Abstract

Full-field swept-source optical coherence tomography (FF-SS-OCT) provides high-resolution depth-resolved images of the sample by parallel Fourier-domain interferometric detection. Although FF-SS-OCT implements high-speed volumetric imaging, it suffers from the cross-talk-generated noise from spatially coherent lasers. This noise reduces the transversal image resolution, which in turn, limits the wide adaptation of FF-SS-OCT for practical and clinical applications. Here, we introduce the novel spatiotemporal optical coherence (STOC) manipulation. In STOC the time-varying inhomogeneous phase masks are used to modulate the light incident on the sample. By properly adjusting these phase masks, the spatial coherence can be reduced. Consequently, the cross-talk-generated noise is suppressed, the transversal image resolution is improved by the factor of2, and sample features become visible. STOC approach is validated by imaging 1951 USAF resolution test chart covered by the diffuser, scattering phantom and the rat skin ex vivo. In all these cases STOC suppresses the cross-talk-generated noise, and importantly, do not compromise the transversal resolution. Thus, our method provides an enhancement of FF-SS-OCT that can be beneficial for imaging biological samples.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

2017 (4)

O. Thouvenin, K. Grieve, P. Xiao, C. Apelian, and A. C. Boccara, “En face coherence microscopy [Invited],” Biomed. Opt. Express 8(2), 622–639 (2017).
[Crossref] [PubMed]

C. Pfäffle, H. Spahr, D. Hillmann, H. Sudkamp, G. Franke, P. Koch, and G. Hüttmann, “Reduction of frame rate in full-field swept-source optical coherence tomography by numerical motion correction [Invited],” Biomed. Opt. Express 8(3), 1499–1511 (2017).
[Crossref] [PubMed]

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

P. Xiao, M. Fink, A. H. Gandjbakhche, and A. Claude Boccara, “A resolution insensitive to geometrical aberrations by using incoherent illumination and interference imaging,” Eur. Phys. J. Spec. Top. 226(7), 1603–1621 (2017).
[Crossref]

2016 (6)

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Pfäffle, H. Sudkamp, G. Franke, and G. Hüttmann, “In vivo optical imaging of physiological responses to photostimulation in human photoreceptors,” Proc. Natl. Acad. Sci. U.S.A. 113(46), 13138–13143 (2016).
[Crossref] [PubMed]

P. Xiao, M. Fink, and A. C. Boccara, “Full-field spatially incoherent illumination interferometry: a spatial resolution almost insensitive to aberrations,” Opt. Lett. 41(17), 3920–3923 (2016).
[Crossref] [PubMed]

H. Sudkamp, P. Koch, H. Spahr, D. Hillmann, G. Franke, M. Münst, F. Reinholz, R. Birngruber, and G. Hüttmann, “In-vivo retinal imaging with off-axis full-field time-domain optical coherence tomography,” Opt. Lett. 41(21), 4987–4990 (2016).
[Crossref] [PubMed]

D. Borycki, O. Kholiqov, and V. J. Srinivasan, “Interferometric near-infrared spectroscopy directly quantifies optical field dynamics in turbid media,” Optica 3(12), 1471–1476 (2016).
[Crossref] [PubMed]

2015 (1)

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J.-S. Lee, Y.-S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9(4), 253–258 (2015).
[Crossref]

2014 (2)

2013 (2)

2012 (2)

2010 (1)

2008 (1)

2006 (1)

2005 (3)

2004 (3)

2002 (3)

2000 (2)

A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, and H. Sattmann, “A thermal light source technique for optical coherence tomography,” Opt. Commun. 185(1-3), 57–64 (2000).
[Crossref]

G. Li, P.-C. Sun, P. C. Lin, and Y. Fainman, “Interference microscopy for three-dimensional imaging with wavelength-to-depth encoding,” Opt. Lett. 25(20), 1505–1507 (2000).
[Crossref] [PubMed]

1994 (1)

Apelian, C.

Arathorn, D. W.

