2.1.

FD-OCT

Figure 1 shows the optical scheme of LF-FDOCT consisting of a 2-D spectrometer, a free-space Michelson interferometer, and a cylindrical lens (CL). This scheme is nearly identical to that of conventional FD-OCT, with the exception of the cylindrical lens and the 2-D CCD. The light source is a superluminescent diode (SLD) with a center wavelength $\left({\lambda }_0\right)$ of $824\mathrm{nm}$ , a bandwidth of $19\mathrm{nm}$ , and maximum output power of $7\mathrm{mW}$ (BWC-SLD-11, B&W TEK Inc., Delaware, USA), and it provides a depth resolution of $11.4\mu \mathrm{m}$ with a refractive index of 1.38. The spectrometer consists of a VHG ( $1200\mathrm{lp}∕\mathrm{mm}$ , Wasatch Photonics, Inc.), an achromatic lens (L4) with a focal length of $150\mathrm{mm}$ and a diameter of $1\mathrm{in.}$ (Thorlabs, Inc.), and a 2-D CCD camera (TI-124B, Nikko Denki Tsushin Co., Ltd., Japan). The diffraction angle of the grating is optimized to maximize the diffraction efficiency. The CCD camera is an NTSC-standard $1∕2\text{‐}\mathrm{in.}$ video camera that uses $640\text{pixels}$ for spectral resolution and $480\text{pixels}$ for lateral resolution (B-scan), the details of which are described later. The signals from the CCD camera are digitized into $10\text{‐}\text{bit}$ numerical values by an NTSC frame grabber (PCI-1409, National Instruments) with a detection speed of $30\text{frames}∕\mathrm{s}$ (fps). Each spectrum that is detected by the CCD camera and the frame grabber is rescaled into frequency space by spline or zero-filling interpolation,^{13, 28, 29} then Hanning windowed, zero-filled from $640\text{pixels}\text{to}2048\text{pixels}$ , and digitally inversely Fourier transformed on a computer to obtain a depth-resolved OCT image.

Fig. 1

Optical scheme of LF-FDOCT: Ls, lenses; CL, cylindrical lens; BS, beamsplitter: Ms; mirrors; and VHG, volume holographic grating.

The relationship between the real depth and the pixel position in the image, which depends on spectrometer specifications, is examined by a plane mirror sample mounted on a micrometer. Figure 2a shows the 1-D OCT signals of the mirror sample with different depths, and Fig. 2b shows the relationship between the real depth positions of the mirror sample and the peak positions of the OCT signals in terms of pixels. On the basis of the gradient of this plot, the calibration coefficient is determined to be $4.2\mu \mathrm{m}∕\text{pixel}$ . The depth measurement range is $2048\text{pixels}\times 4.2\mu \mathrm{m}∕\text{pixel}$ , which equals $8.6\mathrm{mm}$ . However, half of this range is occupied by mirror images,^{30, 31} and the effective depth-measurement range is $4.3\mathrm{mm}$ .

Fig. 2

(a) One-dimensional OCT signals of a mirror sample with different depths and (b) peak positions in (a) plotted against the real depth positions of the mirror sample.

A theoretical effective depth-measurement range can be calculated from the parameters of the spectrometer by

2.2.

Line-Field Configuration

The LF-FDOCT does not require a mechanical A-scan due to its FD-OCT configuration. Moreover, the B-scan is not required because of line illumination and a 1-D imaging optics. As shown in Fig. 1, a CL ( $100\text{‐}\mathrm{mm}$ focal length, Sigma Koki Co., Ltd., Japan) is placed between a collimator lens [L1; a microobjective of 0.13 numerical aperture (NA), Olympus, Japan] and a beamsplitter (BS). As illustrated in Fig. 3a , the cylindrical lens does not affect the horizontal optical perspective, and the optics is identical to that of conventional FD-OCT. On the other hand, in the vertical optical perspective, the cylindrical lens extends the illumination on the sample into a 1-D line, as shown in Fig. 3b. The sample is then illuminated by the line focus, and the illuminated area is imaged on the CCD camera by objective L2 (an achromatic lens with a focal length of $60\mathrm{mm}$ and a diameter of $1\mathrm{in.}$ , Thorlabs, Inc.) and a spectrometer-lens L4 with a transverse magnification of 2.5.

