Design method of structured light field mask plate with spiral linear amplitude distribution

Abstract

The invention relates to a design method of a structured light field mask plate with spiral linear amplitude distribution, which comprises the following steps of: based on a spiral line parameter equation regulation and control technology, obtaining an improved uniform spiral line family parameter equation containing multiple adjustable parameters; based on an arbitrary curve shaping technology, a complex amplitude expression of a structured light field with spiral linear amplitude distribution is obtained, and the complex transmittance function of the mask plate with the structured light field with the spiral linear amplitude distribution is obtained by combining the amplitude, the phase and a blazed grating of a spiral line family light field. And obtaining the structured light field mask plate with spiral linear amplitude distribution. And the mask plate is used for generating spiral line family light beams which are free of spurious interference and accurate and controllable in geometrical characteristic parameters such as opening angle and curvature on a focal plane. Therefore, a customizable optical solution is provided for complex control tasks such as multi-particle spiral sorting and protein spiral assembling, and particularly, the method has remarkable advantages in particle control and micro-nano manufacturing in the field of biomedicine.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical manipulation, and specifically relates to a method for designing a structured light field mask with a helical linear amplitude distribution. Background Art

[0002] By designing the gradient phase and angular momentum distribution, the helical structured light field can achieve multi-dimensional control of the particle motion trajectory in optical manipulation. Due to the symmetric amplitude distribution of the light field of traditional optical tweezers relying on Gaussian beams or annular vortex beams, it is difficult to achieve the function of directional transportation of particles along complex helical paths. The helical linear light field can decompose the transverse light gradient force into a radial constraint component and a tangential driving force component by regulating the light intensity gradient and orbital angular momentum distribution, thereby guiding the particles to perform complex motions along a preset helical trajectory.

[0003] The light field with a helical linear amplitude distribution exhibits important application values in frontier fields such as micro-nano scale particle manipulation, optical information encoding and transmission, and quantum state regulation due to its unique orbital angular momentum transfer characteristics. In recent years, researchers have explored the structured regulation of the helical light field. Alonzo et al. [Opt. Express 2005, 1749] generated a helical cone beam by superimposing vortex phases to achieve the control of the helical motion trajectory of particles, but the endpoint aggregation effect of its intensity distribution limits the stability of particle motion; Tao et al. [Opt. Laser Technol. 2019, 288] innovatively introduced power exponent phase regulation and successfully achieved continuous adjustment of the helical opening angle. However, the interference of stray light in the focal plane significantly reduces the manipulation accuracy of the optical tweezer system; Tian et al. [Opt. Commun. 2020, 124824] further improved the tunability of the helical structure through exponential factor regulation, but failed to break through the problem of coupled control of the helical lobe number and chiral direction. These above-mentioned helical light field generation technologies are limited by single physical quantity regulation and lack of structural flexibility, and cannot meet the requirements of multi-scale particle cooperative manipulation, nor can they dynamically construct a helical light field family with variable pitch, no stray light interference, and geometric characteristic parameters such as opening angle and curvature size precisely controllable.

[0004] In summary, there is currently a lack of a helical light field family with an arbitrarily adjustable helical amplitude distribution to meet the requirements in the technical field of optical manipulation, especially for the complex arrangement of particles and the flexible regulation of multi-parameter helical light field families. Summary of the Invention

[0005] To solve the above technical problems, the object of the present invention is to provide a method for designing a structured light field mask with a helical linear amplitude distribution, and use this mask to generate a helical light field family with no stray light interference and geometric characteristic parameters such as opening angle and curvature size precisely controllable in the focal plane.

