Abstract

Realistic simulation of image formation in optical coherence tomography, based on Maxwell’s equations, has recently been demonstrated for sample volumes of practical significance. Yet, there remains a limitation whereby reducing the size of cells used to construct a computational grid, thus allowing for a more realistic representation of scatterer microstructure, necessarily reduces the overall sample size that can be modelled. This is a significant problem since, as is well known, the microstructure of a scatterer significantly influences its scattering properties. Here we demonstrate that an optimized scatterer design can overcome this problem resulting in good agreement between simulated and experimental images for a structured phantom. This approach to OCT image simulation allows for image formation for biological tissues to be simulated with unprecedented realism.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Corrections

20 June 2018: Typographical corrections were made to the funding section and acknowledgments.


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References

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2017 (2)

2016 (2)

P. R. T. Munro, “Three-dimensional full wave model of image formation in optical coherence tomography,” Opt. Express 24, 27016–27031 (2016).
[Crossref] [PubMed]

T. Brenner, D. Reitzle, and A. Kienle, “Optical coherence tomography images simulated with an analytical solution of Maxwell’s equations for cylinder scattering,” J. Biomed. Opt. 21, 45001 (2016).
[Crossref]

2015 (4)

2014 (2)

2011 (1)

2010 (2)

2008 (2)

I. Meglinski, M. Kirillin, V. Kuzmin, and R. Myllyla, “Simulation of polarization-sensitive optical coherence tomography images by a Monte Carlo method,” Opt. Lett. 33, 1581–1583 (2008).
[Crossref] [PubMed]

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[Crossref]

2007 (1)

2006 (2)

2004 (1)

2002 (1)

2000 (1)

1999 (1)

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44, 2307–2320 (1999).
[Crossref] [PubMed]

1998 (1)

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

1997 (1)

1995 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems ii. structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Almasian, M.

M. Almasian, N. Bosschaart, T. G. van Leeuwen, and D. J. Faber, “Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime,” J. Biomed. Opt. 20, 121314 (2015).
[Crossref]

Andersen, P. E.

Birngruber, R.

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Boppart, S. A.

Bosschaart, N.

M. Almasian, N. Bosschaart, T. G. van Leeuwen, and D. J. Faber, “Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime,” J. Biomed. Opt. 20, 121314 (2015).
[Crossref]

Brenner, T.

B. Krüger, T. Brenner, and A. Kienle, “Solution of the inhomogeneous Maxwell’s equations using a Born series,” Opt. Express 25, 25165–25182 (2017).
[Crossref]

T. Brenner, D. Reitzle, and A. Kienle, “Optical coherence tomography images simulated with an analytical solution of Maxwell’s equations for cylinder scattering,” J. Biomed. Opt. 21, 45001 (2016).
[Crossref]

Bukowska, D.

Carney, P. S.

Chen, Z.

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

Coupland, J. M.

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[Crossref]

Curatolo, A.

Derzsi, L.

Eljaszewicz, A.

Engelhardt, R.

Engelke, D.

Faber, D. J.

M. Almasian, N. Bosschaart, T. G. van Leeuwen, and D. J. Faber, “Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime,” J. Biomed. Opt. 20, 121314 (2015).
[Crossref]

Ferguson, R. A.

P. D. Woolliams, R. A. Ferguson, C. Hart, A. Grimwood, and P. H. Tomlins, “Spatially deconvolved optical coherence tomography,” Appl. Opt. 49, 2014–2021 (2010).
[Crossref] [PubMed]

P. H. Tomlins, R. A. Ferguson, C. Hart, and P. D. Woolliams, “Point-spread function phantoms for optical coherence tomography,” NPL Report OP2 (National Physical Laboratory, 2009).

Gan, X.

Garstecki, P.

Grimwood, A.

Gu, M.

Hart, C.

