In Periodic diffraction correlation imaging (PDCI), the images of several objects located in different spatial positions can be integrated into one image following certain rules, which is named shape merging. In this paper, we proposed and demonstrated this new technique. It can be realized without SLM or beam-splitter. And this effect can find novel application in optical encryption, enabling transmission of object information to a remote place secretly.
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Since the first ghost imaging experiment  based on quantum entangled photon pairs was performed in 1995, over the past decade the phenomenon had attracted much interest in the field of quantum optics. More recently, ghost imaging had been investigated from different aspects, including compressive sensing in ghost imaging , high order ghost imaging [3–6], ghost imaging by measuring reflected photons [7–9], periodic diffraction ghost imaging , ghost imaging under Talbot effect [11, 12], ghost imaging through turbulent [13, 14] and computational ghost imaging (CGI) [15, 16], etc.
Lately a novel correlation imaging mechanism called periodic diffraction correlation imaging (PDCI)  is proposed. This mechanism is based on periodic diffraction effect, in which a periodic intensity pattern is generated at a diffraction plane after a periodic point source array. PDCI can be realized without a beam-splitter, so the complexity of correlation imaging scheme can be reduced sharply comparing with the traditional ghost imaging. Therefore, PDCI can easily realize high-resolution, Nth-order ghost imaging without a beam-splitter and correlation microscopy.
Many optical encryption methods have been proposed recently to secure, store, and decrypt information by using phase, wavelength, spatial frequency and polarization [17–20]. The advantages of optical encryption are its high-speed operation and possibility of hiding data in multiple dimensions. One approach is optical encryption based on CGI. In this method, the encrypted version of the object image is simply an intensity vector, rather than complex-valued matrix, which dramatically reduces the number of bits transmitted by the sender to the receiver. And this approach might benefit from compressive sampling techniques applied to CGI to improve reconstruction quality by using even a fewer number of realizations. This scheme has shown robustness to eavesdropping even when using only a small number of key components. However it is still lack of security features in encrypted images  and the SLM is relatively expensive. So simplifying execution in applications and decreasing the time for encryption are focuses of current research.
In this paper, we demonstrate a novel technique called shape merging which is a useful function of PDCI. We use a periodic point source array to generate the intensity pattern we need. And the achieved intensity is also periodic according to the periodic diffraction effect. Each point source is a sub-source; the objects illuminated by this light source can be merged into one image and appeared in the detecting plane periodically. Based on this technique, a new optical encryption method is proposed, which can realize encryption without SLM or beam-splitter. This method has a smaller computation complexity than that based on CGI.
The paper is organized as follows. In section 2, the shape merging technique is studied experimentally. In section 3, the new optical encryption method is proposed, and its features are demonstrated. And in section 4, the conclusion is made.
2. Shape merging technique
In the classical scheme of second-order correlation imaging, pseudo-thermal light is generated by a rotating ground glass located after a laser. Then the light is separated by a beam-splitter into two spatially correlated beams. One is the reference beam, impinging on a multipixel detector, without ever passing through the object. And the other is the object beam, which, after illuminating the object is collected by a bucket detector, with no spatial resolution. The intensity patterns recorded by the object charge-coupled-device (CCD) and the reference CCD are denoted byand, respectively. Then by calculating, the ghost image is retrieved, where. In this scheme, the beam-splitter is an indispensable optical component for creating point-to-point correlation. While in the PDCI scheme shown in Fig. 1, a beam-splitter is not required, so the complexity of the system is reduced, what’s more, without the use of SLM, it has a rather lower cost than that of CGI. An object CCD placed after the object is used as a bucket detector, while a reference CCD is used for recording the reference diffraction intensity patterns. The schematic diagram shown in Fig. 2 indicates the proper positions for CCDs in this experiment. In Fig. 2, the object CCD is placed at a place marked as a solid line square, and the reference CCD can be placed at any place marked as dotted line squares with shadow. According to the periodic diffraction effect, the intensity pattern generated by a periodic point source array is also periodic. Therefore, the object could be retrieved with a period of T in the image plane, and the T  is found to be
Then we demonstrate the shape merging technique in the PDCI and its useful application. In order to explain this technique clearly, firstly we make a definition of the non-repeated diffraction pattern (NDP) . An arbitrary square area with its side length equal to the period T in the periodic intensity pattern is named a NDP. As mentioned above, the image of the object in the PDCI reappears in the image plane with a period of T. If the size of the object is larger than that of a NDP, and the components of the object have a relative position relation with each other, then a shape-merged image which is different from the original objects is obtained in each NDP, this is named shape merging technique.
