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A method to recover the image of an object behind thin turbid layers is developed by wavefront shaping technique. The optimized wavefront is generated by modulating the scattering light of a known object with a spatial light modulator. A Pearson Correlation Coefficient is introduced as a cost function for the optimization. A beam scanning method based on optical memory effect is proposed to further enlarge the Field-of-View (FOV). The experimental results show good fidelity and large FOV of the recovered image.
©2013 Optical Society of America
1. Introduction
The propagation of light in turbid media leads to scattering and disturbance of the light wavefront. The scattering carries the spatial, temporal, spectral or polarization information of the incident signal, and turns it into a speckle field. While the ability to look through the scattering media was verified more than one decade ago [1], the restoration of scattering-imaging was realized recently. For this purpose, several schemes [2–6] have been proposed. The wavefront shaping technique [7] is one of the most promising methods. The principle is to use an active spatial light modulator (SLM) to modulate the incident (scattering) light and to transform a random medium into a lens [8], a spatial-temporal pulse shaper [9], an active spectral filter [10], an arbitrary polarization convertor [11], or even a scattering imaging system [2]. It has been shows that “looking around corners and through thin turbid layers” can be achieved by two steps [2]. Firstly, the scattered light from a point source is corrected by an optimization process. And then, any object in the vicinity of the point source can be imaged correctly with the help of the “optical memory effect” [12, 13]. The technique can work even with incoherent light and hence does not require the whole information of the scattering matrix [14], raster-scanning [3] or off-line reconstruction [5]. However the size, location, brightness as well as the wavelength of the point light source of reference [2] will affect the fidelity of the reconstructed image, which is in general significantly degraded from the object. Furthermore, it is actually impractical to implant a point light source behind the diffusive medium in many applications. However the knowledge of a certain shaped object under a scattering medium can be achieved. For example, the object detected by noninvasive method [4] can be served as a reference. Besides, the organ detected by X-ray technique below the skin can act as a reference. Meanwhile, in many medical applications, the surroundings of a tested object also play an important role in diagnosis and treatment [15]. So the development of a control scenario with a reference object is potentially possible and necessary.
In this paper, we introduce a scattering-imaging method based on a known object. A phase mask, which can recover the image of the known object, is generated by wavefront shaping technique. With the help of the optical memory effect, any other unknown object can be imaged through the scattering system using the optimized phase mask. This technique requires a global optimization with a Genetic Algorithm (GA). What is more, we further effectively enlarge the field-of-view (FOV) of the system by scanning the incident light. The experimental results show good fidelity and large FOV of the recovered image. It indicates that once a specific object in front of a scattering system is restored, objects around the reference can be identified. This technique will be important toward scattering-imaging in thin turbid media.
2. Scattering light correction based on a reference object
The experimental setup is shown in Fig. 1 . A collimated laser (He-Ne laser) illuminates the object on the object plane (OP, placed at a distance d1 from the scattering medium), and projects the diffraction pattern of the object onto the thin scattering medium (Newport 10° circular light shaping diffuser). The scattered field behind the diffuser is precisely imaged on the phase only SLM (Holoeye Pluto-VIS) by a 4-f system with Lens 1 (f1 = 45 mm) and Lens 2 (f2 = 130 mm). The modulated scattering light is captured by a CCD camera with Lens 3 (f3 = 75 mm).
Fig. 1 Experimental setup for scattered light correction based on a reference object. The back surface of the scattering medium is precisely imaged on the SLM. The focal length of lens 1, lens 2 and lens 3 is 45 mm, 130 mm and 75 mm, respectively.
