2.1.

Delay-Encoded Dual-Beamlet FDOCT System

Figure 1 illustrates the schematic of the dual-beamlet delay-encoded PSFDOCT system. The concept of delay optics is similar to that described in Ref. 8. The illumination source is a superluminecent diode (Superlum, Russia) with a central wavelength of 840 nm and a spectral bandwidth of 45 nm, which provided an axial imaging resolution of $\sim 7\mu \mathrm{m}$ in air. The light source is coupled into the fiber-based Michelson interferometer with a coupling ratio of $10:90$. In the sample arm, the beam is expanded to 7 mm diameter and incorporated a $10\times$, 0.26 NA microscope objective (Mitutoyo, United States) with an effective focal length of 20 mm and a working distance of 30.5 mm, which yield a measured lateral resolution of $\sim 3\mu \mathrm{m}$ in air. The dualangle delay encoding is implemented by inserting a glass slide of thickness 2 mm into the sample path (shown in Fig. 1). The glass slide is inserted midway into the collimated sample path such that half the sample light passes through the glass, which subdivides the probing beam into two beamlets with different optical delay and incident angle on the sample specimen as shown in the inset of Fig. 1. The light emerging at the output of interferometer was sent to a custom-built high-speed spectrometer, which consists of a 30-mm-focal-length collimator, a $1200\text{-}\text{lines}/\mathrm{mm}$ transmitting grating, an achromatic lens with a 100-mm focal length, and a 12-bit, 1024-pixels CCD line scan camera (ATMEL AVIIVA SM2, United States). This spectrometer setup had a designed imaging depth of $\sim 3.0\mathrm{mm}$ on each side of the zero-delay line with a maximum line-scan rate of $\sim 51\mathrm{KHz}$. The introduction of the glass plate divides the back-reflected sample arm signal into four different optical paths: air-air (AA), glass-air (GA), air-glass (AG), and glass-glass (GG). Since the optical path of AG and GA has the same optical path distance, the resultant OCT signal with the delay-encoded optics generates a set of three OCT images [${\mathrm{OCT}}_{\mathrm{AA}}$, ${\mathrm{OCT}}_{\mathrm{AG}-\mathrm{GA}}$, and ${\mathrm{OCT}}_{\mathrm{GG}}$ as shown in Fig. 2(c)] within the total imaging range of the designed spectrometer with a delay separation of $T(n-1)/2$ (where $T$ and $n$ are the thickness and refractive index of the glass plate, respectively). Among these delay-encoded images, the vibration components of the OCT images corresponding to ${\mathrm{OCT}}_{\mathrm{AA}}$ and ${\mathrm{OCT}}_{\mathrm{GG}}$ were used for the calculation of the vibration vector as illustrated in Fig. 2(c). The measured sensitivity of these channels were $\sim 98\mathrm{dB}$ each.

Fig. 1

(a) Experimental set-up of SD-PS OCT system. L1 to L5: lenses, MO: microscopic objective, GP: glass plate, B1: beamlet-1 (through glass), B2: beamlet-2 (through air), $\theta$: separation angle b/w beamlets, v1 and v2: vibration vectors, $\alpha 1\text{and}\alpha 2$: angles of incidence, PC: polarization controller, FC: fiber coupler, DG: diffraction grating, OC: optical circulator, RM: reference mirror, SLD: superluminescent diode, COMP: computer. (b) Angle calibration setup with positioning goniometer. $G$: goniometetric stage, $R$: radius, MT: test mirror.

Fig. 2

(a) Structural image of the apical turn of a guinea pig cochlea (Video 1, MPG, 2.8 MB) [URL: http://dx.doi.org/10.1117/1.JBO.18.3.036003.1]. (b) structural image with delay-encoded optics, and (c) corresponding vibrational image with magnitude in nm (nanometer).

The estimated beam separation angle between the two beamlets is $\sim 16.69\mathrm{deg}$ with an OCT sample beam of diameter 7 mm and a microscope objective ($10\times$, 0.26 NA) with a focal length of 20 mm. In order to experimentally verify the estimated separation angle, we mounted a mirror on a goniometer stage as show in Fig. 1(b) at the sample plane of the OCT system. The optical axis of the sample beam was set normal to the mirror surface, and a 2 mm thick glass plate was introduced halfway into the sample beam to obtain two beamlets. Then the goniometer was scanned over a set of angles at which the back-reflected signal from each of the two beamlets experienced maximum, and the difference of these angles was taken to be the effective separation angle.

