Computational optical coherence tomography [Invited]

Abstract

Optical coherence tomography (OCT) has become an important imaging modality with numerous biomedical applications. Challenges in high-speed, high-resolution, volumetric OCT imaging include managing dispersion, the trade-off between transverse resolution and depth-of-field, and correcting optical aberrations that are present in both the system and sample. Physics-based computational imaging techniques have proven to provide solutions to these limitations. This review aims to outline these computational imaging techniques within a general mathematical framework, summarize the historical progress, highlight the state-of-the-art achievements, and discuss the present challenges.

Keywords: (100.3175) Interferometric imaging; (100.3190) Inverse problems; (110.1085) Adaptive imaging; (110.1758) Computational imaging; (110.4500) Optical coherence tomography.

Figures

Fig. 1

Schematic of a point-scanning spectral-domain OCT system. (a) A fiber-based Michelson interferometer is used to measure the spectral interference from the sample arm and reference arm with a spectrometer. In the sample arm, light is focused into the sample and scanned by the scanners. (b) A scatterer is probed by a Gaussian beam traveling at different angles. Figure adapted from [16].

Fig. 2

Geometry of a Gaussian beam for low- and high-numerical-aperture (NA) lenses. These geometries are contrasted with the assumption of a collimated axial OCT scan. The confocal parameter, b, is the region within which the beam is approximately collimated, and w0 is the beam radius at the focus, which is related to the transverse resolution (2w0). The axial resolution depends on the coherence length of the source, Lc. Figure adapted from [20].

Fig. 3

Simulation of two scattering particles which are in-focus and far-from-focus, respectively. (a) Cross-section image of the standard OCT reconstruction showing strong defocus for the far-from-focus particle. (b) ISAM reconstruction showing depth-invariant high transverse resolution. (c) Phase of the original complex data in the frequency-domain. Black line illustrates ISAM resampling curve. (d) Resampled phase in the frequency-domain, corresponding to the ISAM reconstruction. Adapted from [73].

Fig. 4

Human breast tissue imaged with Fourier-domain OCT according to the geometry illustrated in the top. En face images are shown at two different depths above the focal plane, 591 µm (section A) and 643 µm (section B). ISAM reconstructions (c,f) resolve structures in the tissue which are not decipherable from the standard OCT processing (b,e), and exhibit comparable features with respect to the histological section (a,b). The scale bar indicates 100 µm. Figure adapted from [16].

Fig. 5

Real-time ISAM visualization of highly-scattering in vivo human skin from the wrist region acquired using a 0.1 NA OCT system, after placing the focus 1.2 mm beneath the skin surface. Cross-sectional results of (a) OCT and (b) ISAM. En face planes of (c) OCT and (d) ISAM at an optical depth of 520 µm into the tissue. (e) Variation of SNR with depth shows the improvement of ISAM, which was computed using the 20% (noise) and 90% (signal) quantiles of the intensity histograms. Compared to OCT, ISAM shows significant improvement over an extended depth range. CS, coverslip; GL, glycerol; SD, stratum disjunction; SC, stratum corneum; RD, reticular dermis; SF, subcutaneous fat. Scale bars represent 500 µm. Adapted from [59].

Fig. 6

Digital refocusing of OCT data from an onion. (a) En face plane from outside the focal region. (b) Digital refocusing result for (a). (c) A typical en face image within the focal region. Figure adapted with permission from [96].

Fig. 7

Holoscopic reconstruction of a grape comparing digital refocusing to the one-step reconstruction. (a) Cross-section from the volume refocued in one layer. (b) En face image at the virtual focus after the digital refocusing. (c) En face plane after the same digital recofusing operation as (b), 160 μm above the virtual focus. Since each depth is not independently brought into focus, defocus blur is still visible away from each virtual focus. (d) B-scan of the one-step reconstruction. (e) En face image at same location as (b). (f) En face image at same location as (f). Defocus is corrected since the one-step reconstruction brings every plane into focus. The NA was 0.14 (confocal parameter was 28 μm). Figure adapted with permission from [102].

Fig. 8

Sub-aperture cross-correlation method for estimation of the aberration correction filter. Reconstructions from each sub-pupil function are compared to the central reference sub-aperture to determine the slope of the wavefront. Reproduced with permission from [123].

Fig. 9

Volumetric cellular-resolution imaging of in vivo human skin acquired using a 0.6 NA point-scanning SD-OCM system without depth scanning. (a-e) En face results at different depths based-on the standard OCT processing. (f-j) ISAM and CAO processing for (a-e), respectively. Arrows indicate (f) boundary of the stratum corneum and epidermis, (g) granular cell nuclei, (h) dermal papillae, (i) basal cells, and (j) connective tissue. Scale bar represents 40 µm. Adapted from [119].

Fig. 10

Fovea images of the living human retina. (a) A fundus image showing the location of the acquired en face OCT data. (b) Original en face OCT data. (c) En face OCT data after CAO. N, nasal; S, superior. Scale bars represent 2 degrees in (a) and 0.5 degrees in (b, c). Figure adapted from [124].

Fig. 11

Retinal imaging and response to an optical stimulus. After computational aberration correction, optical path length changes Δℓ can be resolved in individual cones. (A and B) Measurements of independent responses were about 10 min apart. Light stimulus was 3 s for both cases. Most cones reacted to the stimulus, but some exhibited only a small or no response and are indicated by yellow arrows. Some locations pointed by the light blue arrow show abrupt phase changes within a single cone. (C). The proposed technique shows the capability of identifying more complicated stimulation patterns and indicating which photoreceptors contribute to an image seen by the test person. Scale bars represents 200 μm. Figure adapted from [135].

Fig. 12

Simulation of a single point scatterer showing the impact of 1-D Brownian motion (left column), step motion (middle column), and sinusoidal motion (right column). The motion maps in the top row were applied along the axial dimension (second row), fast axis (third row), and slow axis (final row). Within each column, the left image shows the OCT en face plane, while the right image shows the result of computational refocusing. The magnitude of the motion applied is scaled by dn for each image to achieve a representative artifact. The simulation was performed at a central wavelength of λ0 = 1.33 µm. Scale bars represent 50 µm. Reproduced from [138].

Fig. 13

(a) Illustration of the axial motion correction algorithm implemented without an external phase reference. (b) Three-dimensional OCT and computationally-refocused reconstruction of an in vivo human sweat duct. Prior to phase correction, the computational refocusing fails dramatically. Following phase correction, the refocusing succeeds. Adapted from [145].