1. Introduction

Recent interest in the optical properties of turbid media has been fueled by new techniques to control light propagation through scattering materials [1–7]. These techniques rely on the deterministic nature of multiple scattering to shape the incident wavefront and pre-compensate for the scattering effects in the material. The focusing of light through turbid media is achieved by optimizing the incident wavefront to overcome the effects of multiple scattering and constructively interfere many input modes after scattering. This has been done through optical phase conjugation [6,7] or with a feedback system which uses a spatial light modulator (SLM) for wavefront control to maximize the focus spot intensity [1–5]. Most of these studies and techniques focus on the creation of a single focal spot in or through the turbid material [1–10], however little or no emphasis has been placed on focusing to multiple spots [5,8]. Further research has explored the use of turbid material wavefront control for image transmission, but unfortunately none has achieved direct image creation through highly scattering materials [11–13]. For example [11], and [12] require digital image reconstruction and [13] only works in thin (weakly) scattering media while operating on a limited field of view. Alternatively, scanning techniques require point-by-point reconstruction using, for instance, fluorescent particles [14] or second harmonic generation [15]

In this paper, in contrast, we present image creation and projection through highly scattering turbid media using multiple wavelengths without need for reconstruction. The technique requires a global optimization for which we implement a wavefront optimization genetic algorithm (GA) [9]. We show that the GA optimizes multiple spots with high uniformity and intensity. We experimentally demonstrate multiple focal spot and multiple wavelength focusing. We then demonstrate the creation of multi- wavelength images using this technique. The three distinct aspects of this image projection technique relative to prior proposals are: (1) the wide-field image appears without any need of further reconstruction after the adaptive optimization (except for demosaicing when needed), (2) it is amenable to thick, highly scattering media, (3) it can encode color images using RGB channels, and (4) it is capable of creating synthetic light objects.

2. Image projection through turbid media

The task at hand can be understood in two different ways, namely the creation of images using a turbid material in conjunction with a SLM or the creation of images through a given turbid material. The method decomposes the pattern into multiple focal spots and focuses coherent, scattered light at those preselected locations creating an image. From a different perspective the process can be understood as the shaping of the speckle pattern for image formation.

The maximum enhancement or signal to background ratio (SBR) possible in this method is determined by the number of input modes used for wavefront control. The SBR for a single focus spot, η(1), is defined as the ratio between the output mode intensity, I_m, and the initial average intensity, 〈I₀〉. The SBR dependence on input modes is: η(1) = π/4(N-1) [1], where N is the number of optimized input modes. However, by focusing to multiple focus points, M, the maximum SBR is scaled by the number of focus points created: η(M) = η(1)/M, as the enhancement distributes evenly between targets [2,8]. The total number of input modes which can be used is limited by the degrees of freedom of the SLM and the optics. Other factors, such as, sample drift and the diffraction efficiency of the SLM, further degrade the maximum achievable enhancement [3].

To efficiently optimize the wavefront to create the desired image through the turbid material we employ a genetic algorithm (GA) [9]. After verification via simulation we show that the genetic algorithm optimizes multiple points with a smaller standard deviation than the continuous sequential algorithm (CSA) [8] using either an intensity or amplitude metric.

We use a scattering model simulation for comparison of the GA and CSA [8,9]. For multiple spot focusing the GA cost function and the CSA feedback need to take into account multiple targets. We modify the GA cost function to maximize the intensity of the focal spots, while penalizing for large differences in intensity value. Specifically, we modify the cost function, C, to be the summation of all the focus spot intensities, I, minus the number of focus spots, M, multiplied by the standard deviation of the intensities of the focus spots, σ(I):

We compare the algorithms based on the number of measurements. A measurement being defined as the process of measuring the GA cost function or the CSA metric for each phase mask. The CSA with 10 phase samples performs 10 measurements per input mode. Thus, when optimizing a phase mask with N input modes, there are 10∙N measurements to optimize a full phase mask. For this simulation, we compare the GA and CSA algorithm simulations through 2∙10∙N measurements. Each algorithm has N = 256 input modes with an infinitely long persistence time. A Gaussian noise value of 0.3∙〈I₀〉 added to each measurement simulates experimental conditions. For this simulation the GA uses a population size of 50, with a mutation rate of R = (R₀ - R_end)∙exp(-d/λ) + R_end, where R₀ is 0.1, R_end is 0.0025, λ is 1000, and d is the measurement number. Figure 1 shows the mean value of 100 optimizations for the CSA-I, CSA-A, and GA methods compared to 1/N times the CSA-I maximum for single point focusing. The error bar in the figure indicates the mean standard deviation of the enhancement for the various focal spots for the 100 optimizations. The simulations indicate that the GA leads to higher enhancements with lower deviation in the focal spot intensities than the CSA-A, which in turn improves over the CSA-I method with less spot intensity variability [8].

