Mie scattering model for dual-axes confocal architecture

Transcription

1 Mie scattering model for dual-axes confocal architecture Larry K. Wong, a Michael J. Mandella, b Paul Holcomb, c Gordon S. Kino, b Thomas D. Wang a a Division of Gastroenterology, Stanford University School of Medicine, Stanford, CA 9435 b Ginzton Laboratory, Stanford University, Stanford, CA 9435 c Breault Research Organization, Inc., Tucson, AZ ABSTRACT Tissue scattering has a significant effect on the image resolution and light collection efficiency in confocal microscopy. The dual-axes (DA) confocal architecture has many advantages including high axial resolution with low numerical aperture lenses and long working distance for use in vivo as a microendoscope. In addition, less scattered light along the illumination path may be collected and introduced as noise. In this paper, we use Monte Carlo tissue scattering simulations to compare the dual-axes and conventional single-axis (SA) configurations. Simulation results show that the axial response for the dual axes configuration varies with pinhole size and optical thickness of scattering media in a way that differs from the single axis architecture. The DA configuration is able to filter out efficiently multiply-scattered photons and out-of-focus light, thus allowing imaging with greater tissue penetration depths to provide vertical crosssectional images, which has significant implications for in vivo imaging. Keywords: scattering, Mie theory, confocal, microscopy, single-axis, dual-axes, Monte Carlo 1. INTRODUCTION In confocal microscopy a pinhole is used to reject light from out-of-focus layers and light scattered by tissue. In the single-axis (SA) architecture, the pinhole is along the same optic axis of the objective. The SA configuration is the most common architecture for both benchtop systems and fiber-optic confocal microscopes that have been miniaturized for endoscope usage. 1,2 Tissue scattering is one of the most important factors that can significantly degrade image resolution, contrast, and dynamic range. The dual-axes (DA) confocal architecture with low numerical aperture (NA) objectives and separation of the illumination and collection beams has been shown to produce long working distance (WD) with high axial resolution, 3,4 and to provide a sufficient dynamic range to collect vertical cross-sectional (perpendicular to surface) images of tissue. 5,6 Miniaturized DA confocal systems have been produced to demonstrate the above features 7,8 and a fluorescence DA confocal system has also been implemented. 9 In this study we use Monte Carlo simulations to model tissue scattering 1 to show that the DA architecture improves the rejection of multiply-scattered photons considerably, thus providing greater signal-to-noise ratio (SNR) and dynamic range, resulting in better tissue penetration than that of the SA architecture, given the same axial resolution. 2. METHODS In this work a commercially available non-sequential ray tracing program (ASAP 26 Breault Research Organization, Tucson, AZ) is used to model the SA and DA confocal architectures and tissue scattering. This software takes random scattering and ray splitting into account. Figure 1 shows the schematic diagrams for (a) SA and (b) DA confocal configurations. In the SA configuration, the incident beam first passes through a beam splitter (BS) and then an ideal lens (L1) focuses the beam into the tissue block. The reflected rays are then diverted by a beam splitter again and focused onto a detector by an ideal lens (L 2 ). At the focal planes of L1 a mirror (M) is embedded in the tissue to reflect the incident beam. Since the beam splitter reduces the original flux by 25%, the SA results are scaled up accordingly. For the DA architecture, the incident beam is focused by an ideal lens (L 3 ) into the tissue at an angle θ = 3 to the normal axis, and an ideal lens (L 4 ) focuses the reflected rays onto the detector. A mirror (M) is also embedded at the focal planes of the lenses to reflect the incident beam. For the purpose of evaluating the SA and DA configurations with comparable diffraction limited range definitions, the NAs are defined as.58 and.21 respectively to achieve an equivalent -3 db (FWHM) axial resolution.

