2 (i.e., 25 or 12.5μm) is implemented per A-scan to increase the pixel resolution of the spectral camera. As for SDOCT, the ideal cross interference term (prior to camera digitization) between the reference and sample arms can be written as,

where S_{sr}(k)=[S_{s}(k)·S_{r}(k)]^{1/2} is the mutual-correlation spectrum and ΔL is the pathlength mismatch between the sample and the reference arms. Assume that the spectral resolution Δ*λ* resulted from a finite pixel size Δx is Δk (e.g., Δk = (-2*π*/*λ*
^{2})Δ*λ*), the detection response of a pixel can be approximated by a rectangular function,

which is an integration or averaging function over the spectral range of k-Δk/2 and k+Δk/2. If the sampling comb function is defined as

where N=512 or 1024 is the pixel number of the InGaAs in camera and k_{0} is the lowest wave number to be detected, then the measured spectrograph I_{D}(k) will be given as [21]

and the resultant PSF with respect to the pathlength difference ΔL can be derived as,

$$=\mid \mathit{FT}\left[C\left(k\right)\right]\otimes \mathit{FT}\left[{S}_{\mathit{sr}}\left(k\right)\right]\otimes \left[\delta \left(L+\Delta L\right)+\delta \left(L-\Delta L\right)\right]\xb7\mathrm{sin}c(\Delta \mathit{L}\Delta k/2)\mid $$

$$=\mid \frac{\pi}{\Delta k}\sum _{j=-\infty}^{\infty}\left[\delta \left(L-\frac{2j\pi}{\Delta k}+\Delta L\right)+\delta \left(L-\frac{2j\pi}{\Delta k}-\Delta L\right)\right]\otimes \mathit{FT}\left[{S}_{\mathrm{sr}}\left(k\right)\right]\xb7\mathrm{sin}c(\Delta L\Delta k/2)\mid $$

which represents a pair of pulses at ±ΔL whose envelop (i.e., autocorrelatiotion) is determined by the mutual spectrum *S*
_{sr}(*k*). More importantly, as the envelop is multiplied by the sinc(ΔLΔk/2) function which is the FFT product of the detector rectangular function in Eq. (3), Eq. (5) reveals that PSF decays with the increase of either pathlength difference ΔL or camera pixel size Δk (i.e., Δx)[1, 22]. The results of theoretical modeling of Eq. (5) are shown in Fig. 4.

Because of limited spectral resolution Δk, the amplitude of PSF(ΔL) decreases with ΔL resulting in SDOCT signal degradation in the high-frequency range. Further analysis of Eq. (5) indicates that in the sub-Nyquist-sampling region or beyond the Fourier transform window where ΔL≥ΔL_{Nq}=1/2·(j2π/Δk) |_{j=1}=π/Δk≈4.2mm, the PSFs as exemplified by the red low peaks are rolled back to incorrect positions as a result of aliasing, which induces artifacts and increases the noise level in this region.

Figure 5 illustrates the principle of the pixel shift technique in which curve A is the input interference spectrograph, curves B and C are the measured results prior and post half interpixel shift, and curve D is the recombined result. As can be seen that although pixel shift does not enhance the original pixel resolution Δk or Δx (e.g., 25 or 50μm), it doubles the spectral sampling rate and thus preserves the high-frequency components of the interference modulation contributed mostly from deeper places with a higher ΔL. The sampling function for pixel shift is changed to

where Δk′=Δk/2, and the PSF can be rewritten as

$$=\mid \mathit{FT}\left[{C}_{\mathit{ps}}\left(k\right)\right]\otimes \mathit{FT}\left[{S}_{\mathit{sr}}\left(k\right)\right]\otimes \left[\delta \left(L+\Delta L\right)+\delta \left(L-\Delta L\right)\right]\xb7\mathrm{sin}c(\Delta \mathit{L}\Delta k/2)\mid $$

$$=\mid \frac{\pi}{\mathrm{\Delta k\prime}}\sum _{j=-\infty}^{\infty}\left[\delta \left(L-\frac{2j\pi}{\mathrm{\Delta k\prime}}+\Delta L\right)+\delta \left(L-\frac{2j\pi}{\mathrm{\Delta k\prime}}-\Delta L\right)\right]\otimes \mathit{FT}\left[{S}_{\mathrm{sr}}\left(k\right)\right]\xb7\mathrm{sin}c(\Delta L\Delta k/2)\mid $$

