System for realizing optical rotation based on cylindrical lens

Abstract

The invention provides a system for realizing optical rotation based on cylindrical lenses, and the system is provided with at least one cylindrical lens, and when a single cylindrical lens is arranged, the system is used for rotating the intensity distribution of an incident light field; when two cylindrical lenses are arranged, the cylindrical lenses are used for rotating the intensity distribution and the phase distribution of a light field at the same time; wherein the two cylindrical lenses meet the confocal condition, the distance between the input plane and the output plane is twice the focal length, and the two cylindrical lenses are strictly aligned on the plane perpendicular to the optical axis. The problem that in a traditional method, a cumbersome Dove prism and an optical system are difficult to integrate can be solved. Meanwhile, by applying the technical scheme of the invention, the cylindrical lens can be continuously rotated to realize dynamic optical rotation, and the method has application potential and market prospect in image processing, computer vision and related fields.

Description

Technical Field

[0001] The present invention relates to the fields of optical rotation operations and image processing, and particularly to a technical solution for realizing optical rotation based on a cylindrical lens. Background Art

[0002] All-optical processing is an effective method for performing high-speed parallel processing, which is superior to traditional digital processing because traditional digital processing has problems such as complex analog-to-digital conversion, extremely high power consumption, and slow response speed. At the same time, the miniaturization of optical processing systems is an ongoing goal in the fields of science and engineering, while traditional optical selection devices are large in size and difficult to integrate. Planar optical elements can redesigned optical elements into thin planar elements, which is expected to significantly reduce the occupied space and system complexity. Similar to complex signal processing by integrating multiple basic logic gates in digital circuits, complex optical analog calculations are usually also achieved by combining basic optical operations. Translation, scaling, and rotation are three basic operations of light field manipulation, and their miniaturized and lightweight designs can significantly enhance the integration of all-optical computing. Therefore, the development of planar optical technology makes it possible to miniaturize optical devices, but there is a lack of efficient and compact light field rotation schemes in the prior art. Summary of the Invention

[0003] In view of the above problems, inspired by the principle of optical conformal mapping, the present invention proposes a technical solution for realizing optical rotation based on a pair of cylindrical lenses.

[0004] The technical solution of the present invention provides a system for realizing optical rotation based on a cylindrical lens, and at least one cylindrical lens is provided. When a single cylindrical lens is provided, it is used to rotate the intensity distribution of the incident light field. When two cylindrical lenses are provided, it is used to rotate both the intensity distribution and the phase distribution of the light field simultaneously; wherein, the two cylindrical lenses satisfy the confocal condition, the distance between the input plane and the output plane is twice the focal length, and the two cylindrical lenses are strictly aligned in the plane perpendicular to the optical axis.

[0005] Moreover, the optical rotation is realized through the conformal mapping theory, which satisfies the Cauchy-Riemann transformation condition, so that the phase expression of the light field rotation can be resolved into the phase form of the cylindrical lens.

[0006] Moreover, when a single cylindrical lens is provided, the phase expression of the cylindrical lens is,

[0007] wherein, is the wave vector, is the propagation distance, is the rotation angle, are the polar coordinate parameters of the input plane.

[0008] Moreover, when two cylindrical lenses are set, The phase expression of the first cylindrical lens is,

[0009] The phase expression of the second cylindrical lens is,

[0010] Wherein, is the wave vector, is the propagation distance, and are the polar coordinate systems of the input plane and the output plane respectively, is the rotation angle.

[0011] Moreover, by continuously switching the phase expressions of the cylindrical lenses, a dynamic optical rotation effect is achieved, realizing dynamically adjustable optical rotation.

[0012] Moreover, the optical image rotation angle of the system has a double-angle relationship with the rotation angle of the cylindrical lens, and by adjusting the rotation angle of the cylindrical lens, the rotation of the light field at any angle can be achieved.

[0013] Moreover, the system is applicable to any input light field, including off-axis Gaussian beams and fractional-order vortex beams, and can realize a dynamic phase mask through a spatial light modulator, a diffractive optical element or a metasurface.

[0014] Moreover, the system realizes phase modulation through planar optical devices, and as a compact light field rotator, it supports the miniaturization and integration requirements of optical systems.

[0015] Moreover, the system can be cascaded with a planar optical translator or a scaler to realize the composite operations of translation, rotation and scaling of the light field.

[0016] Moreover, the cylindrical lens of the system is manufactured by lithography and integrated into an optical chip or a micro-nano optical device.

