Optical coherence tomography (OCT) is an imaging modality that enables high-resolution cross-sectional imaging of biological tissues and translucent materials.^{1, 2} Spectral domain (SD) OCT is a high-speed and high-sensitivity variant of OCT that largely replaced the older time domain variant in the recent years.

In SD-OCT, the depth-resolved information can be reconstructed by Fourier transform of the cross spectral density measured with a spectrometer located in the detection arm of an interferometer.^{3, 4} However, SD-OCT suffers from two drawbacks that restrict its measurement range.

First, the Fourier transform of the real-valued cross-spectral density is symmetrical about the zero path difference. Therefore, one cannot distinguish between positive and negative optical path differences with respect to the reference mirror. This effect particularly concerns imaging of objects with larger depth extensions, such as the anterior eye segment, where measurement ranges of the order of
$10\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
are needed. In order to suppress the mirror images, the so-called full-range complex (FRC) technique was introduced.^{5} In addition to the amplitude of the spectral interferogram, its phase is measured to reconstruct the full complex spectral interferogram—the analytic function. Inverse Fourier transformation of the analytic function directly yields the true object structures without any mirror terms. Several FRC approaches were developed that differ in the way of generating the
$\pi \u22152$
phase-shifted quadrature function of the spectral interferometric signal.^{6, 7, 8} An elegant method uses the phase modulation that is introduced by off-pivot-point illumination of the galvanometer scanner mirror.^{9, 10, 11} A second drawback of SD-OCT is the spectrometer-intrinsic depth range, which is limited by its spectral resolution. Until now, the depth range of standard SD-OCT systems is
$\sim 3\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
, which can be doubled by applying FRC methods. However, this axial measurement range is not sufficient to cover the entire anterior eye segment.

In this letter, we demonstrate an SD-OCT system with a modified spectrometer design combined with a FRC measurement range doubling that achieves an imaging depth of $14\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ , sufficient to cover the human anterior eye segment from the cornea to the posterior surface of the lens.

Figure 1 shows a schematic diagram of our system. A superluminescent diode (Superlum, Moscow) with a center wavelength of
$835\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
and a bandwidth (FWHM) of
$18\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$
was used as the light source. The round trip coherence length was
$17\phantom{\rule{0.3em}{0ex}}\mu \mathrm{m}$
. The collimated beam (
$1.5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
diam) was divided by a
$50\u221550$
nonpolarizing beamsplitter into a reference and a sample beam. A variable neutral density filter was mounted in the reference arm to adjust the light power so that the line-scan camera of the spectrometer is operated close to the saturation limit to get maximum sensitivity. In the sample arm, a galvanometer scanner was mounted on an
$x\text{-}y$
translation stage for correct adjusting of the scanner position to achieve a
$\pi \u22152$
phase shift between adjacent A scans.^{9} The scanner was driven by a saw-tooth voltage generated by a DAQ-card (National Instruments, PCI 6110, Austin, TX). An achromatic object lens with a focal length of
$80\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
was used to focus the beam onto the sample. This provided a transversal resolution of
$\sim 57\phantom{\rule{0.3em}{0ex}}\mu \mathrm{m}$
with a confocal range of
$6\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
. Sample and reference beams were recombined at the
$50\u221550$
splitter, coupled into a single mode fiber and guided to the spectrometer where the real part of the spectral interferogram
$S(x,\lambda )$
was recorded.

The spectrometer consisted of a transmission diffraction grating (Wasatch Photonics, Logan, Utah) with
$1500\phantom{\rule{0.3em}{0ex}}\text{lines}\u2215\mathrm{mm}$
, an achromatic camera lens with a focal length of
$300\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
, and a
$2048\phantom{\rule{0.3em}{0ex}}\text{pixel}$
line-scan camera (Atmel, Aviiva M2 CL 2014, San Jose, CA) with
$14\times 14\phantom{\rule{0.3em}{0ex}}\mu {\mathrm{m}}^{2}\phantom{\rule{0.2em}{0ex}}\text{pixel}$
size. In our configuration, the spectrometer resolution was
$25\phantom{\rule{0.3em}{0ex}}\mathrm{pm}$
. The SD-OCT intrinsic depth range, which is limited by the Nyquist sampling theorem, was measured with
$7\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
(in air).^{6} After applying the full-range algorithm, the depth range was doubled to an axial imaging range of
$14\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
. The probing beam power on the cornea was
$2\phantom{\rule{0.3em}{0ex}}\mathrm{mW}$
, which is well below the safety limits.^{12} The integration time per A scan was set to
$50\phantom{\rule{0.3em}{0ex}}\mu \mathrm{s}$
to optimize the trade-off between mirror term suppression and sensitivity. With this setting, the sensitivity of the system was measured with
$\sim 106\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
near zero position. The sensitivity decrease was
$\sim 17\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
over three-quarters of the depth range. The system worked with an A-scan rate of
$20\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$
. A single B scan with 2048 A-scans was recorded in
$\sim 100\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$
. The acquisition time for a 3-D scan with 120 B scans was
$\sim 15\phantom{\rule{0.3em}{0ex}}\mathrm{s}$
. The scanning range covered the whole transversal width of the anterior eye segment (
$14\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$
for a single B scan and
$14\times 14\phantom{\rule{0.3em}{0ex}}{\mathrm{mm}}^{2}$
for a 3-D scan).