In our experiment, light from a He-Ne laser emitting at 632.8 nm passed through a rotating ground glass to generate pseudo-thermal light. Then this beam illuminates a periodic array board which consists of 100 × 100 points and has a = 50μm. We use a transmission object which was placed after the array board, shown in the Fig. 3(a) .This object has an English letter ‘c’ at upper left corner, another ‘c’ at upper right corner and an English letter ‘s’ at lower right corner. The three letters ‘c’, ‘c’ and ‘s’ have a relative position relation with each other. Then the transmitted light was collected by a CCD of size 1392 × 1040 pixels which has a distance z = 410 mm with the array board. By using correlation measurement, a shape-merged ‘ccs’ which is the logotype of our lab was retrieved, shown in Fig. 3(b), the function of image is given byFig. 3(b), this depends on the period T and the size of the CCD.
In this experiment, we use only one CCD. We choose one of the NDPs, the information contained in this NDP can be thought of detected by the object CCD. While other NDPs seen as the reference beam. Hence this scheme has a lower complexity than that of traditional correlation imaging.
3. Optical encryption
The shape merging technique extends the PDCI to a novel application, optical encryption. The idea is illustrated in Fig. 4. The sender transmits an encrypted image to the receiver. We assume that they transmit the information of object1 through a private channel, consisting of a vector of N components, , which are detected by a CCD used as a bucket detector. The information of object2 is encoded in another vector of N components, , containing the transmission intensity values. These values are also shared with the receiver privately and recorded by another CCD. These two private channels have different encryption methods. The reference intensity distribution is transmitted to the receiver through a public channel. Then by using coincidence measurement, the complete image can only be obtained between the sum of total signal intensity values and the reference intensity distribution through the following linear operation:
The scheme of optical encryption is similar to the shape merging shown in Fig. 1, in order to reduce the complexity of this experiment, we only use one CCD to record the intensity patterns. In the imaging plane, we choose two NDPs, which contain the transmission light intensities of the two objects, and, respectively. The information should have been detected by independent signal CCDs or bucket detectors. While other NDPs seen as the reference beam. The intensity information of the two objects can be seen as the secret key to each other, if the eavesdropper only obtains the information of one object, he cannot retrieve the complete object. The optical setups were the same as previous experiment; the two objects were shown in Fig. 5(a) and 5(b), we assume the two objects as a flag and the map of a city. Then a merged image obtained by coincidence measurement is shown in Fig. 5(c), the flag is inside the map which stands for the position of the destination, and as for all the parameters are not changed, the result image has the same period T with the Fig. 3(b).
In this mechanism, if the position relationship between these two objects is changed, the result will be different, as shown in Fig. 5(d)-5(f). And if we change any parameter among the wavelength λ, the distance between adjacent point sources a, the distance along the transmission axis z and the size of the detection area of the CCD, the number of images appearing in the image plane will also change. Hence this mechanism is controllable; the sender can change the parameters with the receiver to improve the confidentiality of the system. What’s more, in the encryption method based on CGI mentioned above, the reference intensity pattern has to be computed according to the phase distribution modulated on the SLM for each iteration. Therefore the computation complexity of the encryption based on CGI is remarkably high. Whereas, in the encryption based on PDCI, the reference intensity patterns are measured directly. Consequently, its computation complexity is smaller than that of former.
In this paper, a useful application named shape merging technique is studied. This technique is based on periodic diffraction correlation imaging and can be realized without a beam-splitter at a lower cost comparing with traditional ghost imaging. It can merge several objects into one image with only one CCD periodically. Then we demonstrate a potential application of shape merging technique, optical encryption, which can be used to encrypt and transmit object information to the destination secretly. This method is controllable and has a lower computation complexity comparing with the encryption method based on CGI. In summary, this mechanism provides a flexible way to realize image merging and encryption with a low cost and simple experiment scheme.
This work is supported by the Natural Science Foundation of China (Grants No: 60970109, 61170228).
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