Open Access
Add to BibSonomy
Abstract
A proof-of-principle demonstration of a novel method of background subtraction for optical coherence tomography is presented using a full-field time-domain set-up. This single-shot method is based on time-averaged sampling of a sinusoidal phase modulation in the reference arm. It can significantly suppress motion artifacts as well as entirely eliminate phase-noise induced background subtraction errors that corrupt the images obtained using other methods. When used with Fourier domain set-ups, this technique can also eliminate arbitrarily strong autocorrelation artifacts.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical Coherence Tomography (OCT) provides a three-dimensional view inside a sample using non-ionizing visible or infra-red radiation in a non-destructive manner. The imaging depth resolutions made possible with OCT are of the order of microns while Ultrasonography or Ultrasound scanning commonly used in medicine has resolutions of the order of centimeters [1]. OCT lateral resolutions are determined by confocal considerations, similar to a microscope. Axial resolution in an OCT tomogram depends on the coherence length of the probe illumination. A broad source spectrum results in a short coherence length and hence short axial resolution for the tomogram. A Gaussian-shaped source spectrum results in axial and lateral resolutions of
and respectively, where ${\lambda }$ is the centre wavelength of the illumination, ${\Delta \lambda }$ is the full width at half maximum (FWHM) of the spectral bandwidth of the illumination, f and D being the focal length and aperture size of the objective lens respectively [2,3].OCT debuted in the last decade of the 20th century for in-vivo retinal scans [4,5] and in the years that followed, OCT has been established as a ubiquitous tool in eye care [6]. Advances in OCT technology have improved the resolution of scans while reducing acquisition times. The first generation time-domain systems (TD-OCT) were followed by Fourier-domain systems (FD-OCT) which could be implemented without moving parts. Initial FD-OCT devices were spectral-domain systems (SD-OCT). Swept-source devices (SS-OCT) followed when suitable swept-wavelength sources were developed. High resolutions have been obtained using full-field geometries (FF-OCT) which acquire an entire 2D en-face image in a single exposure, as opposed to point-wise raster scanning with fiber-based geometries. OCT has been applied to cardiology with intravascular imaging, dentistry, pathology and dermatology. Research using OCT in non-destructive materials testing, analysis of artwork and many other fields is ongoing [2].
Full field optical coherence tomography (FF-OCT), or wide-field optical coherence tomography (WF-OCT) [7–10] typically uses a time domain (TD) setup and is preferred for applications requiring high lateral resolution and en-face imaging. This configuration avoids galvo-mirror scanners [3–5,10,11] and swept sources [12–14] while allowing data acquisition over large imaging depths at tens of megavoxels per second if high-speed cameras are used, while typical flying spot OCT configurations acquire at most a few megavoxels per second [15]. One of the crucial steps in post-processing of Time-Domain FF-OCT data is background subtraction. Incoherent reflections from the reference and sample arms make up the background. Unless this background is subtracted, the tomographic information at a particular depth cannot be isolated. Various schemes have been used for background subtraction in FF-OCT like the four-phase shifting interferometric method [15], a single-shot 2-D quaternionic analytic signal processing approach [16], lock-in detection using phase modulation with stroboscopic illumination [8] and other phase shifting methods [7], averaging a large number of frames [17] subtraction of successive frames [17–19] and various lock-in detection methods [20,21]. The method we present below has the advantages of ease of implementation and acquisition speed while being tolerant of phase noise introduced by sample movement or vibrations.
Fourier Domain Optical Coherence Tomography (FD-OCT) is based on the Fourier pair relationship of the optical wavenumber ${k}$ and the path-length difference ${x}$. In FD-OCT, we measure the spectral interferogram at each point instead of just the intensity. The inverse fourier transform of the spectral interferogram yields the sample reflectivity as a function of path length. FD-OCT has the significant advantage of higher signal to noise ratio (SNR) as compared to Time Domain (TD-OCT).
