## Motion artifacts in optical coherence tomography with frequency-domain ranging

Optics Express, Vol. 12, Issue 13, pp. 2977-2998 (2004)

http://dx.doi.org/10.1364/OPEX.12.002977

Acrobat PDF (672 KB)

### Abstract

We describe results of theoretical and experimental investigations of artifacts that can arise in spectral-domain optical coherence tomography (SD-OCT) and optical frequency domain imaging (OFDI) as a result of sample or probe beam motion. While SD-OCT and OFDI are based on similar spectral interferometric principles, the specifics of motion effects are quite different because of distinct signal acquisition methods. These results provide an understanding of motion artifacts such as signal fading, spatial distortion and blurring, and emphasize the need for fast image acquisition in biomedical applications.

© 2004 Optical Society of America

## 1. Introduction

4. S. K. Nadkarni, D. R. Boughner, M. Drangova, and A. Fenster, “In vitro simulation and quantification of temporal jitter artifacts in ECG-gated dynamic three-dimensional echocardiography,” Ultrasound in Med. & Biol. **27**, 211–222 (2001). [CrossRef]

5. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science **254**, 1178–1181 (1991). [CrossRef] [PubMed]

6. J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Optical biopsy and imaging using optical coherence tomography,” Nat. Medicine **1**, 970–972 (1995). [CrossRef]

7. R. C. Youngquist, S. Carr, and D. E. N. Davies, “Optical coherence-domain reflectometry: A new optical evaluation technique,” Opt. Lett. , **12**, 158–160 (1987). [CrossRef] [PubMed]

8. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurements of intraocular distances by backscattering spectral interferometry,” Opt. Comm. **117**, 43–48 (1995). [CrossRef]

12. N. Nassif, B Cense, B. H. Park, S. H. Yun, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express **12**, 367–376 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-367 [CrossRef] [PubMed]

13. F. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. **36**, 6548–6553 (1997). [CrossRef]

16. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express **11**, 2953–2963 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2953 [CrossRef] [PubMed]

16. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express **11**, 2953–2963 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2953 [CrossRef] [PubMed]

21. N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,” Opt. Lett. **29**, 480–482 (2004). [CrossRef] [PubMed]

## 2. Spectral-Domain Optical Coherence Tomography (SD-OCT)

### 2.1 Theory

#### 2.1.1 Principle of operation

*k*=2

*π*/

*λ*where

*λ*is the optical wavelength. A discrete Fourier transform (DFT) of the CCD scan output produces an axial reflectance profile of the sample (A-line). A 2-D tomographic image is obtained by acquiring multiple A-lines as the probe beam is scanned over the sample along a transverse direction.

*T*, of the CCD. The A-line acquisition time

*T*becomes equal to the A-line period if the CCD is operated with a 100% duty cycle. The photocurrent associated with the fringes arising from interference between the reference and sample light can be expressed as [8

8. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurements of intraocular distances by backscattering spectral interferometry,” Opt. Comm. **117**, 43–48 (1995). [CrossRef]

24. J. M. Schmitt and A. Knuttel, “Model of optical coherence tomography of heterogeneous tissue,” J. Opt. Soc. Am. A **14**, 1231–1242 (1997). [CrossRef]

*S*

_{r}(

*k*) and

*S*

_{s}(

*k*) denote the spectral power density of the reference arm and sample arm light,

*γ*is the photon-to-electron conversion efficiency, Re{} denotes the real part (neglected hereinafter for simplicity), (

*x*,

*y*,

*z*) denote the coordinate of a reference frame fixed to the sample,

*r*(

*x*,

*y*,

*z*) represents the complex-valued backscattering coefficient of the sample which is characterized by both local variations of the refractive index and the round-trip attenuation of light in the sample,

*g*(

*x*,

*y*,

*z*) denotes the intensity profile of the probe beam normalized to ∬

*g*

*dxdy*=1, (

*x*

_{b},

*y*

_{b}) denote the transverse coordinates of the probe beam in the sample, and

*z*

_{b}denotes the longitudinal coordinate of the zero path length point of the interferometer. For a Gaussian beam with a large confocal parameter, the intensity profile is given by

*w*

_{0}denotes the full-width-half-maximum (FWHM) of the beam profile. In Eq. (1), the explicit dependence on the intensity profile,

*g*, rather than an electric field profile of the probe beam can be understood by considering the mode field profile of the sample arm fiber, which is by definition given by Eq. (2) at the sample location. The amplitude of the backscattered light received by the sample arm fiber is determined by an overlap integral between the scattered field and the mode field, resulting in the dependence on the intensity beam profile in Eq. (1).

