Abstract

Swept-laser sources offer a number of advantages for Phase-sensitive Optical Coherence Tomography (PhOCT). However, inter- and intra-sweep variability leads to calibration errors that adversely affect phase sensitivity. While there are several approaches to overcoming this problem, our preferred method is to simply calibrate every sweep of the laser. This approach offers high accuracy and phase stability at the expense of a substantial processing burden. In this approach, the Hilbert phase of the interferogram from a reference interferometer provides the instantaneous wavenumber of the laser, but is computationally expensive. Fortunately, the Hilbert transform may be approximated by a Finite Impulse-Response (FIR) filter. Here we explore the use of several FIR filter based Hilbert transforms for calibration, explicitly considering the impact of filter choice on phase sensitivity and OCT image quality. Our results indicate that the complex FIR filter approach is the most robust and accurate among those considered. It provides similar image quality and slightly better phase sensitivity than the traditional FFT-IFFT based Hilbert transform while consuming fewer resources in an FPGA implementation. We also explored utilizing the Hilbert magnitude of the reference interferogram to calculate an ideal window function for spectral amplitude calibration. The ideal window function is designed to carefully control sidelobes on the axial point spread function. We found that after a simple chromatic correction, calculating the window function using the complex FIR filter and the reference interferometer gave similar results to window functions calculated using a mirror sample and the FFT-IFFT Hilbert transform. Hence, the complex FIR filter can enable accurate and high-speed calibration of the magnitude and phase of spectral interferograms.

© 2016 Optical Society of America

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References

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2015 (1)

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” Proc. Natl. Acad. Sci. U.S.A. 112(10), 3128–3133 (2015).
[Crossref] [PubMed]

2014 (2)

S. S. Gao, R. Wang, P. D. Raphael, Y. Moayedi, A. K. Groves, J. Zuo, B. E. Applegate, and J. S. Oghalai, “Vibration of the organ of Corti within the cochlear apex in mice,” J. Neurophysiol. 112(5), 1192–1204 (2014).
[Crossref] [PubMed]

J. Park, E. F. Carbajal, X. Chen, J. S. Oghalai, and B. E. Applegate, “Phase-sensitive optical coherence tomography using an Vernier-tuned distributed Bragg reflector swept laser in the mouse middle ear,” Opt. Lett. 39(21), 6233–6236 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref] [PubMed]

2011 (4)

2010 (2)

2009 (6)

M. Szkulmowski, I. Grulkowski, D. Szlag, A. Szkulmowska, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation by complex ambiguity free joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 17(16), 14281–14297 (2009).
[Crossref] [PubMed]

M. Gora, K. Karnowski, M. Szkulmowski, B. J. Kaluzny, R. Huber, A. Kowalczyk, and M. Wojtkowski, “Ultra high-speed swept source OCT imaging of the anterior segment of human eye at 200 kHz with adjustable imaging range,” Opt. Express 17(17), 14880–14894 (2009).
[Crossref] [PubMed]

L. Thrane, H. E. Larsen, K. Norozi, F. Pedersen, J. B. Thomsen, M. Trojer, and T. M. Yelbuz, “Field programmable gate-array-based real-time optical Doppler tomography system for in vivo imaging of cardiac dynamics in the chick embryo,” Opt. Eng. 48(2), 023201 (2009).
[Crossref]

P. Levesque and M. Sawan, “Real-Time Hand-Held Ultrasound Medical-Imaging Device Based on a New Digital Quadrature Demodulation Processor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(8), 1654–1665 (2009).
[Crossref] [PubMed]

P. K. Meher, J. Valls, T.-B. Juang, K. Sridharan, and K. Maharatna, “50 years of CORDIC: Algorithms, architectures, and applications,” IEEE Trans. Circuits Syst. 56, 1893–1907 (2009).

