Underwater imaging technology plays an essential function in resource development and underwater object detection. To reduce the impact of distortion and loss in underwater imaging, ghost imaging has become one of the important research directions of long-distance underwater imaging because it requires only one-dimensional intensity fluctuation information of the imaging object with good noise resistance. A spatial light modulator (SLM) or a digital micromirror device (DMD) can directly use prefabricated modulated optical fields, then receive the total light intensity by a bucket detector. Additionally, computational ghost imaging has played a more prominent role in advanced light field modulation techniques.

Turbulence is a serious problem with classical imaging. Underwater optical imaging has to combat turbulence induced by temperature and salinity fluctuations. Surprisingly, the fluctuation index disturbance introduced in the optical path can be incorporated into the computational model in ghost imaging. Thus, ghost imaging has capablility of effectively reducing the effect of atmospheric turbulence. Similarly, applying ghost imaging techniques to address turbulence in water has also received attention. This property of ghost imaging is a historic milestone in optical imaging. However, as the propagation distance increases, the attenuation of the light field in the water becomes impossible to ignore. Moreover, the computational models are no longer adaptable in practice. Even now, it is crucial to perform high-quality ghost imaging in water with light field attenuation remains challenging.

Fortunately, the Bessel beam provides a promising solution for light field modulation to reduce attenuation. It can be mathematically formulated by the Bessel function, which is the solution of the Helmholtz Equation in cylindrical coordinates. The Bessel beam has a unique transverse toroidal pattern that does not change when it propagates over a certain distance, thus it is considered diffraction-free propagation and "self-healing". Therefore, Bessel beams can propagate in water with less diffraction scattering effects. In practice, a Bessel beam can be generated by using a Gaussian beam coupled with an axicon. In addition, SLM and DMD can also be used to generate Bessel beams. In ghost imaging, the use of a constantly shifted Bessel light field to overcome the influence of turbulence was reported. However, this would generate strong background noise in the reconstructed image and degrade the imaging quality. Therefore, there is crucial to solve the problem of image quality degradation when utilizing Bessel beams for long-distance ghosting imaging in water.

The research group led by Prof. Xuelong Li from Northwestern Polytechnical University, the researchers from Friedrich Schiller University and Helmholtz Institute Jena focused the underwater ghost imaging scheme using a modulation pattern combining offset-position pseudo-Bessel-ring (OPBR) and random binary (RB) speckle pattern illumination. The obtained ghost images have a better CNR compared to RB beam ghost imaging under the same conditions. The research results are published in Chinese Optics Letters, Vol. 21, Issue 8, 2023: Zhe Sun, Tong Tian, Sukyoon Oh, Jiang Wang, Guanghua Cheng, Xuelong Li. Underwater ghost imaging with pseudo-Bessel-ring modulation pattern[J]. Chinese Optics Letters, 2023, 21(8): 081101.

In this work, the use of lateral Bessel rings with random intensity modulation to form an offset-position pseudo-Bessel-ring (OPBR) speckle pattern was proposed. The OPBR speckle patterns and project them to the DMD in the computational ghost imaging system was designed. The pseudo-Bessel ring beam with the traditional random speckle patterns were combined, which effectively reduced the propagation error of the beam in the water body. Moreover, its special ring structure also facilitates the concentration of the incident light energy. This is a successful combination of practical engineering applications and theories, and this work will also inspire us to explore more beautiful theoretical mechanisms in the field of ghost imaging principles and applications, which will lead to more effective practical values.

To experimentally verify the proposed method, the implementation setup was built. A 10mW laser beam with a wavelength of 532 nm, which is less absorbable to water. A set of digitally OPBR speckle patterns sequentially displayed on DMD and laser beam modulated accordingly in spatial intensity distribution. It must be noted that the micromirrors of DMD are 1280×800 with a pitch of 10.6µm. The modulated beam propagated through the water tank and then fell on the object. To demonstrate the feasibility and performance of OPBR speckle patterns, a laser-cut transmitting digit "3" was prepared as the object. The digit "3" was employed as an object because it contains the frequencies of all directions and it is thus more representative. An image of the digit "3" taken with a high-gain camera for comparison was presented. The transmitted light intensity was collected by a bucket detector. The computer was used to control the ghost imaging system, produce the OPBR speckle patterns, control the patterns exhibition, record the light intensity data, and reconstruct the images. The shape of the object can be calculated by the correlation of the speckle pattern and the single-pixel intensity. The retrieved ghost image was reconstructed by the correlation of the intensity signals and the sequenced random binary (RB) speckle patterns.

From the experiments, the pseudo-Bessel-ring modulation rules for the CNR growth was obtained. For comparison, the image quality by using traditional RB speckle patterns was checked. The results showed that the OPBR speckle patterns are more advantageous in highly scattering media. For the universality and robustness of this method, the CNR scaling is observed for two different digit objects with the same patterns. A simulation in ideal conditions to verify the feasibility of the proposed method was also demonstrated. The results show that using the OPBR speckle pattern can effectively improve image quality compared to traditional ghost imaging. Both experiments and numerical simulations demonstrated that the proposed method can significantly improve the quality of ghost imaging in the scattering medium. This method is very promising for high-quality ghost imaging in turbid water and can be easily applied to SLM-based computational ghost imaging, and axicon-based pseudothermal ghost imaging to replicate the properties of a Bessel beam in the future.

Schematic diagram of ghost imaging setup with the offset-position pseudo-Bessel-ring (OPBR) speckle pattern. A laser incident on a DMD modulated by a sequence of random binary speckle patterns. The modulated light propagates through turbid water, then falls on the object.