2.1.

Experimental System

Figure 1 shows a schematic of the FD-OCT system with three different phase-shifting method configurations. A superluminescent diode (Superlum, County Cork, Ireland) with an $890\text{-}\mathrm{nm}$ central wavelength and $140\text{-}\mathrm{nm}$ full width at half maximum (FWHM) was used as a light source. A fiber-based Michelson interferometer was used with a $90∕10$ fiber coupler sending 10% of the light toward the sample arm. The beam output power on the sample was $450\mu \mathrm{W}$ . The measured axial and lateral resolutions in air were 3.6 and $9.4\mu \mathrm{m}$ , respectively. Light reflected from the sample was combined with the light from the reference arm, and then sent to a spectrometer, where the complementary metal-oxide semiconductor (CMOS) line detector (spL4096- $140\mathrm{km}$ , Basler, Highland, Illinois), maximum $140\text{-}\mathrm{kHz}$ line rate at $4096\text{pixels}$ , and $10\times 10\text{-}\mu \mathrm{m}\text{pixel}$ size, acquired spectral fringes. The operating setup of the detector included 4-tap $12\text{-bit}$ , $80\text{-}\mathrm{MHz}$ , camera link clocks, and the line averaging mode (dual line $10\times 20\mu \mathrm{m}$ ). B-scan imaging frame rates (frames/s or fps) were 100, 50, and $20\mathrm{fps}$ for 1000 A-scans using 2048 detector pixels. The optical components of the spectrometer consisted of a $75\text{-}\mathrm{mm}$ focal length collimator (Thorlabs, Newton, New Jersey), a $1200\text{-line}∕\mathrm{mm}$ volume holographic diffraction grating (Wasatch Photonics, Logan, Utah), and an $\mathrm{f}=100\mathrm{mm}$ achromatic objective lens (Thorlabs). As shown in Fig. 1, the sample arm scanner as well as the reference arm scanner could be used to introduce phase shifts between consecutive A-scans. The galvo scanner at the sample arm is also used to scan the imaging beam over the sample at the zero offset position in two other configurations. In addition, as a separate phase-shifting component we used the piezoelectric translator (P-840.40, Physics Instruments, Auburn, Massachusetts) at the reference arm of the OCT system. The full travel displacement of the PZT is $60\mu \mathrm{m}$ when applying $10\mathrm{V}$ to an open loop PZT amplifier module ( $10\times$ amplification). The mirror attached at the PZT was $7\mathrm{mm}$ in diameter and $22.5\mathrm{g}$ .

Fig. 1

Schematic of the FD-OCT used for evaluating complex conjugate removal methods. Three dotted rectangles represent components that are used to introduce phase shifts that were tested: SLD (superluminescent diode), CMOS (complementary metal-oxide semiconductor) line detector, and PZT (piezoelectric translator).

A Fourier reconstruction algorithm of the OCT image includes DC subtraction and a dispersion compensation method before applying complex conjugate removal procedures.²¹ To process the data and display the image, a main computer unit (HP xw8600, $3.2\text{-}\mathrm{GHz}$ dual processors) with a rapid speed frame grabber (PCIe 1429, National Instruments, Austin, Texas), synchronized B-scan, and camera exposure timing where the FD-OCT algorithm programmed with LabVIEW software (National Instruments) was embedded. The galvo scanner and frame grabber were controlled and triggered by a module-based multifunction DAQ (NI PCIe 6363, National Instruments).

2.2.

Phase-Shifting Methods

Three phase-shifting methods were used in our experiment.

2.3.

Full-Range Image Reconstruction

Several variations of the common algorithm have been proposed for reconstructing the full-range image with phase-shifting methods. These include reconstruction using the Hilbert transformation,⁶ filtering with the Heaviside step function,²¹ and bandpass filtering.²² The Hilbert transformation method is mathematically equivalent to filtering with the Heaviside step function demonstrated by Baumann ²¹ In this work we employed the filtering algorithm with the bandpass filter because this procedure eliminates low and high frequency components, which results in enhancing image quality by suppressing trivial frequency values. For determining the filter bandwidth, it is necessary to consider that the filter output will include all frequency components of the sampled structure. Then, application of additional high pass filter limits low frequency noise. In FD-OCT, the coherence fringe spectrum including phase shifts can be expressed by

2.4.