[0006] The technical solution adopted by the present invention is as follows: A method for designing a structured light field mask with a spiral linear amplitude distribution, and the steps are as follows: S1. Based on the spiral parameter equation regulation technology, obtain an improved unified spiral family parameter equation with multiple adjustable parameters; S2. Based on the arbitrary curve shaping technology, obtain the complex amplitude expression of the structured light field with a spiral linear amplitude distribution: Among them, G i (ξ, η) = Φ{E i (x, y)}, Φ{} is the Fourier transform function, (x, y) are the coordinates before Fourier transform, and (ξ, η) are the coordinates after Fourier transform; S3. Based on the above, combine the amplitude, phase of the spiral family light field with a blazed grating, so as to obtain the complex transmittance function of the structured light field mask with a spiral linear amplitude distribution, and its expression is: T = bw[A0(ξ, η)]exp{i[{angle(F{E(x, y)}) + P0)]} Among them, angle() is the angular function, A0(ξ, η) is the amplitude of the constructed light field, bw[] is the binarization function, exp{} is the exponential function, F{} is the Fourier transform function, and E(x, y) is the transmittance function of the computer-generated hologram; The mask described based on this complex transmittance function is the structured light field mask with a spiral linear amplitude distribution. As a preferred solution, in step S1, the improved unified spiral family parameter equation with multiple adjustable parameters obtained is: In the formula, X(t) and Y(t) are integral functions with respect to the parameter t, representing the spatial position distribution of the spiral on the two-dimensional plane, where t is the parametric angle or parametric distance of the spiral; the two constant coefficients α and β are used to adjust the size of the spiral; (-1) γ and (-1) γ-1 are sign functions, used to change the direction and shape of the spiral; A and B are used to adjust the amplitudes of the spiral in the horizontal and vertical axes; sin m (ξ) and sin n (ξ) The exponents m and n in are used to adjust the periodicity and waveform of the spiral; q is an exponential coefficient, used to adjust the curvature and rotation speed of the spiral; k is used to adjust the symmetry and shape of the spiral. As a preferred solution, in step S2, E i (x, y) is the transmittance function of the computer-generated hologram, and the specific expression is: where |c'2(t)| = [X(t) 2 +Y(t) 2 1 / 2 , t ∈ [0, 2π], X(t) and Y(t) are the parametric equations of the helical family of beams, which determine the shape of the curve, and Φ i is the phase term of the beam. As a preferred solution, in step S3, the phase expression of the blazed grating is P0 = 2πx / d, where d is the period of the blazed grating.

[0007] Technical effects of the present invention: [[ID=URL]]The structured light field mask plate with a helical linear amplitude distribution designed by the present invention realizes high-precision dynamic regulation of the helical family of light fields including various helical types. Compared with the traditional method for generating helical conical beams, the present invention significantly improves the purity and manipulation flexibility of the light field, and supports the customized regulation of helices such as Archimedean spiral, logarithmic spiral, Fermat spiral, linked spiral, hyperbolic spiral, Euler spiral, snail spiral, Doppler spiral, Poncelet spiral, tractrix spiral, atomic spiral, involute, Cotes spiral, sine spiral, cosine spiral, etc. and multi-level nested spiral structures; thus providing a customizable optical solution for complex manipulation tasks such as multi-particle spiral sorting and protein spiral assembly, and showing significant advantages especially in particle manipulation and micro-nano manufacturing in the biomedical field. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 is a mask plate of a partial helical family of light fields generated by the present invention, and the selected helices are atomic helix, Euler helix, Archimedean helix, sine helix when n = 4, sine helix when n = 2, and tractrix helix. Figure 2 is Figure 1 the atomic helix, Euler helix, Archimedean helix, sine helix when n = 4, sine helix when n = 2, and tractrix helix light fields generated by the mask plate shown. DETAILED DESCRIPTION OF THE INVENTION

[0009] The present invention utilizes the principle of computer-generated holography to obtain a structured light field with a helical linear amplitude distribution and multi-parameter adjustable by computer coding, and prepares a digital mask plate using the holographic principle. The present invention can generate a multi-mode helical family of light fields without stray interference and with precisely controllable opening angle and curvature size. Therefore, it has important application value in the field of particle manipulation.