P. D. Woolliams, R. A. Ferguson, C. Hart, A. Grimwood, and P. H. Tomlins, “Spatially deconvolved optical coherence tomography,” Appl. Opt. 49, 2014–2021 (2010).
[Crossref] [PubMed]

P. H. Tomlins, R. A. Ferguson, C. Hart, and P. D. Woolliams, “Point-spread function phantoms for optical coherence tomography,” NPL Report OP2 (National Physical Laboratory, 2009).

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Johnson, S. G.

A. Oskooi and S. G. Johnson, “Accurate FDTD Simulation of Discontinuous Materials by Subpixel Smoothing,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House Antennas and Propagation Series, 2013), pp. 133–148.

Jorgensen, T. M.

Kennedy, B. F.

Kienle, A.

B. Krüger, T. Brenner, and A. Kienle, “Solution of the inhomogeneous Maxwell’s equations using a Born series,” Opt. Express 25, 25165–25182 (2017).
[Crossref]

T. Brenner, D. Reitzle, and A. Kienle, “Optical coherence tomography images simulated with an analytical solution of Maxwell’s equations for cylinder scattering,” J. Biomed. Opt. 21, 45001 (2016).
[Crossref]

Kirillin, M.

Knuttel, A.

Kriezis, E. E.

Krüger, B.

Kuzmin, V.

Lasser, T.

Lindmo, T.

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

Lobera, J.

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[Crossref]

Lu, Q.

Luo, Q.

Marks, D. L.

Martincek, I.

Meglinski, I.

Milner, T. E.

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

Munro, P. R. T.

Myllyla, R.

Nelson, J. S.

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

Oskooi, A.

A. Oskooi and S. G. Johnson, “Accurate FDTD Simulation of Discontinuous Materials by Subpixel Smoothing,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House Antennas and Propagation Series, 2013), pp. 133–148.

Ossowski, P.

Pan, Y.

Raiter-Smiljanic, A.

Ralston, T. S.

Reitzle, D.

T. Brenner, D. Reitzle, and A. Kienle, “Optical coherence tomography images simulated with an analytical solution of Maxwell’s equations for cylinder scattering,” J. Biomed. Opt. 21, 45001 (2016).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems ii. structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Rosperich, J.

Rumble, J.R.

J.R. Rumble, “CRC Handbook of Chemistry and Physics” (CRC, 2018)

Sampson, D. D.

Schmitt, J. M.

Sheppard, C.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Smithies, D. J.

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

Szkulmowska, A.

Tarjányi, N.

Thrane, L.

Tomlins, P. H.

P. D. Woolliams, R. A. Ferguson, C. Hart, A. Grimwood, and P. H. Tomlins, “Spatially deconvolved optical coherence tomography,” Appl. Opt. 49, 2014–2021 (2010).
[Crossref] [PubMed]

P. H. Tomlins, R. A. Ferguson, C. Hart, and P. D. Woolliams, “Point-spread function phantoms for optical coherence tomography,” NPL Report OP2 (National Physical Laboratory, 2009).

Török, P.

Turek, I.

Tycho, A.

van Leeuwen, T. G.

M. Almasian, N. Bosschaart, T. G. van Leeuwen, and D. J. Faber, “Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime,” J. Biomed. Opt. 20, 121314 (2015).
[Crossref]

Villiger, M.

Wang, L. V.

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44, 2307–2320 (1999).
[Crossref] [PubMed]

Wiese, M.

Wilson, T.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Wojtkowski, M.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems ii. structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Woolliams, P. D.

P. D. Woolliams, R. A. Ferguson, C. Hart, A. Grimwood, and P. H. Tomlins, “Spatially deconvolved optical coherence tomography,” Appl. Opt. 49, 2014–2021 (2010).
[Crossref] [PubMed]

P. H. Tomlins, R. A. Ferguson, C. Hart, and P. D. Woolliams, “Point-spread function phantoms for optical coherence tomography,” NPL Report OP2 (National Physical Laboratory, 2009).

Yao, G.

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44, 2307–2320 (1999).
[Crossref] [PubMed]

Yura, H. T.