Arthaber, H.

Aubry, A.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref] [PubMed]

Badon, A.

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref] [PubMed]

Birngruber, R.

Boccara, A. C.

Boccara, C.

Bonin, T.

Borycki, D.

Bourquin, S.

Brown, W. J.

Choi, W.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J.-S. Lee, Y.-S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9(4), 253–258 (2015).
[Crossref]

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J.-S. Lee, Y.-S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9(4), 253–258 (2015).
[Crossref]

Y. Choi, P. Hosseini, W. Choi, R. R. Dasari, P. T. So, and Z. Yaqoob, “Dynamic speckle illumination wide-field reflection phase microscopy,” Opt. Lett. 39(20), 6062–6065 (2014).
[Crossref] [PubMed]

Choi, Y.

Chu, S.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Claude Boccara, A.

P. Xiao, M. Fink, A. H. Gandjbakhche, and A. Claude Boccara, “A resolution insensitive to geometrical aberrations by using incoherent illumination and interference imaging,” Eur. Phys. J. Spec. Top. 226(7), 1603–1621 (2017).
[Crossref]

Culver, J. P.

Dasari, R. R.

de Boer, J. F.

de la Zerda, A.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Drexler, W.

B. Považay, A. Unterhuber, B. Hermann, H. Sattmann, H. Arthaber, and W. Drexler, “Full-field time-encoded frequency-domain optical coherence tomography,” Opt. Express 14(17), 7661–7669 (2006).
[Crossref] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, and H. Sattmann, “A thermal light source technique for optical coherence tomography,” Opt. Commun. 185(1-3), 57–64 (2000).
[Crossref]

Dubois, A.

Ducros, M.

Durduran, T.

Dutta, R.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Fainman, Y.

Fercher, A.

Fercher, A. F.

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27(16), 1415–1417 (2002).
[Crossref] [PubMed]

A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, and H. Sattmann, “A thermal light source technique for optical coherence tomography,” Opt. Commun. 185(1-3), 57–64 (2000).
[Crossref]

Fink, M.

P. Xiao, V. Mazlin, K. Grieve, J.-A. Sahel, M. Fink, and A. C. Boccara, “In vivo high-resolution human retinal imaging with wavefront-correctionless full-field OCT,” Optica 5(4), 409–412 (2018).
[Crossref]

P. Xiao, M. Fink, A. H. Gandjbakhche, and A. Claude Boccara, “A resolution insensitive to geometrical aberrations by using incoherent illumination and interference imaging,” Eur. Phys. J. Spec. Top. 226(7), 1603–1621 (2017).
[Crossref]

A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
[Crossref] [PubMed]

P. Xiao, M. Fink, and A. C. Boccara, “Full-field spatially incoherent illumination interferometry: a spatial resolution almost insensitive to aberrations,” Opt. Lett. 41(17), 3920–3923 (2016).
[Crossref] [PubMed]

Franke, G.

C. Pfäffle, H. Spahr, D. Hillmann, H. Sudkamp, G. Franke, P. Koch, and G. Hüttmann, “Reduction of frame rate in full-field swept-source optical coherence tomography by numerical motion correction [Invited],” Biomed. Opt. Express 8(3), 1499–1511 (2017).
[Crossref] [PubMed]

H. Sudkamp, P. Koch, H. Spahr, D. Hillmann, G. Franke, M. Münst, F. Reinholz, R. Birngruber, and G. Hüttmann, “In-vivo retinal imaging with off-axis full-field time-domain optical coherence tomography,” Opt. Lett. 41(21), 4987–4990 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Pfäffle, H. Sudkamp, G. Franke, and G. Hüttmann, “In vivo optical imaging of physiological responses to photostimulation in human photoreceptors,” Proc. Natl. Acad. Sci. U.S.A. 113(46), 13138–13143 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

D. Hillmann, T. Bonin, C. Lührs, G. Franke, M. Hagen-Eggert, P. Koch, and G. Hüttmann, “Common approach for compensation of axial motion artifacts in swept-source OCT and dispersion in Fourier-domain OCT,” Opt. Express 20(6), 6761–6776 (2012).
[Crossref] [PubMed]

T. Bonin, G. Franke, M. Hagen-Eggert, P. Koch, and G. Hüttmann, “In vivo Fourier-domain full-field OCT of the human retina with 1.5 million A-lines/s,” Opt. Lett. 35(20), 3432–3434 (2010).
[Crossref] [PubMed]

Fujimoto, J. G.