Suppression Ratio and Sensitivity of Fourier-Domain Optical Coherence Tomography System

The suppression ratio (SR) is an intensity difference between maximum values of the FD-OCT sample signal and its complex conjugate suppressed (CCS) mirror signal $(\mathrm{SR}=I_{{\mathrm{OCT}}_{\max }}∕I_{{\mathrm{CCS}}_{\max }})$ . In this experiment the SR is obtained after averaging the signal from 20 A-scans to limit the effect of random phase fluctuations.

The sensitivity of the OCT system is defined by the minimum reflectivity of the sample that can be detected (signal-to-noise ratio equals one).² One of the important parameters describing an FD-OCT system is its sensitivity drop-off due to limited spectral resolution of the detector. This was assessed by measuring sensitivity for different optical path length differences between the sample and the reference arm. Figure 2 shows the sensitivity drop-off measured in our FD-OCT system. The system sensitivity was decreased by approximately $20\mathrm{dB}$ at a $1.5\text{-}\mathrm{mm}$ path length difference between the sample and the reference arm. Additionally, we evaluated sensitivity differences at different line exposure times. As expected, there is an approximately $3\text{-}\mathrm{dB}$ drop between $50\text{-}\mathrm{fps}$ and $100\text{-}\mathrm{fps}$ B-scans at the same path length difference position. The theoretical maximal depth range $z_{\max }$ is given by $z_{\max }={\lambda }^2∕4\delta \lambda$ , where $\delta \lambda$ is the spectrometer resolution.² The calculated $z_{\max }$ of our system is $\pm 2.5\mathrm{mm}$ . Since the maximum sensitivity is obtained at the zero path length difference position, the closer the sample is located to the zero path length difference plane, the better the sensitivity.

Fig. 2

System sensitivity measurement as a function of optical path length difference and different acquisition speeds.

3.1.

Suppression Ratio

The suppression ratio (SR) is the most important parameter for complex conjugate removal methods to quantify the complex conjugate suppression. Figure 3 shows measured SR values for the three different phase-shifting methods using a paperboard as a sample. To measure the SR of the sample and the reference arm modulation methods, we moved the pivot offset position along a diagonal direction, which is a $45\text{-}\mathrm{deg}$ angle between the incident beam and the sample or reference mirror. The galvanometer-based phase-shifting scanned $6\mathrm{mm}$ for the sample arm modulation and $4.5\mathrm{mm}$ for the reference arm modulation. For the PZT-based method, the SR is obtained by changing applied voltages $\left(0\text{to}100\mathrm{V}\right)$ , thereby changing the travel length $\left(0\text{to}60\mu \mathrm{m}\right)$ of the PZT.

Fig. 3

Suppression ratio of complex conjugate artifacts using a paperboard with: (a) pivot offset scanning of the sample arm; (b) pivot offset scanning of the reference arm; (c) phase shifting with the PZT, 1000 A-scans, and $6\text{-}\mathrm{mm}$ scanning range; and (d) phase shifting with the PZT, 300 A-scans, and $1.5\text{-}\mathrm{mm}$ scanning range.