2 In microscopy, a shorter wavelength in general means higher resolution. But for tissue imaging, shorter wavelength reduces tissue penetration because of tissue scattering. Although using a longer wavelength in the near infrared region gives better tissue penetration, it does compromise resolution. We have chosen a wavelength of 633 nm for this Monte Carlo simulation study as a compromise between resolution and tissue penetration depth. Clinical experimental data for tissue scattering parameters are also available at this wavelength. incident Gaussian beam y x z BS L2 L1 WD tissue M incident Gaussian beam x y y z x z L3 θ L4 collection axis WD tissue M detector (a) SA detector (b) DA Fig. 1. Schematic for (a) single axis and (b) dual axes confocal configurations used in the Monte-Carlo ASAP models. From diffraction theory, the theoretical transverse and axial resolutions for this DA geometry with an average tissue refractive index n = 1.4 at a wavelength λ = 633 nm are found to be 3,6. 466λ.466λ x = = 1.16µ m; y = = 1. µ m ; m nα cosθ nα z.466λ = = 2. nα sinθ µ (1) where α refers to the beam half angle and should be sufficiently small so that sinα = α. A Gaussian beam is used to model a light source delivered through a fiber. The mirror at the focal plane for both SA and DA configurations is located 2 µm below the tissue surface. To simplify the model and speed up simulation time, four assumptions were made in this study: 1) multiple scattering of an incoherent beam dominates over diffraction effects, 2) to eliminate aberrations the non-scattering medium surrounding the lenses and the tissue (the scattering medium) is index matched, 3) absorption is not included for there is much larger attenuation due to the scattering of ballistic photons, and 4) the lens system has a magnification of 1 from the focal plane to the detector pinhole. The angular dependence of scattering and the optical properties of non-absorbing spheres is calculated from the Henyey-Green phase scattering function given by 11,12,13,14 where g, the anisotropy factor, is defined as g p( θ ) = (2) 2 3 / 2 4π (1 + g 2g cosθ ) 2π g = cosθ = cosθ p( θ )sinθdθdϕ. (3) π The attenuation coefficient µ s and anisotropy g are determined by the size, refractive index, and concentration of tissue scatterers and then used as the ASAP simulation parameters. We consider a tissue phantom composed of polystyrene microspheres suspended in water with a diameter of.48 µm, refractive index 1.59, and a concentration of.394 spheres/µm 3, and Mie theory is used to calculate g =.81 and µ s = 5. mm -1 at λ = 633 nm. 14