[0010] First, based on any curve shaping technology, the complex amplitude expression of the helical family of beams is constructed as follows: ​ Among them, G i (ξ, η) = Φ{E i (x, y)}, where Φ{} is the Fourier transform function, (x, y) are the coordinates before Fourier transform, (ξ, η) are the coordinates after Fourier transform, and E i (x, y) is the transmittance function of the computer-generated hologram. It can be expressed as: Among them, |c'2(t)| = [X(t) 2 +Y(t) 2 , where t ∈ [0, 2π], X(t) and Y(t) are the parametric equations of the curve, which determine the shape of the curve, and Φ 1 / 2 is the phase term of the light beam. i To facilitate obtaining a spiral family light field with no stray interference and precisely controllable opening angle and curvature size, for the purpose of the spiral family light field, the unified parametric equation of the spiral family can be written as: For the purpose of obtaining a spiral family light field with no stray interference and precisely controllable opening angle and curvature size, the unified parametric equation of the spiral family can be written as: In the formula, X(t) and Y(t) are integral functions with respect to the parameter t, representing the spatial position distribution of the spiral in the two-dimensional plane, where t is the parametric angle or parametric distance of the spiral; the two constant coefficients α and β are used to adjust the size of the spiral; (-1) γ and (-1) γ-1 These two terms are sign functions, used to change the direction and shape of the spiral; A and B are used to adjust the amplitude of the spiral in the horizontal and vertical axes; sin m (ξ) and sin n (ξ) The exponents m and n in are used to adjust the periodicity and waveform of the spiral; q is an exponential coefficient, used to adjust the curvature and rotation speed of the spiral; k is used to adjust the symmetry and shape of the spiral; therefore, by setting different structural parameters, the transformation characteristics between different types of spirals can be regulated. The phase expression of the blazed grating is: P0 = 2πx / d. Where d is the period of the blazed grating, and its function is to perform interference recording on the above-mentioned spiral family light beam containing various adjustable parameters. A structured light field with a spiral-shaped amplitude distribution has the advantages of including various spiral-shaped amplitude distributions and being multi-parameter adjustable. By combining the amplitude and phase of the spiral family light field with a blazed grating, the complex transmittance function of the structured light field mask with a spiral-shaped amplitude distribution is obtained. The specific expression of its complex transmittance function is: T = bw[A0(ξ, η)]exp{i[{angle(F{E(x, y)}) + P0)]} Among them, angle() is the angular function, A0(ξ, η) is the amplitude of the constructed optical field, bw[] is the binarization function, exp{} is the exponential function, F{} is the Fourier transform function, E(x, y) is the transmittance function of the computer-generated hologram, and P0 is the phase of the blazed grating. The mask described by this complex transmittance function is the mask of the structured light field with a spiral amplitude distribution according to the present invention.

[0011] In the experiment, using the unified spiral parametric equation and the principle of computer-generated holography, here we take the masks of atomic spiral, Euler spiral, Archimedes spiral, sine spiral with n = 4, sine spiral with n = 2, and tractrix spiral, and generate the corresponding spiral structured light fields, as Figure 2 shown. Embodiment

[0012] Taking a mask with a size of 1024×1024 as an example, masks of atomic spiral, Euler spiral, Archimedes spiral, sine spiral with n = 4, sine spiral with n = 2, and tractrix spiral for a laser with a working wavelength of 532 nm are given. This mask generates a structured light field with a spiral amplitude distribution. According to the mask complex transmittance function in the specific implementation manner, a mask of a structured light field with a spiral amplitude distribution including multiple spiral amplitude distributions and multiple adjustable parameters is finally obtained.

[0013] Figure 1 That is, the masks of atomic spiral, Euler spiral, Archimedes spiral, sine spiral with n = 4, sine spiral with n = 2, and tractrix spiral used in the embodiment. Such a mask of the spiral structured light field can be realized by a spatial light modulator. Taking the PLUTO-VIS-016 type phase spatial light modulator of German Holoeye company as an example, its pixel size is 8μm, the fill factor is 93%, and the resolution is 1920pixel×1080pixel. In the experiment, a continuous-wave solid-state laser with a wavelength of 532 nm and a power of 50 mW is used.

