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We demonstrated experimental comparison between ghost imaging and traditional non-correlated imaging under disturbance of scattering. Ghost imaging appears more robust. The quality of ghost imaging does not change much when the scattering is getting stronger, while that of traditional imaging declines dramatically. A concise model is developed to explain the superiority of ghost imaging. Due to its robustness against scattering, ghost imaging will be useful in harsh environment.
© 2015 Optical Society of America
1. Introduction
Since the first experiment was realized with entangled photons [1], ghost imaging(GI), especially with the pseudo-thermal source [2,3], has attracted more and more attention [2–22]. In GI experiments, the thermal source, for example, created by lighting a laser on a rotating ground glass, is separated into two correlated beams by a beam splitter. One beam illuminates the object, with the transmission (or reflected) light collected by a bucket (single-pixel) detector. The other beam is recorded by a spatial-resolving detector, such as a CCD camera. The image of the object can be reconstructed by combining results from two detectors. Recent researches improved GI in many aspects, such as reconstruction algorithms for better quality and/or higher spatial resolution [11, 15, 16], and single-pixel camera was also realized [13, 14]. Due to its novel features, especially its ability to form images without a spatial-resolving detector toward the object, people are discussing possible applications of GI, especially in the harsh noisy environment, such as a technique for biomedical imaging or remote sensing.
Considering applications of GI over a long distance, people have to understand the influences of the atmosphere, especially scattering and turbulence. The influence of turbulence has been discussed in many papers [17–20], while only a few papers reported on GI in atmosphere scattering. According to the size of scattering particles and the wavelength, scattering can be classified into Rayleigh scattering, and Mie scattering. In the atmospheric environment, Mie scattering is dominant when considering influences on imaging. Gong and Han [21] proposed a modified correlated imaging method which can enhance the quality of imaging in a Mie scattering media. Li et al [23] demonstrated periodic diffraction ghost imaging through a scattering layer. Bina et al [22] got a high-contrast image of an absorbing object immersed in a Rayleigh scattering turbid medium via ghost imaging. They point out that the scattered light is totally uncorrelated to the incident reference and they observed similar behavior for ghost imaging and diffusion imaging under scattering. However, whether their conclusion is suitable for Mie scattering is unclear. At the same time, it is still not clear whether GI contains any intrinsic advantage, compared with traditional imaging under atmospheric scattering. In this paper, we clarify possible intrinsic advantages of GI, by experimentally comparing GI with traditional imaging, under disturbance of Mie scattering. With the strength of scattering increasing, experimental results show that the quality of ghost imaging is slightly influenced, while that of traditional imaging degrades dramatically. Different behaviors are observed for ghost imaging and non-correlated imaging when the scattering is stronger than that of Ref [22]. This can be explained by considering the changes of the illumination field due to the scattering disturbance. Usage of correlation makes the imaging method more robust against scattering.
When comparing between two imaging methods on the intrinsic features, we try to reveal the advantages implied from the mechanism, and exclude advantages or disadvantages results from the difference in device performance. In order to make a fair comparison, it is reasonable to set the following parameters to be comparable, which are related to the performances of the devices. (1) The sensitivity of the detectors. The bucket detector in ghost imaging system only consists of a single pixel, which is technically easier to improve its sensitivity than that of the multi-pixel array detectors in traditional imaging. This might help GI to be more sensitive. (2) The integration time of measurements or the total number of the detected photons. Many times of measurements are required to reconstruct the image with GI, which can be mathematically treated as weighted averaging. Such averaging over times usually helps to enhance the quality of image, since typically the more photons are detected, the more information can be achieved. (3) The intensity of illumination and the features of the scattering media. Behaviors of light propagation related to those parameters might affect the results of imaging.
2. Experimental setup
To compare the performance of GI with traditional imaging under scattering conditions, we designed experiments satisfying the above requirements, with the setup illustrated in Fig. 1. In the experiment, the pseudo-thermal source is created by lighting a laser of λ = 532nm on a rotating ground glass. The light field in the reference arm is recorded by a CCD camera, CCD1 in Fig. 1. In the object arm, the light illuminates the object, and the transmitted light is collected by another camera CCD2. For traditional imaging, the object, lens f3, and CCD2 comprise a typical imaging system, with CCD2 located on the imaging plane. Namely, CCD2 serves as the array detector for traditional imaging, and the bucket detector for GI as well. The magnifications of ghost imaging and traditional imaging are all set to be 1, with z3 = z4 = 400mm, z5 = z6 = 100mm and f3 = 50mm. The pseudo-thermal source can also serve as the illumination for traditional imaging. To obtain the image, we also do averaging over many frames for traditional imaging. By sharing the object arm of GI for traditional imaging, we are using the same light source and detectors, averaging over the same number of frames, and acquiring the images with both techniques simultaneously, therefore the above requirements can be easily satisfied.
