CN105334195A - Method for determining detector position with atomic maximum fluorescence collection efficiency - Google Patents

Abstract

The invention discloses a method for determining the detector position of the maximum fluorescence collection efficiency of atoms. Firstly, the atomic flux fluorescence collection system is simulated and modeled based on the Monte Carlo principle; surface (that is, the function of fluorescence collection efficiency with respect to the spatial position relationship of the detector), and finally, the maximum value of the fluorescence collection efficiency and the corresponding spatial position coordinates of the detector are calculated within the movable space range of the detector. The invention solves the problem of the position of the detector to maximize the collection efficiency of the atomic fluorescence when the atomic fluorescence diverges greatly (as a cylindrical light source), and can also evaluate the error caused by the inaccurate placement of the detector to the light collection efficiency.

Description

A Method for Determining Detector Positions for Maximum Fluorescence Collection Efficiency of Atoms

technical field

The invention relates to the problem of light collection efficiency of a light source of arbitrary shape passing through a lens system, more particularly applicable to the problem of light collection efficiency of a light source of arbitrary shape passing through a lens system while a detector moves within a certain spatial range, and belongs to the field of non-imaging optics.

Background technique

Cold atomic beams are widely used in basic physics research and various ultra-precision metrology and testing technologies, such as atomic lithography, atomic frequency standards, atomic gravimeters, atomic gyroscopes, and atomic gravity gradiometers. Its performance indicators, such as flux, have an important impact on the measurement accuracy of these applications. Flux test methods generally include fluorescence method and absorption method. In the process of detecting atomic flux by fluorescence method, a lens system is often used to collect atomic fluorescence. The measurement result of fluorescence collection efficiency will affect the flux size, and then affect to the measurement accuracy for the above applications.

In flux detection, it is generally desirable to place the fluorescence (light source) at the focal point of the lens system, and the detector at the other focal point of the lens, so as to obtain the maximum fluorescence collection efficiency (high signal-to-noise ratio), and then use The concept of spatial solid angle is used to calculate fluorescence collection efficiency. This method is only suitable for the calculation model of the maximum fluorescence collection efficiency of a point light source in an ideal optical system, and has great limitations. This method is invalid if the fluorescence divergence is large (as a cylindrical light source) or if the error caused by the inaccurate detector position to the fluorescence collection efficiency is to be evaluated. In addition, when the lens system cannot be regarded as an ideal optical system, using this method to calculate the maximum fluorescence collection efficiency will also produce errors.

Contents of the invention

The object of the present invention is to solve the above problems, and propose a method for determining the detector position for the maximum fluorescence collection efficiency of atoms. The device consists of a light source, a lens system, and a detector (Figure 1). Due to the limitation of the experimental device, the detector can only move within a certain space range. Its implementation steps are as follows:

(1) Move the detector along the three directions of x, y, and z according to the step size h _x , h _y , h _z within the movable space range of the detector, and use the Monte Carlo principle to obtain the fluorescence collection efficiency corresponding to each position value and record it (n values);

(2) Using polynomials as basis functions to construct an approximation hypersurface b=b(x, y, z). In order to ensure that the constructed hypersurface has C ₂ continuity in E ⁴ space, while ensuring stability and reducing the amount of calculation, a cubic polynomial is selected as the basis function to construct the approximate hypersurface b=b(x,y,z).

b＝A ₁ +A ₂ z+A ₃ z ² +A ₄ z ³ +y(A ₅ +A ₆ z+A ₇ z ² )+y ² (A ₈ +A ₉ z)

+A ₁₀ y ³ +x(A ₁₁ +A ₁₂ z+A ₁₃ z ² )+xy(A ₁₄ +A ₁₅ z)+A ₁₆ xy ² +x ² (A ₁₇ +A ₁₈ z)

