Laguerre-Gaussian transform for rotating image processing

Abstract

Rotation is a common motional form in nature, existing from atoms and molecules, industrial turbines to astronomical objects. However, it still lacks an efficient and reliable method for real-time image processing of a fast-rotating object. Since the Fourier spectrum of a rotating object changes rapidly, the traditional Fourier transform (FT) techniques become extremely complicated and time consuming. Here, we propose a Laguerre-Gaussian (LG) transform to analyze the rotating object with LG-mode 5-7 basis. The rotation operation provides a feasible way to acquire LG spectrum, which is similar to the function of lens in FT. Particularly, the obtained LG spectrum does not change even the object working at a high rotating speed. By analyzing the LG spectrum, one can perform image processing such as reconstruction, edge enhancement, and pattern replication. Such LG transform provides an efficient and convenient way to real-time monitor and analyze a fast-rotating object in scientific research and industry.FT decomposes a temporal signal into its constituent frequencies. Because many linear operations including differentiation and convolution are much easier to perform in the frequency domain, FT has been widely applied in analysis of differential equations, FT spectroscopy, and signal processing [1]. In Fourier optics, FT from an optical pattern to its spatial frequency components can be readily achieved by using an optical lens [2]. Based on such optical FT, powerful tools, such as image reconstruction, edge recognition, spatial filtering, computer generated hologram, and image compression [3], have been developed for image processing schemes. However, in real-time monitoring of a rotating object (such as a biological molecule, industrial centrifuge and turbine, and an astronomical object), the typical optical FT techniques wouldn't work as efficiently as usual. Since its Fourier spatial frequency spectrum is changing along with the rotating object, FT-based image processing schemes become complicated and time consuming. In this Article, we propose and experimentally demonstrate to use a Laguerre-Gaussian (LG) transform of a rotating object to overcome this problem. The obtained LG spectrum does not vary with the rotation, which provides great convenience and a nature way for further image processing of a fast-rotating object.

Symmetry detection of rotating patterns based on rotational Doppler effect of light

“…In 2020, Wei et al performed imaging and image processing of a rotating object by analyzing the LG spectrum [22] . As the RDE is closely objects on incident light by means of mode expansion, which explained the phenomenon of topological charge change of scattered light and the generation of RDE [23] . Furthermore, Qi et al found in the experiment that the amplitude of the RDE signal reaches its maximum when the topological charge of the optical vortex matches the geometric symmetry of the object [24] .…”

Spatially Structured-Mode Multiplexing Holography for High-Capacity Security Encryption

“…5,18−23 Laguerre−Gaussian (LG) modes and Hermite−Gaussian (HG) modes are the eigensolutions of a paraxial wave equation, which are capable of composing complete and orthogonal bases. LG modes feature a circular symmetry and are directly related to the OAM of photons, which play an important role in rotational Doppler shift, 24 optical image processing, 25,26 and optical communications. 27 LG modes are characterized by an azimuthal index l and a radial index p. HG modes have a rectangular symmetry and are defined by the indices of m and n along x-and y-directions, respectively.…”

Laguerre–Gaussian-Domain Rotational Image Restoration beyond the Camera Response

“…Laguerre–Gaussian (LG) modes are the Eigen solutions of the paraxial wave equation, which are capable of composing a complete and orthogonal basis to form arbitrary optical fields. − LG mode features a circular symmetry, which is characterized by an azimuthal index l (i.e., orbital angular momentum (OAM)) , and a radial index p . By utilizing the l index, researchers have developed digital spiral imaging (DSI) techniques to analyze the object’s azimuthal information. − One can also input an OAM-carrying light to measure the rotational speed , based on the rotational Doppler effect. − Recently, the measurement of full LG spectrum has been demonstrated to reconstruct the image of a rotating object within the camera response speed …”

“…34−37 Recently, the measurement of full LG spectrum has been demonstrated to reconstruct the image of a rotating object within the camera response speed. 38 In this article, we propose and experimentally demonstrate a novel LG-domain image processing method to restore the rotation-blurred image beyond the camera response. The process of capturing an optical image of a rotating object is equivalent to an integration during the exposure time.…”