Single camera based spectral domain polarization sensitive optical coherence tomography.

We developed a new spectral domain polarization sensitive optical coherence tomography (SD PS-OCT) system that requires only a single spectrometer CCD camera. The spectra of the horizontal and vertical polarization channels are imaged adjacent to each other on a 2048 pixel line scan camera, using 1024 pixels for each channel. Advantages of the system are reduced costs and complexity, lower demands on timing and triggering circuitry, and higher robustness against camera misalignments. We discuss the additional postprocessing required to accommodate for spectral distortions, show calibration measurements in a test sample, and finally demonstrate the system for measuring human ocular tissue in vivo.


Introduction
Optical coherence tomography (OCT) is a noninvasive imaging technique for recording high-resolution cross-sectional images of transparent and translucent samples [1][2][3]. Conventional OCT measures backscattered intensity with a resolution on the order of a few μm. Polarization sensitive (PS) OCT takes advantage of the additional polarization information carried by the reflected light [4,5]. Thereby, PS-OCT can reveal important information about biological tissue that is unavailable in conventional OCT. Several possible applications of PS-OCT to medical diagnostics have been suggested, e.g., birefringence measurements can be useful for burn depth estimation in skin [6], caries diagnostics [7], glaucoma [8] and keratoconus [9] diagnostics in ophthalmology, while measurement of polarization scrambling has recently been suggested for diagnosing the retinal pigment epithelium (RPE) in age related macula degeneration (AMD) [10].
Different methods of PS-OCT have been reported in literature. While early work on PS-OCT [4,5] measured only reflectivity and retardation of a sample, in recent years many proposals have been made to extract more information, e.g. on Stokes vectors [11,12], Müller [13] and Jones matrix [14] distribution, birefringent axis orientation [11,15], and diattenuation [16][17][18]. We developed a method that combines the PS low coherence interferometry setup first devised by Hee et al. [4] with a phase sensitive recording of the interferometric signals in the two orthogonal polarization channels [15,19], thus allowing to measure three parameters, reflectivity, retardation, and birefringent axis orientation simultaneously.
While the original OCT technique was based on mechanically scanning a reference mirror to perform so called A-scans in time domain (TD), spectral domain (SD) OCT [20] has gained considerable interest since it has been shown that SD OCT has huge advantages in terms of sensitivity and acquisition speed [21][22][23]. After these advantages had been demonstrated for intensity based imaging, the SD-OCT technology was also transferred to PS-OCT. After initial demonstrations of SD PS-OCT with a slow scan system [24], state of the art high speed SD PS-OCT systems were recently reported [25][26][27][28].
PS-OCT systems usually require a two-channel polarization sensitive detection unit where a polarizing beam splitter splits the beam at the interferometer exit into a horizontal and a vertical polarization channel whose interferometric signals are recorded separately. In SD PS-OCT this usually requires two separate spectrometer cameras [25][26][27][28]. This adds additional costs and poses high demands on the triggering hard-and software to avoid any time delays between the signal acquisition of the two cameras which is required if phase based PS-OCT algorithms are used.
In this paper, we report on the development of a single-camera SD PS-OCT system that avoids these problems. We describe the system design, discuss requirements of the spectral re-shaping necessary to accommodate spectral distortions, and show the results of calibration measurements. Finally, we demonstrate, to the best of our knowledge for the first time, applications of the system to PS-OCT imaging of external ocular tissue as conjunctiva, sclera, and ocular tendon in the living human eye.

System description
A sketch of our new single camera SD PS-OCT setup is shown in Figure 1. The interferometer part of the system, which is based on the original polarization sensitive low coherence interferometer design first described by Hee et al. [4], is similar to a SD PS-OCT instrument published recently [27]. For the current setup we used a super luminescent diode (SLD) emitting at 840 nm (Superlum SLD-371-HP) with an FWHM bandwidth of 50 nm to illuminate the interferometer. In the sample arm, the light passed a quarter wave plate oriented at 45° to yield a circularly polarized state and was focused onto the sample by an 80 mm focal length lens. Scanning was performed by an x-y galvanometer scanning unit. In the reference arm, a quarter wave plate set at 22.5° was used to generate, after double pass, a plane polarization state oriented at 45°, providing equal reference power in both detection channels. After recombination of the beams from sample and reference arm, the light was split into two orthogonally polarized beam components by a polarizing beam splitter.