[0014] Figure 2 Shown, that is, a structured light field with a spiral amplitude distribution including multiple spiral amplitude distributions and multiple adjustable parameters generated in the embodiment.

[0015] In summary, the present invention proposes a specific design scheme and implementation scheme of a structured light field mask with a spiral amplitude distribution that includes various spiral light intensity distributions and multiple parameter adjustments, and takes the atomic helix, Euler helix, Archimedes helix, sine helix when n = 4, sine helix when n = 2, and tractrix helix as examples. For a laser with a working wavelength of 532 nm, a technical implementation route of a design method for a structured light field mask with a spiral amplitude distribution is proposed.

[0016] The above design of a class of structured light field masks that generate various spiral light intensity distributions and are adjustable with multiple parameters only represents a specific implementation manner of the present invention, and should not be construed as a limitation on the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the basic idea of the present invention, several deformations and improvements can be made to the specific implementation details proposed in this patent, and these all fall within the protection scope of the present invention.

Claims

1. A method for designing a structured light field mask with a spiral linear amplitude distribution, characterized in that: The steps are as follows: S1. Based on the spiral parameter equation regulation technology, obtain an improved unified spiral family parameter equation with multiple adjustable parameters; S2. Based on the arbitrary curve shaping technology, obtain the complex amplitude expression of the structured light field with a spiral amplitude distribution: Among them, G i (ξ, η) = Φ{E i (x, y)}, where Φ{} is the Fourier transform function, (x, y) are the coordinates before the Fourier transform, and (ξ, η) are the coordinates after the Fourier transform; S3. Combine the amplitude and phase of the spiral family light field with a blazed grating to obtain the complex transmittance function of the structured light field mask with a spiral amplitude distribution, and its expression is: T = bw[A0(ξ,η)]exp{i[a{ngle(F{{E(x,y)})+P0)]} where angle() is the angular function, A0(ξ,η) is the amplitude of the constructed light field, bw[] is the binarization function, exp{} is the exponential function, Φ{} is the Fourier transform function, and E(x,y) is the transmittance function of the computer-generated hologram; The mask described by this complex transmittance function is the structured light field mask with a spiral amplitude distribution.

2. A method for designing a structured light field mask with a spiral amplitude distribution according to claim 1, wherein: In step S1, the improved unified spiral family parameter equation with multiple adjustable parameters obtained is: In the formula, X(t) and Y(t) are integral functions with respect to the parameter t, representing the spatial position distribution of the helix in the two-dimensional plane, where t is the parameterized angle or parameterized distance of the helix; the two constant coefficients α and β are used to adjust the size of the helix; (-1) γ and (-1) γ-1 are sign functions, used to change the direction and shape of the helix; A and B are used to adjust the amplitudes of the helix in the horizontal and vertical axis directions; sin m (ξ) and sin n (ξ) The exponents m and n in are used to adjust the periodicity and waveform of the helix; q is an exponential coefficient used to adjust the curvature and rotation speed of the spiral; k is used to adjust the symmetry and shape of the spiral.

3. A method for designing a structured light field mask with a spiral amplitude distribution according to claim 2, wherein: In step S2, E i (x, y) is the transmittance function of the computer-generated hologram, and the specific expression is: where |c'2(t)| = [X(t) 2 + Y(t) 2 1 / 2 , t ∈ [0, 2π], X(t) and Y(t) are the parametric equations of the helical family of beams, determining the shape of the curve, Φ i is the phase term of the beam.​ 4. A method for designing a structured light field mask with a spiral amplitude distribution according to claim 1, wherein: In step S3, the phase expression of the blazed grating is P0 = 2πx / d, where d is the period of the blazed grating.

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