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Imaging through a scattering medium has been a main challenge in modern optical imaging field. Recently, imaging through scattering medium based on wavefront shaping has been reported. However, it has not been clearly investigated to apply the optical memory effect based iterative wavefront shaping technique in speed estimation of a moving object through scattering medium. Here, we proposed to combine the iterative wavefront shaping technique with laser speckle contrast analysis method to detect the relative speed changes of moving objects through scattering medium. Phantom experiments were performed to validate our method.
© 2016 Optical Society of America
1. Introduction
Imaging through scattering medium is essential for numerous applications, ranging from astronomical observations through the turbulent atmosphere [1] to microscopic imaging in biological tissues [2]. However, it is difficult to achieve clear image because the random refractive index variations within the media distort the spherical wavefronts generated by every point source, resulting in a smeared image (or specked image with coherent illumination [3,4]). Recently, several methods have been proposed for imaging through scattering media, for example optical phase conjugation [5,6], measurement of the transmission matrix [7,8], speckle intensity correlation [9–11], and wavefront shaping [4,12]. Optical phase conjugation can force a transmitted light field to retrace its trajectory through a target and recover the original light field [5], which needs two processes separately: recording and recovering. Measurement of the transmission matrix, based on a spatial phase modulator together with a full-field interferometric measurement on a camera, can allow light focusing and imaging through the random medium and might give important insight into the mesoscopic properties [7]. The spatial speckle intensity correlations method can also be used to detect and identify objects within a heavily scattering medium using the phase retrieval algorithm. It has been attempted in fluorescence image with the speckle scanning technique [10], single-shot imaging [9] through the heavily scattering medium, and imaging the light field through heavily scattering random medium [11]. This method is limited by some conditions, such as object’s sparsity, camera full well capacity and the number of statistical speckle grains [9]. The wavefront shaping technique is based on the optical memory effect of scattering medium, in which the phase of the light is controlled spatially to compensating the phase distortion due to random scattering so that the real-time wide-field imaging using scattered light can be achieved [4,13]. It has been used in fluorescence image [14–16], depth-enhanced two dimensional optical coherence tomography [17,18] through the scattering medium.
In recent years, not only the static object imaging through the scattering medium, but also the moving object imaging through the scattering medium aroused people’s interest with a variety of methods. Newman et al. [19] demonstrated spatial speckle intensity correlations can be used to detect and identify objects moving within a heavily scattering medium. By taking the difference between time-varying scattering fields caused by a moving object and applying optical time reversal, Zhou et al. [20] showed light can be focused back to the location previously occupied by the object and demonstrated this approach with discretely moved objects. Ma et al. [21] demonstrated real-time focusing in dynamic scattering media and moving-object tracking by rapidly measuring the perturbed optical field followed by adaptively time reversing the phase-binarized perturbation. However, it has not been clearly investigated to apply the iterative wavefront shaping technique based on the optical memory effect in detection of moving object through scattering medium.
In this paper, we combined the wavefront shaping technique with laser speckle temporal contrast analysis method [22,23] to achieve relative speed changes evaluation of moving objects through scattering medium.
2. Experimental setup and methods
The experimental setup shown in Fig. 1 is based on the wavefront shaping technique and laser speckle temporal contrast analysis method.
Fig. 1 Experimental setup is shown for speed detection of moving object through scattering medium. Laser, Neutral density filter (ND), Collimating lens (CL), Moving diffuser (MD), Object plan (OP), Beam dump (BD), Beam splitter (BS), Objective (O1 and O2), Lens (L1 and L2), Charge coupled device (CCD), Spatial Light Modulator (SLM). Moving diffuser is a piece of moving ground glass or a fluid sample set at the speed of v.