Gandjbakhche, A. H.

P. Xiao, M. Fink, A. H. Gandjbakhche, and A. Claude Boccara, “A resolution insensitive to geometrical aberrations by using incoherent illumination and interference imaging,” Eur. Phys. J. Spec. Top. 226(7), 1603–1621 (2017).
[Crossref]

Graf, R. N.

Grajciar, B.

Grieve, K.

Hagen-Eggert, M.

Hain, C.

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

Hee, M. R.

Hermann, B.

Hillmann, D.

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, and H. Sattmann, “A thermal light source technique for optical coherence tomography,” Opt. Commun. 185(1-3), 57–64 (2000).
[Crossref]

Hosseini, P.

Hüttmann, G.

C. Pfäffle, H. Spahr, D. Hillmann, H. Sudkamp, G. Franke, P. Koch, and G. Hüttmann, “Reduction of frame rate in full-field swept-source optical coherence tomography by numerical motion correction [Invited],” Biomed. Opt. Express 8(3), 1499–1511 (2017).
[Crossref] [PubMed]

H. Sudkamp, P. Koch, H. Spahr, D. Hillmann, G. Franke, M. Münst, F. Reinholz, R. Birngruber, and G. Hüttmann, “In-vivo retinal imaging with off-axis full-field time-domain optical coherence tomography,” Opt. Lett. 41(21), 4987–4990 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Hain, H. Sudkamp, G. Franke, C. Pfäffle, C. Winter, and G. Hüttmann, “Aberration-free volumetric high-speed imaging of in vivo retina,” Sci. Rep. 6(1), 35209 (2016).
[Crossref] [PubMed]

D. Hillmann, H. Spahr, C. Pfäffle, H. Sudkamp, G. Franke, and G. Hüttmann, “In vivo optical imaging of physiological responses to photostimulation in human photoreceptors,” Proc. Natl. Acad. Sci. U.S.A. 113(46), 13138–13143 (2016).
[Crossref] [PubMed]

D. Hillmann, T. Bonin, C. Lührs, G. Franke, M. Hagen-Eggert, P. Koch, and G. Hüttmann, “Common approach for compensation of axial motion artifacts in swept-source OCT and dispersion in Fourier-domain OCT,” Opt. Express 20(6), 6761–6776 (2012).
[Crossref] [PubMed]

T. Bonin, G. Franke, M. Hagen-Eggert, P. Koch, and G. Hüttmann, “In vivo Fourier-domain full-field OCT of the human retina with 1.5 million A-lines/s,” Opt. Lett. 35(20), 3432–3434 (2010).
[Crossref] [PubMed]

Izatt, J. A.

Jeong, S.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J.-S. Lee, Y.-S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9(4), 253–258 (2015).
[Crossref]

Joo, J. H.

S. Kang, S. Jeong, W. Choi, H. Ko, T. D. Yang, J. H. Joo, J.-S. Lee, Y.-S. Lim, Q. H. Park, and W. Choi, “Imaging deep within a scattering medium using collective accumulation of single-scattered waves,” Nat. Photonics 9(4), 253–258 (2015).
[Crossref]

Kang, S.

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Lerosey, G.

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Lew, M. D.

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A. Badon, D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry, “Smart optical coherence tomography for ultra-deep imaging through highly scattering media,” Sci. Adv. 2(11), e1600370 (2016).
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Liba, O.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
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Sticker, M.