After routing them to the novel spectrometer unit using single mode fibers, both beams were collimated by two fiber couplers with focal lengths of 50 mm and directed onto the center of the same transmission grating (1200 lines/mm, Wasatch Photonics). Thereby, the incident angles onto the grating were chosen to be slightly larger and smaller than Littrow's angle, α L , respectively. Due to the unequal incident angles, the two beams were exiting the grating spectrally dispersed at two differently oriented sectors of exiting angles in the same plane. Assuming the same wavelength range [λ min , λ max ] for both incident beams, the incident angles α 1 = α L -Δα and α 2 = α L + Δα were chosen such that the least diffracted wavelength of beam 1, i.e. λ min , and the strongest diffracted wavelength of beam 2, i.e. λ max , were diffracted into the same exiting angle β c . In doing so, after passing the achromatic camera lens with a focal length of 150 mm, the two spectra were imaged side by side onto a single 2048 element line scan camera (Atmel Aviiva M2 CL 2014).
With the aid of the grating equation and a trigonometric theorem, the angular deviation Δα from Littrow's angle α L can be expressed as (1) where G is the spatial frequency of the grating. For G = 1200 mm −1 and a wavelength range λ max -λ min = 70 nm (this turned out to be a good compromise between achievable depth range and separation of the two spectra on the CCD camera), an angular deviation Δα = 2.7° is required to achieve one spectrum imaged next to the other. According to the data sheet of the grating, the diffraction efficiency is the same for the center wavelength for both S and P polarization states when incident angles with similar deviations from α L (Δα < 4°) are chosen. S and P efficiency differ by up to ~ 7% for peripheral wavelengths of the source spectrum. This mismatch was corrected for during spectrometer alignment where equal sensitivity for both spectrometer channels was adjusted.
The spectral interferograms were digitized by the line scan camera with a resolution of 12 bits per pixel and transferred to a personal computer (P4, 3.2 GHz, 1 GB RAM) via Camera Link by means of a high speed frame grabber board (National Instruments PCI-1428). The read out of frames was triggered by the galvanometer scanner. One frame (B-scan) was composed of 2000 A-lines. Using an integration time of 50 μs for each A-line of 2 × 1024 pixels and a power of 660 μW onto the sample, which is below the limits drawn by ANSI and IEC laser safety standards [29,30], a sensitivity of 96 dB was measured. Due to finite spectrometer resolution the sensitivity dropped by 17.5 dB along ¾ of the total depth range of 2.7 mm.
After the data had been acquired, several steps of post-processing were performed. First the average over 2000 A-lines was subtracted from the raw data, followed by fixed pattern noise removal. Then the raw data lines were split into two halves of 1024 pixels, thus representing the spectral interferograms of the horizontal and vertical polarization channels. Thereafter, zero-padding to 4096 data points per channel was performed, and the data were rescaled to k-space, which will be described in detail in the following section. Finally, an inverse FFT of both spectral interferograms was performed to yield the A-scan signals of the object structure in form of A H,V (z)exp[iΦ H,V (z)], where H and V refer to the signals obtained from the horizontal and vertical polarization channels, respectively. From these signals sample reflectivity R, retardation δ, and (cumulative) fast axis orientation θ can be calculated as reported before [15]: (2) (3) (4) where ΔΦ = Φ V -Φ H is the phase difference between the signals of the two polarization channels. Measured values for δ and θ are unambiguous in the range from 0° to 90° and −90° to +90°, respectively.

Rescaling and spectrometer calibration
In contrast to the two-camera based SD PS-OCT instruments presented so far [25][26][27][28], the spectral sampling and remapping process requires a slightly different approach. For polarization sensitive measurements using SD-OCT, an exact pixel-to-pixel correspondence of the spectral interferograms of the horizontal and vertical polarization channel is required. Any mismatch of the spectra in k-space will result in polarization mimicking artifacts, which has been discussed for translational shifts and for size distortions [25,27].