However, FD-OCT needs several computational steps before the inverse fourier transform can accurately give us the sample reflectivity. One of the important steps is the removal of autocorrelation terms from the spectral interferogram to prevent artifacts in the resultant tomogram. Many methods have been used for this, including the historical use of comparatively stronger reference arm reflectivity so that the autocorrelation terms become weaker [12], averaging spectra over multiple points [22], using resonant acquisition [23], using an off-axis reference beam [24] and various balanced detection methods [25,26]. In this paper, we explain theoretically how our simple technique is also effective in removing arbitrarily strong autocorrelation artifacts in FD-OCT images.
2. Theoretical background
2.1 J0 null technique for time domain FF-OCT
In the following discussion, we follow the treatment of Sudarshanam and Srinivasan [27] and assume the sample and reference arms of the FF-OCT interferometer are illuminated with monochromatic plane waves. The intensity at a particular pixel would be
where A is the amplitude of the interference signal and ${I_{inc}}$ the incoherent background intensity. ${\phi }$ is the phase difference between the sample and reference arms. If we introduce a sinusoidal phase modulation in the reference arm, the intensity additionally becomes a function of time, where M is the amplitude of the modulation of angular frequency ${\omega }$ and initial phase ${\theta }$. Expanding this expression using trigonometric identities and the series and where ${J_n(x)}$ are Bessel functions of the first kind, we can write2.2 ${J_0}$ null technique for FD-OCT autocorrelation artifact removal
In the frequency domain, the intensity at a particular point on the image plane is represented by the spectral interferogram [28]
If the reference arm undergoes a phase modulation as in Eq. (3), the spectral interferogram in Eq. (9) becomes
2.3 π phase-shifting for OCT
In the ${\pi }$ phase-shifting method, a second interferogram is obtained by shifting the reference mirror to induce a phase shift of ${\pi }$ radians, which has an intensity pattern,
In this case, subtracting ${I_{\pi }}$ from the original interferogram of Eq. (3) yields ${2 \cdot A(x,y)cos[\phi (x,y) ]}$ and the Hilbert transform once again gives us the amplitude, as ${2 \cdot A(x,y)}$. In spite of giving double the signal strength in noise-free conditions, in case there is a phase fluctuation due to vibration leading to an additional phase-shift close to ${\pi }$ radians, subtraction produces an amplitude close to zero in place of ${2 \cdot A(x,y)}$. This leads to missing areas in the en-face image and the resulting tomogram as noted by other researchers also [17].Even in the case of FD-OCT, the spectral fringes will get washed out due to such phase fluctuations while subtracting frames. Since the fringes are Fourier transformed to get the reflectivity data point by point, it would lead to an entire missing A-scan, appearing as a missing line along the depth axis.
Similarly, in four-phase shifting and multiple phase shifting techniques also, the output critically depends on the accuracy of phase-shifting which requires expensive, robust and vibration-free optics, or expensive high-speed imaging systems.
2.4 Adjacent frame subtraction for FF-OCT
When adjacent frames are subtracted, the second interferogram has a random phase shift ${\beta }$, and the corresponding interferogram is
Subtracting this from the original interferogram in Eq. (3) would give us ${A(x,y)\Big \{-2 \cdot sin[\phi (x,y) + \beta / 2] \cdot sin(\beta / 2) \Big \}}$on which the Hilbert transform would once again give us ${2 \cdot A(x,y)\cdot sin(\beta / 2)}$. Clearly, for certain values of ${\beta }$, the measured amplitude would vanish, as discussed in the case of ${\pi }$ phase-shifting. This method also assumes that the adjacent slice falls well within the coherence length of the source, and that the reflectivities of adjacent slices are similar.
In conclusion, among all these background subtraction schemes, only the ${J_0}$ null technique is insensitive to phase fluctuations which could happen between the first and second image acquisitions. This advantage of the ${J_0}$ null technique is convincingly demonstrated by our experiments.