Supposed an identified object, e.g. a 1 mm tall letter “S”, is placed on the object plane. If a flat phase pattern is displayed on the SLM, the image recorded on the CCD is a typical speckle pattern [Fig. 2(b) ]. However, when an appropriate phase pattern is loaded on the SLM, the distortion introduced by the scattering medium can be corrected and object is re-imaged on the CCD [Fig. 2(d)]. The SLM now acts as a phase modulator that can reorganize the speckle pattern. For example, the scattered light can be constructively interfered on the specified speckles and destructively interfered on the undesired speckles. In our experiment, GA was used to search for the appropriate phase pattern, and a LabVIEW program was built to control the SLM and the CCD. As the reference object “S” is known in advance, the target image of “S” can be constructed in computer [Fig. 2(a)]. The size of the target image can be determined according to the system arrangement and the speckle feature. A Pearson Correlation Coefficient [16] is introduced as the similarity judgment and as a cost function during the optimization process:
where, and . s and t denote the coordinates of the image. f(s,t) is the image captured by the CCD, and w(s,t) is the target image. This cost function is simple and effective. It can work well for different complex target pattern, even for a grayscale one. It is worth noting that the reference object can be of any shape. But its size and fineness will affect the speckle size. To attain the best optimization result, the speckle size should be about the pixel size of the CCD. To lower the memory requirement of the computer hardware and reduce the optimization time, only 96 × 54 pixels of the SLM is used (20 × 20 physical pixels were combined as an effective pixel). The GA program (Matlab Optimization Toolbox) involved a population size of 30, crossover fraction of 0.6, a random mutation of 0.5% of the segments, and elite count of 4. The optimization process is shown in Fig. 2(c). After about 3000 generations of iteration, the optimization program almost tended to converge. The correlation coefficient calculated with the recovery image and the target image is about 0.8. The whole optimization process costs tens of minutes, depending on the complexity of the target image.Fig. 2 Optimization process and results. (a) Constructed image of the reference object: a letter “S” with the size of about 1 mm. (b) Before correction, the reference object “S” is directly imaged through scattering system (with a flat pattern on SLM). (c) The evolution of correlation coefficient in the optimization process. (d) The optimized result. Inset: the optimized phase pattern (0~2π). (e),(f)Images of replacing the letter “S” with letters “O” and “E”, respectively. Scale bars, 1mm.
After the optimization process, the optimized phase pattern (inset in the Fig. 2(d)) is determined. The reference object is replaced with any other unknown object. And at the same time, the optimized phase pattern is kept displaying on the SLM. With the help of the memory effect, the image of the tested object can be detected in real time. Figure 2(e) is the recovered image of the letter “O” and Fig. 2(f) is the recovered image of the letter “E”. They both contain most of the essential information of the tested object and the recovered images are of a high fidelity.
To demonstrate the memory effect and test the Field-of-View (FOV) of the system, a pinhole-tracking experiment was conducted. With the same phase pattern that recovered the image of letter “S”, we replaced the letter “S” with a 200 μm pinhole and moved it laterally (along the x axis). The series of images of the pinhole are shown in Fig. 3 . Figure 3(a) shows the image of the pinhole (green) at different positions. The imaging results of the pinhole at different positions (green) are overlapped with the reference target image (red). Figure 3(b) displays the normalized intensity of the image spot, where the red line shows the relative intensity that drops to 1/2 of the peak value. The tracking results indicate that the optimized phase pattern can help to recover the image from the scattered light with certain amount of FOV. On the other hand, in contrast to the image recovery with a point-based optimization method [2], the peak intensity is not at the center, and the curve does not show symmetric property around the center. It is believed that the formation of the desired image point is not only contributed from a single corresponding object point, but is also the interference result of the whole illuminated object. For example if the reference object is replaced by a pinhole, the image of the pinhole is the total memory effect of points on the whole reference object. The nearest reference point always contributes mainly to the imaging result. Although this effect may cause the intensity variation in the recovered image, it will not reduce the fidelity greatly. As shown in Fig. 3(b), the Full-Width-at-Half-Maximum (FWHM) is about 1.5 mm. Hence the FOV of this system is estimated to be 3 mrad.
Fig. 3 Pinhole tracking experiment. (a) Images of a pinhole shifting laterally on the object plane (green), overlapped by the optimized image of the reference letter “S” (red). (b) Normalized intensity of images of the pinhole (blue line). The red line indicates the intensity that drops to 1/2.
3. FOV enlargement
The optical memory effect found by Feng et al [13] indicated that two incident light waves with a certain correlation will maintain some of the correlation after passing through scattering media. When object points from different lateral positions diffract onto the surface of the scattering medium, their diffraction centers will not overlap. So the correlation between them will become little. As a result, it causes a limited FOV, as shown in Fig. 3(b). However, rotating the incident light while keeping the same illumination region could result in stronger correlation and a wider FOV. In this situation, the correlation function C(qL) has the form of [13]
where q = 2πθ/λ, θ is the tilting angle, λ is the wavelength of light, and L is the effective thickness of the turbid medium. Equation (2) shows that FOV of the system is proportion to λ/L. If the scattering medium is relatively thin (L is small), the FOV will be large.As shown in Fig. 4(a) , only the reference object (Fig. 4(b), the letter “S”) is illuminated if incident beam is shrinked to the size of the FWHM of the shifting correlation range (1.5 mm). The tested object is consisted of three letters: “O”, “S”, and “A” [Fig. 4(b)]. Assuming that only the “S” in the middle is a priori known, the others are to be identified. After the execution of the optimization algorithm, the phase distribution used for calibration is found and the desired recovery image of the reference letter [Fig. 4(c)] is obtained. If the incident light is expanded to cover the size of the whole tested object, only small part of the adjacency around “S” can be imaged [Fig. 4(d)]. For a larger detection range, a different scheme is needed to enlarge the FOV. Basically, the shrinked incident light is tilted by a reflection mirror to illuminate the other unknown area of the tested object. The illumination region on the scattering media surface should be the same while scanning. With the optimized phase displayed on the SLM, the information of the unknown tested object can be detected and identified [Fig. 4(e), Fig. 4(f)]. Finally, the scanning results are overlapped and the full view of the tested object is shown in Fig. 4(g). Compared to the direct illumination method [Fig. 4(d)], the imaging result is much wider and clearer. This result confirms the validity of the approach. By tilting the illumination, the objects around the reference can be detected. Besides, the speckle noise will be suppressed when the illumination area is reduced, as the disturbance from the undetected area of the tested object can be effectively excluded.