Due to the different incident angles, the shapes of the spectra recorded by the line scan camera of our system are distorted with respect to each other. Park et al. [25] derived a theoretical equation representing the wavelength distribution observed at the line scan camera of a spectrometer. By applying the Taylor series expansions of the sine and arc tangent functions, an expression can be derived which, to a first approximation, shows a linear dependency of wavelength on the spatial position at the CCD line. The advantage of assuming a linear wavelength distribution over the camera pixels is the reduction of the number of free variables.
Owing to the different incident angles of the beams of the horizontal and vertical polarization channel, the width of the same spectral range imaged onto the CCD will be somewhat different. In fact, beam 1 hitting the grating at the smaller angle α 1 = α L -Δα will be dispersed to a greater extent than beam 2 and therefore a smaller wavelength range will be covered by the same number of pixels. Since we assigned the same number of pixels (1024) to each polarization channel, the detected wavelength range of channel 2 will be larger than that of channel 1, i.e. a distortion of the spectral width occurs. To correct for this distortion, the wavelength range covered by channel 1 was used as a window size for channel 2. It is possible to assign more pixels to the more-broadly dispersed spectrum of beam 1, however, as the wavelength range covered by the camera pixels of beam 1 and 2 differs just by approximately 4%, which corresponds to ~ 40 pixels, equal portions of 1024 pixels were chosen for simplicity.
Still, the spectra recorded are linear in wavelength-space. To achieve a depth profile resembling the object structure, i.e. a depth profile that is linear in z-space, the spectral data has to be remapped to equal sampling intervals in k-space [31]. The values of the scaling parameters obtained from theoretical wavelength mapping (based on the grating equation) were iteratively optimized to yield perfectly linear A-line depth mapping. The finally received parameter values allow computing the actual wavelength distributions for both channels.
In total, the rescaling procedure, after splitting the spectral data in two arrays of 1024 data points each, consists of three steps: First, the window width in channel 2 has to be set corresponding to the wavelength range detected in channel 1, then the window has to be shifted to the correct position along the pixels of the spectral data of beam 1 such that the first and the last pixel of each array correspond to the same wavelengths λ min and λ max , respectively. Finally the spectral interferograms of both channels are remapped to uniform sampling intervals in k-space by means of linear interpolation within these windows. To keep the rescaling operation short and avoid spectral distortions by repeated interpolation, our software performed the three steps at once. The first two steps (window size, window shift) are controlled by one variable scaling parameter each, the last step (remapping from λ-space to k-space) requires two variables, i.e. one for each channel, because the widths of the spectra are dispersed over different numbers of pixels on each half of the CCD array. The signal quality provided by the algorithm was improved by performing zero padding of the spectral data prior to remapping [32]. Figure 2 shows the steps of the rescaling process: In Fig. 2(a), the raw spectral data as recorded by the line scan camera is plotted. After the 3-step rescaling process described above (zero padding omitted here), the same spectral data are shaped to the form shown in Fig. 2(b). One can see that the spectra do not have exactly the same shape although they are equally ranged in k-space now. Those discrepancies are mainly caused by the camera lens which does not allow perfect imaging onto the camera and alignment of the spectrometer. As the spectrally dispersed beams cover most of the lenses horizontal diameter, aberrations are likely to distort the spectra. During the alignment process one has to trade perfect conservation of the spectra's shapes for preserving the sensitivity properties of the system. The slight overlapping of the two spectra in Fig. 2(a) is the result. However, this slight overlap has only negligible impact on amplitude and phase of the OCT A-scan signals (this causes artifacts in channel 1 that are 32 dB below the signal in channel 2; no influence of channel 1 signals on channel 2 images was observed). Figure 2(c) shows the coherence functions obtained from a mirror in the sample arm. To receive an equal intensity in both polarization channels, the quarter wave plate in the sample arm was turned to an orientation of 22.5°. Although the shape of the central part of the coherence functions is the same, the side lobes due to the deviation from Gaussian spectral shapes are somewhat different. In retardation and axis orientation images, this will cause deviations of the values obtained in the central part of the coherence peaks from those of their surroundings.