A. F. Fercher, C. K. Hitzenberger, M. Sticker, E. Moreno-Barriuso, R. Leitgeb, W. Drexler, and H. Sattmann, “A thermal light source technique for optical coherence tomography,” Opt. Commun. 185(1-3), 57–64 (2000).
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C. Pfäffle, H. Spahr, D. Hillmann, H. Sudkamp, G. Franke, P. Koch, and G. Hüttmann, “Reduction of frame rate in full-field swept-source optical coherence tomography by numerical motion correction [Invited],” Biomed. Opt. Express 8(3), 1499–1511 (2017).
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Supplementary Material (2)

NameDescription
» Visualization 1       presents the ability of STOC manipulation to correct for image deformations caused by the tailored micro diffuser,
» Visualization 2       shows the ability of the STOC manipulation to suppress the speckle pattern

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Figures (14)

Fig. 1
Fig. 1 The cross-talk-generated noise is induced by high spatial coherence. (a) The optical fields from parallel detection channels (drawn schematically as tubes) are within the same coherence area A c . So, as shown in the second column, fields add coherently (red and blue waves produce a wave with larger amplitude), and intensities recorded by detector pixels (squares in the last column) contain cross-talk-generated noise, which is represented here as random spheres. (b) Contrary, for low spatially coherent light, fields from parallel detection channels are independent (each channel is within different coherence area,   A c,1 and A c,2 ). Thus, optical fields do not interfere, and the cross-talk-generated noise is absent.
Fig. 2
Fig. 2 Quantification of the spatial coherence with scattering coherency matrix, G. (a) When STOC manipulation is disabled, the spatial coherence is unchanged and high (non-diagonal G). In practice, blue lines (low values) in matrix G appear, when region used for matrix calculation contains pixels of zero values. (b) After enabling STOC manipulation, the low spatial coherence is synthesized. This is confirmed by a diagonal G.
Fig. 3
Fig. 3 Full-field swept-source optical coherence tomography supplemented by the STOC manipulation. (a) A light from the rapidly tunable laser ( λ=840 nm) is linearly polarized and split into the object and reference arms. Optical field in the object path is modulated in time by phase masks displayed on the spatial light modulator (SLM). The modulated light illuminates the sample covered by the layer inducing cross-talk-generated noise (Distorting Layer, DL). A light back-reflected from the sample is then recombined with the reference field and the resulting superposition is recorded by a two-dimensional camera. Abbreviations: SM – single mode optical fiber; C – collimator; P1 polarizer (0 degree polarization); BS1, BS2, BS3, BS4 – non-polarizing beam splitters (50:50); SLM – spatial light modulator; L1, L2, L3, L4, L5, L6, L7 – lenses; M1, M2 – flat mirrors; MOb – microscope objective; D1, D2 – diaphragms; DF – density filter; DL – distorting layer, DC – dispersion compensation module; * – conjugated planes. (b) Synchronization of light modulation with data acquisition. A phase mask is displayed on the spatial light modulator (SLM), and modulates the light from a tunable laser at every instantaneous wavelength ( λ 1 , λ 2 ,, λ 512 ) leading to the corresponding spectral fringe pattern recorded at the 2D camera. The above process is repeated for consecutive phase masks until the last phase mask is reached.
Fig. 4
Fig. 4 STOC manipulation suppresses the spatial coherence and improves spatial resolution. (a) Intensity images of the high-resolution resolution test chart with two ROIs (red line and yellow rectangle) used for further analysis. (b,c) High spatial frequency bars of the resolution test chart [yellow ROI in (a)] cannot be resolved when STOC is off but become clearly distinguishable after enabling STOC. Cross-sectional plots were obtained by averaging 3D plots from subfigure (b) along the x-direction. (d) The resulting improvement in spatial resolution is quantified with the width, σ of the Edge Spread Function [determined from red ROI in (a)]. As shown in figure titles, ESF width is reduced by a factor of 2 after enabling STOC manipulation.
Fig. 5
Fig. 5 STOC manipulation controls the degree of spatial coherence by varying the number of phase masks, M. (a) Intensity images with two rectangles showing ROIs used to calculate scattering coherency matrix G (b,c). For M<32, the intensity image contains speckle noise. The corresponding matrices G are not diagonal, which indicate the high degree of spatial coherence. For M32 this degree is reduced (diagonal G), so the speckle contrast in the corresponding intensity images is diminished.
Fig. 6
