阅读说明：本技术 一种圆环形结构光的解析描述方法 (Analytic description method of annular structured light ) 是由 楼宇丽 杨力 刘庆伟 陈晓雪 代梦诗 李重光 于 2019-10-25 设计创作，主要内容包括：本发明涉及一种圆环形结构光的解析描述方法,属于光学技术领域。首先将激光通过轴锥镜-透镜光束变换系统,得到环形光；在获取轴锥镜-透镜光束变换系统的几何光学参数；最后得到环形光的强度分布。本发明可以直接计算轴锥镜-透镜组合中,透镜后焦面上环形光的强度分布,无需使用数值积分的方法。根据所需要的环形光强度分布要求,调整轴锥镜、透镜及其组合的几何光学参数,即可完成光路设计。(The invention relates to an analytic description method of ring-shaped structured light, and belongs to the technical field of optics. Firstly, passing laser through an axicon-lens beam transformation system to obtain annular light; obtaining the geometrical optical parameters of the axicon-lens light beam transformation system; and finally obtaining the intensity distribution of the annular light. The method can directly calculate the intensity distribution of the annular light on the focal plane behind the lens in the axicon-lens combination without using a numerical integration method. And according to the requirement of the required annular light intensity distribution, adjusting the geometrical optical parameters of the axicon, the lens and the combination of the axicon and the lens to complete the light path design.)

1. An analytic description method of ring-shaped structured light is characterized in that:

step 1: passing the laser through an axicon-lens beam transformation system to obtain annular light;

step 2: acquiring geometrical optical parameters of an axicon-lens beam transformation system;

step 3: obtaining the intensity distribution of the annular light through a formula (1);

in the formula, I (x)_f,y_f) Is the intensity distribution on the back focal plane 4 of the lens, (x)_f,y_f) Is a rectangular coordinate on the back focal plane 4 of the lens, I_maxIs the maximum value of the light intensity,

Technical Field

The invention relates to an analytic description method of ring-shaped structured light, and belongs to the technical field of optics.

Background

The annular structured light (hereinafter referred to as "annular light") is applied to the fields of super-resolution microscopic imaging, particle micro-control, laser micromachining, nonlinear optics and the like, and the annular light is obtained by using an axicon-lens combination, which is the method preferentially adopted at present. However, no mathematical description of the analytical form of the annular light distribution has emerged to date, which affects the design of the optical system producing the annular light, as well as the practical application of the annular light. The parallel light vertically irradiates the axicon to obtain Bessel light beams, and the Bessel light beams are still Bessel light beams after being converted by the axisymmetric optical system. According to the mathematical theory, the first kind of integer order Bessel function is analyzed in the universe. For dark field microscopy, particle manipulation, etc. applications, it is currently of most concern that the annular light in the axicon-lens combination be accurately distributed at the back focal plane of the lens, and in the presence of a slight defocus.

Disclosure of Invention

The invention aims to solve the technical problem of providing an analytical description method of annular structured light aiming at the defects of the current annular light distribution theory research, accurately describing the annular light intensity distribution on the rear focal plane of a lens, disclosing the exact relation between the geometrical optical parameters of an axicon and the lens and the annular light distribution, and providing a theoretical basis for the design of an axicon-lens combined optical system. The invention also provides convenience for practical application in consideration of the long focal depth characteristic of the Bessel beam.

The technical scheme of the invention is as follows: an analytic description method of ring-shaped structured light comprises the following specific steps:

step 1: passing the laser through an axicon-lens beam transformation system to obtain annular light;

step 2: acquiring geometrical optical parameters of an axicon-lens beam transformation system;

step 3: obtaining the intensity distribution of the annular light through a formula (1);

in the formula, I (x)_f,y_f) Is the intensity distribution on the back focal plane 4 of the lens, (x)_f,y_f) Is a rectangular coordinate on the back focal plane 4 of the lens, I_maxIs the maximum value of the light intensity,

{. is the square of a first-order Bessel function of the first kind, R is the axis coneThe clear radius of the mirror 2, n the refractive index of the axicon material, β the conical base angle of the axicon 2, f the focal length of the lens 3, and λ the wavelength of the uniform parallel beam 1.

The invention takes Fourier optics as a theoretical basis, researches the light wave transformation characteristics of the axicon and the lens, deduces the light wave complex amplitude distribution on the focal plane behind the lens by means of a Fresnel (Fresnel) diffraction formula, and further obtains the intensity distribution. The first-order Bessel function of the first kind is used for describing the normalized intensity distribution formula of the analytic form, and the annular light intensity distribution can be directly calculated by the formula without numerical integral calculation.

The orthogonal property of Fourier-Bessel series, the differential property of first-order Bessel function, the integral property of zero-order Bessel function, the screening property of delta function, the translation scaling property of Fourier transform and the definition of limit of first-order Bessel function by Dirac.

The invention has the beneficial effects that: the intensity distribution of the annular light on the focal plane behind the lens in the axicon-lens combination can be directly calculated without using a numerical integration method. And according to the requirement of the required annular light intensity distribution, adjusting the geometrical optical parameters of the axicon, the lens and the combination of the axicon and the lens to complete the light path design.

Drawings

FIG. 1 is a schematic view of an axicon-lens optical path used in the present invention;

FIG. 2 is a two-dimensional distribution plot of the ring light as simulated by the computer of the present invention;

FIG. 3 is a real picture of the ring light taken by the experiment of the present invention;

fig. 4 is a cross-sectional profile of the annular light of the present invention along a certain direction.

In the figure: 1-uniform parallel beam, 2-axicon, 3-lens, 4-lens back focal plane

Detailed Description

The invention is further described with reference to the following drawings and detailed description.

As shown in fig. 1, the axicon-lens beam transformation system is composed of a uniform parallel beam 1, an axicon 2, a lens 3 and a lens back focal plane 4. After laser is emitted, the laser needs to be expanded and collimated to form a uniform parallel light beam 1 which just can fill the whole axicon 2, the uniform parallel light beam perpendicularly irradiates the axicon 2, a Bessel light beam is generated on the rear surface (or the vertex of the cone), a lens 3 is added in the range (the maximum class diffraction-free distance) where the light beam is generated to be converted into another Bessel light beam, and annular light is obtained on a rear focal plane 4 of the lens.

Under fresnel approximation, mathematical derivation is performed by fresnel diffraction formula to obtain annular light on the lens back focal plane 4, whose normalized (or relative) light intensity distribution is given by the following formula:

left side of the formula, I (x)_f,y_f) Is the intensity distribution on the back focal plane 4 of the lens, (x)_f,y_f) Is a rectangular coordinate on the back focal plane 4 of the lens, I_maxIs the maximum value of the light intensity. On the right side of the formula,

is the square of the first-order Bessel function of the first type, R is the clear radius of the axicon 2, n is the refractive index of the axicon material, β is the cone base angle of the axicon 2, f is the focal length of the lens 3, and λ is the wavelength of the uniform collimated beam 1.

While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit and scope of the present invention.