† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11847062 and 61871234), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20180755), and the Science Fund from NUPT (Grant No. NY218098).
We propose a compressed ghost imaging scheme based on differential speckle patterns, named CGI-DSP. In the scheme, a series of bucket detector signals are acquired when a series of random speckle patterns are employed to illuminate an unknown object. Then the differential speckle patterns (differential bucket detector signals) are obtained by taking the difference between present random speckle patterns (present bucket detector signals) and previous random speckle patterns (previous bucket detector signals). Finally, the image of object can be obtained directly by performing the compressed sensing algorithm on the differential speckle patterns and differential bucket detector signals. The experimental and simulated results reveal that CGI-DSP can improve the imaging quality and reduce the number of measurements comparing with the traditional compressed ghost imaging schemes because our scheme can remove the environmental illuminations efficiently.
Ghost imaging (GI) is a special optical imaging scheme,[1–7] where one of the two spatially correlated optical beams illuminates an object and is detected by a bucket detector without any spatial resolution, and the other beam is measured by a spatially resolving detector or computing offline. Then the object could be imaged by correlating the speckle patterns and corresponding bucket detector signals. However, the number of measurements are required much more to obtain a clear image. Subsequently, compressed ghost imaging (CGI)[8] was proposed to obtain a high quality image of object by exploiting the compressed sensing (CS)[9] algorithm from far fewer measurements than what is usually considered necessary in traditional GI schemes. CS can be used in CGI to reduce both the acquisition time and the number of measurement significantly by the aid of the redundant structure of the images. Since then, CGI has been received much attention and considerable number of methods and applications based on CGI has been proposed.[10–14]
However, the imaging quality of CGI is susceptible to the environmental illuminations. Complementary CGI (CCGI)[15] is proposed to solve this issue, which uses the complementary speckle pattern pairs[16,17] consisting of the speckle pattern and its inverse speckle pattern to illuminate the object and then acquire the differential signals by taking the difference among two bucket detector signals corresponding to the speckle pattern and its inverse speckle pattern. Instead of the bucket detector signals, the differential signals are used to reconstruct the images. Due to the inference of environmental illuminations can be removed efficiently in the differential signals, the image quality can be dramatically improved. However, the number of measurement of this method is large, which is twice as much as the traditional CGI (TCGI).
In this paper, we present a compressed ghost imaging scheme based on differential speckle patterns, named CGI-DSP. In the scheme, a series of bucket detector signals are acquired when an unknown object is illuminated by a series of random speckle patterns, and then the differential speckle patterns (differential bucket detector signals) are obtained by taking the difference between present random speckle patterns (present bucket detector signals) and previous random speckle patterns (previous bucket detector signals). Finally, the image of object can be obtained directly by performing the compressed sensing algorithm on the differential speckle patterns and differential bucket detector signals. The advantage of the CGI-DSP scheme is that the number of measurements could be reduced and the imaging quality can be improved comparing with traditional CGI (TCGI) and complementary CGI (CCGI).
The remainder of the paper is arranged as follows. CGI-DSP is presented in Section
The schematic diagram of the CGI-DSP is shown in Fig.
The speckle pattern Ii(x,y) interacts with an object through a projector lens and then is measured by a bucket detector to get a bucket detector signal Bi,
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Furthermore, we can obtain a differential speckle pattern, ΔIi(x,y), by taking the difference between present random speckle patterns Ii(x,y) and previous random speckle patterns Ii − 1(x,y),
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Therefore, a differential bucket detector signal ΔBi between the present bucket detector signal Bi and the previous bucket detector signals Bi − 1 is
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Above steps are repeated M to accumulate M random speckle patterns
Finally, the image of object is reconstructed by compressed sensing algorithm.[8] Here, TVAL3 algorithm[20] is used, which has the advantage of the reconstruction of a quality image. Therefore, the object’s image
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![](cpb_29_2_024204/cpb_29_2_024204_ieqn6.gif)
![](cpb_29_2_024204/cpb_29_2_024204_ieqn7.gif)
![](cpb_29_2_024204/cpb_29_2_024204_ieqn8.gif)
We discuss the performance of the CGI-DSP scheme by experiments and numerical simulations in this section.
The experimental system of CGI-DSP is shown in Fig.
![]() | Fig. 2. A schematic diagram of the CGI-DSP scheme experimental system. DMD: digital micro-mirror device; BF: bandpass filter; BD: bucket detector, and ADC: analogue-to-digital converter. |
Additionally, mean square error (MSE) is used to evaluate the imaging quality quantitatively,[14]
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![](cpb_29_2_024204/cpb_29_2_024204_ieqn9.gif)
To verify the feasibility of CGI-DSP, we first perform the numerical simulations, and compare the results of CGI-DSP with those results using CCGI and TCGI with different number of measurements and SNRs, which are shown in Figs.
![]() | Fig. 3. The numerical simulation results of the “NUPT” logo by using CGI-DSP scheme, where MSE is presented together. |
![]() | Fig. 4. The numerical simulation results of the “NUPT” logo by using CCGI scheme, where MSE is presented together. |
![]() | Fig. 5. The numerical simulation results of the “NUPT” logo by using TCGI scheme, where MSE is presented together. |
The simulated results shown in Figs.
Furthermore, the performance of reconstructed images’ MSE as a function of the SNR for CGI-DSP, CCGI, and TCGI is shown in Fig.
In addition, we perform the experiments and the results are shown in Figs.
![]() | Fig. 7. The experimental results of the “NUPT” logo by using CGI-DSP scheme, where MSE is presented together. |
![]() | Fig. 8. The experimental results of the “NUPT” logo by using CCGI scheme, where MSE is presented together. |
We have proposed a compressed ghost imaging scheme based on differential speckle patterns (CGI-DSP) in this paper. We have verified the feasibility of CGI-DSP by simulations and experiments. Moreover, we have compared the performance of CGI-DSP, CCGI, and TCGI. The results show that CGI-DSP can improve the imaging quality and decrease the number of measurements comparing with TCGI and CCGI.
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