In conventional SD-OCT, the intensity distribution $I(x,z)$ (which represents the depth profiles) is retrieved by inverse Fourier transform of the recorded spectral interferogram $I(x,z)={\mathrm{FT}}_{k\to z}^{-1}\left\{S(x,k)\right\}$ , where $x$ is the transversal scanning direction, $z$ the axial depth range, and $k$ the wavenumber. Prior to the Fourier transform, fixed pattern noise and dc term were removed by subtracting a mean spectrum (averaged over 2048 A scans) from each spectral data set, followed by rescaling the spectral data from $\lambda $ space into $k$ space.

As mentioned above, the Fourier transform of a real valued function is Hermitian, and therefore, the depth profile is symmetrical about zero path difference, giving rise to mirror artifacts in conventional SD-OCT. To suppress these mirror artifacts and double the measurement range, we used a phase shift introduced by the
$x$
scanning mirror.^{9, 10, 11} In brief, the sample beam hits the fast scanning mirror slightly away from the scanner pivot axis. Therefore, during the transversal scan, the optical path length is changed. A constant phase shift between adjacent A scans is generated that depends on the mirror axis offset. If the phase difference is set appropriately
$(\pi \u22152)$
, one can reconstruct the complex spectral interferogram by Hilbert transform of
$S(x,k)$
along the transverse coordinate
$x$
for each wavenumber
$k$
. Finally, an inverse Fourier transform of each complex spectral A scan yields the depth profiles with suppressed mirror images.

The measured spectral interferograms were transferred via camera link and a high-speed frame grabber card (National Instruments, PCI 1428, Austin, Taxas) to a personal computer, where the data were stored and postprocessed.

We demonstrate the performance of our system by 2-D and 3-D imaging of the human anterior eye segment *in vivo*. Figure 2 shows a B scan. The signal intensity was plotted on a logarithmic gray scale and covers an image size of 14
$\left(x\right)\times 14$
(
$z$
, optical distance)
${\mathrm{mm}}^{2}$
. Figure 2a shows a SD-OCT image obtained by inverse fast Fourier transform (FFT) of the spectral interferogram without applying FRC reconstruction. The object structure is disturbed by overlapping of mirror images. Figure 2b shows the same data set with FRC postprocessing. Note that the imaging depth ranges from the front surface of the cornea to the posterior surface of the lens. Even the epithelium of the cornea and backscattered intensity within the lens can be observed, as well as the lens capsule. However, there are still some residual mirror artifacts from highly backscattering structures, such as the iris.

To quantify the mirror term suppression of our system, the extinction ratio was measured within a highly backscattering structure (iris *in vivo*) and at a weakly scattering black synthetic (nonmoving) surface.^{9} Only pixels with an intensity level above a certain threshold (noise level) in both imaging regions (corresponding to the positive and negative frequencies) were used to calculate the extinction ratio. With this convention, the extinction ratio was measured from Fig. 2b with
$22\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
in contrast to the nonmoving sample with
$36\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$
. The reduced extinction ratio might be caused by sample motion that leads to phase instabilities and loss in mirror term suppression efficiency. Axial sample motion of
$>2\phantom{\rule{0.3em}{0ex}}\mathrm{mm}\u2215\mathrm{s}$
would inverse the suppression effect (suppressing the real image and enhancing the mirror image).^{9}

Figure 3 shows the anterior eye segment during the accommodation from the far point (a) to the near point (b). The bright lines in both figures indicate the lens surfaces and demonstrate the thickness-change of the lens.
Videos 1 shows a 3-D scan of the anterior eye segment. It contains 120 sequenced B scans, which were recorded during one sweep of the
$y$
scanner mirror. The size of the 3-D scan is approximately
$14\left(x\right)\times 14\left(y\right)\times 14\left(z\right)\phantom{\rule{0.3em}{0ex}}{\mathrm{mm}}^{3}$
.
Videos 2 shows the same 3-D data set in the *en face* plane.

One drawback of this method is that only a fixed scanning pattern (transversal range and speed) can be used for a specific scanning-mirror pivot-point offset. To overcome this problem, a motorized mount for the transverse scanner can be used. However, this would result in a more expensive and more complex system.

## Conclusion

In conclusion, we have developed a SD-OCT system with an extended depth range. With the high sensitivity and high speed of the instrument, the whole anterior eye segment from the cornea to the posterior surface of the lens could be imaged *in vivo* with a recording time of
$\sim 100\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$
per B scan at an A scan rate of
$20\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$
; 120 sequenced B scans formed a 3-D scan, which was recorded in
$\sim 15\phantom{\rule{0.3em}{0ex}}\mathrm{s}$
. Possible clinical applications of our system may be in cataract and glaucoma (chamber angle) diagnostics, as well as in accommodation studies.

## Acknowledgments

Technical support by C. Wölfl and financial support by the Austrian Science Fund (FWF Grant No. P 19624-B02) are gratefully acknowledged.

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