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
[Crossref] [PubMed]

2008 (1)

H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
[Crossref]

2007 (2)

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

A. K. Ellerbee and J. A. Izatt, “Phase retrieval in low-coherence interferometric microscopy,” Opt. Lett. 32(4), 388–390 (2007).
[Crossref] [PubMed]

2005 (2)

2004 (1)

J. Rogowska, N. A. Patel, J. G. Fujimoto, and M. E. Brezinski, “Optical coherence tomographic elastography technique for measuring deformation and strain of atherosclerotic tissues,” Heart 90(5), 556–562 (2004).
[Crossref] [PubMed]

2003 (1)

2000 (1)

1998 (1)

1994 (1)

A. Reilly, G. Frazer, and B. Boashash, “Analytic Signal Generation - Tips and Traps,” IEEE Trans. Signal Process. 42(11), 3241–3245 (1994).
[Crossref]

Andersen, P. E.

H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
[Crossref]

Applegate, B. E.

Azeredo-Leme, C.

C. Azeredo-Leme, “Clock Jitter Effects on Sampling: A Tutorial,” IEEE Circuits Syst. Mag. 11(3), 26–37 (2011).
[Crossref]

Bajraszewski, T.

Barry, S.

Baumann, B.

Boashash, B.

A. Reilly, G. Frazer, and B. Boashash, “Analytic Signal Generation - Tips and Traps,” IEEE Trans. Signal Process. 42(11), 3241–3245 (1994).
[Crossref]

Boppart, S. A.

Bouma, B.

Bouma, B. E.

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
[Crossref] [PubMed]

Bower, B. A.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

Braaf, B.

Brezinski, M. E.

J. Rogowska, N. A. Patel, J. G. Fujimoto, and M. E. Brezinski, “Optical coherence tomographic elastography technique for measuring deformation and strain of atherosclerotic tissues,” Heart 90(5), 556–562 (2004).
[Crossref] [PubMed]

Cable, A. E.

Carbajal, E. F.

Chaney, E. J.

Chen, X.

Chen, Z.

Choi, W.

Choudhury, N.

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref] [PubMed]

de Boer, J.

de Boer, J. F.

Desjardins, A. E.

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
[Crossref] [PubMed]

Drexler, W.

Duker, J. S.

Ellerbee, A. K.

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” Proc. Natl. Acad. Sci. U.S.A. 112(10), 3128–3133 (2015).
[Crossref] [PubMed]

A. K. Ellerbee and J. A. Izatt, “Phase retrieval in low-coherence interferometric microscopy,” Opt. Lett. 32(4), 388–390 (2007).
[Crossref] [PubMed]

Fercher, A.

Frazer, G.

A. Reilly, G. Frazer, and B. Boashash, “Analytic Signal Generation - Tips and Traps,” IEEE Trans. Signal Process. 42(11), 3241–3245 (1994).
[Crossref]

Fujimoto, J.

Fujimoto, J. G.

Gao, S. S.

Gora, M.

Groves, A. K.

S. S. Gao, R. Wang, P. D. Raphael, Y. Moayedi, A. K. Groves, J. Zuo, B. E. Applegate, and J. S. Oghalai, “Vibration of the organ of Corti within the cochlear apex in mice,” J. Neurophysiol. 112(5), 1192–1204 (2014).
[Crossref] [PubMed]

Grulkowski, I.

Hornegger, J.

Hsu, K.

Huang, D.

Huber, R.

Izatt, J. A.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

A. K. Ellerbee and J. A. Izatt, “Phase retrieval in low-coherence interferometric microscopy,” Opt. Lett. 32(4), 388–390 (2007).
[Crossref] [PubMed]

Jacques, S. L.

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref] [PubMed]

Jayaraman, V.

Jorgensen, T. M.

H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
[Crossref]

Juang, T.-B.

P. K. Meher, J. Valls, T.-B. Juang, K. Sridharan, and K. Maharatna, “50 years of CORDIC: Algorithms, architectures, and applications,” IEEE Trans. Circuits Syst. 56, 1893–1907 (2009).

Kaluzny, B. J.

Karnowski, K.

Kowalczyk, A.

Kraus, M. F.

Larsen, H. E.

L. Thrane, H. E. Larsen, K. Norozi, F. Pedersen, J. B. Thomsen, M. Trojer, and T. M. Yelbuz, “Field programmable gate-array-based real-time optical Doppler tomography system for in vivo imaging of cardiac dynamics in the chick embryo,” Opt. Eng. 48(2), 023201 (2009).
[Crossref]

H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
[Crossref]

Lee, H. Y.