3 The simulations given here are performed using two 2.8 GHz Dual-Core Pentium computers, each equipped with 2 GB of RAM. A typical simulation takes about 7 CPU hours to process 1.2 billion photons. By segmenting the simulation into four parts and using two such dual-processors running in parallel, the effective simulation time is reduced to about 2 CPU hours for each processor. 3. RESULTS 3.1. Signal and noise characteristics between DA and SA configurations To study the photons from multiple scattering we define a detector of 1 µm diameter which captures a sizable portion of the scattered photons. Since the SA detector is on the y-z plane, we let P(y, z) be the photon flux distribution on the SA detector and look at only one slice of this distribution along the y-axis. We define the normalized photon flux distribution to be P * (y) = P(y, )/P max where P max is the maximum flux at the detector. This normalized flux distribution P * (y) for the SA model is shown in Fig. 2(a). The photon flux distribution consists of two components the ballistic photons (signal) and multiply-scattered photons (noise) and the maximum flux of ballistic photons is at the center of the detector. Some multiply-scattered photons will also arrive at the detector center. Placing a pinhole in front of the detector can eliminate some but not all these noise components. If there were sufficient ballistic photons available, we would choose the pinhole size to be comparable to the spot diameter given by diffraction theory, as shown in Fig. 2(a), otherwise we might have to compromise and use a larger pinhole to get sufficient signal. For the DA case, the detector is tilted by 3 from the x-y plane, as shown in Fig. 1(b). Let P(x, y) be the photon flux distribution on the DA detector projected onto the x -y plane where x is a coordinate axis at 3 to the x-axis and z a coordinate at 3 to the z-axis. Figure 2(b) shows the normalized photon flux distribution P * (x ) = P(x, )/P max for the DA configuration along the x -axis. The choice of the x -axis is because multiply-scattered photons are symmetrically distributed along the y-axis but asymmetrically distributed along the x -axis, which is clearly seen in the isometric view of P(x, y) as shown in Fig. 2(c). Fig. 2(b) also exhibits both the ballistic and noise components. The major difference for DA is that most of the multiply-scattered photons reaching the detector are systematically swept to one side of the detector and away from the center of the pinhole. As a result, a higher ratio of ballistic photons to multiply-scattered photons are collected at the center of the DA detector, thus increasing SNR at the pinhole location Ballistic vs. multiply-scattered photons The ASAP program provides the capability to track the paths of all rays, thus making it very versatile to analyze the tissue scattering processes. The ASAP command SELECT enables users to isolate a subset of rays to analyze the number of scattering events. The command CONSIDER selects a set of optical components, such as the detector or the mirror, for ray tracing. Combining these two commands, ASAP can isolate those rays that reached the detector and count the number of scattering events for each ray so as to study the ballistic and multiply-scattered photons components for a particular confocal configuration. We consider a slab of tissue, with µ s = 16 mm -1, thickness t = 1 µm. For each ray reaching the DA detector, we trace its path history. Let N scatt be the number of scattering events for each ray reaching the detector. Starting with unit flux for the incident beam (F o =1), we plot a histogram N scatt for all rays at the detector and calculate their respective fluxes F(N scatt ) relative to F o. Figure 3 shows this histogram of F(N scatt ) for all the rays collected at the DA detector. The case N scatt = 1 refers to the ballistic photons that are scattered only once by the mirror at the focal plane. Using this method the ballistic photons and the multiply-scattered photons can be identified and sorted by order, thus providing a better understanding of the scattering process, which may potentially lead to a more efficient confocal microscope design.

4 1 ballistic photons (signal) pinhole P*(y).5 noise from multiply-scattered photons (a) SA y, µm 1 ballistic photons (signal) pinhole P*(x ).5 noise from multiply-scattered photons (b) DA x, µm P(x',y) y, µm -5 5 x', µm (c) DA isometric view Fig. 2. Normalized photon flux distribution P * at the detector for (a) single axis and (b) dual axes confocal configurations showing the ballistic component and the noise from multiply-scattered photons. (c) Isometric view of the DA photon flux distribution P(x,y).

5 Relative flux F(Nscatt) N scatt Fig. 3. A histogram of N scatt, the number of scattering events for each ray reaching the DA detector (tissue model parameters: µ s = 16 mm -1, thickness t = 1 µm) Axial response study Performing the axial response simulation by moving the mirror in the tissue along the z-axis over the range -1 µm < z < +1 µm and measuring the flux at the detector, we can show that the DA confocal architecture has improved dynamic range over the SA configuration. In this axial response study, a detector of 1 µm in diameter is divided into 11 bins along its length. The sum of the photon flux is determined for all the bins that fall within a given pinhole diameter (D). We define f( z) to be the detector flux where the mirror is at location z with respect to the focal plane at z = and let f*( z) = f( z)/f() be the normalized flux. Plotting this normalized flux f*( z) versus z gives the axial response. We define L, the total optical length of the tissue region, to be two times the product of the scattering coefficient µ s and the tissue depth t, or L = 2µ s t. The factor of two comes from the fact that the total path length is two times the tissue depth. Figure 4(a) shows the axial response on a logarithmic scale (1 log 1 f*( z)) for the SA and DA configurations with pinhole diameters D = 1, 2 and 3 µm, corresponding to typical fiber core dimensions, and L = 6.4, corresponding to typical colon epithelium parameters (µ s = 16 mm -1 and t = 2 µm). This plot indicates clearly improved dynamic range for the DA architecture compared to that of SA with all 3 pinhole diameters. The result does not take diffraction of the ballistic component into consideration, which will be developed in future Monte Carlo simulation study. Figure 4(b) shows the normalized axial responses f*( z) on a logarithmic scale for SA and DA at total optical lengths L of 4.8, 6.4 and 8. and D = 3 µm. The scattering coefficient µ s at λ = 633 nm for esophagus epithelium tissue 15 is about 7 mm -1, 2 mm -1 for normal colon mucosa, and 22 mm -1 for adenomatous colon mucosa. 16 The range of tissue depths spanned by L = 4.8 to 8 for esophagus is 34 µm to 57 µm and from 12 µm to 2 for normal colon mucosa. Even for a relatively thick tissue at L= 8, the simulation still provides sufficient photon statistics; e.g., for L = 8, an incident beam of unit flux (F o =1) with 28 million photons results in approximately 14, photons reflected from the focal plane and about 7 collected when the mirror is 1 µm away from the focal plane. For a given pinhole diameter, in this case D = 3 µm, the DA configuration has significantly better dynamic range than that of the SA over a range of optical lengths relevant to biological imaging. Fig. 4(b) also shows that by varying the optical thickness L by almost a factor of 2, scattering does not appear to alter the FWHM of the axial response for both SA and DA. Over this thickness range, the dynamic range for SA has only minimal changes, while for DA only the signal levels outside the pinhole changes significantly.