3. Experimental procedure
We present a proof-of-principle demonstration of our method using Time Domain FF-OCT. A schematic of our setup is shown in Fig. 1. A single-emitter 850 nm IR LED of bandwidth 35 nm was used as the illumination source for our samples. Spatial filtering and intensity control was achieved by an aperture placed after the light-gathering lens. Path length variation was achieved by a linear translation stage driven by a micro-stepping motor controlled by a low-cost microcontroller (Arduino Due), utilizing a locally sourced micro-stepping driver (Bholanath BH MSD 2A). Though the driver allowed micro-stepping up to 39 nm micro-steps (1/25600 of a rotation, with 1 mm translation stage pitch), our experiments were done with micro-steps of 5 microns (1/200 rotation). This stepping range falls well within the coherence length of our source, and allows for quicker translations over longer optical path lengths.
The front surface of an OD2 neutral density filter (NDF) was used as the reflector in the reference arm. Uncoated lenses were used in the proof-of-concept OCT assembly. The cube beam-splitter (Thorlabs BS014) was placed at a slight angle to the beams to avoid multiple back reflections from the beam-splitter surfaces. The camera used was an astronomy monochrome CMOS planetary imager (QHY5L-II M) which can image upto 200 frames per second. Image acquisition and processing was done by custom cross-platform OpenCV-based [29] software [30] written in C++, which we have open-sourced. The ${J_0}$ null technique was implemented using on-off keying, a subset of Amplitude Shift Keying (ASK) commonly used in digital communication systems. The carrier signal driving the phase modulator was ASK modulated with the on-state amplitude exactly corresponding to the ${J_0}$ null. This is the reason for the multiple references to ”ASK” in our software.
We used an 8${\Omega }$ loudspeaker coil to produce the reference arm phase modulation. The ${J_0}$ null amplitude for the 850 nm IR LED illumination was determined by visual inspection of the camera output in free-running video mode. The frequency used was a resonance of the loudspeaker, at 456 Hz. The peak-to-peak sine-wave drive voltage at ${J_0}$ null, where the fringes vanish, was 800 mV. Similarly, the voltage required for a ${\pi }$ phase-shift was also determined by visual inspection to be 39 mV DC, while driving the speaker coil at 1 Hz. The exposure times needed for our camera was chosen to vary from 10 ms to 30 ms depending on the sample. The samples were illuminated with around 80 ${\mu W/cm^2}$ of illumination as measured by a Newport 1830C power meter.
We needed to attenuate the reference arm illumination with an NDF (OD 0.5) for the biological samples. The axial PSF in air with our IR LED illumination was experimentally determined to be 7.1 ${\mu m}$ without the reference arm NDF, and 7.8 ${\mu m}$ with the NDF. Imaging a USAF 1951 target determined that each pixel of the camera ranged 5.8 ${\mu m}$ on the sample. Noise reduction was done by 10x10 pixel binning of individual frames, resulting in a final 58 ${\mu m}$ lateral resolution in our proof-of-principle demonstration setup. Custom-written software [30] was used to automate the entire process of image acquisition and processing. On-the-fly background subtraction, Hilbert transform and averaging enabled real-time display of the OCT images on the PC screen as well as on a rudimentary web interface, which could also be used on mobile devices.
4. Results
A proof-of-principle demonstration of the effectiveness of the ${J_0}$ null technique in OCT was done using Time Domain FF-OCT. In preliminary tests, we acquired en-face images of an irregularly shaped metallic reflector, and found that some of the en-face images had missing areas when using the ${\pi }$ phase-shift or alternate frame subtraction methods, but such missing areas were not noticed with the ${J_0}$ null technique. Moreover, the image using the ${J_0}$ null technique most closely resembles the actual object shape. We notice that only in case of the ${J_0}$ method the single-shot image is almost as good as the image obtained after averaging, clearly indicating that fast single shot imaging results in artifacts with the other methods in the presence of vibration induced phase noise. Representative results of this sample are presented in Fig. 2. To further validate our technique, we also imaged biological samples.
Fig. 2. Comparison of background subtraction methods when imaging a metallic sample. En-face single-shot and averaged images using, (a) and (b) the ${J_0}$ null technique, (c) and (d) ${\pi }$ phase-shifting, (e) and (f) alternate frame subtraction. The ${J_0}$ null technique is tolerant to phase noise induced by sample vibration, while the other techniques result in banding artifacts and distortion. A lateral area of 7.5 mm x 5.6 mm is imaged here.