+A ₁₉ x ² +A ₂₀ x ³

Substituting the recorded n fluorescence collection efficiency values into the above formula, there are:

where G _i,1 =1,G _i,2 = _zi ,G _i,3 = _zi ² ,G _i,4 = _zi ³ ,...,G _i,20 = _xi ³ ,(i=1, 2,3,…,n), which can be abbreviated as

b=GA

Using the generalized inverse solution method, the generalized inverse G ⁺ of the matrix G can be obtained, and the minimal least squares solution (best approximation) with the smallest 2-norm can be obtained, namely:

A = G ⁺ b

Among them, G ⁺ is the fourth kind of generalized inverse of G, which satisfies 1~4 of the Penrose-Moore equations and is unique. So the minimal least squares solution of the equation system b=GA is unique. Finally, the empirical formula b=b(x, y, z) can be obtained.

(3) Find the maximum value of b and the corresponding spatial position coordinates of the detector within the movable space range of the detector.

The advantages of the present invention are:

(1) It can solve the problem of light collection efficiency calculation in the case of non-point light sources;

(2) When the optical system cannot be regarded as an ideal optical system, this method can establish the relationship between the light collection efficiency and the spatial position of the detector, and find the detector position with the highest light collection efficiency within the range where the detector can move;

(3) It is possible to evaluate the error caused by the inaccurate placement of the detector to the light collection efficiency;

Description of drawings:

Fig. 1 is a schematic diagram of the overall structure of the present invention;

Fig. 2 is the structural representation of embodiment;

detailed description

The present invention will be further described in detail with reference to the accompanying drawings and embodiments.

The lens system used to test the atomic flux by the fluorescence method is generally a double-lens or single-lens system. Generally, there are more double-lens systems. Here is a fluorescence collection system based on a double-lens (as shown in Figure 2: the fluorescence is a cylindrical light source, and the Uniformly emits light with the same sex, and the receiving surface of the detector is a circular surface. Due to the limitation of the experimental device, it can only move in a certain cuboid area)) as an example for illustration.

Select appropriate optical simulation software (lighttools is used as an example here) to establish a simulation model of fluorescence collection efficiency. Move the detector along the three directions of x, y, and z according to the step size h _x , h _y , h _z within the space range of the cuboid where the detector can move, perform simulation, and record the fluorescence collection efficiency value corresponding to each position ( A total of n values).

Use polynomials as basis functions to construct an approximation hypersurface b=b(x, y, z), in order to ensure that the constructed hypersurface has C ₂ continuity in E ⁴ space, while ensuring stability and reducing the amount of calculation, a cubic polynomial is selected The approximating hypersurface b=b(x,y,z) is constructed as a basis function.

b＝A ₁ +A ₂ z+A ₃ z ² +A ₄ z ³ +y(A ₅ +A ₆ z+A ₇ z ² )+y ² (A ₈ +A ₉ z)

+A ₁₀ y ³ +x(A ₁₁ +A ₁₂ z+A ₁₃ z ² )+xy(A ₁₄ +A ₁₅ z)+A ₁₆ xy ² +x ² (A ₁₇ +A ₁₈ z)

+A ₁₉ x ² +A ₂₀ x ³

Substituting the recorded n fluorescence collection efficiency values into the above formula, there are:

where G _i,1 =1,G _i,2 = _zi ,G _i,3 = _zi ² ,G _i,4 = _zi ³ ,...,G _i,20 = _xi ³ ,(i=1, 2,3,…,n), which can be abbreviated as

b=GA

Use the pinv function in matlab to find the generalized inverse G ⁺ of the matrix G, and you can get the minimal least squares solution (best approximation) with the smallest 2-norm:

A = G ⁺ b

Since G ⁺ is the fourth kind of generalized inverse of G, it satisfies 1-4 of the Penrose-Moore equations and is unique. So the minimal least squares solution of the equation system b=GA is unique. The above calculation process is carried out in matlab, and finally the empirical formula b=b(x, y, z) can be obtained.