As shown in Fig. 3, the maximum complex conjugate SR with a paperboard is around $25\mathrm{dB}$ . The phase shifting between consecutive A-scans is $\Delta \phi =0.5\pi$ , and the pivot offset position is $1.6\mathrm{mm}$ for the sample arm pivot offset scanning. As indicated in Figs. 3 and 3, the SR is not restricted by the speed of line acquisition for the galvo-scanner-based phase-shifting methods. Our experimental SR data by the galvo-scanner-based phase-shifting methods yield similar results to those described by Leitgeb ¹³ When a mirror was placed in the sample, we observed that the maximum SR is $32\mathrm{dB}$ , which was similar to the result as explained by Fig. 2 in Ref. 13. The reason that the maximum SR of the mirror is higher than that of the paperboard is that the mirror sampling density $\left(\rho \right)$ is higher than the paperboard one. In this work, however, we only investigated SR using real samples, a paperboard or skin, instead of using a mirror. In Figs. 3 and 3, the SR of the sample arm pivot offsetting method is approximately $4\mathrm{dB}$ higher than that of the reference arm pivot offsetting method. The two phase-shifting methods, however, should be theoretically symmetric, since the phase shift is generated in the same way. There were intensity fluctuations in both the sample arm pivot offsetting method and the reference arm pivot offsetting method. Unlike the sample arm phase-shifting method, the reference arm pivot offsetting method uses two scanners that introduce additional phase errors that limit the maximum SR achievable. In addition, the reference beam fluctuations are more prominent than the sample arm’s due to a DC subtraction procedure used in our OCT data processing algorithm. The DC intensity fluctuates across B-scans so that the averaged DC level cannot properly correct individual A-scans. This can also explain the differences in maximum SR between two phase-shifting techniques.

The phase modulation with PZT generates $15\text{to}17\text{-}\mathrm{dB}$ suppression of 1000 A-scans and the $6\text{-}\mathrm{mm}$ scanning range, which is shown in Fig. 3. Here, the PZT travels the full length $60\mu \mathrm{m}$ by applying $100\mathrm{V}$ , which is close to $0.45\pi$ phase shifts. For this acquisition scheme, the $60\text{-}\mu \mathrm{m}$ displacement of the PZT is not enough to obtain the maximum SR. To achieve the half cycle of full phase modulation with the PZT method, we instead use 300 A-scans for one B-scan and $1.5\mathrm{mm}$ of the scanning size. In Fig. 3, we noticed the maximum SR $\left(20\mathrm{dB}\right)$ with the PZT method has a value close to the SR $\left(21\mathrm{dB}\right)$ of the reference pivot offsetting method. As discussed earlier, the constraint of the PZT method is limitation of the PZT displacement, which confines the maximum phase shifts. During SR measurement with the PZT, moreover, we used a supplementary and concrete PZT mount to alleviate mechanical vibrations when the actuator is traveling.

3.2.

In Vivo Full-Range Images

Full-range images of in vivo human tissues with different line exposure times were performed to compare image quality for the different phase-shifting schemes. We show B-scan images of the human fingerpad and nail as well as the human retina. Figure 4 shows standard FD-OCT images and full-range images of the human fingerpad and nail in vivo acquired with the sample arm pivot offsetting method for different acquisition speeds. The fast B-scan images, $100\mathrm{fps}$ , have lower intensity at a fingerpad region compared to $20\text{-}\mathrm{fps}$ images (due to the sensitivity difference), but it is still possible to discriminate epidermis and the dermis layers on the fingerpad. This is expected because, as indicated in Fig. 2, the high-speed acquisition image has lower sensitivity than the slow-speed acquisition image at the same path length difference position. Complex conjugate artifacts are clearly removed for all imaging acquisition speeds using the sample arm phase-shifting method.

Fig. 4

In vivo images of human fingerpads and fingernails acquired at different image acquisition speeds with standard FD-OCT reconstruction (left column) and the full-range reconstruction with the sample arm pivot offset phase-shifting $(\Delta \phi =0.5\pi )$ method (right column). Human fingerpad at (a) $20\text{-}\mathrm{fps}$ , (b) $50\text{-}\mathrm{fps}$ , and (c) $100\text{-}\mathrm{fps}$ B-scans. Human fingernail at (d) $20\text{-}\mathrm{fps}$ , (e) $50\text{-}\mathrm{fps}$ , and (f) $100\text{-}\mathrm{fps}$ B-scans. The lateral scanning range is $6\mathrm{mm}$ .