The necessity of accurate alignment of a SD PS-OCT system to avoid birefringence artifacts in PS tomograms has been pointed out in previous literature [25,27]. The spectrometer alignment and calibration procedure of our novel single camera SD PS-OCT system consists of several steps.
First, the fiber couplers are positioned such that the two collimated beams hit the center of the grating at the angles calculated by equation (1). The spectrometer's camera lens is removed to position the CCD line with the central pixel being located in the central minimum of the spectrally dispersed light beams to ensure straight alignment. Now the lens is inserted to image the spectra obtained in the polarization channels onto the camera. To ensure the same sensitivity decay to be observed in both channels, a mirror is placed in the sample position and the quarter wave plate in the sample arm is turned to 22.5° to provide an OCT signal with equal power in the horizontal and vertical polarization state. The spectrometer is now adjusted so that the sensitivity decays are minimal and identical. If the sensitivity in one channel -due to different spectral resolution, aberrations of the lens or misalignment of the camera -drops faster than in the other one, an artificial retardation will be the result. When maximal sensitivity performance is achieved, the quarter wave plate in the sample arm is reset to an orientation of 45° and an additional retarder is inserted in front of the sample mirror. Then the software scaling parameters controlling shift and window width are adjusted in such a manner that the phase difference of ΔΦ (proportional to axis orientation) keeps a constant value for OCT signals along the whole accessible depth range.

Results
In order to analyze the accuracy of the SD PS-OCT instrument we performed measurements on a test target consisting of a retarder and a mirror. First we investigated the linearity of measurements of fast axis orientation by changing the retarder's axis orientation at a fixed path length difference of 0.93 mm, while also monitoring the retardation (which should stay at a constant value). The unambiguous range of axis values was covered by setting the optic axis of the retarder to values increasing in equidistant steps of 15°. The results of these measurements are shown in Figure 3(a). The measured values of axis orientation are plotted as a function of set axis orientation. The measured values are in good agreement with the set orientations of the retarder. However, a slight oscillation around the set values is to be noticed. Also in the plot of retardation values derived from the same data set (Fig. 3(b)) an oscillation of the measured values around the mean value of 78° can be observed. The amplitude of the oscillation amounts to ± 8° for axis orientation values and ± 3° for retardation values. These deviations are probably caused by imperfect polarization properties of the optical components of the interferometer (similar deviations were observed in time domain PS-OCT systems [15]).
In a second series of measurements we examined the system performance when changing the path length difference between sample and reference mirror while keeping the axis orientation of the retarder at a fixed value. Each measurement was repeated 5 times. Figure 4 shows the results of these measurements. The measured retardation remains constant along the whole depth range; the mean value is 78°, the distribution of data points around this mean value varies along depth position with a standard deviation (SD) of ~ 0.6° (the SD of 5 measurements at a given depth is even smaller, as indicated by the error bars). The average measured axis orientation is 22°, with an SD of 1.4° for data points obtained at different depths. The SD of measurements obtained at a given depth is indicated by error bars. It increases in the last third of the depth range, probably because of the poorer signal quality caused by the intensity decay with depth.