We imaged an onion-skin sample using the three background subtraction techniques, repeating the acquisition multiple times with each technique. We made the sample oscillate with an amplitude of around 400 nm with frequencies in the 1 to 10 Hz region, using a piezo disk to mimic motion artifacts from an in-vivo biological sample. We present the single shot B-scan images in the top row in in Fig. 3 along with the results obtained for each method using an average over ten readings. It can again be seen that the single-shot B-scan image obtained using the ${J_0}$ null technique does not have missing regions and resembles the averaged image. The other techniques necessarily require averaging to remove vibration-induced artifacts.
Fig. 3. Comparison of background subtraction methods when imaging an onion skin moving at 2 ${\mu m/s}$. B-scan single-shot and averaged images respectively using the ${J_0}$ null technique (a) and (b), ${\pi }$ phase-shifting (c) and (d), and alternate frame subtraction (e) and (f). The ${J_0}$ null technique is tolerant to phase noise induced by sample motion, while the other techniques result in missing layers in the single-shot B-scans. The lateral extent along the x-axis is 7.5 mm and the axial extent is 100 ${\mu m}$ for these B-scans.
Since the vibrations in the previous examples were artificially created, we further verified our results by imaging the forefinger of a human volunteer, keeping it as stable as possible by pressing it against a glass plate. As seen in Fig. 4, parts of the en-face image are again missing sections in the other subtraction methods as compared to the ${J_0}$ null technique, while the single shot image for the ${J_0}$ method is similar to the averaged version. In this case, the only source of vibration was the natural motion of the finger instead of the piezo disk.
Fig. 4. Comparison of background subtraction methods when imaging a volunteer’s finger, stabilized by pressing it against a glass plate. En-face single-shot and averaged images respectively using the ${J_0}$ null technique (a) and (b), ${\pi }$ phase-shifting (c) and (d), and alternate frame subtraction (e) and (f). The ${J_0}$ null technique is tolerant to phase noise induced by sample motion, while the other techniques result in en-face images with banding artifacts pointed out by the arrows. The area imaged here is 7.5 mm by 5.6 mm.
5. Discussion
This method has the following advantages -
(a) Only a single background acquisition needs to be taken for each slice, speeding up the acquisition process and enabling processing to be done in real-time. This is an advantage over methods which use a large number of acquisitions [17] to create the background to be subtracted.
(b) Most importantly, background subtraction is robust and less sensitive to vibrations - missing areas are avoided in the tomograms, both in TD and FD OCT configurations when acquiring images subject to phase noise. Our technique is a single-shot background subtraction technique which is independent of the sample phase. Another technique that is independent of the sample phase fluctuations is the one that uses hundreds of images [17] to create the background by averaging the fringes to zero, which also requires a larger number of averages when working with higher SNRs.
(c) We also note that motion artifacts can be almost eliminated in Time Domain FF-OCT en-face images using high frequency piezos with sufficiently small detector exposure times when using the ${J_0}$ null technique. In other methods, even under noiseless conditions, the subtracted frame requires the sample or reference arm to be displaced by some amount. In our method, the mean position of both the sample and reference mirror remain absolutely unchanged. This leads to perfect background elimination on subtraction.
(d) In the case of FD-OCT, especially when the autocorrelation artifacts are strong, our technique can still result in artifact-free images in the presence of vibration, using short exposure times. This becomes an added advantage for FD-OCT using spectrometers with 2-D sensors (cameras) which result in single-shot B-scans. The other subtraction techniques would result in missing areas in the tomograms.
(e) Even when the modulation amplitude is not exactly at the ${J_0}$ null value, the degradation in SNR is negligible, since the amplitude can easily be kept near the null point by visual inspection. Moreover, error in the null position will not produce missing regions or artifacts, since the phase dependent terms in Eq (12) will always average to zero.