The images shown in Fig. 5 were acquired using phase-shifting methods with the reference arm pivot offset method and the PZT-based phase-shift method. Complex conjugate artifact-free images acquired at $20\mathrm{fps}$ in Figs. 5 and 5 retain some residual mirror artifacts, since the SR cannot suppress the mirror signal completely, where the signal-to-noise ratio is over the maximum SR. In addition to Figs. 5 and 5, the reference-arm-based phase modulation methods have higher coherence noise than the sample arm phase modulation method illustrated in Figs. 4 and 4. Displacement of the reference arm mirror position reduces the reference beam stability when the sample is scanned. Thus, the reference beam intensity changes during the phase modulation, requiring an additional DC subtraction algorithm to compensate the DC value variations over A-scans. Furthermore, the reference arm phase modulation methods demand careful attention to the reference beam alignment for reducing reference beam intensity changes. Note that the fast acquisition images, Figs. 5 and 5, have less visible mirror artifacts than $20\text{-}\mathrm{fps}$ B-scan images. The system sensitivity drops by approximately $6\mathrm{dB}$ between $20\mathrm{fps}\text{to}100\mathrm{fps}$ , as shown in Fig. 2; however, the SR drop from $20\mathrm{fps}\text{to}100\mathrm{fps}$ is approximately $2\mathrm{dB}$ , demonstrated in Fig. 3. This is the reason that we can see more artifacts in Fig. 5 with $20\mathrm{fps}$ than Fig. 5 with $100\mathrm{fps}$ , because the sample structure signal at $20\mathrm{fps}$ is stronger than that at $100\mathrm{fps}$ . Comparing Figs. 4 and 5, we note that the phase-shifting method of the sample arm has better complex conjugate suppression than that of the reference arm. However, the sample arm phase-shifting method may not be easily implemented with some existing OCT systems or more complex ones, such as those involving adaptive optics.²⁰ Thus, the reference arm pivot offsetting method is an interesting alternative to sample-arm-based phase shifting. The maximum phase shift achieved with our PZT was $0.45\pi$ for 1000 A-scans due to the limit of the PZT displacement. Note that the standard FD-OCT imaging method does not allow placement of the sample at the zero path length difference position. This is because of overlap in the complex conjugate images and the potential for flipping complex conjugate images by sample motion. Also, positioning of the sample further away from the zero path length difference line diminishes the maximum achievable sensitivity. However, when using full-range imaging with the complex conjugate removal method, it is possible to achieve maximum sensitivity, which is critical in high-speed imaging where short exposure times lower the system sensitivity.

Fig. 5

In vivo human fingerpad images for different phase-shifting methods with standard FD-OCT reconstruction (left) and full-range image reconstruction (right). (a) $20\text{-}\mathrm{fps}$ B-scans with the reference arm pivot offset method $(\Delta \phi =0.5\pi )$ . (b) $100\text{-}\mathrm{fps}$ B-scans with the reference arm pivot offset method $(\Delta \phi =0.5\pi )$ . (c) $20\text{-}\mathrm{fps}$ B-scans with the PZT-based phase-shifting method $(\Delta \phi =0.45\pi )$ . (d) $100\text{-}\mathrm{fps}$ B-scans with the PZT-based phase-shifting method $(\Delta \phi =0.45\pi )$ . The lateral scanning range of images is $8.5\mathrm{mm}$ .

One limitation of acquiring full-range images in vivo is reduction of the suppression ratio due to sample movement.²¹ Figure 6 illustrates the suppression ratio differences between one stationary position Nail 1 and a moving sample Nail 2. The SR for those images is calculated by subtraction of the two strongest signals, a real image (positive side) and a suppressed mirror image (negative side), across the zero delay. Comparing SR of the paperboard in Fig. 3 to the SR of the fingernails in Fig. 6, different scanning structures and areas can have different maximum SR values because of signal intensity differences from these structures. The SR cannot be higher than signal-to-noise ratio for a given structure. Additional phase shifts by sample motion reduce the SR due to changing the $\Delta \phi$ value. When the sample was moving, the complex conjugate suppression ratio diminished by as much as $10\mathrm{dB}$ for the $20\text{-}\mathrm{fps}$ acquisition. Despite sample movement, $100\text{-}\mathrm{fps}$ B-scan images are virtually free of this artifact and have stable SR across B-scans compared to the slow-speed acquisition images.