[0017] In summary, the present invention designs a scheme for realizing optical rotation with a cylindrical lens system. Using a single cylindrical lens can realize the rotation of the pure optical image intensity, and using a pair of cylindrical lenses can realize the rotation of the optical intensity and phase. The present invention provides a novel, simple and general method, which can continuously rotate the light field to any angle, and significantly reduces the size compared with the previous complex and space-consuming strategies.

[0018] The present invention also conveniently demonstrates the phase mask of the cylindrical lens using a spatial light modulator to verify its function. The present invention recognizes that the phase mask can be replaced by a planar optical element to further enhance the integration level and possibly achieve more powerful functions by utilizing the huge design freedom. The cylindrical lens system proposed by the present invention for optical field rotation can, together with the planar optical element for optical field translation and scaling, constitute the basic component of complex optical field transformation. Therefore, the present invention envisions that such a compact optical field rotator can be applied in the miniaturization and integration applications in the fields of image processing, computer vision, and large-scale optical processing systems, etc. Description of the Drawings

[0019] Figure 1 It is a schematic diagram of the cylindrical lens realizing optical rotation in an embodiment of the present invention; Figure 2 It is a schematic diagram of the optical path for verifying the optical rotation function in an embodiment of the present invention; Figure 3 It is a comparison diagram of simulation and experiment of a single cylindrical lens realizing the rotation of optical intensity in an embodiment of the present invention; Figure 4 It is a comparison diagram of simulation and experiment of a single cylindrical lens rotating the intensity of an off-axis Gaussian beam in an embodiment of the present invention; Figure 5 It is a comparison diagram of simulation and experiment of a cylindrical lens pair composed of two cylindrical lenses rotating a split vortex beam in an embodiment of the present invention. Detailed Embodiments

[0020] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0021] The present invention proposes a system for optical rotation based on cylindrical lenses. The present invention simulates the rotation effect of Dove prism on the light field, and derives the phase expression of the optical rotator in combination with the conformal mapping theory. Its expression is in the form of a cylindrical lens in the Cartesian coordinate system. Therefore, the present invention designs an optical system for rotating the light field intensity with a single cylindrical lens, and cascades two confocal cylindrical lens groups to simultaneously rotate the light field intensity and phase. Based on a single cylindrical lens group, the present invention demonstrates the rotation of holographic images and off-axis Gaussian beams by the rotator. In addition, the present invention demonstrates the rotation of fractional vortices based on two cylindrical lens groups, thus verifying the feasibility of the design scheme of the present invention. At the same time, in this method, the phase expression of the cylindrical lens can be implemented as a phase mask through planar optical devices such as spatial light modulators, diffractive optical elements, and metasurfaces. Therefore, problems such as the difficulty of integrating the bulky Dove prism with the optical system in the traditional method can be solved. At the same time, the present invention notes that the cylindrical lens can be continuously rotated to achieve dynamic optical rotation, which has great application potential in image processing, computer vision and related fields.

[0022] This lens element can rotate any light field distribution to the desired angle without relying on the optical path accumulation in the Dove prism. This method not only facilitates the miniaturization of the optical system, but also solves the inevitable polarization change problem of obliquely incident light at the interface of traditional bulk prisms. As a demonstration, the present invention also realizes dynamic optical rotation by using a programmable spatial light modulator, thus constructing a compact and adjustable image processing system. The discovery of using cylindrical lenses to achieve optical rotation, like similar devices in other optical elements, fills the gap in planar optical rotation devices and opens up the possibility of all-optical image processing in integrated systems. In addition, planar cylindrical lenses can be mass-produced by mature nanofabrication technologies such as lithography.

[0023] Example 1 In this embodiment, a single cylindrical lens is set to rotate the intensity distribution of the incident light field. To achieve optical rotation, the conformal mapping condition needs to be satisfied during optical rotation processing so that there is an analytic phase for modulating the light field rotation, thereby solving the phase expression of the rotator that satisfies the coordinate mapping condition. By solving, the phase expression form of the rotator is the expression of a classical cylindrical lens, thereby constructing a cylindrical lens rotation system. By rotating the phase of the cylindrical lens, the optical rotation operation is realized.

[0024] For spatial rotation, the optical element should be described by a rotation operator acting on the transmitted light, and accompanied by a light field coordinate transformation, which can be described as:

[0025] where, and The Cartesian coordinate systems of the input plane and the output plane respectively, is the rotation angle.

[0026] In the present invention, simulating the rotation effect of the Dove prism on the light field, the relationship of polar coordinate transformation between the input plane and the output plane in optical rotation is:

[0027] Wherein, and are the polar coordinate systems of the input plane and the output plane respectively, is the rotation angle.