A collimated laser (He-Ne laser, Melles Griot, America; 632.8 nm and 15 mW) illuminates the object on the object plane, and then the diffraction pattern of the object passes through a thin scattering medium (Thorlabs 20°circular light shaping diffuser). The distance between the object plane and the thin scattering medium is 20 cm. The scattered field behind the diffuser is imaged on a phase only spatial light modulator (SLM, Holoeye Pluto-VIS) using the objective 1 (0.30NA, × 10 objective) and the lens 1 (f = 80 mm). This yields a magnification of the diffuser surface by a factor ~3 on the SLM. The surface of SLM is imaged on the plane of the lens 2 (f = 200 mm) with demagnification of ~3 using the lens 1 and the objective 2 (0.25NA, × 10 objective). A CCD is placed at the back focal plane of the lens 2.
The experimental procedure was divided into two stages: the optimization stage and imaging stage. In the optimization stage, a point object was produced by a 100 um pinhole, placed on the object plane and illuminated by a collimated laser beam. In order to balance among the memory requirement of the computer, the optimization time and the optimization result, the SLM was divided into 192 × 108 equally sized square segments. The phase of different segments was optimized using a genetic optimization algorithm, which used a population size of 30, crossover fraction of 0.7, a random mutation of 0.05% of the segments, and elite count of 4. An image with a circle bright spot about 100 um in diameter at the central of the image [Fig. 2(a)] is used as the optimized target, which is used to calculate the Pearson Correlation Coefficient [12] with the image recorded by CCD after loading a new phase pattern on the SLM. The spatial correlation coefficient between the image recorded by CCD camera and the target image was used as the similarity judgment and as a cost function in the genetic algorithm during the optimization process. The genetic algorithm was written by C language and a dynamic link library file was generated to be used in a home-made LabVIEW system control program. The CCD exposure time was set to be longer than the refresh period of the SLM to reduce the flipping noise of the SLM. In the optimization stage, the exposure time was 30 ms to balance the flipping noise and the whole optimization time.
Fig. 2 Optimization process and results: a, An optimized target image corresponding to the pinhole: an image with a circle bright spot about 100 μm in diameter at the central of the image. b, Before correction: point light source is directly imaged through scattering system (with a flat pattern on SLM). c, After correction: a point image is generated when an appropriate phase pattern is loaded on the SLM. Inset: the optimized phase mask. d, The optimization process is shown by the correlation coefficient along the iteration times in the genetic algorithm. e, The imaging of a double-hole aperture after correction. f, The imaging of a ‘-’ shape aperture after correction. Scale bars: 500 μm.
In Fig. 2, the optimization process [Fig. 2(d)] is shown by the maximal correlation coefficient in the population along the iteration times in the genetic algorithm. During the optimization process, the maximum correlation coefficient could reach 0.88 after 3000 iterations and an appropriate phase pattern can be finally obtained. The speckle image [Fig. 2(b)] was captured by CCD camera when a flat pattern was loaded on SLM before correction, while the distortion introduced by the scattering medium can be corrected significantly and a point image [Fig. 2(c)] was obtained on the CCD camera when an appropriate phase pattern [shown at the bottom-left corner in Fig. 2(c)] is loaded on the SLM. Based on the optical memory effect [24–26], if the wavefront of the light beam is tilted within a certain angular range, the output wavefront could be regarded as equally tilted, resulting in the translation of the far-field speckle pattern at a distance behind the scattering medium. So the object near the point source can be imaged on the receiving plane (CCD camera) by using the same correcting phase pattern of SLM. In the imaging stage, we tested the correcting performance by replacing the pinhole with a double-hole aperture and a ‘-’ shape aperture. Figure 3(e) and Fig. 3(f) showed the images obtained by CCD camera when the double-hole aperture and ‘-’ shape aperture were used as objects respectively. The field of view (FOV) of the scattering imaging system is inversely proportional to diffuser thickness L and directly proportional to the distance R of the scattering medium from the object plan. It is given by FOV≈Rλ/(πL), where λ is the optical wavelength [4].