The ${J_0}$ null technique has the following limitations -
(a) The acquisition speed is limited by the modulation frequency of the phase-shifting device used - the ${J_0}$ null technique needs the exposure time to be at least as long as the time period of the periodic phase-shifting. This limitation could easily be overcome by using piezo transducers driven at high frequencies. Typical piezo drivers at kilohertz frequencies would permit sub-millisecond exposures.
(b) The ${J_0}$ null technique results in 3 dB lower SNR than with ${\pi }$ phase-shift subtraction in a completely vibration-free acquisition system as discussed in Section 2. However, the impact of this condition can easily be overcome by choosing appropriate reference arm reflectivity as well as light sources.
(c) The null of the ${J_0}$ will not occur at the same amplitude of reference arm modulation for all optical wavelengths. But using the slope of the ${J_0}$ function around the null point, it is seen that the fall in SNR after subtraction, for a source bandwidth of 50 nm, is negligible (less than 0.08 dB) when the center wavelength (850 nm) is at the null point. Even for a source of 200 nm bandwidth centered at 850 nm the fall in SNR is less than 0.2 dB. Due to the approximately linear variation of ${J_0}$ near the null point, the fall in SNR is approximately ${\Delta \lambda / 4 \lambda }$, where ${\Delta \lambda }$ is the full-width at half-maximum (FWHM) of the source spectrum.
6. Conclusions
This study proposes the application of the ${J_0}$ null technique to single shot background subtraction in Time Domain FF-OCT and to autocorrelation removal in FD-OCT. For the first time to the best of our knowledge, the ${J_0}$ null technique has been applied to OCT imaging and demonstrated to be robust and relatively insensitive to phase noise. These advantages of the ${J_0}$ null technique and its simplicity of implementation make it an attractive option when building fast and vibration tolerant TD-OCT devices and FD-OCT devices free of autocorrelation artifacts.
Funding
Department of Science and Technology, Government of India (DST FIST 2012-2017 SR/FST/PSI-172/2012).
Acknowledgments
The authors wish to convey their gratitude to Bhagawan Sri Sathya Sai Baba, the founder Chancellor of their University, who guided and inspired them throughout this project.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. C. A. Puliafito, J. S. Schuman, M. R. Hee, and J. G. Fujimoto, Optical coherence tomography of ocular diseases (SLACK Inc., 1996).
2. W. Drexler and J. G. Fujimoto, Optical Coherence Tomography: Technology and Applications, Second Edition (Springer International Publishing, 2015).
3. E. A. Swanson, D. Huang, C. P. Lin, C. A. Puliafito, M. R. Hee, and J. G. Fujimoto, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17(2), 151–153 (1992). [CrossRef]
4. A. F. Fercher, K. Mengedoht, and W. Werner, “Eye-length measurement by interferometry with partially coherent light,” Opt. Lett. 13(3), 186–188 (1988). [CrossRef]
5. C. K. Hitzenberger, W. Drexler, and A. F. Fercher, “Measurement of corneal thickness by laser Doppler interferometry,” Invest. Ophthalmol. Visual Sci. 33, 98–103 (1992), https://iovs.arvojournals.org/article.aspx?articleid=2160990.