To demonstrate the system performance in biological tissue, tomograms of human ocular tissue were recorded in vivo. Figure 5 shows polarization sensitive images of a region localized nasally to the cornea of a healthy subject's left eye. The tomograms were derived from a set of 2000 A-lines. An area of 10 (horizontal) × 2.7 (vertical, optical distance) mm 2 is displayed. Figure 5(a) shows the intensity image, Fig. 5 While the tissue appears quite homogeneous in the intensity image, apart from the dark band on the right (Fig. 5(a)), it is the polarization sensitive measurement that reveals details of the structure of the ocular tissue. In the retardation image ( Fig. 5(b)) the non-birefringent conjunctiva (CJ) appears blue; below, the sclera (S) can be observed. The retardation and axis orientation of scleral tissue strongly depend on position, especially near the corneal limbus, where collagen fiber orientation varies considerably. The dark band in the right part of the intensity image turns out to be strongly birefringent tissue, probably tendon (T) of the muscle affixed at the nasal part of the eye (musculus rectus medialis). One can clearly see two oscillations of retardation within the tendon along the whole displayed range starting from the onset of the tendon in the center of the image to the right image border. The same tissue properties are also evident in the axis orientation image (Fig. 5(c)). Also here, the oscillations perpendicular to the tendon are visible (these oscillations do not represent axis changes but are caused by the algorithm used to calculate the axis orientation which causes axis jumps of 90° at depth positions where δ crosses 90°-isolines (or multiples thereof) [15]).

Discussion and conclusion
The advantages of SD-OCT, high sensitivity and imaging speed, have recently been extended to PS-OCT [25][26][27][28]. The systems reported so far worked well, however, needed two CCD cameras operating in parallel to record both polarization channels simultaneously. The operation of two CCD cameras in parallel has the drawback of higher costs, greater system complexity, high sensitivity to misalignments, and the need for sophisticated timing and triggering schemes.
In this paper, we demonstrated a single camera SD PS-OCT system that overcomes these problems to a large extent. The costs are reduced and any triggering problems are avoided because the spectra of both, the horizontal and the vertical polarization channel, are recorded by the same camera simultaneously. The method of imaging the two spectra on the left and right hand sides of the CCD array, however, also has drawbacks.
An obvious drawback is the reduced number of pixels available for each spectrum. At a given depth resolution, this means that the imaging depth is reduced by a factor of two. However, in our previous two-camera setup [27] we also used just 1024 pixels of each camera to reduce the data stream and obtained images of sufficient depth (3 mm) for retinal imaging. Our single camera system has an imaging depth of 2.7 mm (because of a different spectrometer geometry) which is sufficient for imaging of superficial tissues (cf. Fig. 5) and also should be sufficient for retinal imaging.
A drawback related to that mentioned above is that the total width of both spectra on the camera is twice as large as that of a single spectrum, imposing higher demands on the imaging lens. Narrow oscillations near the edges of the image field of the spectrometer lens are likely to show poorer contrast as compared to those in the center. This is probably the reason for the stronger sensitivity decay with depth of the single camera system (17.5 dB instead of 14 dB of the two-camera system [27]). This problem might be solved by using a higher quality lens than our simple achromatic lens.
Previously it has been shown that a pixel-to-pixel correspondence of the recorded spectra of the two channels is required to avoid artifacts in the PS-OCT images [25,27]. In a twocamera system, this can be achieved by a careful alignment of the two cameras [27] or by a software based calibration step [25]. Since the single camera system has not enough degrees of freedom to achieve the pixel-to-pixel correspondence by a pure hardware alignment, software based correction of the distorted spectra is required. Apart from a shift correction, also a size correction of the spectra is now required which means an additional calibration step. The total computation time for spectral re-shaping plus remapping into k-space is now 4 seconds for an OCT image consisting of 2000 A-scans (Pentium 4, 3.2 GHz, LabView code). This can, of course, be improved by developing dedicated parallel code.
In conclusion, we have developed a new, single camera based SD PS-OCT instrument that operates at a state of the art A-scan rate of 20000 A-scans/s. We have applied the new system to image external ocular tissue that has not been imaged before by PS-OCT. Thereby, we have demonstrated the usefulness of the system to distinguish between conjunctiva, sclera, and tendon, which is difficult to accomplish by standard intensity based OCT. The new system is more robust against camera misalignments and should therefore be well suited for operation in a clinical setting.     Retardation and axis orientation measured as a function of depth. A retarder set to a fixed axis orientation was placed in front of a mirror in the sample position. Different path length differences with respect to the reference mirror were obtained by shifting the sample mirror in beam direction. Retardation values are depicted in blue, values of axis orientation are shown in red.  Europe PMC Funders Author Manuscripts