Noninvasive optical tomographic imaging by speckle ensemble

Transcription

1 Invited Paper Noninvasive optical tomographic imaging by speckle ensemble Joseph Rosen and David Abookasis Ben-Gurion University o the Negev Department o Electrical and Computer Engineering P. O. Box 653, Beer-Sheva 84105, Israel ABSTRACT We survey recently invented methods o optical tomographic imaging through scattering medium. The threedimensional structure o an object hidden between two biological tissues is recovered rom many noisy speckle pictures obtained on the output o a multi-channeled optical imaging system. Keywords: Scattering Medium, Speckled Images, Microlens Array, Optical tomography. 1. INTRODUCTION Medical tomography techniqes such as X-ray Computed Tomography (CT) 1 oer great advantages and are still widely used despite the act that they suer rom several drawbacks such as ionizing radiation, a complex structure and highcost. The advantage o optical tomography over other medical tomography techniques is that they provide quantitative inormation on unctional properties o tissues, while being non-harmul (the radiation is non-ionizing). Accordingly, in the recent years researchers have invested considerable eort towards developing optical tomography systems that use near-inrared (NIR) light. The most well-known system is the optical coherence tomography (OCT) system. 2 OCT synthesizes cross-sectional images rom a series o laterally adjacent depth-scans with high depth and transversal resolution. However, OCT involves a cumbersome intererometric process with complicated reconstruction algorithms to generate accurate cross-section images o various body parts. In the present study we suggest a simple optical tomography technique that is based on speckled images. The proposed system is an extension toward three dimensional (3D) imaging o our previous works, reerred as Noninvasive Optical Imaging by Speckle Ensemble (NOISE) 3,4 and its modiied version 5 NOISE-2. Thereore, we term the present technique as NOISE-3D. In the irst NOISE system the hidden object was reconstructed rom many speckled images ormed by a microlens array (MLA). Each microlens rom the array projects a small dierent speckled image o the hidden object onto a CCD camera. In the reconstruction algorithm, all the noisy images rom the array are shited to a common center and then accumulated to a single average picture thereby revealing the shape o the hidden object. In NOISE-2, a dierent algorithm was implemented on the same optical system, preventing the need to shit the speckled images to a common center. In addition to recording the speckled images o the object, we recorded speckled images o a point-like object generated by illumination through the medium with a point-source. Each sub-image o the speckled object with a corresponding sub-image o the speckled point-like object were placed together side by side in the computer. Then, by computing the autocorrelation o each joint sub-image, and averaging over all the autocorrelations, a cross-correlation between the object unction and a narrow point-like unction is reveled. This method resulted in a better reconstruction o the hidden object compared to that achieved by the irst NOISE technique. The improvement can be attributed to the averaging process by which avoids the need to estimate the common center o each noisy sub-image. In NOISE-2, as long as all the objects images have the same distance to their corresponding point-like images, all the sub-images are automatically averaged as i they are all centered at the same point. In this study we extend NOISE-2 in order to develop a new imaging technique or embedding objects in a scattering medium. In addition to reconstructing the object, its location in the 3D space is also extracted. Thereore, the proposed system has the advantage o revealing and acquiring depth inormation o objects seen through a scattering medium. This technique diers rom recently proposed depth extraction systems using lens array 6,7 since our system observes scenes hidden beneath a scattering media and uses a dierent algorithm or depth acquiring. Optical Inormation Systems III, edited by Bahram Javidi, Demetri Psaltis, Proceedings o SPIE Vol (SPIE, Bellingham, WA, 2005) X/05/$15 doi: / Proc. o SPIE

2 Scattering Layers T 1 MLA- Right Right Channel CCD Laser Beams T 2 Hidden Objects Adjustable Pinhole L R MLA- Let L L CCD Let Channel Computer Pinhole Image Speckled Images o the Object Average Spectrum Fourier Transorm 2 Fourier Transorm Average Autocorrelation Recovered Objects Figure 1: Schematic diagram o the proposed stereoscopic NOISE system. The lower block diagram describes the computational process o each channel. Proc. o SPIE

3 Figure 1 is a schematic diagram o the proposed 3D imaging system. The coniguration consists o two MLAs accompanied by imaging lenses, a pinhole (implemented by an adjustable iris) placed behind the second scattering layer T 2 and conventional CCD cameras. Each path, let and right separately, is equivalent to that given in Re [5]. However, it should be noted that unlike NOISE-2, in the present setup the point-source is placed in ront o the scattering medium, and thus serves as a reerence point instead o as a point-source o illumination. We ind that this change improves the reconstructed image because now light rom the pinhole is no longer scattered. Thereore the pinhole's image is narrower and so is its cross-correlation with the object's image. The idea behind this point technique is to ascribe the location o an object to a location o some known point in space. The computational process at each channel is schematically described in the lower part o Fig. 1. Like in NOISE-2, the computational process yields three spatially-separated terms at the output o each path. One term is the zero-order at the vicinity o the output plane origin. This term is equal to the sum o the pinhole autocorrelation and the object autocorrelation. The other two terms correspond to the cross-correlation between the object and the pinhole and thus, assuming the average pinhole image is close to a point, these terms approximately yield the object reconstruction. The image o the hidden object can thereore be retrieved by reading it rom one o these orders. Note that in this scheme the distance o the reconstructed object rom the output plane origin is related directly to the transverse gap between the object and the reerence point. θ Right Detection Plane T 2 MLA-RIGHT d R x R Object Reerence Point φ h B R z B L n t MLA-LEFT z p x L d L Let Detection Plane z o Figure 2: Perspective projection geometry o the object and the reerence point through each channel. Proc. o SPIE