Appl. Opt. (4)

Biomed. Opt. Express (1)

J. Biomed. Opt. (2)

T. Brenner, D. Reitzle, and A. Kienle, “Optical coherence tomography images simulated with an analytical solution of Maxwell’s equations for cylinder scattering,” J. Biomed. Opt. 21, 45001 (2016).
[Crossref]

M. Almasian, N. Bosschaart, T. G. van Leeuwen, and D. J. Faber, “Validation of quantitative attenuation and backscattering coefficient measurements by optical coherence tomography in the concentration-dependent and multiple scattering regime,” J. Biomed. Opt. 20, 121314 (2015).
[Crossref]

J. Opt. Soc. Am. A (5)

Meas. Sci. Technol. (1)

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[Crossref]

Opt. Express (8)

P. R. T. Munro and P. Török, “Calculation of the image of an arbitrary vectorial electromagnetic field,” Opt. Express 15, 9293–9307 (2007).
[Crossref] [PubMed]

A. Curatolo, B. F. Kennedy, and D. D. Sampson, “Structured three-dimensional optical phantom for optical coherence tomography,” Opt. Express 19, 19480–19485 (2011).
[Crossref] [PubMed]

P. R. T. Munro, D. Engelke, and D. D. Sampson, “A compact source condition for modelling focused fields using the pseudospectral time-domain method,” Opt. Express 22, 5599–5613 (2014).
[Crossref] [PubMed]

P. R. T. Munro, A. Curatolo, and D. D. Sampson, “Full wave model of image formation in optical coherence tomography applicable to general samples,” Opt. Express 23, 2541–2556 (2015).
[Crossref] [PubMed]

P. Ossowski, A. Raiter-Smiljanic, A. Szkulmowska, D. Bukowska, M. Wiese, L. Derzsi, A. Eljaszewicz, P. Garstecki, and M. Wojtkowski, “Differentiation of morphotic elements in human blood using optical coherence tomography and a microfluidic setup,” Opt. Express 23, 27724–27738 (2015).
[Crossref] [PubMed]

P. R. T. Munro, “Exploiting data redundancy in computational optical imaging,” Opt. Express 23, 30603–30617 (2015).
[Crossref] [PubMed]

P. R. T. Munro, “Three-dimensional full wave model of image formation in optical coherence tomography,” Opt. Express 24, 27016–27031 (2016).
[Crossref] [PubMed]

B. Krüger, T. Brenner, and A. Kienle, “Solution of the inhomogeneous Maxwell’s equations using a Born series,” Opt. Express 25, 25165–25182 (2017).
[Crossref]

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Med. Biol. (2)

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998).
[Crossref] [PubMed]

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44, 2307–2320 (1999).
[Crossref] [PubMed]

Proc. Roy. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems ii. structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253, 358–379 (1959).
[Crossref]

Other (5)

J.R. Rumble, “CRC Handbook of Chemistry and Physics” (CRC, 2018)

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

A. Oskooi and S. G. Johnson, “Accurate FDTD Simulation of Discontinuous Materials by Subpixel Smoothing,” in Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, A. Taflove, A. Oskooi, and S. G. Johnson, eds. (Artech House Antennas and Propagation Series, 2013), pp. 133–148.

P. H. Tomlins, R. A. Ferguson, C. Hart, and P. D. Woolliams, “Point-spread function phantoms for optical coherence tomography,” NPL Report OP2 (National Physical Laboratory, 2009).