6 -5 SA(2µm) SA(3µm) 1 Log1f*( z), db SA(1µm) DA(2µm) DA(3µm) -3 DA(1µm) (a) z, µm 1 Log1f*( z), db L= 6.4 L=4.8 L=8. L= 6.4 L=4.8 SA DA L= (b) z, µm Fig. 4. Axial response of normalized photon flux shows improved dynamic range for the single axis (SA) configuration compared to that of dual axes (DA) at λ=633 nm: (a) Pinhole diameters D = 1, 2 and 3 µm for optical length L = 6.4, (b) optical lengths L = 4.8, 6.4 and 8. for pinhole diameter of D = 3 µm.

7 4. DISCUSSION The superior DA axial response can be explained by simple geometry (see Figure 5). In the SA geometry, photons scattered from the vicinity of the focal planes (± ) in the direction of the ballistic photons are all gathered by the detector through the pinhole. But in the DA case, when the mirror moves away from the focal plane by ±, the center of the beam also moves away by ±2 sinθ from the center of the pinhole. Even taking diffraction and the broadening of the out-of-focus beam into consideration, the beam flux decreases exponentially when > D/2 (for θ = 3 ). Thus, the spatial filtering effect by a pinhole for DA is more efficient than for SA as a result of this simple geometric effect. The DA confocal configuration is not only more efficient in filtering out-of-focus photons, it also collects fewer multiply-scattered photons. Consider those multiply-scattered photons that are scattered near the tissue surface (the dotted arrows in Figure 5), and suppose it is also scattered in the direction of the ballistic photons. In the SA case, these scattered photons will be gathered by the detector in spite of a pinhole to filter out-of-focus light (Fig. 5(a)). This is true for all layers starting from the tissue surface to very deep within the tissue. Of course, those multiply-scattered photons are also attenuated by the tissue. The noise component originating from the first few tens of microns of tissue dominates. This also explains the large noise volume underneath the ballistic spike of Fig. 2(a). But for the DA case, just as the out-of-focus photons are filtered efficiently by the pinhole when > D/2, it also filters out efficiently multiply-scattered photons that are in the direction of the ballistic photons as shown in Fig. 5(b). pinhole D BS tissue surface θ pinhole - focal plane + (a) SA (b) DA Fig. 5. Geometric explanation for the superior axial response of the DA configuration over the SA. The dotted arrows denote simplified paths of photons scattering near the tissue surface and shows how this relatively large component of scattered light is rejected by the DA pinhole, whereas the SA pinhole accepts this scattered light more easily. The solid arrows denote simplified paths of out-offocus light, which is also better rejected by the DA pinhole. As a result of this spatial filtering effect, the dual-axes confocal architecture provides optical sectioning capability that is superior to that of the conventional single-axis configuration in terms of SNR and dynamic range, and thus, the DA architecture allows for imaging with greater tissue penetration depths to provide vertical cross-sectional images, which has significant implications for in vivo imaging.