4 To extract the depth inormation about the object we initially use the principle o stereoscopic vision, ignoring, or the time being, the eect o the scattering medium T 2. In the diagram depicted in Fig. 2, the projection o the object and the point-reerence on the image planes o both arrays can be presented as ollows: xr cosθ BR ( xr d R ) cosθ BR h, z (1a) p zo or the right channel, and xl cosθ BL ( x L d L ) cosθ BL + h, (1b) z p zo or the let channel. z o and z p are the distance o the object and the pinhole rom the center o the array respectively. B R and B L represent the distance o each array rom the z axis. d R and d L are the gaps between the images o the reerence point and the observed object, in the right and let channels, respectively. x R and x L are the displacements o the reerence point images rom the horizontal axis which crosses the center o each microlens, in the right and let channels, respectively. h is the transverse gap between the object and the pinhole, and θ is the tilt angle o each array. Solving the our equations o Eqs. (1), yields the distance between each array plane to the object, given by z o B z p = B z D cosθ p where B=B R +B L is the baseline and D=d R +d L is the sum o the object-reerence point gaps at the two channels. It is clear rom Eq. (2) that dierent perspectives lead to a slight displacement o the object in the two views o the scene. Equation (2) has the advantage that one needs only to measure D which is related to the sum o the distances o the reconstructed object rom the output plane origin at the two channels. Accordingly, we achieve a simple method or obtaining the object s depth since in our coniguration the baseline B, the ocal length and the pinhole distance rom the MLA z p are known parameters. Calculating D, as described below, we can estimate the depth inormation z o o an object rom the MLAs in an imaged scene. Note that by using the pinhole there is no need to know the object and the reerence point locations which are diicult to estimate in such a noisy scattering system. This is an additional advantage or using a method with a reerence point. Since objects are covered under the layer T 2 with higher-than-one index o reraction, while the reerence point is positioned in ront o T 2, the obtained gap between each object and the reerence point in each channel is dierent than the situation without the layer T 2. Considering the Snell law, and the act that the layer T 2 is tilted relatively to the optical axis o each array, the corrected displacement D rom the measured displacement D ~ is ~ 2 t sin φ cosφ D = D + 1 () 3 z 2 2 sin o n φ ~ ~ ~ where D = d R + d L is the sum o the object-reerence point gaps at the two channels measured ater introducing the layer T 2, t and n are the thickness and the reractive index o the scattering layer, respectively and φ is the angle between the z axis and the ray connecting the centers o the object and the MLA. The second term in Eq. 3 describes the size change o the image as a consequence o the layer T 2. Since φ and z o are unknown beore calculating Eq. (1), φ and z o are initially approximated as θ and z p, respectively, in order to yield an initial estimation or D. The next step is to extract the inormation about the displacement D ~ rom the reconstructed image. According to the technique o NOISE-2 (depicted in the lowchart o Fig. 1) or each path, each sub-image o the speckled point reerence with a corresponding sub-image o the object (recorded by a dierent exposure where the iris is opened) is Fourier transormed and the square magnitude o each sub-spectrum is accumulated with all the other sub-spectrums. This average joint power spectrum is then Fourier transormed, which yields the output correlation plane. This plane in turn yields a symmetric image reconstruction around the plane origin. By taking one o the irst orders, we count the number o pixels that range rom this order to the plane origin. The distance in pixels is converted to a real distance at the arrays image plane by subtracting the sub-matrix width, by multiplying the pixel number with the size o the CCD pixel and by dividing it by the magniication o the imaging lenses L R and L L. These operations are implemented on each path in order to estimate D ~. By calculating D using Eq. 3 we can now calculate the object depth by using Eq. 2. ( 2) Proc. o SPIE