A comparison between Eq. (5) and Eq. (7) reveals that the decay of PSF amplitude with ΔL, determined by sinc(ΔkΔL/2), remains unchanged; whereas the Fourier transform window or the Nyquist sampling range is doubled, i.e., ΔL’_{Nq}=2ΔL_{Nq}=(2π/Δk)≈8.4mm because Δk’=Δk/2. Figure 6 shows that as pixel shift doubles the Fourier transform window, the high-frequency components that are rolled back as noise and artifacts as discussed above can be restored. As reflected in Fig. 4, the two blue curves beyond the Nyquist regime (ΔL≥ΔL_{Nq}) can be recovered and the artifacts, i.e., the displaced two red curves are eliminated. Thus, the results of theoretical modeling suggest that interpixel shifted SDOCT can enhance the system SNR in the high ΔL range and increase the effective imaging depth of SDOCT.

## 3. Results

To verify the theoretical prediction that interpixel shifted SDOCT enhances the system SNR in the high ΔL range and increase the effective imaging depth of SDOCT, we performed the following experimental studies. We first characterized interpixel shifted SDOCT by comparing the degradation of the autocorrelation functions measured without and with pixel shift. Then we performed *ex vivo* imaging of scattering biological tissue to examine the utility of interpixel shifted SDOCT in enhancing image contrast and imaging depth.

In the characterization experiments, we used the specular reflection from the surface of a microscope cover glass slide (R≈4%) in the sample arm to avoid saturation of the camera. As the spectral spreading range for a 512-pixel camera is half of that for a 1024-pixel camera with the same pixel size, the optical setup of the spectral radar needs to be changed to accommodate the difference. To avoid the complication in changing optical setup and the complication induced by phase variation due to slow camera stepping (<10ms), a 1024-pixel camera was employed and binning of adjacent 2 pixels were used to simulate the 512-pixel camera with and without pixel shift. Fig. 6 shows an example of the experimental results. According to Nyquist sampling criterion, the field of view of a FDOCT system is determined [23] by Δz_{Nq}=ΔL_{Nq}/2=π/(2Δk)=*λ*
^{2}/(4Δ*λ*)≈ 2.1mm (here the refractive index is assumed n=1 for free space), as indicated by the dashed blue line in Fig. 6. As predicted by Eq. (5), the PSF of the cover glass at Δz=2.8mm (Δz∾Δz_{Nq}) is rolled back to Δz≈1.3mm as artifacts in SDOCT image. Whereas with pixel shift, this pulse is fully restored at Δz=2.8mm, shown as the red curve. It is interesting to see that the restored curve has almost 4-fold enhancement in the peak amplitude over the artifact curve. More importantly, the elevated noise in this range (e.g., ~3dB over the baseline noise level) induced by spectral sub-sampling or aliasing is effectively eliminated by pixel shift. It is important to be noted that this SNR enhancement (~13.6dB) can be crucial because it affects the SDOCT image in the deep area (e.g., Δz> 1.5mm) where image SNR is usually low for scattering tissue imaging.

Figure 7 summarizes the results of PSF measurements for different depths. As can be seen, the measured Nyquist sampling point is at Δz_{Nq}≈2.0mm, consistent with the theoretical prediction of Δz_{Nq}≈2.1mm. The red dotted curve (no pixel shift) and the blue dotted curve (with pixel shift) converge up to Δz≈ 1.5mm at which the red curve drops significantly due to decreased sampling rate and starts to roll back (aliasing effect) at the Nyquist sampling point Δz_{Nq}≈2.1mm. With simple pixel shift, both problems of aliasing and excessive decrease of signal amplitude with Δz are solved; therefore, the advantages of interpixel shifted SDOCT are demonstrated. For comparison, the result of a true N=1024 line camera is included as shown by the dark dotted line. As predicted by Eq. (5) and Eq. (7) in which the envelop term is changed to sinc(ΔLΔk/4), PSF decays with Δz at a reduced slope, thus providing increased depth of field for SDOCT imaging.