The movable area of the detector is a cuboid area, and the extremum of b=b(x, y, z) is calculated within this range. b=b(x, y, z) calculate the partial derivatives for x, y, z respectively, and make the respective partial derivatives be 0, and combine the three equations, there are:

From the above formula, the extreme points of the fluorescence collection efficiency and the corresponding fluorescence collection efficiency can be obtained (removing the points not in the movable area of the detector), and then b=b in the six planes where the moving area of the detector is a cuboid (x,y,z) to find the extremum. All obtained extreme values of fluorescence collection efficiency are compared to find out the maximum fluorescence collection efficiency value and its corresponding detector position coordinates.

According to the above method, the maximum value of the fluorescence collection efficiency and the corresponding detector position coordinates can be obtained. In addition, it is also possible to analyze the errors brought about by the fluorescence collection efficiency when the detectors are placed inaccurately.

The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments, and can also be made without departing from the gist of the present invention within the scope of knowledge possessed by those of ordinary skill in the art. Variations. The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. Anyone familiar with this field Those skilled in the art, without departing from the scope of the technical solution of the present invention, may use the above-disclosed technical content to make some changes or modify them into equivalent embodiments with equivalent changes. The technical essence of the invention, within the spirit and principles of the present invention, any simple changes, equivalent replacements and improvements made to the above embodiments still fall within the protection scope of the technical solutions of the present invention.

Claims (2)

1. determine a method for the detector position of atom maximum fluorescence collection efficiency, it is characterized in that, the method is:

(1) in the moveable spatial dimension of detector, step-length h is pressed along x, y, z three directions _x, h _y, h _zmobile detector, utilizes Monte Carlo principle to obtain phosphor collection efficiency value corresponding to each position and records (n value);

(2) to construct as basis function with polynomial expression and approach hypersurface b=b (x, y, z).In order to ensure that constructed hypersurface is at E ⁴in space, there is C ₂continuously, ensure stability simultaneously, reduce calculated amount, select cubic polynomial to construct as basis function and approach hypersurface b=b (x, y, z).

b＝A ₁+A ₂z+A ₃z ²+A ₄z ³+y(A ₅+A ₆z+A ₇z ²)+y ²(A ₈+A ₉z)

+A ₁₀y ³+x(A ₁₁+A ₁₂z+A ₁₃z ²)+xy(A ₁₄+A ₁₅z)+A ₁₆xy ²+x ²(A ₁₇+A ₁₈z)

+A ₁₉x ²+A ₂₀x ³

N the phosphor collection efficiency value substituting into record, to above formula, has:

Wherein G _{i, 1}=1, G _{i, 2}=z _i, G _{i, 3}=z _i ², G _{i, 4}=z _i ³..., G _{i, 20}=x _i ³, (i=1,2,3 ..., n), can be referred to as

b＝GA

Utilize generalized inverse solution, obtain the generalized inverse G of matrix G ⁺, the minimal least sqares solution (the best is approached) of 2 Norm minimums can be obtained namely:

A＝G ⁺b

Wherein G ⁺be the 4th class generalized inverse of G, it meets 1 ~ 4 of Penrose-Moore equation, has uniqueness.So the minimal least sqares solution of system of equations b=GA has uniqueness.Finally can obtain experimental formula b=b (x, y, z).

(3) in the moveable spatial dimension of detector, ask the maximal value of b and the detector locus coordinate of correspondence.

2. according to a kind of method determining the detector position that atomic fluorescence collection efficiency is maximum described in claim 1, it is characterized in that described step (2) selects cubic polynomial as basis function to construct the function b=b (x of phosphor collection efficiency about detector spatial relation, y, z).

b＝A ₁+A ₂z+A ₃z ²+A ₄z ³+y(A ₅+A ₆z+A ₇z ²)+y ²(A ₈+A ₉z)

+A ₁₀y ³+x(A ₁₁+A ₁₂z+A ₁₃z ²)+xy(A ₁₄+A ₁₅z)+A ₁₆xy ²+x ²(A ₁₇+A ₁₈z)

+A ₁₉x ²+A ₂₀x ³。