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

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Figures (12)

Fig. 1
Fig. 1 Schematic diagram of the modelled OCT system and the model itself. Sill and Sdet represent the planar surfaces upon which the illumination is introduced and the scattered field is detected, respectively. Scattering in free space is simulated by using a perfectly matched layer (PML) which absorbs incident radiation with very low reflection.
Fig. 2
Fig. 2 Schematic representation of the OBEL phantom, showing its orientation relative to the OCT objective (left) along with a typical B-scan of the phantom.
Fig. 3
Fig. 3 Three different discrete approximations to a sphere of diameter 1μm using cubic elements of width λ0/6 (red) with a rendering of an ideal sphere of diameter 1μm (blue) superimposed. We refer to a), b) and c) as discretisations 1, 2 and 3, respectively.
Fig. 4
Fig. 4 Plots of g (left) and μs (right) within the OCT system’s spectrum for discretisations 1, 2 and 3 and the optimized design.
Fig. 5
Fig. 5 Plot of ( n ) versus the number of PSTD simulations executed during execution of optimization algorithm.
Fig. 6
Fig. 6 The optimized scatterer design, n opt, at non-negative PSTD cell indices. The complete scatterer design can be obtained by noting that the refractive index of cell (i, j, k) is equal to that of (|i|, |j|, |k|).
Fig. 7
Fig. 7 Comparison of B-scans of the OBEL and PSF phantoms displayed on an SNR scale ranging from 0 to 60 dB.
Fig. 8
Fig. 8 Plots of data extracted from the PSF phantom. a) Shows the average lateral FWHM of point objects as a function of axial location. The error bars span two standard deviations. b) Shows the average of measured lateral PSFs located within the region |zzref − 400μm| < 20μm with error bars spanning two-standard deviations along with the simulated in-focus lateral PSF. c) Shows the average of axial PSFs of the same point objects considered in b) along with the simulated axial PSF. The error bars span a total of two standard deviations.
Fig. 9
Fig. 9 Comparison between experimental (left) and simulated (right) images of the OBEL phantom. The lower image in each column is an expanded view of the region bounded by a red rectangle in the full image of the same column. The white right-angle in each image denotes 50μm. The blue rectangle in the expanded images denotes the region used to calculate the autocovariance plots in Fig. 10. The axial dimension is scaled to physical distance in both cases.
Fig. 10
Fig. 10 Plots of normalized autocovariance along the axial and transverse directions, for simulated and experimental phantoms.
Fig. 11
Fig. 11 Histograms of pixel values for the experimental and simulated images. Pixels were taken from the top 35μm of the image occupied by the letters, as is illustrated in the right image. a) Shows the histogram when the entire rectangular region depicted in the right image is considered. b) Shows the histogram when only pixels falling within the stencil of the letters are considered and c) shows an amplitude probability distribution (p(|A|)) of the noise-free simulated pixels from within the ROI (indicated by yellow boxes), along with a fitted Rayleigh distribution.
Fig. 12
Fig. 12 The left plot contains averaged A-scan intensities for different arrangements of the modelled TiO2 scatterers and particles with a low scattering cross-section in order to produce a calibration A-scan. The right plot presents a plot of the ratio between the two plots from the left axis along with an exponential fit to this data.

Equations (8)

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

J * ( t ) = { k ^ × e ill ( r 3 , k 0 ) exp ( i ω 0 ( t t 0 ) ) exp ( π ( ( t t 0 ) / W ) 2 ) } ,
H y t = 1 μ [ E x z J y * ] E x t = 1 H y z ,
H y | τ + Δ t / 2 H y | τ Δ t / 2 Δ t = 1 μ [ E x z J y * ] | τ H y | τ + Δ t / 2 = Δ t μ [ E x z J y * ] | τ + H y | τ Δ t / 2 ,
α tot ( k ) = S det ( T e ill ( r 3 , z det , k ) ) ( T e tot ( r 3 , z det , k ) ) d 2 r 3
i ( k ) | α tot ( k ) α ill ( k ) + α ref ( k ) α ill ( k ) | 2 ,
n ( k ) = η i ( k ) ,
A ( z 3 z ref ) = 1 2 π 0 S ( k ) n ˜ ( k ) exp ( i k 2 ( z 3 z ref ) ) d k ,
( n ) = m = 1 N λ S ( λ m ) i j k F | ν ^ i j k A i j k 3 l = i , j , k ( S ˜ l ( n , λ m ) S l ( λ m ) ) | 2 i j k F | ν ^ i j k A i j k 3 l = i , j , k S l ( λ m ) | 2