*T*gives the number of electrons as

*k*

_{0}is the center wavenumber of the light source and Δ

*k*is FWHM spectral width in wavenumber, we get

*δz*

_{0}=4ln2/Δ

*k*denotes the axial resolution [25

25. E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “1,” Opt. Lett. **17**, 151–153 (1992). [CrossRef] [PubMed]

*F*(

*Z*) is proportional to a coherent sum of all backscattered light generated from a coherence volume at

*Z*=

*z*with a size given by the probe beam area and coherence length of the light source.

## 2.1.2 Axial motion

*r*(

*x*,

*y*,

*z*)=

*r*(

*x*,

*y*)

*δ*(

*z*-

*z*(

*x*,

*y*)). As a result of the axial motion,

*z*

_{b}is no longer a constant but is given by

*z*

_{b}-

*v*

_{z}

*t*where

*v*

_{z}denotes the axial velocity of the sample. The backscattering amplitude

*r*(

*x*,

*y*,

*z*) is invariant as we assume that the scattering layer is under rigid motion. For a sample consisting of multiple internal structures moving at different velocities between each other, the analysis described here can be extended simply by applying it to individual structures separately.

*N*

_{0}denotes the number of signal electrons obtained at

*v*

_{z}=0, and Δ

*z*=|

*v*

_{z}

*T*| is the amount of axial displacement of the sample during the integration time

*T*. Equations 7 and 8 imply two motion-induced phenomena. First, in performing the Fourier transform of Eq. (8) via. Eq. (4), the factor sin(

*k*Δ

*z*)/(

*k*Δ

*z*) can be approximated by a constant sin(

*k*

_{0}Δ

*z*)/(

*k*

_{0}Δ

*z*) in the case of |Δ

*z*|≪|

*z*-

*z*

_{b}|. Therefore, Eq. (8) asserts that the axial motion gives rise to an SNR penalty by a factor of sin

^{2}(

*k*

_{0}Δ

*z*)/(

*k*

_{0}Δ

*z*)

^{2}. The SNR penalty can be understood in terms of the fringe washout due to the continuous phase change of fringes during the integration time. Second, when

*k*Δ

*z*≫1 broadening of the axial resolution arises because the Sinc function in Eq. (7) limits the effective spectral bandwidth. This effect may be described as a convolution of the original image with a rect function given by the Fourier transform of the sinc function.

## 2.1.3 Transverse motion

*x*. Without loss of generality, we will assume a stationary probe again and consider a scattering layer (sample) moving at constant velocity

*v*

_{x}. Replacing

*x*

_{b}to

*x*

_{b}-

*v*

_{x}

*t*in Eq. (3) we get

*g*to

*G*defined in Eq. (11).

*G*(

*x*,

*y*) is referred to as the effective beam profile and represents the amount of beam exposure at the location (

*x*,

*y*). Physically,

*G*(

*x*,

*y*) represents an enlarged area illuminated by the probe beam during the integration time. Examples of the effective beam profile are shown in Fig. 3(a) for the Gaussian probe beam defined in Eq. (2).

*G*(

*x*,

*y*=0) is shown for four different values of the transverse displacement, Δ

*x*=|

*v*

_{x}

*T*|, normalized to the beam size,

*w*

_{0}. The area of the profile is conserved i.e. ∬

*G dxdy*=∬

*g dxdy*.

## 2.2. Experiments

### 2.2.1 SD-OCT system

*w*

_{0}=18 µm. The spectrometer consisted of a diffraction grating, focusing lens, and InGaAs line scan camera (LSC) with a 512-pixel CCD array. The output of the camera was digitized using a 12-bit data acquisition board (DAQ). The acquired data were interpolated to correct for nonlinearity in

*k*-space and processed via a DFT to produce images. The camera was operated at a readout rate of 18.94 kHz with an integration time of 24.4 µs (46% duty cycle). The sensitivity of the SD-OCT system was measured to be greater than 105 dB over a depth range of 2 mm. The free-space axial resolution was measured to be between 12 and 14 µm FWHM over the depth range of 2 mm. The operating conditions and performance of the system are described in detail in Ref. 11.

