Ординатура / Офтальмология / Английские материалы / Handbook of Optical Coherence Tomography_Bouma, Tearney_2002
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applications, the tight focusing of OCT probe beams that is required for high spatial image resolution does produce intensities approaching established optical exposure limits. A number of international bodies recommend human exposure limits for optical radiation; in the United States, one well-known set of guidelines for optical radiation hazards are ANSI Z1361, produced by the American National Standards Institute [56]. Unfortunately, these guidelines are specified for laser radiation exposure and are provided only for exposures to the eye and skin. Nonetheless, many analyses of OCT radiation safety have used these standards. The applicable ANSI standards for cw laser exposure to the eye and skin both recommend a maximum permissible exposure (MPE) expressed as a radiant exposure, which is a function of the exposure duration, and tabulated spectral correction factors.
ACKNOWLEDGMENTS
We acknowledge research support from the National Science Foundation (BES9624617), the Whitaker Foundation, an Olympus Graduate Research Fellowship (A.M.R.), and a National Institutes of Health Research Traineeship (S.Y.).
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7
Speckle Reduction Techniques
J. M. SCHMITT, S. H. XIANG, and K. M. YUNG
Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China
7.1INTRODUCTION
The word ‘‘coherence’’ in optical coherence tomography (OCT) conveys both a primary strength and a primary weakness of this new imaging technology. On the one hand, the measurement technique on which OCT is based, interferometry, relies inherently on the spatial and temporal coherence of the optical waves backscattered from a tissue. On the other hand, this same coherence gives rise to speckle, an insidious form of noise that degrades the quality of OCT images. Speckle arises as a natural consequence of the limited spatial-frequency bandwidth of the interference signals measured in optical coherence tomography (OCT). In images of highly scattering biological tissues, speckle has a dual role as a source of noise and as a carrier of information about tissue microstructure.
This chapter gives an overview of speckle in OCT and attempts to clarify some of the issues that makes its origins and consequences difficult to understand. The first section addresses a central question: Is speckle a source of noise in OCT or is it the signal itself? The concepts of signal-carrying and signal-degrading speckle are defined in terms of the phase and amplitude disturbances of the sample beam. Four speckle noise-reduction methods—polarization diversity, spatial compounding, frequency
The first three sections of this chapter are an edited version of a paper published in the Journal of Biomedical Optics 4:95–105, 1999.
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compounding, and digital signal processing—are discussed, and the potential effectiveness of each method is analyzed briefly. The final sections of the chapter are devoted to examples of speckle-reduction techniques that rely on digital signal processing: a modified zero-adjustment procedure (ZAP) and an optimal nonlinear wavelet threshold (ONWT) technique.
7.2CHARACTERISTICS OF SPECKLE IN OCT
Speckle came to the forefront soon after it was discovered that the reflection of a laser beam from a rough surface has a distinctive granular or mottled appearance [1]. Having no obvious relationship with the texture of the surface, the dark and bright spots formed by the reflected beam change their pattern whenever the surface moves slightly. This phenomenon, known as laser speckle, was found by early researchers to result from random interference between reflected waves that are mutually coherent. It has taken several decades, however, for researchers to realize the full significance of speckle as a fundamental property of signals and images acquired by all types of narrowband detection systems, which include radar, ultrasound, and radio astronomy. In addition to the optical properties and motion of the target object, speckle is influenced by the size and temporal coherence of the light source, multiple scattering and phase aberrations of the propagating beam, and the aperture of the detector. All of these variables contribute to the observed characteristics of speckle in optical coherence tomography of living tissue. A thorough analysis of each of these variables alone and in combination is not possible within the narrow confines of this chapter. We ask the reader to settle instead for a barebones analysis of a small subset of these variables whose effects have been studied at this early stage of development of OCT. Many of the missing elements in the analysis presented in this section can be pieced together from the theoretical analyses given in Ref. 2. Other elements are truly missing, and an analysis of their influence on OCT awaits further research.
7.2.1Origin
In optical coherence tomography the sample is placed in one of the arms of an interferometer at the focus of a converging lens. As the optical path in the other arm of the interferometer varies during the scanning operation, an ac current is generated by a photodetector at the output of the interferometer. This photocurrent is proportional to the real part of the cross-correlation product of the reference optical field Ur and the optical field Us backscattered from the sample,
i Re U U ð1Þ
d r s
where the brackets h i denote an average over time and space. When the light source satisfies the quasi-monochromatic condition (i.e., its center frequency, 0, greatly exceeds its bandwidth ) and the sample field backscatters from a single scattering center, the photocurrent can be expressed in terms of the optical path difference, , between the two arms,
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þ ð Þ& |
ð2Þ |
id ð Þ ¼ K gð Þ cos½2 0 |
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where K is a constant of proportionality that relates the optical and electronic variables and jgð Þj and ð Þ are, respectively, the argument and phase of the cross-correlation in Eq. (1). The function jgð Þj represents the envelope of the temporal coherence function, given by gð Þ ¼ hUsðtÞUs ðt þ Þi. We see from Eq. (2) that id ð Þ responds to both the phase and the amplitude of the crosscorrelation of the scattered and reference optical fields. It is the sensitivity of the photocurrent to the phase that makes OCT susceptible to the effects of speckle. For the ideal case of a perfectly flat reflector placed at the focus of the lens in the sample arm, the complex autocorrelation function of the source determines the magnitude of the phase term ð Þ in Eq. (2). However, when the sample is a tissue containing densely packed scatterers, both gð Þj and ð Þ can no longer be treated as deterministic variables because waves from multiple scattering centers combine randomly to form the interference signal [3].