6. J. Fujimoto and E. Swanson, “The development, commercialization, and impact of optical coherence tomography,” Invest. Ophthalmol. Visual Sci. 57(9), OCT1–OCT13 (2016). [CrossRef]
7. E. Beaurepaire, A. C. Boccara, M. Lebec, L. Blanchot, and H. Saint-Jalmes, “Full-field optical coherence microscopy,” Opt. Lett. 23(4), 244–246 (1998). [CrossRef]
8. A. Dubois, L. Vabre, A.-C. Boccara, and E. Beaurepaire, “High-resolution full-field optical coherence tomography with a Linnik microscope,” Appl. Opt. 41(4), 805–812 (2002). [CrossRef]
9. H. M. Subhash, “Full-field and single-shot full-field optical coherence tomography: A novel technique for biomedical imaging applications,” Adv. Opt. Technol. 2012, 1–26 (2012). [CrossRef]
10. O. Thouvenin, C. Apelian, A. Nahas, M. Fink, and C. Boccara, “Full-field optical coherence tomography as a diagnosis tool: recent progress with multimodal imaging,” Appl. Sci. 7(3), 236 (2017). [CrossRef]
11. 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, et al., “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef]
12. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995). [CrossRef]
13. S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22(5), 340–342 (1997). [CrossRef]
14. A. Grebenyuk, A. Federici, V. Ryabukho, and A. Dubois, “Numerically focused full-field swept-source optical coherence microscopy with low spatial coherence illumination,” Appl. Opt. 53(8), 1697–1708 (2014). [CrossRef]
15. E. Auksorius and A. C. Boccara, “Fingerprint imaging from the inside of a finger with full-field optical coherence tomography,” Biomed. Opt. Express 6(11), 4465–4471 (2015). [CrossRef]
16. M. S. Hrebesh and M. Sato, “Real-time single-shot full-field OCT based on dual-channel phase-stepper optics and 2D quaternionic analytic signal processing,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XIII, vol. 7168 (International Society for Optics and Photonics, 2009), p. 71681H.
17. Y. Watanabe and M. Sato, “Quasi-single shot axial-lateral parallel time domain optical coherence tomography with Hilbert transformation,” Opt. Express 16(2), 524–534 (2008). [CrossRef]
18. Y. Watanabe and M. Sato, “Three-dimensional wide-field optical coherence tomography using an ultrahigh-speed CMOS camera,” Opt. Commun. 281(7), 1889–1895 (2008). [CrossRef]
19. H. Nandakumar, A. K. Subramania, and S. Srivastava, “Sub-4-micron full-field optical coherence tomography on a budget,” Sadhana 43(6), 97 (2018). [CrossRef]
20. P. Egan, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field optical coherence tomography with a complimentary metal-oxide semiconductor digital signal processor camera,” Opt. Eng. 45(1), 015601 (2006). [CrossRef]
21. S. Bourquin, P. Seitz, and R. P. Salathé, “Optical coherence topography based on a two-dimensional smart detector array,” Opt. Lett. 26(8), 512–514 (2001). [CrossRef]
22. R. K. Wang and Z. Ma, “A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography,” Phys. Med. Biol. 51(12), 3231–3239 (2006). [CrossRef]
23. M. Shalaby and S. S. Al-Sowayan, “Autocorrelation noise free optical coherence tomography using the novel concept of resonant oct (roct),” J. Eur. Opt. Soc. Publ. 12(1), 10 (2016). [CrossRef]
24. D. Hillmann, H. Spahr, H. Sudkamp, C. Hain, L. Hinkel, G. Franke, and G. Hüttmann, “Off-axis reference beam for full-field swept-source oct and holoscopy,” Opt. Express 25(22), 27770–27784 (2017). [CrossRef]
25. W.-C. Kuo, C.-M. Lai, Y.-S. Huang, C.-Y. Chang, and Y.-M. Kuo, “Balanced detection for spectral domain optical coherence tomography,” Opt. Express 21(16), 19280–19291 (2013). [CrossRef]
26. E. Bo, X. Liu, S. Chen, X. Yu, X. Wang, and L. Liu, “Spectral-domain optical coherence tomography with dual-balanced detection for auto-correlation artifacts reduction,” Opt. Express 23(21), 28050–28058 (2015). [CrossRef]
27. V. Sudarshanam and K. Srinivasan, “Universal dynamic phase-calibration technique for fiber-optic interferometric sensors and phase modulators,” Opt. Lett. 14(22), 1287–1289 (1989). [CrossRef]
28. L. V. Wang and H.-i. Wu, Biomedical optics: principles and imaging (John Wiley & Sons, 2012).
29. G. Bradski, “The OpenCV Library,” Dr. Dobb’s Journal of Software Tools (2000).
30. H. Nandakumar, “ASKlive,” https://github.com/hn-88/ASKlive (2018).