Fig. 4 Experiment for FOV enlargement. (a) Experimental setup of scanning mechanism. The parts (not shown here) after the scattering medium are the same as those in Fig. 1. (b) Tested object placed on the object plane. (c) Optimization result of the reference object. (d) Image of directly illuminating the whole tested object. (e) Image of tilting the incident light to illuminate the letter “O”. (f) Image of tilting the incident light to illuminate the letter “A”. (g) Combination of the figures (c), (e) and (f). Scale bars, 1mm.
In our experiment, a strongly scattering polycarbonate diffuser is used as a scattering medium. Although it may severely disturb the incident wavefront (phase only), the thickness of the scattering sample is about 1.2 μm. The observation angle due to memory effect is about tens of milliradian. This result is in agreement with the reported result in the supplementary material of reference [4]. The corresponding field is approximately 6.6 mrad in this experiment, which is till well within the range of the memory effect.
4. Discussion
This system can be also applied to the reflection situation, such as a piece of paper or a wall. In the situation of reflection geometry, the effective thickness L in Eq. (2) should be replaced by the scattering mean free path l. Although only two-dimensional objects were tested in this experiment, the system should work in principle to resolve the image along the axial as well. By shifting the tested object in z direction or multiplying the illumination light by a quadratic wavefront, we can make use of the axial memory effect [17] to detect the axial information. The resolution of a typical scattering lens system is given by δx = λd1/πw at lateral and δz = (2λ/π)(d1/w)2 at axial [1], where w is the diameter of the illumination on scattering surface, d1 is the distance between the tested object and the scattering medium in Fig. 1. The size of the letters used in the experiment is 4 point (font size), about 1 mm tall, which is much bigger than the system’s resolution. By precisely adjusting the system and working in a higher index medium, it is possible to provide a resolution exceeding sub-100 nm [18]. By modulating the phase of each incident channel and making them constructive interference at one spatial area, the signal of an optimized single speckle to noise (the average background) can reach to η~(π/4)NSLM, where NSLM is number of segments of the SLM [19]. When an object to be optimized is N times larger, the intensity enhancement of the desired region will reduce to ηN = η/N. Besides, the increase of N is harmful to the convergence rate of the optimization program and reduces the image recovery quality. Thus, appropriate choices of the system resolution and speckle size are necessary and helpful.
The optimized phase pattern can effectively suppress the speckle background. The speckle artifacts in the recovered images are relatively small compared to other speckle imaging systems. The speed of GA algorithm is mainly limited by the refresh rate of the SLM. By using Micro Optoelectro Mechanical System based SLM and high-speed camera, it is possible to reduce the optimization time to seconds or even shorter. It will be beneficial to the applications in life science [20]. Finally, the application of this system is mainly limited by the effective thickness of the scattering media. This technique will work most efficiently in situations with a thin scattering material. Besides, detection of objects surrounded by the scattering media is not available in this experiment, since a scatter-free laser beam is needed to illuminate the tested object.
5. Conclusions
A technique for reconstructing scattered light imaging is presented. A known reference object is applied to the wavefront shaping system. After a GA-based optimization search, an appropriate phase distribution can be found to reshape the scattered light. Once the reference is replaced with any other unknown tested object, its image behind the thin scattering medium can be recovered with the help of optical memory effect. Besides, a scanning scheme of the incident beam for FOV enlargement and imaging quality improvement is proposed and demonstrated. With the Person Correlation Coefficient as a cost function, the achieved image quality is of high fidelity.
In conclusion, this technique has potential applications in image recovery. Examples of the potential application include security monitoring, biomedical imaging, as well as damaged imaging-device repairing.
Acknowledgment
This work is supported by the Chinese National Natural Science Foundation (10934011) and the National Basic Research Program of China (2012CB921904). The authors gratefully acknowledge Li Li and Yan Sheng for helpful discussion on this work.
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