Fig. 6 Quantification of the speckle contrast in STOC manipulated FF-SS-OCT for the variable number of phase masks. (a) The intensity image with two ROIs used for calculations (red and yellow rectangles). Pixels from red ROI are used to determine mean signal intensity, I . Pixels from yellow ROI are used to calculate standard deviation, σ. (b) I and σ yield C=σ/ I for a variable number of phase masks M (red circles). These are compared to theoretical prediction of C( M )=C( 1 )/ M (black solid line).
Fig. 7
Fig. 7 Statistical analysis of the STOC-manipulated FF-SS-OCT intensities for the variable number of phase masks, M. (a) Images with red rectangle denoting the region used for statistical analysis. (b) Experimentally determined intensity histograms were fit with the modified Rician probability density function to estimate the standard deviation of the cross-talk-generated noise ( σ n ) and the useful signal intensity ( I d ). As M increases, the intensity distributions become narrower. Consequently, the noise quantified with σ n decreases, while the useful signal intensity, I d increases.
Fig. 8
Fig. 8 STOC manipulation controls the extent of the spatial coherence by varying the SLM block size R. (a) For R4×4, the intensity images do not change significantly. Contrary, for R>4×4, an additional regular, dark pattern appears. This pattern is due to diffraction from edges of the phase mask blocks. (b) The coherence area, which corresponds to the diagonal thickness of the scattering coherency matrix, starts to increase for R>4×4 due to larger spatial blocks that are manipulated. Larger blocks reduce the number of controllable degrees of freedom. (c) This behavior is also confirmed through intensity distributions, which become wider for R=6×6 and R=8×8. Red rectangles in subfigure (a) denote the region of interest which was used to determine matrix G and intensity distributions.
Fig. 9
Fig. 9 Quantification of the cross-talk-generated noise and useful signal for the variable number of phase masks, M and block size, R. The standard deviation of the noise, σ n decreases with M (a), while the ratio σ n (M=1)/ σ n (M=128) decrease with R (inset in a). The signal, I d expresses the opposite behavior and increases with M (b). The total intensity I T =2 σ n 2 + I d received by all channels approaches 1 [inset in (b)]. The maximum improvement in I d is observed for R4×4. Larger block sizes lead to a decrease in I T .
Fig. 10
Fig. 10 STOC manipulation in FF-SS-OCT imaging of the sample covered by diffusing and scattering phantoms. (a) The sample image is distorted due to high spatial coherence, which is represented as non-diagonal matrix G and wide intensity distributions. (b) The cross-talk noise is suppressed by STOC manipulation as confirmed by diagonal matrix G and narrow intensity distributions.
Fig. 11
Fig. 11 Characterization of wavefront deformations caused by the optical system (the first row), the TMD (second row) and the MSD (the third row).
Fig. 12
Fig. 12 STOC manipulation suppresses the cross-talk-generated noise in FF-SS-OCT (see Visualization 1 and Visualization 2). USAF test target covered by two different diffusers [TMD (a) and MSD (b)] was imaged without (STOC OFF) and with STOC manipulation (STOC ON). After enabling STOC manipulation image deformations (TMD) and speckles (MSD) are suppressed without any prior information about the distorting layer.
Fig. 13
Fig. 13 Qualitative analysis of the STOC performance for compensating image deformations (see Visualization 1). An undistorted reference FF-SS-OCT image of the sample [first column in (a)] was used to extract contours [first column in (b)]. The resulting contour map is overlaid on the distorted image to show that the TMD deforms and displaces sample features from their correct locations (STOC OFF). This effect can be corrected for by STOC manipulation (see STOC ON column).
Fig. 14
Fig. 14 STOC manipulation suppresses the cross-talk-generated noise in FF-SS-OCT imaging of the high-resolution 1951 USAF resolution chart covered by the 100 μm-thick rat skin ex vivo. (a) When STOC manipulation is disabled, the sample features hidden by the scattering layer cannot be seen due to cross-talk-generated noise. In that case, the scattering coherency matrix (middle column) is non-diagonal and the intensity distribution is wide (right column). (b) By enabling STOC manipulation we suppress the cross-talk-generated noise, so the previously hidden scrambled fragments of the sample become visible. Scattering coherency matrix is now diagonal (middle column) and the intensity distribution is narrow (right column). Red rectangle denotes the ROI used to determine scattering coherency matrix and intensity distributions.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