Fig. 3 The moving ground glass experimental results: the raw images through a highly scattering diffuser and the speed maps with laser speckle temporal contrast analysis at different speeds. a and b, the raw images without correction (loading the flat pattern on the SLM) at different speeds: lower speed (3.06 mm/s) and higher speed (7.64 mm/s). c and d, the speed maps obtained with the laser speckle temporal contrast analysis corresponding to (a) and (b). e and f, the raw images with correction (loading the optimized pattern on the SLM) at different speeds: lower speed (3.06 mm/s) and higher speed (7.64 mm/s). g and h, the speed maps obtained with the laser speckle temporal contrast analysis corresponding to (e) and (f). Scale bars: 500 μm.
By using the wavefront shaping technique based on the optical memory effect, an object can be imaged through the scattering system. When the object is moving, the motion of scattering particles can cause spatial-temporal intensity fluctuations of imaged speckle when a coherent light is incident on a dynamic turbid medium. The speed map can then be obtained with the laser speckle temporal contrast analysis method [23]. The value of the speckle temporal contrast Kt at pixel (x, y) was calculated as
where Ix,y(n) is the CCD counts at pixel (x, y) in the nth raw laser speckle image, N is the number of images acquired, and <Ix,y> is the mean value of CCD counts at pixel (x, y) over the N images. Laser speckle contrast imaging (LSCI) maps the two-dimensional changes in speed of scatters based on analyzing speckle contrast linked to the electric field autocorrelation time of fluctuating speckle (τc). It is usually accepted that the τc is inversely proportional to velocity of the moving scatters [27]. However, the relation between temporal speckle contrast Kt and correlation time τc of electric field autocorrelation function is affected by many factors such as, static scattering, speckle size, the velocity distribution of moving scatters [27]. Although it is still difficult for laser speckle contrast imaging to get the absolute speed of moving particles until now, the changes in 1/τc measured by laser speckle contrast imaging showed good linear relationship with the relative speed changes of moving scatters in previous studies [22, 28]. For the case of T/τc →∞ (T is the CCD camera exposure time), 1/K2 was reported to be an approximate estimation of T/τc [28].3. Result
To validate the method we proposed here, two phantom experiments were performed by using the moving ground glass and the fluid phantom.
3.1 Moving ground glass experiment
In the moving ground glass experiment, a piece of moving ground glass was placed at the back of a rectangular aperture (1 mm × 0.2 mm). The speed of the moving ground glass, driven by a stepper motor, was set at the range from 0.76 mm/s to 8.40 mm/s and the speed step was set to 0.76 mm/s. The CCD exposure time used in the image stage was 40 ms. A stack of 100 speckle images were recorded by the CCD camera for each speed.
Then, speed maps were reconstructed by using the laser speckle temporal contrast analysis method at each speed. The value of speckle temporal contrast Kt at pixel (x, y) was calculated with Eq. (1). And then, 1/K2, is used as an approximate estimation for the speed of the moving object [27]. Raw laser speckle images and the speed maps at the different speeds of the moving object are given in Fig. 3. Figure 3(a) and Fig. 3(b) show the raw laser speckle images without correction (loading the flat pattern on the SLM) at different speeds: lower speed (3.06 mm/s) and higher speed (7.64 mm/s), while Fig. 3(e) and Fig. 3(f) are the laser speckle raw images with correction (loading the optimized pattern on the SLM) at different speeds. It can be clearly seen that there is a clear “-” shape object (the rectangular aperture) in the raw images with correction while the raw images without correction only show uniform speckles. The raw images with correction can extract the speed information of the moving object. Based on the laser speckle temporal contrast analysis method, Fig. 3(g) and Fig. 3(h) represent the speed maps obtained corresponding to Fig. 3(e) and Fig. 3(f). In the speed maps, it is easy to see that there are both the shape and speed information of the object, and the higher speed the object moves with the bigger speed value it has.