## 2.2.2 Axially moving mirror

^{2}(

*k*

_{0}Δ

*z*)/(

*k*

_{0}Δ

*z*)

^{2}where Δ

*z*was calculated by assuming a perfect sinusoidal oscillation of the speaker with the measured amplitude of 1.76 mm and frequency of 40 Hz. The theoretical curve agrees well with the experimental results. Harmonic distortion in the speaker motion and a depth-dependent reflectivity of the mirror due to finite confocal parameter of the probe beam may account for the slight offset in the peak positions and dissimilar peak values compared to the experimental curve. Figures 5(c) and (d) show the results of a similar experiment conducted for a mirror displacement amplitude of 0.22 mm and frequency of 80 Hz.

## 2.2.3 Transverse beam scanning

*x*/

*w*

_{0}=0.19 [V

^{-1}]. Images obtained at 10 and 20 V exhibit significant blurring particularly along the transverse direction and exhibit disconnected surface lines.

26. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. **4**, 95–105 (1999). [CrossRef] [PubMed]

*x*/

*w*

_{0}=4. One may anticipate that the FWHM should increase with increasing Δ

*x*/

*w*

_{0}simply because the probe beam moves over a slanted surface. However, because our sample had a relatively large scatterer size of approximately 15 µm, only a few to several scatterers might be illuminated during a single A-line acquisition at Δ

*x*/

*w*

_{0}up to 4. Apparently in the A-line with the minimum FWHM, a single scatterer generated a dominant signal over the others. In this case, the FWHM would be expected to have a value similar to the intrinsic axial resolution of the SD-OCT system. The flat line (blue) at 13 µm represents the mean axial resolution of the system measured with a stationary mirror sample.

_{0}=0.25. At this low value, the previous results in Fig. 7 predict that the SNR decrease and resolution broadening should be negligible. Indeed, no signature of such degradation is seen in Fig. 8. The skin fold region with steep structural lines appears as sharp as other areas, despite a depth change by several hundreds optical wavelengths during a single A-line acquisition time.

## 2.3 Discussion

*in vivo*. The main causes include patient motion, physiological phenomena such as cardiac motion, blood flow, pulsation, and catheter movement associated with beam scanning or uncontrolled movement of operator’s hand. Furthermore, environmental changes such as mechanical vibration, sound waves, and temperature drift can alter the path length difference in the interferometer, resulting in SNR degradation through fringe washout. The SNR penalty from fringe washout is given by sin

^{2}(

*k*

_{0}Δ

*z*)/(

*k*

_{0}Δ

*z*)

^{2}. An SNR margin of 10 dB limits Δ

*z*to be less than 0.37

*λ*

_{0}. This is equal to 0.48 µm for

*λ*

_{0}=1.3 µm and corresponds to 19.7 mm/s in velocity for

*T*=24.4 µs. This value may be large enough so that the effect of typical environmental changes or slow patient motion is negligible. However, fast physiological motions such as the cardiac motion in cardiovascular imaging may cause a significant SNR penalty. The maximum velocity of heart motion can be as high as 100 mm/s [27

27. S.-M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart **86**, 432–437 (2001). [CrossRef] [PubMed]

*in vivo*[28

28. M. V. Sivak Jr., K. Kobayashi, J. A. Izatt, A. M. Rollins, R. Ung-runyawee, A. Chak, R. C. K. Wong, G. A. Isenbert, and J. Willis, “High-resolution Endoscopic imaging of the GI tract using optical coherence tomography,” Gastrointest. Endosc. **51**, 474–479 (2000). [CrossRef] [PubMed]

29. G. J. Tearney, H. Yabushita, S. L. Houser, H. T. Aretz, I. K. Jang, K. Schlendorf, C. R. Kauffman, M. Shishkov, E. F. Halpern, and B. E. Bouma, “Quantification of macrophage content in atherosclerotic plaques by optical coherence tomography,” Circulation **106**, 113–119 (2003) [CrossRef]

*x*/

*w*

_{0}=1. For the SD-OCT system used in this study, the parameters

*w*

_{0}=18 µm,

*T*=24.4 µs, and 46 % duty cycle require that the shift of the probe beam during the A-line period should be less than 39 µm. This requirement puts a limit on the minimum number of A-lines that need to be acquired per image during one revolution of the catheter. A ranging depth of 4 mm requires a minimum of 644 A-lines per image.