Fig. 6

Decreasing suppression ratio by sample movement. B-scan images with the sample arm pivot offset method $(\Delta \phi =0.5\pi )$ of in vivo human fingernail images at a stationary position Nail 1, and the sample moved Nail 2 (left), and complex conjugate suppression ratio of Nail 1 and Nail 2 (right). Fingernails at (a) $20\text{-}\mathrm{fps}$ B-scan, (b) $100\text{-}\mathrm{fps}$ B-scan, and the suppression ratio. The lateral scanning range of each nail image is $6\mathrm{mm}$ .

Figure 7 demonstrates standard FD-OCT images and our full-range FD-OCT images of a fingernail, a 3-D fingerpad, and a 3-D human retina acquired at $100\mathrm{fps}$ . Figure 7 is a high resolution image of full-range fingernail with an average of 20 frames to reduce speckles. Clearly fast acquisition speed helped to reduce motion artifacts. In addition, Fig. 7 shows volumetric representation of the human fingerprint image before and after removal of the complex conjugate artifacts. Although the fingerpad is placed at the zero path length difference line, an overlapped complex conjugate image is removed by the method. Note that the sample arm power was about $450\mu \mathrm{W}$ . Figure 7 shows complex conjugate removed volumetric representation of the human retina of a healthy volunteer using the reference arm pivot offsetting method and the $100\text{-}\mathrm{fps}$ acquisition speed. Here, the dashed line indicates the zero path length difference position.

Fig. 7

In vivo standard FD-OCT images (left) and full-range images (right) after reconstruction of the complex-conjugate-free methods. (a) High resolution fingernail images at $100\text{-}\mathrm{fps}$ B-scan without and with the sample arm pivot offset method $(\Delta \phi =0.5\pi )$ . The lateral scan range of the images is $6\mathrm{mm}$ . (b) 3-D visualization of a human fingerpad at $100\text{-}\mathrm{fps}$ B-scan without and with the reference arm pivot offset method $(\Delta \phi =0.5\pi )$ . The image size is $8.5\left(x\right)\times 8.5\left(y\right)\mathrm{mm}$ . (c) In vivo 3-D human retinal imaging at $100\text{-}\mathrm{fps}$ B-scan without and with the reference arm pivot offset method $(\Delta \phi =0.5\pi )$ . The region of interest is $3\left(x\right)\times 3\left(y\right)\mathrm{mm}$ . The dashed line is the zero path length difference position.

3.3.

Comparison Among Three Phase-Shifting Techniques

To evaluate proposed phase-shifting schemes, Table 1 compares all three techniques: the pivot offset scanning of the sample arm, the pivot offset scanning of the reference arm, and the PZT at the reference arm. Here, image quality is determined as the maximum SR, which indicates the quantity of the complex conjugate suppression. The sample arm pivot offsetting method can only use a fixed scanning pattern, because the sample arm performs both image scanning and phase modulation. Therefore, this method leads to limited accessible sampling patterns. However, there is no restriction on selection of beam scanning patterns for the reference arm phase-shifting methods. As demonstrated in Figs. 3 and 3, the PZT method at the reference arm operates complex conjugate removal with limited phase shifts. By contrast, pivot offsetting methods based on the scanning mirror accomplish full phase shifting and are adequate for fast acquisition schemes. Supplementary DC subtraction processing is necessary to lower coherence noise of the reference arm phase modulation methods. Although these complex conjugate removal methods depend on sample motion, we note that increased acquisition speed can minimize the motion artifacts of the phase-shifting methods.