In order to further show the capability of detecting the speed changes of moving object through scattering medium by wavefront shaping technology and laser speckle contrast analysis method, the same region of interest (ROI, about 30 × 30 pixels) is chosen from the speed maps obtained at different speeds and the average speeds within the ROI of the moving object at different speeds were calculated and plotted in Fig. 4. The linear relationship between the actual speed of moving object and the measured relative speed with the laser speckle temporal contrast analysis method is shown in Fig. 4. It is clear to see that our proposed method can detect the changes in speed of moving object through scattering medium very well. After compensating the wavefront distortion caused by scattering medium with SLM, the object can be imaged on the CCD camera through the scattering medium. Then the temporal statistics of the light field imaged on the CCD can be related to the speed of moving objects.
Fig. 4 1/K2 versus the actual speed both with correction and without correction in the moving ground glass experiment. (1/K2) is calculated from the same region of interest (ROI) in the raw images of the moving object at a range of different speeds without wavefront correction (the red square, ROI chosen in Fig. 3(d)) and with wavefront correction (the blue circle, ROI chosen in Fig. 3(h)).
3.2 Fluid phantom experiment
In the fluid phantom experiment, the moving ground glass was replaced with a fluid sample in Fig. 1. 0.5g/100 mL PMMA (Poly methyl methacrylate microsphere, 10 μm in diameter) solution was pushed into a glass tube with inner size of 5.7 mm × 1 mm by a syringe-based infusion pump (Stereotaxic Syringe Pump, Stoelting CO., USA). The speed of the fluid was set from 2.00 mm/s to 8.07 mm/s and the speed step was set to 1.009 mm/s. The CCD exposure time used in the image stage was 40 ms. A stack of 150 speckle images were recorded by the CCD camera for each speed.
As in the moving ground glass experiment, speed maps were reconstructed by using the laser speckle temporal contrast analysis method at each speed. Raw laser speckle images and the speed maps at the different speeds of the fluid are given in Fig. 5. Figure 5(a) and Fig. 5(b) show the raw laser speckle images without correction (loading a flat pattern on the SLM) at different velocities: lower speed (5.05 mm/s) and higher speed (8.07 mm/s), while Fig. 5(e) and Fig. 5(f) are the laser speckle raw images with correction (loading the optimized pattern on the SLM) at different speeds. It can be also clearly seen that there is a clear “-” shape object (the rectangular aperture) in the raw images with correction while the raw images without correction only show uniform speckles. Based on the laser speckle temporal contrast analysis method, Fig. 5(g) and Fig. 5(h) represent the speed maps obtained corresponding to Fig. 5(e) and Fig. 5(f). In the speed maps, it is also easy to see that there are both the shape and speed information of the object, and the higher speed the particles moves with the bigger speed value it has. And then, the relationship between the actual speed of fluid and the measured relative speed changes with the laser speckle temporal contrast analysis method is shown in Fig. 6.
Fig. 5 Fluid experimental results: the raw images through a highly scattering diffuser and the speed maps with laser speckle temporal contrast analysis at different speeds. a and b, the raw images without correction (loading the flat pattern on the SLM) at different speeds: lower (5.05mm/s) and higher speed (8.07 mm/s). c and d, the speed maps obtained with the laser speckle temporal contrast analysis corresponding to (a) and (b). e and f, the raw images with correction (loading the optimized pattern on the SLM) at different speeds: lower speed (5.05 mm/s) and higher speed (8.07 mm/s). g and h, the speed maps obtained with the laser speckle temporal contrast analysis corresponding to (e) and (f). Scale bars: 500 μm.
Fig. 6 1/K2 versus the actual speed both with correction and without correction in the fluid phantom experiment. 1/K2 is calculated from the region of interest (ROI, about 20×10 pixels) in the raw images of the moving object at a range of different speeds without wavefront correction (the red square, ROI chosen in Fig. 5(d)) and with wavefront correction (the blue circle, ROI chosen in Fig. 5(h)).