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” Proc. Natl. Acad. Sci. U.S.A. 112(10), 3128–3133 (2015).
[Crossref] [PubMed]

Leitgeb, R.

Levesque, P.

P. Levesque and M. Sawan, “Real-Time Hand-Held Ultrasound Medical-Imaging Device Based on a New Digital Quadrature Demodulation Processor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(8), 1654–1665 (2009).
[Crossref] [PubMed]

Liu, J. J.

Lu, C. D.

Maharatna, K.

P. K. Meher, J. Valls, T.-B. Juang, K. Sridharan, and K. Maharatna, “50 years of CORDIC: Algorithms, architectures, and applications,” IEEE Trans. Circuits Syst. 56, 1893–1907 (2009).

Meher, P. K.

P. K. Meher, J. Valls, T.-B. Juang, K. Sridharan, and K. Maharatna, “50 years of CORDIC: Algorithms, architectures, and applications,” IEEE Trans. Circuits Syst. 56, 1893–1907 (2009).

Moayedi, Y.

S. S. Gao, R. Wang, P. D. Raphael, Y. Moayedi, A. K. Groves, J. Zuo, B. E. Applegate, and J. S. Oghalai, “Vibration of the organ of Corti within the cochlear apex in mice,” J. Neurophysiol. 112(5), 1192–1204 (2014).
[Crossref] [PubMed]

Nelson, J. S.

Nguyen, C. T.

Nguyen-Huynh, A.

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref] [PubMed]

Nilsson, R. T.

H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
[Crossref]

Norozi, K.

L. Thrane, H. E. Larsen, K. Norozi, F. Pedersen, J. B. Thomsen, M. Trojer, and T. M. Yelbuz, “Field programmable gate-array-based real-time optical Doppler tomography system for in vivo imaging of cardiac dynamics in the chick embryo,” Opt. Eng. 48(2), 023201 (2009).
[Crossref]

Nuttall, A. L.

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref] [PubMed]

Oghalai, J. S.

Park, J.

Patel, N. A.

J. Rogowska, N. A. Patel, J. G. Fujimoto, and M. E. Brezinski, “Optical coherence tomographic elastography technique for measuring deformation and strain of atherosclerotic tissues,” Heart 90(5), 556–562 (2004).
[Crossref] [PubMed]

Pedersen, F.

L. Thrane, H. E. Larsen, K. Norozi, F. Pedersen, J. B. Thomsen, M. Trojer, and T. M. Yelbuz, “Field programmable gate-array-based real-time optical Doppler tomography system for in vivo imaging of cardiac dynamics in the chick embryo,” Opt. Eng. 48(2), 023201 (2009).
[Crossref]

H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
[Crossref]

Potsaid, B.

Raphael, P. D.

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” Proc. Natl. Acad. Sci. U.S.A. 112(10), 3128–3133 (2015).
[Crossref] [PubMed]

S. S. Gao, R. Wang, P. D. Raphael, Y. Moayedi, A. K. Groves, J. Zuo, B. E. Applegate, and J. S. Oghalai, “Vibration of the organ of Corti within the cochlear apex in mice,” J. Neurophysiol. 112(5), 1192–1204 (2014).
[Crossref] [PubMed]

S. S. Gao, P. D. Raphael, R. Wang, J. Park, A. Xia, B. E. Applegate, and J. S. Oghalai, “In vivo vibrometry inside the apex of the mouse cochlea using spectral domain optical coherence tomography,” Biomed. Opt. Express 4(2), 230–240 (2013).
[Crossref] [PubMed]

Reilly, A.

A. Reilly, G. Frazer, and B. Boashash, “Analytic Signal Generation - Tips and Traps,” IEEE Trans. Signal Process. 42(11), 3241–3245 (1994).
[Crossref]

Rogowska, J.

J. Rogowska, N. A. Patel, J. G. Fujimoto, and M. E. Brezinski, “Optical coherence tomographic elastography technique for measuring deformation and strain of atherosclerotic tissues,” Heart 90(5), 556–562 (2004).
[Crossref] [PubMed]

Sawan, M.