5 LEFT LEFT Object gaps One image rom the array (a) with T2 (b) without T2 (c) One image rom the array (d) with T2 (e) without T2 () d=0mm d=2mm d=4mm Figure 3: Summary o the imaging results obtained by NOISE-3D. Experiments with two separated cylindrical sticks as observed objects were carried out using the coniguration shown in Fig. 1. The sticks had a length o 20mm and a diameter o 2.1mm each. During the experiments, the let-stick was constantly attached to tissue T 1 while the right stick was moved longitudinally toward the MLAs, at three dierent positions. Thus, the relative longitudinal displacements between the sticks were: 0mm (the objects are at the same plane), 2mm and 4mm. The sticks were embedded between two slabs o chicken breast separated by a distance o 12mm. This scattering medium is characterized by a scattering coeicient o µ s =128±9(cm -1 ) [see Re. 4] and absorption coeicient o µ a 0.2(cm -1 ). 8 The thicknesses o the rear tissues T 1 and the ront tissue T 2, were about 3mm and 4.5mm, respectively. The reerence point was created by placing a pinhole with an adjustable aperture at a short distance (22mm) behind tissue T 2, between T 2 and the MLAs. The rear tissue T 1 was illuminated by two diagonal collimated plane waves emerging rom o He-Ne laser at 632.8nm with 35mw. The two MLAs (AdaptiveOptics, S) were placed at a distance o z p =162mm rom the pinhole. Each MLA consists o micro-lenses, but only 3 8 were used in this experiment. Using more than 3 columns per channel introduces a considerable dierent perspective o the object into the averaged image, and thus the reconstructed image is degraded. The diameter o each micro-lens is 0.6mm and its ocal length 6.3mm. The image plane o each MLA is projected onto the CCD (PCO, PixelFly, with 1024x1280 active pixels and pixel size o µm) plane by a single spherical lens L L and L R respectively, each with a ocal length o 120mm and a diameter o 150mm. These lenses, with magniication o 1.3, matches the MLA size with the CCD size and are suiciently large to cover the MLAs. At each channel the distance rom the MLA to the imaging lens is 210mm and the distance rom the MLA to the CCD plane is 280mm. The baseline B is 80mm. Ater acquiring the sets o the observed image in each path, a computer program was employed to reconstruct the sticks and to determine their distance rom the MLAs according to Eqs. (2) and (3). A summary o all the results is displayed in Fig. 3. Columns (a) and (d) show typical sub-images obtained rom a typical microlens without using the averaging process. The reconstructed images derived rom the averaging process on the images o the hidden sticks with dierent relative displacements between the objects are shown in column (b) or the let channel, and (e) or the right channel. Note that the reconstruction o one o the sticks (the right-one rom Fig. 1) in the Proc. o SPIE

6 pictures is improved as a consequence o its closeness to the scattering layer T 2, while the other stick (the let-one rom Fig. 1) remains ar rom T 2. Columns (c) and () show the same reconstructed images obtained by removing the second tissue T 2 on the same setup. The eect o stereoscopic vision is clearly demonstrated in these igures by observing that in the right path the relative distance between the sticks gets smaller while in the let path the distance grows as a consequence o moving the right stick longitudinally towards the MLAs. Measuring corresponding distances in dierent igures can succeed only when there are well-seen indicators on the objects that are viewed rom the two channels. In our almost vertical sticks we choose to reer to the central point o each stick as the object point or the distance measurements. Using these measurements, and applying Eq. 3 and Eq. 2, our results indicate that the relative distances between the sticks without taking T 2 into account are 0.302mm, 2.414mm and 4.397mm instead real distances o 0mm, 2mm and 4mm while when taking T 2 into account the relative distances between the sticks are 0.24mm, mm and 4.548mm. The average error in measuring z o is less than 0.1%. In conclusion, we presented an optical tomography system which enable us to observe the relative gap between objects hidden in a scattering medium. The system was veriied experimentally with a low error o deviation. The proposed system operates with low computational complexity and is robust to the object depth variations. This research was supported by the Israel Science Foundation grant 119/03. Reerences 1. J. G. Webster, Minimally Invasive Medical Technology, (IoP, Bristol and Philadelphia, 2001), A. F. Fercheri, W. Drexler, C. K. Hitzenberger and, T. Lasser, "Optical coherence tomography principles and applications," Rep. Prog. Phys. 66, (2003). 3. J. Rosen and D. Abookasis, "Seeing through biological tissues using the ly eye principle," Opt. Exp. 11, (2003). 4. J. Rosen and D. Abookasis, "Noninvasive optical imaging by speckle ensemble," Opt. Lett, 29, (2004). 5. D. Abookasis and J. Rosen, "NOISE 2 imaging system: seeing through scattering tissue with a reerence point," Opt. Lett, 29, (2004). 6. Y. Frauel and B. Javidi, "Digital three-dimensional image correlation by use o computer-reconstructed integral imaging," Appl. Opt, 41, (2002). 7. J.-H. Park, S. Jung, H. Choi, Y. Kim, and B. Lee, "Depth extraction by use o a rectangular lens array and onedimensional elemental image modiication," Appl. Opt, 43, (2004). 8. G. Marquez, L. V. Wang, S-P Lin, J. A. Schwartz, and S. L. Thomsen, "Anisotropy in the absorption and scattering spectra o chicken breast tissue," Appl. Opt, 37, (1998). Proc. o SPIE