[0028] The output optical image corresponds to the inverted version of the input image, and its rotation angle is determined by the rotation parameter The core idea of this transformation is that the angular position in the polar coordinate system rotates before and after the transformation, while the radial position remains unchanged. To achieve the required transformation, the present invention applies the conformal mapping theory that supports ray optical coordinate transformation, and the mapping needs to satisfy the conditions of the Cauchy-Riemann transformation:

[0029] Fortunately, substituting Equation 2 into Equation 3 reveals that the conditions for conformal mapping are satisfied, thus ensuring the solvability of the equation. Next, using the stationary phase approximation of the Fresnel-Kirchhoff integral, the present invention obtains the transformation conditions in the paraxial propagation background, and the gradient of the optical conversion phase can be expressed as:

[0030] Where is the wave vector of the space, is the propagation distance of the space. Therefore, the phase distribution of the designed rotation device can be obtained by integration, and its distribution is expressed as:

[0031] Wherein, is the phase of a single cylindrical lens.

[0032] There is a double-angle relationship between the rotation angle of the specific optical image of the cylindrical lens optical rotation system designed by the present invention and the rotation angle of the cylindrical lens. By precisely rotating the phase of the cylindrical lens, arbitrary-angle rotation of the image can be achieved.

[0033] Figure 3It respectively shows the rotational phase distribution of a single cylindrical lens designed by the present invention, as well as the simulation results and experimental results of the rotated images at different angles when the transmission parameter d = 230 mm. It can be observed that as the rotation angle increases, the triangular image rotates counterclockwise. Whether it is the shape of the rotated image or the rotation angle, the experimental results are in good agreement with the simulation results.

[0034] Figure 4 summarizes the intensity distributions of simulation and experiment when performing off-axis rotation at intervals of in the azimuthal angle space. The single cylindrical lens of the present invention can achieve the rotation of an off-axis beam.

[0035] Example 2 In this example, two cylindrical lenses are provided to simultaneously rotate the intensity distribution and phase distribution of the light field. After the incident light is phase-modulated by the first rotating cylindrical lens at the input plane and propagates a certain distance, the distribution of the light field rotates, causing the intensity to rotate. After using the second cylindrical lens to compensate for the phase at the output plane, the rotation of the phase can be achieved, and collimated light output can be realized.

[0036] Furthermore, the present invention proposes that the rotation of the optical phase can be achieved by two confocal cylindrical lenses. The positions of the two cylindrical lenses are required to satisfy the confocal condition. The distance between the input plane and the output plane is twice the focal length 2f, and the two cylindrical lenses are required to be strictly aligned in the x-y plane (the plane perpendicular to the optical axis).

[0037] It should be noted that Equation 5 is the expression of the cylindrical lens in the Cartesian coordinate system. From the above theoretical derivation, it is known that after the light field propagates a certain distance through the cylindrical lens, the rotation of the intensity distribution is achieved. The expression of the correction phase is the same as that of the cylindrical lens phase. Therefore, the optical rotation system proposed in this example consists of two customized cylindrical lenses: the first is used to convert the image intensity, and the phase of the first cylindrical lens refers to Equation 5. The other is located at the propagation distance and is used to correct the phase distortion. The phase of the second cylindrical lens refers to Equation 6: The present invention considers that regardless of the shape and size of the input beam, the optical rotation through the cylindrical lens is always effective, which indicates that the rotation scheme based on conformal mapping has universal applicability. This characteristic provides a way to achieve arbitrary optical rotation through pure-phase planar optical elements (such as metasurfaces or diffractive optical elements). If the present invention needs to achieve the rotation of the phase, it is required to compensate for the phase at the output plane position. In the ray reversal direction, the phase corrector performs an inverse coordinate transformation, that is , and similarly, the expression of the corrected phase can be deduced and expressed as: ​

[0038] Among them, is the phase of the second cylindrical lens.

[0039] The schematic diagram of the optical rotation scheme based on the cylindrical lens is as Figure 1 shown. The cylindrical lens system performs phase modulation on the incident light field, causing the rotation of the light field distribution after propagation and evolution.

[0040] The cylindrical lens rotation system can rotate any target object, showing the universality of optical rotation. The present invention verifies the rotation ability of the system for off-axis beams by rotating an off-axis Gaussian beam, and verifies the rotation ability of the system for phase by rotating a fractional-order vortex beam.