P. Levesque and M. Sawan, “Real-Time Hand-Held Ultrasound Medical-Imaging Device Based on a New Digital Quadrature Demodulation Processor,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56(8), 1654–1665 (2009).
[Crossref] [PubMed]

Saxer, C.

Schmetterer, L.

Schmitt, J.

Schuman, J. S.

Shelton, R. L.

Sicam, V. A. D. P.

Sridharan, K.

P. K. Meher, J. Valls, T.-B. Juang, K. Sridharan, and K. Maharatna, “50 years of CORDIC: Algorithms, architectures, and applications,” IEEE Trans. Circuits Syst. 56, 1893–1907 (2009).

Stewart, C. N.

Subhash, H. M.

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
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Trojer, M.

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Wojtkowski, M.

Xia, A.

Xiang, S.

Yelbuz, T. M.

L. Thrane, H. E. Larsen, K. Norozi, F. Pedersen, J. B. Thomsen, M. Trojer, and T. M. Yelbuz, “Field programmable gate-array-based real-time optical Doppler tomography system for in vivo imaging of cardiac dynamics in the chick embryo,” Opt. Eng. 48(2), 023201 (2009).
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Yun, S. H.

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Zawadzki, R.

Zhao, Y.

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S. S. Gao, R. Wang, P. D. Raphael, Y. Moayedi, A. K. Groves, J. Zuo, B. E. Applegate, and J. S. Oghalai, “Vibration of the organ of Corti within the cochlear apex in mice,” J. Neurophysiol. 112(5), 1192–1204 (2014).
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H. E. Larsen, R. T. Nilsson, L. Thrane, F. Pedersen, T. M. Jorgensen, and P. E. Andersen, “Optical Doppler tomography based on a field programmable gate array,” Biomed. Signal Process. Control 3(1), 102–106 (2008).
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IEEE Trans. Med. Imaging (1)

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
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J. Biomed. Opt. (2)

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

H. M. Subhash, A. Nguyen-Huynh, R. K. Wang, S. L. Jacques, N. Choudhury, and A. L. Nuttall, “Feasibility of spectral-domain phase-sensitive optical coherence tomography for middle ear vibrometry,” J. Biomed. Opt. 17(6), 060505 (2012).
[Crossref] [PubMed]

J. Neurophysiol. (1)

S. S. Gao, R. Wang, P. D. Raphael, Y. Moayedi, A. K. Groves, J. Zuo, B. E. Applegate, and J. S. Oghalai, “Vibration of the organ of Corti within the cochlear apex in mice,” J. Neurophysiol. 112(5), 1192–1204 (2014).
[Crossref] [PubMed]

Opt. Eng. (1)

L. Thrane, H. E. Larsen, K. Norozi, F. Pedersen, J. B. Thomsen, M. Trojer, and T. M. Yelbuz, “Field programmable gate-array-based real-time optical Doppler tomography system for in vivo imaging of cardiac dynamics in the chick embryo,” Opt. Eng. 48(2), 023201 (2009).
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Proc. Natl. Acad. Sci. U.S.A. (1)

H. Y. Lee, P. D. Raphael, J. Park, A. K. Ellerbee, B. E. Applegate, and J. S. Oghalai, “Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea,” Proc. Natl. Acad. Sci. U.S.A. 112(10), 3128–3133 (2015).
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Figures (12)

Fig. 1
Fig. 1

The proposed architecture for continuous real-time spectral calibration and linearization.

Fig. 2
Fig. 2

Block diagram illustrating several types of FIR filter approaches to generate an analytic signal (a): Delay element and Hilbert FIR approach (b): Bandpass and Hilbert FIR approach (c): complex FIR approach. In (a), Z-d is a delay element to delay an input signal by d samples and Hilbert FIR is Hilbert transform implemented by FIR filter. The complex FIR filter has two kinds of filter coefficients: real and imaginary coefficients which are described as Complex FIR - Real and Complex FIR - Imag in (c), respectively.