## 3. Optical Frequency Domain Imaging (OFDI)

### 3.1 Theory

#### 3.1.1 Principle of operation

*k*(

*t*)=

*k*

_{0}+

*k*

_{1}

*t*, where

*k*=2

*π*/

*λ*is the wavenumber,

*λ*is the optical wavelength,

*t*is the time spanning from -

*T*/2 to

*T*/2, and

*T*is the tuning period or equivalently A-line period. Further we assume a Gaussian tuning envelope given by

*P*

_{out}(

*t*) denotes the output power of the source and σ

*T*the full width at half maximum (FWHM) of the tuning envelope. Equation (12) also describes the Gaussian spectral envelope of the source, where σ

*k*

_{1}

*T*corresponds to the FWHM tuning range in wavenumber.

*r*(

*x*,

*y*,

*z*) denote the backscattering amplitude of the sample at the point (

*x*,

*y*,

*z*) in a reference frame fixed to the sample characterized by refractive index variations and roundtrip attenuation by absorption and scattering. For a singly reflected sample, the photocurrent generated from the interference between the reference and sample light can be expressed as

*P*

_{r}(

*t*) denotes the optical power returned from the reference arm,

*P*

_{s}(

*t*) the optical power returned from the sample arm when a sample with 100% reflection is used,

*γ*is the photon-to-electron conversion efficiency, The real-part operator, Re{}, will be neglected hereinafter for simplicity, (

*x*

_{b},

*y*

_{b},

*z*

_{b}) denotes the coordinates of the probe beam at zero path length difference of the interferometer, and

*g*(

*x*,

*y*,

*z*) is the normalized intensity profile of the probe beam [Eq. (2)].

*κ*=2

*k*

_{1}

*t*yields a complex-valued depth profile (A-line):

^{2}<1, we can approximate the range of the integral to [-∞,∞], which results in

*δz*

_{0}=4ln 2/(

*k*

_{1}

*T*σ) denotes the FWHM axial resolution neglecting the effect of truncation of a Gaussian spectrum. Equation (17) states that the amplitude of

*F*(

*Z*) is proportional to a coherent sum of all backscattered light from a coherence volume that has a size

*w*

_{0}×

*w*

_{0}×

*δz*

_{0}and is located at a depth

*Z*in the sample.

## 3.1.2 Axial motion

*z*

_{b}(

*t*)=

*z*-

*z*

_{0}-

*v*

_{z}

*t*into Eq. (13) where

*z*

_{0}=

*z*-

*z*

_{b}(0) denotes the mean path length difference, and

*v*

_{z}the axial velocity of the sample. The depth profile is obtained via the Fourier transform:

*z*=

*v*

_{z}

*T*denotes the axial displacement of the sample during a single A-line acquisition time. Equation (18) illustrates two effects of axial motion. First, the depth in the image is given by

*z*

_{D}, originates from the Doppler frequency shift generated by the moving sample. A moving sample would create a signal modulation even in the absence of tuning with the Doppler frequency given by

*kv*

_{z}/

*π*. For wavelength-swept light, the Doppler frequency is added to the original modulation frequency of the OFDI signal, resulting in an erroneous depth offset. Typical values for σ and

*δz*

_{0}/

*λ*may be 0.5–0.8 and 4–12, respectively. Therefore, the Doppler error could be 5 to 22 times the actual displacement Δ

*z*. The second effect is broadening in axial resolution, given by

*κ*

^{2}term in the phase in Eq. (17). Even a modest displacement equal to the unperturbed axial resolution, i.e. Δ

*z*=

*δz*

_{0}, could result in a 70% broadening for

*σ*=0.71.