 

Fig. 1 Simulation results comparing the mean enhancement and standard deviation of enhancement for the CSA-I, CSA-M, and GA methods to the ideal case of 1/N times CSA-I max.

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3. Experimental demonstration of multiple spot and multiple wavelength focusing

The GA is tested using a highly scattering 425 micron thick chicken eggshell. A total intensity transmission measurement verifies the mean free path of the eggshell is less than ten times its thickness [14]. Qualitatively this is confirmed through the observation that no detectable ballistic photons transmit through the eggshell. The illumination sources consist of HeNe (633 nm), frequency doubled Nd:YAG (532 nm), and Argon (455 nm or 514 nm) lasers collimated and combined on the same path. A phase-only SLM (Holoeye HEO 1080P) generates N = 1024 propagating input modes, which are focused with an objective lens (40X, NA = 0.65) onto the surface of the scattering sample (Fig. 2(a) ). A second objective (20X, NA = 0.4) images a plane 1 mm behind the eggshell. The target is to create multiple foci on the opposing side of the eggshell, with either one or two colors. Single color focusing uses 633 nm illumination, while two color focusing uses 633 nm and 514 nm. The intensity measurements are provided by a 12-bit monochrome CCD (Point Grey Research Grasshopper) or a 12-bit RGB CCD camera (Point Grey Research Flea2). This camera has a RGB Bayer filter, thus providing color separation. The red, green, or blue pixels are used to create foci of red, green, or blue color, respectively The algorithm runs until the GA cost function stops improving. Each measurement is obtained at a rate of ~4.5 Hz.

 

Fig. 2 (a) The experimental setup. (b) Experimental results of focusing multiple spots with one and two colors with the GA. Each data point is experimentally optimized ten times.

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Initial experiments reveal that under the experimental conditions the ideal GA population size depends on the number of desired focal spots, with larger populations optimizing more focal spots more efficiently. Therefore, in this experiment the GA population size is varied depending on the number of desired focal spots. Furthermore, unlike the simulations the number of measurements required to maximize the focal spot intensities increases with the number of foci, thus, each iteration is run until the GA cost function is maximized. Each data point represented in Fig. 2(b) is the average of ten experimental optimizations.

The experiment reveals that the GA intensity enhancement scales with the number of foci as shown in simulation and that multiple colors may be focused with enhancement values similar to a single color. This result can be explained by considering a second wavelength to have a unique transmission matrix through the sample, just as any individual focus spot has a unique transmission matrix from the input modes.

Interestingly, the experimental data also reveals the variability of the GA with initial parameter selection, which resulted in a rather significant enhancement increase with the number of focal spots (from 4 to 6). An additional source of variability is the sample drift during the long experimental runs. The results of Fig. 2(b) are presented to illustrate the sensitivity of the optimization to initial conditions and experimental perturbations.

4. Image formation

To test image creation using wavefront control and turbid media we create an image generating the CU logo by superposition of a number of focal points. Using 4096 input modes and a single color (633 nm) the GA optimizes the image, composed of 49 focal points, as shown in Fig. 3(a) . After running through 55,000 measurements the image shown in Fig. 3(b) is created. This image achieves an average SBR of 12.8 with a standard deviation in the SBR of the target points of 2.0. During the optimization 2x2 pixel binning with the monochrome CCD is used to match the size of a binned pixel to the size of a speckle grain. Figure 3(c) shows the image captured without binning at a higher resolution. Interestingly, the image has high intensity throughout the targeted region, unlike typical reconstructions in computer generated holography (CGH) which suffer from speckle effects [16].

 

Fig. 3 Single color image creation. (a) The target intensity distribution. (b) Experimentally generated intensity distribution through an eggshell using binned CCD pixels. (c) High resolution image intensity distribution.