Fig. 3
Fig. 3

(a): The desired frequency response for complex FIR filter (b): The frequency response for the prototype LPF after left-shifting (a) by 0.25.

Fig. 4
Fig. 4

(a): The frequency spectrum of reference interferogram (b): the desired frequency spectrum of reference interferogram after complex FIR filtering.

Fig. 5
Fig. 5

Frequency spetra of three FIR approaches. (a): delay element and Hilbert FIR filter (b): bandpass and Hilbert FIR filter (c): complex FIR filter.

Fig. 6
Fig. 6

(a) Example reference interferogram overlaid with its Hilbert phase. The signal had a center frequency of 19.36 MHz and 0.0775 in digital frequency. (b) Reference interferograms in the frequency domain (c): filtered by delay element and Hilbert FIR approach (d): filtered by bandpass and Hilbert FIR approach (e): filtered by complex FIR approach. These spectra are obtained from 300 reference interferograms.

Fig. 7
Fig. 7

B-scan images of a mouse cochlea. (a): image from FFT-IFFT Hilbert transform (b): image from the delay element and Hilbert FIR approach (c): image from the bandpass and Hilbert FIR approach (d): image from the complex FIR approach. For reference the top of the images are near zero delay with digital frequency 0.024,and the bottom has a zero delay of 0.292.

Fig. 8
Fig. 8

Effect of spectral down-shifting of the reference signal: frequency spectra of the down-shifted reference signal (a) before filtering, (b) bandpass and Hilbert FIR approach and (c) complex FIR approach. A-scans from (d) FFT-IFFT Hilbert transform, (e) bandpass and Hilbert FIR approach and (f) complex FIR approach. Red arrow indicates an artifact that arises due to incomplete suppression of the negative frequencies in the bandpass and Hilbert FIR approach.

Fig. 9
Fig. 9

Frequency responses of displacement of a piezo, from (a) FFT-IFFT Hilbert transform (b) delay element and Hilbert FIR approach (c) bandpass and Hilbert FIR approach (d) complex FIR approach.

Fig. 10
Fig. 10

Frequency responses of displacement of a piezo, (a) from FFT-IFFT Hilbert transform (b) from complex FIR approach

Fig. 11
Fig. 11

Phase noise and B-scan image in accordance with filter order. (a) shows phase noise calculated by Root Mean Square (RMS) according to the filter order ranging from 4 to 40. (b), (c), (d), (e) show B-scan images in accordance with the filter order of 4, 8, 12 and 18, respectively.

Fig. 12
Fig. 12

Comparison of methods for calculating a custom window. (a): axial point spread functions from current and proposed procedures without chromatic correction (b): axial point spread functions from current and proposed procedures with chromatic correction. For comparison, the axial point spread function with no windowing is also shown.

Tables (1)

Tables Icon

Table 1 Comparison of device utilization of FPGA

Equations (10)

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I RI ( k(n) )= ρ 4 [ s(k( n ))( R 1 + R 2 )+2s(k(n)) R 1 R 2 cos( 2k(n) Δz RI ) ]
I RI ( n )=αA+Acos( 2k(n) Δz RI )
δ( n )+ jh Hilbert (n)
( αA+Acos( k(n) Δz RI ) )*( δ( n )+ jh Hilbert (n) )=αA+Acos( k(n) Δz RI )+jAsin( k(n) Δz RI )
tan 1 ( Asin( k(n) Δz RI ) αA+Acos( k(n) Δz RI ) )= tan 1 ( sin( k(n) Δz RI ) α+cos( k(n) Δz RI ) )
H[ h BPF (n) ] h Hilbert (n)
h LPF ( n ) e j2 πf 0 n = h LPF ( n )cos( 2 πf 0 n ) jh LPF ( n )sin( 2 πf 0 n )
( αA+Acos( k( n ) Δz RI ) )*( h Real ( n )+ jh Imag ( n ) )=Acos( k( n ) Δz RI )+jAsin( k( n ) Δz RI )
tan 1 ( sin( k(n) Δz RI ) cos( k(n) Δz RI ) )=k(n) Δz RI
I OCT ( n )= ρ 2 s(k(n)) R R R S cos( 2k( n ) Δz OCT )

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