## 3.1.3 Transverse motion

*v*

_{x}. Substituting x

_{b}(t)=x

_{b}-v

_{x}t in Eq. (13), we get

*x*=

*v*

_{x}

*T*denotes the transverse displacement of the sample during the acquisition of a single A-line. Performing a Fourier transform, we get

*κ*can find an approximate solution which yields

*x*/

*w*

_{0}for

*σ*=0.71. The broadening in transverse resolution is obvious because the effective size of the probe beam is increased by the transverse motion. The broadening in axial resolution occurs because the spectral width that each scattering point on the sample experiences during a single A-line acquisition is reduced as a result of the transverse motion. For a mirror-like sample, represented by

*r*(

*x*,

*y*,

*z*)=

*r*

_{0}

*δ*(

*z*), Eq. (23) can be readily solved by performing the space integration first to show that both transverse and axial resolution are invariant as anticipated since the beam scanning over a mirror does not alter the signal. Equations (24) and (25) are valid for a random scattering sample.

*F*

_{s}(

*z*)|

^{2}/|

*F*

_{n}(

*z*)|

^{2}where

*F*

_{s}(

*z*) and

*F*

_{n}(

*z*) denote the signal and noise components, respectively, obtained from a DFT of signal and noise photocurrents via Eq. (14). The change in SNR by motion depends on the specific type of a sample. For a mirror-like sample, SNR is invariant since the transverse motion does not alter the signal and noise, as can be derived from Eq. (23). For a single point scatterer sample expressed as

*r*(

*x*,

*y*,

*z*)=

*r*

_{0}

*δ*(

*x*)

*δ*(

*y*)

*δ*(

*z*), it can be shown from Eq. (24) that the SNR decrease is given by (1+

*σ*

^{2}Δ

*x*

^{2}/

^{-1}. For a bulk random scattering medium which leads to a fully-developed speckle [26

26. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. **4**, 95–105 (1999). [CrossRef] [PubMed]

*x*-

*y*or

*y*-

*z*plane, the SNR is given by (1+

*σ*

^{2}Δ

*x*

^{2}/

^{-0.5}. The scattering property of actual biological sample may vary between a point scatterer and bulk homogenous random scattering medium. Therefore, we may expect that the SNR decrease for a biological sample may be given by

*α*ranges from 0 to 1 depending on the sample. Figure 10(b) depicts the SNR decrease for three different

*α*values.

*σT*is equal to the FWHM width of optical intensity profile and, therefore, can be interpreted as an effective integration time of the signal. This accounts for the appearance of

*σ*in Eqs. (20), (21), (25) and (26) since Δ

*z*and Δ

*x*were defined as total displacements integrated over the entire A-line acquisition time of

*T*rather than

*σT*.

## 3.1.4 Nonlinear tuning slope

*k*-space. In this case, the wavenumber can be expressed as a Taylor series of time i.e.

*k*(

*t*)=Σ

*k*

_{m}

*t*

^{m}where

*m*=0, 1, 2… It is well known that nonlinear sampling in

*k*-space gives rise to a poor spatial resolution [23

23. E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. **26**, 413–414 (1990). [CrossRef]

*k*-space. Alternatively, the detector output may be sampled with a uniform time interval, and subsequently the acquired data is re-sampled by interpolation to a uniform spacing in

*k*-space. This method is commonly implemented in practice. Mathematically, both methods are equivalent to a coordinate transform from

*t*to a normalized time variable

*τ*, defined as:

*τ*spans from -0.5 to 0.5 for a single A-line acquisition. The wavenumber function then becomes linear in

*τ*, i.e.

*k*(

*τ*)=

*k*

_{0}+

*k*

_{1}

*Tτ*. The depth profile is readily obtained with transform limited spatial resolution by a Fourier transform with respect to

*κ*=

*k*

_{1}

*Tτ*.

*z*

_{b}(

*t*)=

*z*-Σ

*z*

_{m}

*t*

^{m}where

*z*

_{0}=

*z*-

*z*

_{b}(0) denotes the mean path length difference,

*z*

_{1}=

*v*

_{z}the velocity, and

*z*

_{2}the acceleration. Using Eq. (27), we get

*ω*

_{0}is a constant phase term.

*ω*

_{1}corresponds to the signal frequency in

*τ*and is responsible for the Doppler shift in Eq. (19).

*ω*

_{2}represents quadratic signal chirping and therefore results in broadening of the axial resolution. The coefficient of the cubic term,

*ω*

_{3}plays a similar role to third-order chromatic dispersion, leading to asymmetry of the point spread function [31].