In addition to system characterization study, *ex vivo* imaging study of biological tissue was performed to examine the enhancement of interpixel shifted SDOCT on image contrast and imaging depth. For instance, Fig. 8shows the comparative results of a dog bladder tissue imaged by 512-pixel SDOCT (panel A), 512-interpixel shifted SDOCT (panel B), and 1024-pixel SDOCT (panel C). All three images were taken at approximately 7.7fps and post image processing was implemented to reconstruct the 2D OCT images, representing image size (lateral × axial) of 6mm × 1.2mm (panel A) and 6mm × 1.8mm (panel B and C). The results show that all three images can well delineate the bladder morphology such as the low-scattering urothelium (U), the lamina propria (LP), and the muscularis (MS), but the image depth of panel A) is significantly less. As imaging was performed at 24 hours post formalin fixation, artifacts such as several large dark holes in the region of low lamina propria (connective tissue layer) induced by formalin infusion can be seen in all three panels. The SNRs, based on the measured maximum signal value against the noise background, are: 47.9dB (panel A), 48.2dB (panel B) and 48.8dB (panel C) respectively. It must be noted, however, that this SNR quantization does not reflect the influence of aliasing noise effect because the noise level is taken from the dark area above the bladder, which is the shot noise induced mostly by the reference light. For example, the SNRs at point M in panels A), B) are comparable, and that in C) is 0.5dB higher, which is close to 0.9dB as shown in Fig. 7. More interestingly, pixel shift can not only enlarge the image depth but also enhance the SNR in the deeper tissue region. For instance, in one of the dark holes N induced by formalin fixation in panel A), the noise level, induced by aliasing or roll-back artifacts, is 1.5dB higher than the corresponding spot in panels B) and C). In other words, pixel shift can effectively eliminate the aliasing noise due to sub-Nyquist sampling and bring the system back to shot-noise limit. This noise reduction, although 1.5dB, is critical to scattering tissue imaging because the SNR at deeper tissue region is usually very low as exemplified in Fig. 7. For comparison, SNR in the muscularis in panel C) is slightly higher than that in panel B), which is in agreement with the theoretical prediction of Eq. (7) and with the experimental results in Fig. 7. The increase of imaging depth by interpixel shift and the removal of the aliasing noise, although 1.5dB, are important for scattering tissue imaging. For instance, it is found in our clinical trial of SDOCT diagnosis of bladder cancers that due to bladder or scope motion or bladder asperities or invaginations (e.g., caused by tumorigenesis), the displayed OCT image or movie may slightly fall out of the designated axial position; therefore a larger depth of field such as 2.5mm or 3mm can be very useful. In this case, a simple modification using interpixel shifted SDOCT can not only increase the depth of field to 3mm but also enhance the SNR in deeper region (e.g., Δz>1.5mm) by eliminating aliasing noise induced by sub-Nyquist sampling.