Fig. 3

(a) Horizontal and (b) vertical perspectives of optics. A reflection optics is illustrated in the form of a transmitting optics; thus, the BSs and L2s on both side of the sample are identical. Red region represents the beam shape and the green lines indicate imaging rays.

The vertical optical resolution of the LF-FDOCT system is defined by the NA of L2 by using Rayleigh’s criterion:

The vertical measurement range of the LF-FDOCT system is dominated by the magnification $M$ and the size of the CCD, or the height of the line focus. In the proposed LF-FDOCT, the first and the second parameters dominate the measurement range of $2.6\mathrm{mm}$ , and this field is sampled by $480\text{pixels}$ on the CCD.

2.3.

Configuration for 3-D Measurement

The LF-FDOCT can measure a 2-D tomogram without mechanical scanning. To extend LF-FDOCT for 3-D measurements, we introduce a 1-D mechanical C-scan. A gold-protected mirror mounted on a 1-D galvanometer (Model 6220, Cambridge Technology) is placed at the back focal plane of L2, and it swings the probe beam horizontally. A function generator board with a $12\text{‐}\text{bit}$ digital-to-analog resolution (DAQ-2502, ADLINK Technology, Inc.) plugged into a Windows 2000 computer generates the control signal for the galvanometer. The function generator board, and thus the galvanometer, are synchronized with the operation of the CCD camera by a trigger signal from the frame grabber. Owing to this synchronization scheme, the 3-D measurement speed of this LF-FDOCT system is limited only by the driving speed of the CCD. The B-scan rate of the 3-D acquisition is 30 B-scans∕s and it is identical with that of 2-D acquisition.

The maximum horizontal measurement field— $25\mathrm{mm}$ —is dominated by the maximum rotation angle of the galvanometer and the focal length and the diameter of L2.

The horizontal resolution is defined in the same manner as that in conventional TD-OCT and FD-OCT, i.e., it is based on probe beam diameter and the focal length of the objective. In the proposed LF-FDOCT, the horizontal resolution is $15.8\mu \mathrm{m}$ .

4.1.

System Sensitivity

We examine the sensitivity of the LF-FDOCT system by measuring a mirror sample with an exposure time of $1\mathrm{ms}$ , a probe power of $1.1\mathrm{mW}$ , and a probe attenuation of $-36.6\mathrm{dB}$ . The dynamic range is $39\mathrm{dB}$ , therefore the system sensitivity is $75.6\mathrm{dB}$ , while the theoretical sensitivity is $83.9\mathrm{dB}$ . The degradation in the sensitivity may be due to the nonuniformity of the line illumination and vignetting of the CCD. Because an SLD is a spatially coherent light source, coherent crosstalk among the lateral points, which is not evident in the measurement of the mirror but is evident in that of biological samples, may cause additional degradation of the sensitivity. This coherent crosstalk can be suppressed by using spatially incoherent light source with a line slit, which is used to enhance the spatial coherence in one dimension, although this configuration sacrifices great portion of the optical power of the light source.

The exposure time dependency of the signal-to-noise ratio (SNR) and the sensitivity are examined, as shown in Fig. 8 . Figure 8a reveals that the SNR is proportional to the exposure time, as theoretically predicted, and Fig. 8b shows the theoretical shot-noise-limited sensitivity (solid curve) and experimentally measured sensitivity (×). A formula from Ref. 9 and the following parameters are used to calculate the theoretical sensitivity; $480\text{pixels}$ , 6.5% quantum efficiency of the camera, and 80% spectrometer efficiency. The fill factor of the CCD camera, which is not disclosed by its manufacturer, is assumed to be 100%. This assumption may have resulted in the disagreement between the theoretical curve and the experimental values.