*k*tuning and linear motion. For linear-

*λ*tuning (linearly varying output wavelength in time), the axial resolution is found to be independent of

*z*

_{1}; a pure linear motion does not affect the axial resolution in this special case.

## 3.2 Experiments

### 3.2.1 OFDI system

32. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. **28**, 1981–1983 (2003). [CrossRef] [PubMed]

*σ*=~0.71. The tuning repetition rate could be varied by controlling the polygon rotation speed from <1 kHz up to 15.7 kHz. The tuning coefficients of the laser were measured using an unbalanced Michelson interferometer. The measured values were:

*k*

_{0}=4.76×10

^{6}m

^{-1},

*k*

_{1}

*T*/

*k*

_{0}=-0.051,

*k*

_{2}

*T*/

*k*

_{1}=-0.128, and

*k*

_{3}

*T*

^{2}/

*k*

_{1}=-0.075.

*w*

_{0}=18 µm. The light returned from the reference mirror and the sample was combined at a 50/50 coupler. The interference signal was measured with a dual balanced InGaAs photodetector followed by a differential transimpedance amplifier and a low pass electronic filter with a cutoff at 5 MHz. A total of 600 samples were acquired during each wavelength sweep with 94% duty cycle using a 12-bit data acquisition board. Therefore, the A-line acquisition time,

*T*, was nearly equal to the tuning period. The acquired data was interpolated to correct for nonlinearity in

*k*-space before DFT processing to create an image. At the maximum tuning repetition rate of 15.7 kHz, the sensitivity of the OFDI system was measured to be approximately 110 dB over the entire depth range of 3.8 mm. Details of the system is described in Ref. 16.

## 3.2.2 Moving mirror

*f*

_{m}, Eq. (20) predicts that the amplitude in the image, normalized to the actual oscillation amplitude, is given by [1+(2

*π*

*f*

_{m}

*k*

_{0}/

*k*

_{1})

^{2}]

^{1/2}, where

*f*

_{m}=30 Hz in the experiment. The theoretical curve is shown in Fig. 13 as a solid line, and agrees well with the experimental values.

*k*

_{3}. The results of the simulation are presented in Fig. 14(b). The profile labeled 0 is a reference profile calculated assuming a stationary mirror. Curves labeled 1 to 16 depict A-line profiles predicted for an oscillating sample mirror with a vibration amplitude of 0.78 mm. The A-line profiles obtained by the simulation show similar features to those in Fig. 14(a), reproducing the oscillation with similar peak-to-peak amplitude and degree of asymmetric broadening. Curve 17 depicts the position of the moving mirror assumed in the simulation (open circles and solid line, green). It is clearly seen that the oscillation amplitude in the image was exaggerated by a factor of approximately 2 due to the Doppler shift. Additionally, there is a phase shift between curve 17 and the peaks of the A-lines. This shift arises from the velocity dependence of the Doppler shift.

## 3.2.3 Transverse scanning

*α*=~0.4. (red line, Fig. 17a).

*x*/

*w*

_{0}=1. At this low value, as expected from previous results in Fig. 17, negligible degradation in spatial resolution and SNR was observed in the tissue image. The skin fold region is seen as sharp as other areas despite the fact that the depth change between adjacent A-lines corresponds to several hundreds of optical wavelength.

## 3.3 Discussion

*M*times the axial resolution, the maximum allowable axial displacement would be given, using Eq. (20), by Δ

*z*

_{max}(0.44/σ)

*Mλ*. For

*M*=10,

*σ*=0.71,

*λ*=1.3 µm, we get Δ

*z*

_{max}=8 µm. This corresponds to a velocity of 130 mm/s for

*T*=62.5 µs (A-line rate of 16 kHz) or 16.3 mm/s for

*T*=500 µs (A-line rate of 2 kHz).