J( r 1 , r 2 )= U * ( r 1 ,t )U( r 2 ,t ) t  = lim T 1 T T 2 T 2 U * ( r 1 ,t )U( r 2 ,t )dt,
j( r 1 , r 2 )= J( r 1 , r 2 ) I( r 1 )I( r 2 ) ,
I=I( r 1 )+I( r 2 )+2 I( r 1 )I( r 2 ) | j( r 1 , r 2 ) |cos( α ),
U ~ ( r,t )=U( r,t )exp[ iφ(r,t) ],
J ~ ( r 1 , r 2 )= U * ( r 1 ,t )U( r 2 ,t )exp{ iΔφ( r 1 , r 2 ,t ) } t ,
J( r 1 , r 2 )I( r 1 )δ( r 1 r 2 ),
J ~ ( r 1 , r 2 )= U * ( r 1 ,t )U( r 2 ,t ) 1 M m=1 M e iΔφ( r 1 , r 2 , t m ) t .
1 M m=1 M exp{ iΔφ( r 1 , r 2 , t m ) }=δ( r 1 r 2 ).
J ~ ( r 1 , r 2 )= U * ( r 1 ,t )U( r 2 ,t )δ( r 1 r 2 ) t =I( r 1 )δ( r 1 r 2 ).
G=[ J ~ 11 J ~ 12 J ~ 1N J ~ 21 J ~ 22 J ~ 2N J ~ N1 J ~ N2 J ~ NN ]
m=1 M exp[ i φ k ( m ) ]exp[ i φ j ( m ) ]=M δ kj ,
G=[ I 1 0 0 0 I 2 0 0 0 I N ].
S( r,ω )= S DC ( r,ω )+2Re[ W rs ( r,ω )],
I( r,z )= F 1 { S( r,ω ) }= Γ rs ( r,z )+ Γ rs * (r,z),
Γ ~ rs ( r,z,t )= Γ rs ( r,z,t )exp[iφ( r,z,t )].
J( r 1 , r 2 )= Γ ~ rs * ( r 1 ,z,t ) Γ ~ rs ( r 2 ,z,t ) t = Γ rs * ( r 1 ,z,t ) Γ rs ( r 2 ,z,t ) e iΔφ( r 1 , r 2 ,z,t ) t
J( r 1 , r 2 )= Γ rs * ( r 1 ,z,t ) Γ rs ( r 2 ,z,t ) 1 M m=1 M e iΔφ( r 1 , r 2 ,z, t m ) t .
V ( m ) =[ Γ 11 ( m ) , Γ 12 ( m ) ,, Γ 1 N ( m ) , Γ 21 ( m ) , Γ 22 ( m ) ,, Γ 2 N ( m ) ,, Γ N N ( m ) ].
G= m=1 M ( V (m) ) V (m) ,
ESF( x )= a 2 [ 1+Erf( xμ 2 σ ) ],
PSF( x )= 1 2πσ exp[ ( xμ 2 σ ) 2 ].
p( I )= I σ n 2 exp{ I+ I d 2 σ n 2 } I 0 ( I I d σ n 2 ),