2.2.

Image Acquisition and Vibration Analysis

For measuring the vibration amplitude a MB-mode scanning protocol is employed to acquire data during acoustic stimulation. M-scans where acquired over a B-frame at 200 measurement points with a lateral scan range of 500 µm. Each M-scan consists of 1000 A-lines at fixed lateral position on the sample, and 10 M-scans were averaged at each lateral positions of the B-scan to improve the noise floor of the system. The system requires $\sim 800\mathrm{s}$ for capturing a set of MB-mode OCT data at an A-line rate of 2.5 kHz. A custom processing algorithm was used to analyze the MB-mode OCT data.^7,9 First, the reference background OCT image was subtracted from the data sets, and fast Fourier transformations were taken for each column of the M-mode data sets to calculate the complex OCT signals from the spectral data. The phase was calculated for each corresponding pixel of the M-mode image. Then the phase difference between adjacent A-lines was computed, which was proportional to modulation of the optical path difference induced by the acoustic stimulation. The phase difference between adjacent A-scans, $j$ and $j-1$, can be calculated as

The “signal” in this measurement is defined as the peak magnitude of FFT within a $\pm 10\mathrm{Hz}$ window of the modulation frequency, and “noise” is defined as the peak FFT amplitude within the same window without any acoustic stimulation. The minimum noise floor of the system measured without averaging was $\sim 0.01\mathrm{nm}$ at an A-scan rate of 51 kHz and $\sim 2\mathrm{nm}$ at an A-scan rate of 1.5 kHz; With averaging 10 measurements, the system noise floor was $\sim 0.0083\mathrm{nm}$ at 51 kHz and 0.7 nm at 1.5 kHz, respectively. Figure 3 shows the noise floor measurements of the system at seven different A-line rates. As the A-line rate of the system increased, the vibration detection sensitivity of the system also increased by providing a better noise floor as shown in Fig. 3. This trend is due to the fact that the power spectrum of pink noise is inversely proportional to frequency. However, at a higher line rate, the short exposure time of the line detector limits the system performance for imaging highly scattering tissue specimens. In order to overcome this tradeoff between the available optical power and the short exposure time of the line detector, we operate the camera at an optimal line rate of 2.5 kHz for tissue imaging.

Fig. 3

Noise floor of the system measured at various A-scan rates.

2.3.

System Calibration

To test the feasibility of the delay-encoded PSFDOCT system to measure absolute vibration and Doppler angle, a calibrated vibrating piezostack (AE0505D08F, Thorlabs Inc., United States) with a stimulation frequency of 300 Hz (400 mV driving volt) was used as sample. The piezostack was mounted on a goniometer stage as shown in Fig. 1(b), and measurements were carried out at various incident angles ($-20\mathrm{deg}$ to 35 deg) with a step incremental angle of 5 deg. Then the vibration amplitudes were extracted from the two delay-encoded channels by using the above-mentioned method⁷ with averaging five measurements at a single scan point on the surface of the piezostack. Figure 4(a) shows the measured vibration amplitudes and corresponding simulated vibration amplitude for the two channels of the delay-encoded PSFDOCT system. Once the vibration components ($v_1$, $v_2$) from the two delay-encoded channels were extracted, the Doppler angle and the corresponding absolute vibration can be calculated using Eqs. (2) and (3).^8,10 Figure 4(a) shows the estimated vibration amplitudes and corresponding simulated results for beamlet-1(air) and beamlet-2 (glass) for a scan angle range of $-20\mathrm{deg}$ to 35 deg.

Fig. 4

(a) Simulated and measured vibration amplitude plot with the dual beam delay-encoded optics and the corresponding absolute vibration amplitude at preset tilt angles. (b) Set and the measured Doppler angle.

Figure 4(b) shows the set value of the Doppler angle and the corresponding estimated Doppler angles using the measured vibration vectors from the delay-encoded optics. Table 1 shows the estimated RMS error of absolute vibration for 10 measurements at each scan angle. The correlation between the measured and calculated result was excellent with an averaged RMS error of vibration magnitude of 0.68 nm.

Table 1

RMS errors for estimation of absolute vibration amplitude for each scan.