Fig. 1 Experimental setup for comparing GI and traditional imaging. A half wave plate and a polarized beam splitter (PBS) are employed to modify the ratio between two arms, such that both detectors can work in proper regime. Lens f1 and f2 are used to adjust parameters of the field. The effect of scattering is simulated by small particles in salt solution, inside two containers. A binary object is located between two containers. CCD2 is on the imaging plane of the object under help of lens f3, which serves as the array detector for non-correlated imaging and as the bucket detector for GI.
We employ small particles of polymer latexes suspended in salt solution to simulate the effect of scattering media. The diameter of the particles is a ∼ 3.26μm thus 2πa/λ = 38.5, satisfying the condition of Mie scattering [24,25], while more details of the particles can be found on the website [26]. Two identical containers of 2cm × 1cm × 4.3cm are used to hold the solution, with the object located between them. Thus both beams coming to and from the object experience scattering. The strength of the scattering can be controlled by changing the number density of the small particles. Noticing that the scattering media also causes attenuation to the beam, we have to modify the illumination intensity to match the detection regime of the detectors. The driving current of the laser is controlled to adjust the output power. A half wave plate and a polarized beam splitter are used to control the ratio between two arms to keep the intensity in both arms at proper level. The lens f2 = 120mm, reduces the divergence angle of the thermal beam to enhance the availability of the laser energy.
3. Results and discussions
Images of a binary object are obtained with both techniques, as shown in Fig. 2, under different strengths of scattering. The size of the image is 160 × 120 (pixels on CCD) and the number of frames for both techniques is 20000. We use transmission ratio of the scattering media as a measure of the strength of scattering. The lower β is, the stronger the scattering is. The influence of the salt solution itself is ignored, and we define β = 100% when there is no particle in the solution. As shown in Fig. 2, when the scattering is not very strong, both techniques are barely affected. When the scattering is strong, those images from traditional imaging become more and more blurred. By contrast, those of GI still appears insignificantly changed. To quantitatively analyze the results, mean-squared error (MSE) of the image compared to the object is employed. The bigger the value of MSE is, the worse the quality of image is, which means the image is less close to the perfect image of the object. Signal-to-noise (SNR) is also calculated as another evaluation of image quality. The results of MSE and SNR are shown in Fig. 3. Every point in the plot is obtained over statistic of 5 separate experiments. As shown in Fig. 3, the results of MSE and SNR lead to the same conclusion that the quality of traditional imaging declines dramatically with increasing strength of scattering, while that of GI experiences negligible influence. That is, GI shows stronger robustness against Mie scattering than traditional imaging.
Fig. 2 Imaging results of a double slit achieved with both methods. From set (a) to (f), the strength of scattering is increasing, where β shows the transmission ratio of the scattering media as a measure of strength of scattering. For each set, the left one is the result of GI and the right one is that of traditional non-correlated imaging.
Fig. 3 MSE and SNR of the images achieved from two techniques, varying with the strength of scattering. Each point is obtained by a statistic over 5 times of imaging. It shows that the quality of non-correlated imaging declines with the scattering, while that of GI appears robust against scattering.
Furthermore, we examine the behavior of the spatial resolution of ghost imaging. The width of degree of second-order coherence is usually used to estimate the spatial resolution of ghost imaging. We calculate the degree of second-order coherence between the object path and the reference path when the scattering is strong (β = 6.44%), with the results shown in Fig. 4. The peak value of second order of coherence is decreased when there is scattering compared to that of no scattering, as well as the magnitude of background noise. So the SNR remains stable as the results shown above. To compare the width, the results are normalized and shown in the right part of Fig. 4. From the normalized results, the degree of second-order coherence for both cases almost overlap with each other at the dominant part. From those results, GI does appear robust against scattering. Influence of scattering on GI is much less than that of traditional imaging, when considering the imaging quality. That means GI filters out those noise caused by scattering. Roughly speaking, usage of correlation provides the superiority of ghost imaging in scattering environment, as we will explain below.
Fig. 4 Degree of second-order coherence, with and without scattering. This shown in the right plot is normalized. When there is scattering, the peak value of degree of second-order coherence is decreased, while the magnitude of background noise is also decreased. After normalization, it can be seen that the width of the degree of second-order coherence function keeps unchanged, which is related to spatial resolution of GI. Thus, the spatial resolution of GI does not change under disturbance of scattering.