*k*-space. If the resolution broadening can be tolerated up to a factor of

*M*

^{′}, we obtain Δ

*z*

_{max}=

*δz*

_{0}(

*M*

^{′}

^{2}-1)

^{1/2}(2

*σ*). For

*M*

^{′}=2,

*σ*=0.71, and

*δz*

_{0}=10 µm, we obtain Δ

*z*

_{max}=12.2 µm, which corresponds to a velocity of 195 mm/s for

*T*=62.5 µs or 24.4 mm/s for

*T*=500 µs. Motions that might occur in medical imaging

*in vivo*may have a velocity range less than 100 mm/s. Therefore, we expect that the Doppler distortion and image blurring may be negligible for high A-line acquisition rate beyond 10 kHz. However, for a slow acquisition rate, the motion effects may need to be taken into account.

*M*

^{″}, the maximum allowable transverse displacement is given by Δ

*x*

_{max}=

*w*

_{0}(

*M*

^{″}

^{2}-1)

^{1/2}/σ. For

*M*

^{″}=1.41,

*σ*=0.71,

*w*

_{0}=18 µm, we obtain Δ

*x*

_{max}=25 µm. This corresponds to 400 mm/s in velocity for

*T*=62.5 µs. For an application using a rotating fiber-optic catheter [30], the radius-circumferential image will be blurred more at large radius along both radial and circumferential directions. A maximum allowable amount of blurring puts a limit on the minimum number of A-lines to be acquired per image (one revolution of the catheter) as

*A*

_{min}=2

*πR*/Δ

*x*

_{max}, where

*R*is the ranging depth (radius). For example, for

*R*=4 mm and Δ

*x*

_{max}<25 µm, a minimum 1000 A-lines needs to be acquired per one revolution of the catheter.

## 4. Summary

## Acknowledgment

## References and links

1. | N. Bankman, |

2. | R. J. Alfidi, W. J. Mac, R. Intyre, and Haaga, “The effects of biological motion in CT resolution,” Am. J. Radiol. |

3. | M. L. Wood and R. M. Henkelman, “NMR image artifact from periodic motion,” Med. Phys. |

4. | S. K. Nadkarni, D. R. Boughner, M. Drangova, and A. Fenster, “In vitro simulation and quantification of temporal jitter artifacts in ECG-gated dynamic three-dimensional echocardiography,” Ultrasound in Med. & Biol. |

5. | D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science |

6. | J. G. Fujimoto, M. E. Brezinski, G. J. Tearney, S. A. Boppart, B. Bouma, M. R. Hee, J. F. Southern, and E. A. Swanson, “Optical biopsy and imaging using optical coherence tomography,” Nat. Medicine |

7. | R. C. Youngquist, S. Carr, and D. E. N. Davies, “Optical coherence-domain reflectometry: A new optical evaluation technique,” Opt. Lett. , |

8. | A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurements of intraocular distances by backscattering spectral interferometry,” Opt. Comm. |

9. | G. Hausler and M. W. Lindner, “Coherence radar and spectral radar - new tools for dermatological diagnosis,” J. Biomed. Opt. |

10. | M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, “Real time in vivo imaging by high-speed spectral optical coherence tomography,” Opt. Lett. |

11. | S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-speed spectral domain optical coherence tomography at 1.3 µm wavelength,” Opt. Express |

12. | N. Nassif, B Cense, B. H. Park, S. H. Yun, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express |

13. | F. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. |

14. | S. R. Chinn, E. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. |

15. | B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr |

16. | S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express |

17. | T. Mitsui, “Dynamic range of optical reflectometry with spectral interferometry,” Jap. J. of App. Phys. |

18. | R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express |

19. | J. F. de Boer, B. Cense, B.H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. |

20. | M. A. Choma, M. V. Sarunic, C. Uang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express |

21. | N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,” Opt. Lett. |

22. | W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” App. Phy. Lett. |

23. | E. Brinkmeyer and R. Ulrich, “High-resolution OCDR in dispersive waveguide,” Electron. Lett. |

24. | J. M. Schmitt and A. Knuttel, “Model of optical coherence tomography of heterogeneous tissue,” J. Opt. Soc. Am. A |

25. | E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “1,” Opt. Lett. |

26. | J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. |

27. | S.-M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, “Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,” Heart |

28. | M. V. Sivak Jr., K. Kobayashi, J. A. Izatt, A. M. Rollins, R. Ung-runyawee, A. Chak, R. C. K. Wong, G. A. Isenbert, and J. Willis, “High-resolution Endoscopic imaging of the GI tract using optical coherence tomography,” Gastrointest. Endosc. |