8 5. ACKNOWLEDGEMENTS This work was funded, in part, by grants from the National Institutes of Health, including K8 DK67618 (TDW), U54 CA15296 and R33 CA This work has also been supported by the Center for Biophotonics, a National Science Foundation Center managed by the University of California, Davis, PHY (LKW). We thank Dr. Christopher Contag for critical review of the manuscript. We also thank Breault Research Organization, Inc., for the academic license for ASAP 26 and their excellent optical software support. L. K. Wong s address is lkcwong@stanford.edu. REFERENCES 1. D. L. Dickensheets, G. S. Kino, Micromachined scanning confocal microscope. Opt. Lett. 21, (1996). 2. D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, G. J. Tearney, Three-dimensional miniature endoscopy, Nature 443, 765 (26). 3. T. D. Wang, M. J. Mandella, C. H. Contag, and G.S. Kino, Dual axes confocal microscope for high-resolution in vivo imaging, Opt. Lett. 28, (23). 4. R. H. Webb and F. Rogomentich, Confocal microscope with large field and working distance, Appl. Opt. 38, (1999). 5. T. D. Wang, C. H. Contag, M. J. Mandella, N. Y. Chan, and G.S. Kino, Dual axes confocal microscope with postobjective scanning and low coherence heterodyne detection, Opt. Lett. 28, (23). 6. J. T. C. Liu, M. J. Mandella, S. Friedland, R. Soetikno, J. H. Crawford, C. H. Contag, G. S. Kino, and T. D. Wang, Dual-axes confocal reflectance microscope for distinguishing colonic neoplasia. J. Biomed. Opt. 11, (26). 7. J. T. C. Liu, M. J. Mandella, H. Ra, L. K. Wong, O. Solgaard, G. S. Kino, W. Piyawattanametha, C. H. Contag, and T. D. Wang, Miniature near-infrared dual-axes confocal microscope utilizing a two-dimensional microelectromechanical systems scanner. Opt. Lett. 32 (in press). 8. H. Ra, W. Piyawattanametha, Y. Taguchi, O. Solgaard, Dual-Axes Confocal Fluorescence Microscopy with a Two-Dimensional MEMS Scanner", 26 IEEE/LEOS International Conference on Optical MEMS and Their Applications, Big Sky, Montana, August 26, pp T. D. Wang, C. H. Contag, M. J. Mandella, N. Y. Chan, and G. S. Kino, Confocal fluorescence microscope with dual-axis architecture and biaxial postobjective scanning. J. Biomed. Opt. 9, (24). 1. X. Gan and M. Gu, Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media, Opt. Lett. 24, (1999). 11. L. Henyey and J. Greenstein, Diffuse radiation in the Galaxy. Astrophys. Journal 93, 7-83 (1941). 12. C. Bohren, D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983). 13. A. Kokhanovsky, Optics of light scattering media (Springer, 21). 14. S. Prahl, Mie Scattering Calculator R. Bays, G. Wagnieres, D. Robert, D. Braichotte, J. -F. Savary, P. Monnier, and H. van den Bergh, Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry, Appl. Opt. 35, (1996). 16. H. J. Wei, Da Xing, Guo-Yong Wu, Huai-Min Gu, Jian-Jun Lu, Ying Jin, and Xiao-Yuan Li, Differences in optical properties between healthy and pathological human colon tissues using a Ti:sapphire laser: an in vitro study using the Monte Carlo inversion technique. J. Biomed. Opt. 1, (25).