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The ability to create images with two colors is tested through the creation of a number of focal points placed together to create a person riding a bike, with the rider composed of green light and the bike wheels composed of red light. Figure 4(a) shows the intensity distribution designed for a Bayer RGB filter. Using 3840 input modes and two colors (633 nm and 514 nm) the GA runs to optimize the image, which is composed of 49 separate focal points: 24 red and 25 green. After running through 35,000 measurements the image shown in Fig. 4(b) is created with the RGB filter. This image achieves average SBR of 10.2 for the red and 9.6 for the green, with standard deviations of 1.1 and 0.9 respectively. The demosaiced color image, created using the MATLAB function “demosaic” [17], is shown in Fig. 4(c) and clearly displays the two color target image. The SBR achieved for the two colors is similar to the SBR obtained with a single color for the same number of focal spots. These results verify the experiment demonstrated in Fig. 2(b) on a larger scale.

 

Fig. 4 Two color image creation. (a) The desired intensity distribution designed for an RGB Bayer filter CCD. (b) Experimentally obtained intensity distribution through an eggshell with RGB CCD. (c) Two color image obtained after demosaicing the image in (b) with same resolution.

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Finally, we test three color image formation designed for RGB demosaicing to create full-color images. We place a number of focal points in the desired image to create a rainbow. By designing a target intensity distribution for the Bayer RGB filter (Fig. 5(a) ) a full color image of a rainbow is generated through demosaicing (Fig. 5(b)). Using 2048 input modes and three colors (633 nm, 532 nm, and 455 nm) the GA runs to optimize the image, which is composed of 49 separate focal points: 16 red, 26 green, and 8 blue. After running through 20,000 measurements the image shown in Fig. 5(c) is created. This image achieves an average SBR of 5.5, 10.8, and 7.0 for the red, green, and blue, respectively. The standard deviations are 0.6, 2.4 and 0.8 for the red, green, and blue, respectively, this measure scales the various SBR values by their target intensity (Fig. 5(a)). The large disparity in the SBR of the different wavelengths is a side effect of the 532 nm laser having poor power stability. This also affects the time the algorithm can run. Despite this technical issue, the demosaiced image (Fig. 5(d)) clearly shows a rainbow following the desired image pattern (Fig. 5(b)).

 

Fig. 5 Three color pattern projection for full color image creation. (a) The target intensity distribution designed for an RGB Bayer filter CCD. (b) Rainbow created by demosaicing the target intensity distribution. (c) Experimentally obtained intensity distribution captured with RBG CCD through an eggshell. (d) Rainbow obtained after demosaicing the image in (c).

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5. Discussion and conclusions

Similarly to computer generated volume holography and CGH the color image projection technique uses diffraction, but it is notably different in that it also takes advantage of multiple scattering for pattern formation. Therefore, it is the scattering which ultimately determines the image resolution, not the NA of the optics, as in CGH. Thus, the speckle size will ultimately yield the resolution [4]. The bandwidth of the light which can be focused through turbid media is also limited by the scattering properties of the material [18]. The more highly scattering the material is, the narrower the bandwidth required. This is particularly useful when focusing multiple wavelengths, as the material uncouples the transmission matrix of different wavelengths. The method spatially multiplexes the input modes to create multiple focused wavelengths simultaneously. Limitations in the experimental system are a result of the spatial modulator device, which has a low fill factor, decreasing the maximum possible SBR. Furthermore, this device has a slow modulation speed, thus causing sample drift to limit the algorithm run time [8,9]. Both of these issues can be addressed, for example, with the use of a deformable mirror device for wavefront control [10,19] with a high speed camera.

In conclusion, we have demonstrated the use of wavefront control with highly scattering media for image creation using multiple focus spots and wavelengths. We have shown that a GA, with a cost function designed for the task, can be used for efficient creation of multiple, high intensity focal spots with small variations in intensity. This algorithm was used experimentally for the creation of multiple wavelength images. These images show uniform spot intensity with low standard deviations. Interestingly, the adaptive optimization reduces the negative speckle effects common in image creation with CGH.

Image formation with highly scattering materials could find applications in various fields. For example, focused patterns could be used to activate deep neurons with light using photochemical uncaging probes and allow near arbitrary excitation patterns, thus enabling three dimensional neuronal connections to be mapped by the simultaneous excitation of multiple neurons [20]. Furthermore, multiple wavelength focusing could be used for the excitation of different fluorophores in deep tissue fluorescence imaging. Pattern generation through turbid media could also be used for materials processing or energy delivery for various medical treatments.