To explain the robustness against scattering, let us briefly review the procedure of ghost imaging at first. In the general lensless pseudo-thermal ghost imaging setup [2–6] without scattering, the speckle field irradiating the object is the same as the speckle field recorded by the CCD. They have second-order coherence or intensity correlation. The light through the object is collected by a bucket detector, with the results being [4–6],
where T(x′) is the transmission function of the object and Iobj(x′) is the intensity distribution of the speckle field illuminating the target in the object arm. The image of object is obtained via calculating the second-order correlation [4–6], where 〈·〉 means averaging over many frames and Iref (x) shows the intensity distribution of speckle field in the reference path, which is recorded by CCD1. g(2)(x, x′) is the degree of second-order coherence defined asWhen there exists scattering media around the object, the light field irradiating the object is not the same as the reference field due to the scattering disturbance. Mie scattering will destroy the coherence of incident light [24, 25]. Roughly speaking, the light on the detection plane can be classified as transmission light and scattered light. Interacted with the particles, part of the incident light can transmit straight through the media while others will propagate into different directions and gain randomly different phase shifts. The scattered light experience a stochastic process. While the transmission light keeps unchanged. Because of the randomness of the phase shifts by scattering process, the scattered light loses the coherence with the transmission light, in the first order. Since scattering will change the light field intensity distribution, it loses the correlation with the transmission light, in the second order. Based on this, the effects of scattering can be written as
supposing the detected intensity distribution is I(x) when there is no scattering. α (0 < α < 1) shows the percentage of the transmission light to the total detected light, which is related to the transmission ratio of the scattering media. Is(x) represents the intensity of scattered light.For traditional imaging, we take the detected intensity distribution as the image. With the scattering getting stronger, α will be smaller and Is(x) gets larger. There will be more and more scattered light around the object. This results in higher and higher noise around the true image on the detection plane. Thus MSE becomes higher and SNR becomes smaller. The contrast of image will decrease and Is(x) will blur the image or even submerge the signal. That is, the quality of traditional imaging will decline due to scattering.
For ghost imaging, effects from those scattering between the source and the object are dominant, since the bucket detector will collect light transmitted through the object without detecting the spatial distribution. With scattering, the results of bucket detector turn out to be
Since the correlation between the scattered and the transmission light is lost, we have Therefore the results of ghost imaging under scattering will be That is, the signal and the contrast of GI are also decreased by a factor of α, the same as that of traditional imaging. However, noise caused by scattering is canceled out because of correlation imaging method. Therefore, MSE and SNR, or the quality of image do not change much with the strength of scattering increasing. This explains the robustness of GI against scattering. In the view of combined influence by scattering, the model is suitable for single scattering and multiply scattering. All the influences due to scattering are reflected in the changes of illumination field. Nevertheless, in real experiments Iref(x)Is(x′) and 〈Iref(x)〉 〈Is(x′)〉 are not strictly equivalent. When scattering disturbance is strong, the image of ghost imaging will be distorted, as shown in Fig 2. Equation (7) also explains why the peak value of degree of second-order coherence get smaller when there is scattering, since it can be treated as a ghost image of a single point. For traditional imaging, the scattered light is first-order noise which cannot be filtered out. For ghost imaging, the first-order noise is filtered out since second-order correlation is employed to reconstruct the image. Usage of correlation helps to enhance the performance of imaging. Such correlation method can also be used in other fields, such as communication or metrology, when infected by scattering noise.Besides, in our experiments we increase the laser power to compensate for the attenuation caused by scattering media. In practice, GI can obtain images of objects at a longer distance compared with that of traditional imaging, with the same illumination power. The reason lies in that GI employs single-pixel detector and collects all the light within the clear aperture of the receiver. The sensitivity of single-pixel can be higher than array detectors. Number of photons on each pixel will be higher when the light is collected, instead of detected with array detectors. This makes GI more sensitive than traditional imaging. In addition, it is easy to combine compressed sensing algorithm with GI, which can further enhance the quality of image.
4. Conclusion
In conclusion, we designed contrast experiments to compare the imaging ability between ghost imaging and traditional imaging under disturbance of scattering. Ghost imaging can weaken the influence of scattering and behaves better than traditional imaging under the same experimental conditions. The quality of images appears trifling decreased with increasing strength of scattering. The spatial resolution of GI also keeps unchanged. While the image quality of traditional imaging declines dramatically. The superiority of GI under scattering comes out from the second-order correlation method. Since GI is more robust and sensitive than traditional imaging under scattering, GI is a good option for imaging over harsh environment.
Acknowledgments
We are grateful to Xiao-jun Xu and Wen-lin Gong for useful discussions. This work is supported by the National Natural Science Foundation of China under Grant Nos. 11374368 and 11004248.
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