29. | G. J. Tearney, H. Yabushita, S. L. Houser, H. T. Aretz, I. K. Jang, K. Schlendorf, C. R. Kauffman, M. Shishkov, E. F. Halpern, and B. E. Bouma, “Quantification of macrophage content in atherosclerotic plaques by optical coherence tomography,” Circulation |

30. | G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, “Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography,” Opt. Lett. |

31. | A. E. Siegman, |

32. | S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. |

**OCIS Codes**

(110.4500) Imaging systems : Optical coherence tomography

(170.0110) Medical optics and biotechnology : Imaging systems

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.4500) Medical optics and biotechnology : Optical coherence tomography

**ToC Category:**

Research Papers

**History**

Original Manuscript: March 5, 2004

Revised Manuscript: June 17, 2004

Published: June 28, 2004

**Citation**

S. H. Yun, G. Tearney, J. de Boer, and B. Bouma, "Motion artifacts in optical coherence tomography with frequency-domain ranging," Opt. Express **12**, 2977-2998 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-13-2977

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### References

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- N. Nassif, B Cense, B. H. Park, S. H. Yun, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, ???In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,??? Opt. Express 12, 367-376 (2004), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-367">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-367</a> [CrossRef] [PubMed]
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- B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, ???Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+:forsterite laser,??? Opt. Lett. 22, 1704-1706 (1997). [CrossRef]
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- T. Mitsui, ???Dynamic range of optical reflectometry with spectral interferometry,??? Jap. J. of App. Phys. 38, 6133-6137 (1999). [CrossRef]
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- M. A. Choma, M. V. Sarunic, C. Uang, and J. A. Izatt, ???Sensitivity advantage of swept source and Fourier domain optical coherence tomography,??? Opt. Express 11, 2183-2189 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2183">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2183</a> [CrossRef] [PubMed]
- N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, ???In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,??? Opt. Lett. 29, 480-482 (2004). [CrossRef] [PubMed]
- W. Eickhoff and R. Ulrich, ???Optical frequency domain reflectometry in single-mode fiber,??? App. Phy. Lett. 39, 693-695 (1981). [CrossRef]
- E. Brinkmeyer and R. Ulrich, ???High-resolution OCDR in dispersive waveguide,??? Electron. Lett. 26, 413-414 (1990). [CrossRef]
- J. M. Schmitt and A. Knuttel, ???Model of optical coherence tomography of heterogeneous tissue,??? J. Opt. Soc. Am. A 14, 1231-1242 (1997). [CrossRef]
- E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, ???High-speed optical coherence domain reflectometry,??? Opt. Lett. 17, 151-153 (1992). [CrossRef] [PubMed]
- J. M. Schmitt, S. H. Xiang, and K. M. Yung, ???Speckle in optical coherence tomography,??? J. Biomed. Opt. 4, 95-105 (1999). [CrossRef] [PubMed]
- S.-M. Stengel, Y. Allemann, M. Zimmerli, E. Lipp, N. Kucher, P. Mohacsi, and C. Seiler, ???Doppler tissue imaging for assessing left ventricular diastolic dysfunction in heart transplant rejection,??? Heart 86, 432-437 (2001). [CrossRef] [PubMed]
- M. V. Sivak Jr., K. Kobayashi, J. A. Izatt, A. M. Rollins, R. Ung-runyawee, A. Chak, R. C. K. Wong, G. A. Isenbert, and J. Willis, ???High-resolution Endoscopic imaging of the GI tract using optical coherence tomography,??? Gastrointest. Endosc. 51, 474-479 (2000). [CrossRef] [PubMed]
- G. J. Tearney, H. Yabushita, S. L. Houser, H. T. Aretz, I. K. Jang, K. Schlendorf, C. R. Kauffman, M. Shishkov, E. F. Halpern, and B. E. Bouma, ???Quantification of macrophage content in atherosclerotic plaques by optical coherence tomography,??? Circulation 106, 113-119 (2003) [CrossRef]
- G. J. Tearney, S. A. Boppart, B. E. Bouma, M. E. Brezinski, N. J. Weissman, J. F. Southern, and J. G. Fujimoto, ???Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography," Opt. Lett. 21, 1-3 (1996).
- A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986), Chap. 9.
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