[0041] The present invention designs a specific experiment to verify the rotation function of the device of the present invention, as Figure 2 shown. The Gaussian beam emitted from a helium-neon laser is filtered and expanded by a spatial filter composed of two lenses (lens 1 and lens 2) and a pinhole. The collimated beam is adjusted by a polarizer to be consistent with the working polarization direction of the spatial light modulator. After passing through the folded optical path, holographic phase and rotation phase are respectively obtained on the left and right lobes of the spatial light modulator. Specifically, beam splitter 1 reflects the beam to the left lobe of the spatial light modulator, and the reflected beam is redirected to the right lobe of the spatial light modulator through a right-angle prism and beam splitter 2. The light beam modulated twice by the spatial light modulator is collected by a charge-coupled device camera. At the same time, a black paper is placed between beam splitter 1 and beam splitter 2 to prevent light transmission from affecting the observation results. In the design of the present invention, the hologram calculated based on the holographic angular spectrum diffraction principle is encoded into the SLM to generate a triangular pattern.

[0042] To verify the engineering ability of the cylindrical lens to rotate the optical phase in the entire space, the present invention uses a fractional-order vortex beam as the input target object. As is well known, due to the discontinuous azimuth-dependent phase, the propagation of the fractional-order vortex beam will cause the appearance of radially open rings. The fractional-order vortex mode can be generated by loading the vortex phase diagram onto the spatial light modulator. For convenience, the present invention superimposes the vortex phase and the transformation phase onto the left lobe of the SLM. Under this experimental configuration ( ), the rotating fractional-order vortex mode can be directly observed after passing through two phase masks, as Figure 5 shown. As expected, the opening direction of the fractional-order vortex mode rotates at the designed rotation angle, which means that the overall phase of the vortex mode also rotates in the plane. In addition, the opening direction and shape are highly consistent with the simulation results, which further proves the fidelity and accuracy of the rotation function of the proposed cylindrical lens system.

[0043] In specific implementation, a phase mask can be realized by using the spatial light phase modulation technology, and a dynamic optical rotation effect can be realized by continuously switching the expression of the cylindrical lens, thereby realizing dynamically adjustable optical rotation.

[0044] The phase expression of the rotator is the phase expression of the cylindrical lens. The present invention can realize a rotating phase mask by means of planar optics, realize phase modulation on a spatial light modulator, a diffractive optical element, and a metasurface, and does not require bulk optical elements such as volume lenses, thereby realizing the planarization and compactness of the optical system.

[0045] As described above, the above are only specific implementation manners of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A system for realizing optical rotation based on a cylindrical lens, characterized in that: At least one cylindrical lens is provided, When a single cylindrical lens is provided, it is used to rotate the intensity distribution of the incident light field; When two cylindrical lenses are provided, they are used to simultaneously rotate the intensity distribution and the phase distribution of the light field; wherein the two cylindrical lenses satisfy the confocal condition, the distance between the input plane and the output plane is twice the focal length, and the two cylindrical lenses are strictly aligned on a plane perpendicular to the optical axis.

2. The system for realizing optical rotation based on cylindrical lenses according to claim 1, characterized in that: Optical rotation is realized through conformal mapping theory, which satisfies the Cauchy-Riemann transformation conditions, so that the phase expression of light field rotation can be resolved into the phase form of cylindrical lens.

3. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: When a single cylindrical lens is provided, the phase expression of the cylindrical lens is: in, is the wave vector, is the propagation distance, is the rotation angle, are the polar coordinate parameters of the input plane.

4. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: When two cylindrical lenses are set up, The phase expression of the first cylindrical lens is: The phase expression of the second cylindrical lens is: in, is the wave vector, is the propagation distance, and are the polar coordinate systems of the input plane and the output plane, respectively. is the rotation angle.

5. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: A dynamic optical rotation effect is achieved by continuously switching the phase expression of the cylindrical lens, thereby realizing dynamically adjustable optical rotation.

6. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: The rotation angle of the optical image of the system is in a two-fold relationship with the rotation angle of the cylindrical lens, and the rotation of the light field at any angle can be achieved by adjusting the rotation angle of the cylindrical lens.

7. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: The system is applicable to arbitrary input light fields, including off-axis Gaussian beams and fractional-order vortex beams, and can realize dynamic phase masks through spatial light modulators, diffractive optical elements or metasurfaces.

8. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: The system realizes phase modulation through planar optical devices and supports the miniaturization and integration requirements of optical systems as a compact light field rotator.

9. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: The system can be cascaded with a planar optical translator or zoomer to achieve composite operations of translation, rotation and zoom of the light field.

10. The system for realizing optical rotation based on cylindrical lenses according to claim 2, characterized in that: The cylindrical lens of the system is manufactured by photolithography and integrated into an optical chip or a micro-nano optical device.

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