## 4. Discussion and conclusion

Spectral-domain OCT offers enormous advantages over time-domain OCT in terms of imaging rate and signal-to-noise ratio and has been replacing time-domain OCT in many applications. However, one of the drawbacks of SDOCT is the degradation of image contrast with in the increase of pathlength difference ΔL or imaging depth Δz. As many OCT diagnoses are based on intensity variations, it may cause artifacts or misinterpretation of image features. This phenomenon of image degradation with depth is resulted primarily from limited spectral sampling resolution of the SDOCT system to resolve high-frequency spectral interference modulations from deeper areas with higher Δz. There are several parameters in the spectral radar design that may limit the detectable spectral resolution, which includes input beam size, grating diffraction efficiency, lens quality (spherical aberration, chromatic aberration, and field flatness), and the camera pixel size and number. With advanced CCD technology to date, cameras for short-wavelength SDOCT (e.g., from visible to 900nm region) may not be an issue in terms of sensitivity, speed, and pixel resolution, but line InGaAs arrays for 1300nm SDOCT are limited in both sensitivity and speed, and pixel resolution (e.g., N=512 or 1024 pixels). As previous study[10] and our theoretical analysis show that this may lead to problems such as coupling of sampling and spectral resolution, limiting the useful depth of field and inducing aliasing artifacts or noise. In this study, we propose to tackle the problem with pixel shift technique. This simple technique enables visualization of features beyond the field of view of conventional FDOCT and enhances image contrast in deeper image region with Δz≥ 1.5mm, as has been demonstrated theoretically and experimentally. Nevertheless, a careful comparison between theoretical analysis (Fig. 4.) and experimental results (Fig. 6 and Fig. 7) reveals two major problems for the reconstructed point-spread function, i.e., profile skewness and additional amplitude drop. Theoretically, although aliasing occurs whenever undersampled, neither the amplitude nor the shape of PSF will be altered as shown by the red curve in Fig. 4. On the contrary, significant artifacts are induced around the PSF if undersampled experimentally as shown by the dark curve in Fig. 6, which may be partly attributed to imperfect k-space linearization. No matter how the system is calibrated, error is inevitably introduced in the processes of either curve fitting or numerical iteration. And the influence of this error on SDOCT signal reconstruction is highly depth dependent. If the spectral interferogram is undersampled, depth uncertainty is very sensitive to the calibration accuracy, resulting in signal skewness with calibration errors. Pixel shift, however, increases sampling rate, and thus provides more raw spectral data for image reconstruction to eliminate PSF skewness. In terms of excessive PSF amplitude drop with depth, as previously reported [22], it is resulted from the convolution (i.e., averaging) effect of finite focal spot size on the camera pixel, which can be seen by comparing the slope of experimental curves in Fig. 7 with the slope of theoretical modeling (i.e. the green line) in Fig. 4. This effect reduces the applicable depth range of pixel shift technique due to vanished useful information in deep image region, e.g., with Δz≥3mm. However, improvement on optical design and alignment may further enhance the spectral resolution and thus recovery of PSF amplitude in this region. Both theoretical modeling (Eq.(7)) and experiment (Fig. 7) show that a 1024-pixel system has higher PSF amplitude level; however, the difference is unremarkable, in particular, in case of scattering tissue imaging such as exemplified in Fig. 8. In other words, a 512-interpixel shifted system may offer the advantage of cost effectiveness and image rate. It must be noted that for proof of principle, a 1024 pixel camera with pixel binning was used to simulate an interpixel-shifted 512-pixel camera. Currently pixel shift is limited to >10ms per step by stepping the bulky InGaAs camera. High-speed pixel shift (e.g., 7.7kHz or 0.1ms per step) can be implemented by direct PZT stepping of the InGaAs chip, as has been commonly used in interpixel shifted commercial CCD cameras. It should also be pointed out that in this preliminary study, only one-step interpixels shift with half pixel stepsize was performed. As a matter of fact, two-step interpixels shift with 1/3-pixel stepsize has be frequently used to date in high-resolution CCD camera technology, and thus may further improve the image quality of SDOCT, in particular ultrahigh resolution SDOCT at 1300nm range, in which limited pixel resolution of InGaAs remains a technical challenge.

Swept-source SDOCT excels in imaging speed and may permit *in vivo* 3D OCT and functional imaging (e.g., tracking of dynamic blood flow). However, the sweeping wavelength range of current swept sources is insufficient to permit ultrahigh-resolution OCT. A line camera based SDOCT has limited imaging rate, e.g., 30fps or less. However, the technique is of low cost, compact and reliable, and easy to handle, it is highly suitable for most clinical applications (2D OCT at 4 fps is sufficient for most clinical diagnosis, such as endoscopic cancer imaging). More importantly, the technique is suitable for ultrahigh-resolution OCT (uOCT). For instance, spectral-domain uOCT at 800nm wavelength range has been reported using high-resolution CCD array (e.g., 2048 pixel or 4096 pixel). However, high-resolution InGaAs array (e.g., >1024 pixels) is not available. Therefore, the pixel shift technique may provide a viable solution for ultrahigh-resolution line scan camera based SDOCT in the 1.3μm wavelength region.

In conclusion, a simple pixel shift technique is reported to improve the sampling rate and resolution of spectral-domain OCT. Both theoretical analysis and experimental comparison are presented. The results show that although interpixel shifted SDOCT does not necessarily increase the axial resolution, it increases the depth of field of SDOCT image and eliminates the artifacts induced by aliasing effect and therefore enhance the image contrast in the image areas with large depths (e.g., Δz≥1.5mm). Examples of *ex vivo* dog bladder tissue study clearly demonstrate the improvement of imaging depth and the image contrast in deeper layers such as low lamina propria and muscularis (e.g., Δz>1.5mm), which is critical in clinical OCT application. If combined with our MEMS-based SDOCT endoscope, this technique has the great potential to enhance image fidelity and depth of field in our clinical diagnosis of bladder cancers and cartilage degeneration. The technique can also be of great interest to ultrahigh-resolution SDOCT at 1.3μm in which high-resolution and high pixel-density InGaAs cameras remain unsolved.

## Acknowledgments

This work is supported in part by NIH grants 2R01–DK059265 and R01–DK068401. Correspondence can be addressed to yingtian.pan@sunysb.edu

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