Consider the changes that a focused wave incident on the tissue undergoes as it propagates through the tissue to the sample volume, scatters back, and then propagates once again through the tissue back to the lens (Fig. 1). Two main processes influence the spatial coherence of the returning wave: (1) multiple backscattering of the beam inside and outside of the desired sample value and (2) random delays of the forward-propagating and returning beam caused by multiple forward scattering. Although the first of these is the primary source of speckle in rough-surface imaging, the second must also be considered in coherent imaging systems, like OCT, that utilize penetrating waves. The common feature of the two processes is that they alter the shape of the wave front of the returning beam and create localized regions of constructive and destructive interference that appear as speckle in OCT images [4].
Figure 1 Propagation of a focused beam in tissue. The two main processes that distort the wave front of the returning wave—multiple forward scatter and multiple backscatter—are depicted here.
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Multiple backscattering can occur in spite of the short coherence time of the sources used in OCT (usually less than 100 fs). For speckle to form, all that is required is that two or more scatterers in the sample volume backscatter waves that reach some point on the detector out of phase within an interval of time less than the coherence time of the source. Waves backscattered from any pair of point scatterers separated by an optical distance close to an odd multiple of one-half of the wavelength can generate speckle, provided that the optical distance does not exceed the coherence length of the source in the medium. Waves backscattered from different facets of a single large particle can generate speckle in a similar manner. Recent studies suggest that closely packed subwavelength-diameter particles contribute a large fraction of the total optical cross section of the tissue [5–7]. Therefore, the likelihood of finding a pair of scatters or clusters of scatterers within the sample volume that satisfy the conditions for speckle generation is high.
The simulation results in Fig. 2 illustrate how interference noise caused by multiple backscattering can distort the envelope of an OCT signal generated as the sample beam scans along a single line (an OCT A-line). The coherent A-line
Figure 2 Simulation of the distortion of an OCT A-line caused by the coherent detection process. The uppermost plot shows the ideal backscatter profile generated by a dense random distribution of point particles with cross sections modulated by a cosinusoidal function. Below this plot is the incoherent signal that was formed by convolving the backscatter profile with the Gaussian envelope of the simulated OCT point spread function (15 m FWHM). The coherent signal was found in a similar way by convolving the backscatter profile with the coherent PSF containing the optical carrier frequency. The lowermost plot is a low-pass-filtered version of the coherent signal.
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shown in this figure was computed by convolving a random sequence of scatterers (top line of the figure) with the theoretical coherent point spread function (PSF) of an OCT scanner; the incoherent A-line was computed by convolution with the envelope of the PSF. Details of the simulation method are described in Ref. 8. Note that, unlike those of the incoherent A-line, the variations in the magnitude of the coherent A-line track the density of scatterers poorly. In two-dimensional OCT images formed from a series of A-lines, this type of distortion manifests itself as speckle.
7.2.2Statistical Properties
Figure 3 is an example of an OCT image that shows high-contrast speckle in regions of strong backscatter below the surface of skin. Note that the appearance of the speckle noise has no obvious dependence on depth, which suggests that the statistical properties of the speckle are dominated by the effects of multiple backscatter rather than by phase aberrations incurred during propagation through overlying tissue. Decorrelation of the incident and returning beams undoubtedly also occurs, but its effects are difficult to discern because the phase aberrations caused by the multiple forward scattering and multiple backscattering process surperimpose. When a large number of polarized quasi-monochromatic waves with random phase combine, a fully developed speckle pattern is formed in which the probability of measuring an intensity I at a given point is described by the negative exponential density function [9],
1 |
1 |
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pðIÞ ¼ |
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exp |
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ð3Þ |
hIi |
hIi |
|||
where hIi is the mean intensity. The image of a speckle pattern that obeys negative exponential statistics has a signal-to-noise ratio (SNR) equal to 1, where the SNR is defined as the ratio of the mean and standard deviation of the intensity,
Figure 3 Example of an OCT image (dorsal aspect of a finger) containing high-contrast speckle. The interference signals from which the image was formed were sampled at 1:2 m intervals in both dimensions, and the overall size of the image is approximately 1 mm 1 mm.
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SNR ¼ hIi=I . Because intensities close to zero are probable, fully developed speckle patterns are riddled with dark spots.
Although the ac photocurrent, id , measured by OCT scanners is proportional to the complex cross-correlation hUrUs i, not the intensity I ¼ hUsUs i ¼ hjUsj2i in Eq. (3), its squared magnitude M ¼ id2 can nevertheless be treated as an analog of the intensity for characterization of the statistical properties of speckle in OCT images. To study these properties, we employed a quadrature-demodulation technique to record the instantaneous phase and amplitude of the ac photocurrent from an OCT scanner [11]. Figure 4 presents the results of a typical set of measurements. Histograms of the intensities and phases of the OCT signals acquired from a highly scattering region of the skin are shown in the right half of the figure. As expected from the random nature of the signals, the phase was found to be almost uniformly distributed between and (Fig. 4c). The lack of correlation between the real and
Figure 4 Statistics of the amplitude and phase variations of the OCT interference signal derived from a highly scattering region of living skin tissue. (a) OCT image of the region of
the tissue from which the signals were extracted. (b) Histogram of the signal magnitude p
M ¼ A2s þ A2c , where As and Ac are the amplitudes of the real (cosine) and imaginary (sine) components of the quadrature-demodulated interference signal. The measured data are fit by the solid-line curve, which is a plot of Eq. (4). (c) Histogram of the measured phase, defined as tan 1ðAs=Ar). (d) Plot of the real and imaginary components of three A- line signals plotted together in the complex plane.