4. Discussion
We have demonstrated detecting the speed changes of moving object through scattering medium by combining the wavefront shaping technique with laser speckle temporal contrast analysis. The optimized phase pattern can effectively suppress the speckle background. The speckle artifacts in the recovered images are significant smaller than those obtained by the optical imaging system without the wavefront compensation. However, there are some noises at the background region in the image from the Figs. 3(e)–3(h). According to the optical memory effect, only the location at the original corrected point has the best corrective performance. The correction performance will decrease as the object locates far away from the original corrected point position. In other words, if the position is too far away from the corrective target, the phase distortion will not be corrected very well and the residual phase distortion will lead to the background noise, which will disturb the image obtained and reduce the contrast of the speed maps.
In principle the detection of speed changes can be obtained whether wavefront distortion is corrected or not. However, it cannot realize imaging through scattering medium without wavefront correction. Moreover, it is worth noting that the linear relationship between 1/K2 and the actual speed could be influenced by the light intensity. In Fig. 7, the changes of 1/K2 with the increase of actual speed were shown at the different light intensity level in the ground glass experiment when wavefront correction was not performed. The averages of the light intensity in the raw images were 15, 31 and 200 respectively. 1/K2 was calculated from the same region (about 30×30 pixels) in the raw images. There were no obvious changes in 1/K2 with the changes in actual speed of moving ground grass when the average light intensity is lower than 15 which indicates a low signal to noise ratio level. This is why the changes of the 1/K2 are not obvious when the wavefront distortion is not corrected in Fig. 4. As the light intensity increases, the changes of the relative speed become obvious. In the moving ground glass experiment shown in Fig. 3 and Fig. 4, the wavefont distortion was compensated after wavefront correction, so the object behind scattering medium can be imaged on the CCD and the light scattered by the scattering medium can be converged in the imaging plane. And then, the changes of relative speed were obvious because the light intensity at the position of the object’s image increase significantly compared with that before correction.
Fig. 7 1/K2 versus the actual speed at different light intensity level without wavefront correction in the moving ground glass experiment. The averages light intensity in the raw images are 15, 31 and 200 respectively. 1/K2 is calculated from the same region (about 30×30 pixels) in the raw images at different speed.
Our method needs two steps: the optimization stage and imaging stage. In the optimization stage, the optimization time includes the flash period of the SLM (limited by the flash rate of the SLM), the computation time (limited by algorithm, computer hardware and memory) and the run time of the camera (limited by the frame rate of the camera). If the microelectromechanical-based SLMs or faster SLMs based on piezoelectric mirrors and high-speed cameras are used, the optimization process can be completed in a fraction of a second [4, 29]. Potentially the operation speed could be improved by more than an order of magnitude. Thereby it may be possible to apply in imaging through the static scattering medium or the slow-change medium scattering, in which the time scale of the changes in scattering medium is shorter enough than the whole optimization time of SLM. Furthermore, the signal to noise ratio of system can be further improved by exploiting higher resolution SLM to improve the compensation of phase distortion of scattering light. If multi-conjugate large area wavefront correction method [30] is adapted, the FOV in the imaging system will be larger though scattering medium. In addition, the new anisotropic memory effect [31] may also open new possibilities for thick scattering medium. By using the optical memory effect, the phase shift leads to a shift of the interference based focus in the deep direction, thus three dimensional imaging has been developed in the scattered light fluorescence microscopy [15]. So the technique may be investigated to realize three dimensional velocity imaging through scattering medium.
5. Conclusion
In conclusion, the method of combining wavefront shaping technique with laser speckle temporal contrast analysis to evaluate the relative speed changes of moving objects through scattering medium is demonstrated, and a linear relationship between estimated speed and actual speed of moving object is shown.
Acknowledgment
The authors thank Fei Zhang, Anle Ge for preparing the pinhole and the sample model. This work was supported by the National Natural Science Foundation of China (Grant Nos. 91332121, 31471083, 61405065) and the Director Fund of Wuhan National Laboratory for Optoelectronics.
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