Fig. 8

(a) Experimentally measured SNR on a linear scale and (b) theoretical system sensitivity (solid curve) and experimental system sensitivity (×).

As shown in Fig. 8, a longer exposure time leads to higher sensitivity, and we can use a longer exposure time in LF-FDOCT than in conventional FD-OCT. This is because in an LF-FDOCT, the exposure time can be identical to the acquisition time of a single B-scan while the maximum exposure time of a conventional FD-OCT is equal to the acquisition time of a single A-scan. Hence, in principle, the sensitivity of LF-FDOCT is greater than that of a conventional FD-OCT by a factor of $10\log N\mathrm{dB}$ , where $N$ is the number of A-scans in a single B-scan. This discussion is analogous²³ to that of an FF-OCT. In our setup, the maximum gain in the sensitivity is $10\log 480=26.8\mathrm{dB}$ . However, note that the long exposure time enhances the motion artifacts and may degrade the sensitivity. The effect of the motion artifacts is discussed in the following section.

The system sensitivity also depends on the depth in the measurement field, as seen in Fig. 2a. This figure indicates that the sensitivity at the end of the measurement range is $36\mathrm{dB}$ lower than the highest sensitivity, which is at the center of the measurement range (zero delay point). This degradation may be due to the limited resolution of the spectrometer, because the dimensions of optical elements limit the resolution so that it is slightly worse than the sufficient resolution. And the numerical error of the wavelength-frequency rescaling also may be the cause of the degradation.

4.2.

Effect of Motion Artifacts

Although a longer exposure time leads to the higher sensitivity, it can deteriorate the image quality because of the motion artifacts.³⁴

The effect of the motion artifacts in the LF-FDOCT is identical to that in a conventional FD-OCT, however, this effect is relatively large in the former because the exposure time is longer than that in a conventional FD-OCT. On the basis of a formula derived by Yun, ³⁴ the maximum allowable velocity for the SNR decay of $-10\mathrm{dB}$ along the depth is

The maximum allowable lateral velocities are also calculated from the formula by Yun as $\Delta y∕T=10.8\mathrm{mm}∕\mathrm{s}$ for vertical motion and $\Delta x∕T=15.8\mathrm{mm}∕\mathrm{s}$ for horizontal motion, where $\Delta y$ and $\Delta x$ are vertical and horizontal resolutions, respectively.

These estimations suggest that the LF-FDOCT is approximately 20 times more sensitive to axial sample motion than to transversal motions.

4.3.

Potential System Speed

In the measurement described in Sec. 3, the exposure time for a single B-scan is $1\mathrm{ms}$ . Within this duration, 480 A-scans are acquired, hence, the A-scan rate of a single B-scan is $480\mathrm{kHz}$ , however, the overall A-scan rate for the 3-D measurement is $14.4\mathrm{kHz}$ because of the limited duty cyle of 3%, which is due to the fixed frame rate of the NTSC camera. However, if we use a high-speed CCD camera and a high-speed sampling device, the overall A-scan rate for 3-D measurements can be improved up to $480\mathrm{kHz}$ . This would potentially enable a 2-D OCT measurement at a rate of $1000\mathrm{fps}$ , and a 3-D OCT measurement at a rate of $3.3\text{volumes}∕\mathrm{s}$ .

4.4.

Aberrations

With the exception of the cylindrical lens, all of the lenses in the LF-FDOCT system are achromatic doublets, which are designed to correct both achromatic and monochromatic aberrations. The cylindrical lens, which is a planoconvex singlet, can cause an achromatic aberration. The spectral width at the top and bottom perimeters of the line focus can be slightly degraded by the aberration when compared to the spectral width of the light source itself. However, these perimeters are not used for the OCT measurement, therefore, the effect of the achromatic aberration is negligible.

The cylindrical lens also causes a comatic aberration. If the rays do not impinge perpendicularly on the cylindrical lens, the comatic aberration can degrade the quality of the line focus. However, the proposed LF-FDOCT is free from comatic aberration, because the rays enter the cylindrical lens perpendicularly, as shown in Fig. 3a.