Patent ID: 11874475
Assignee: ZHENGZHOU UNIVERSITY OF LIGHT INDUSTRY
Field: Optics (Instruments)
Classification: CPC G  Y | IPC G

Claim 0:
1. A vortex beam-excited precision grating measurement method, the measurement method is based on a vortex beam-excited precision grating measurement apparatus, the measurement apparatus comprising an exciter, wherein a phase modulation device is arranged at an outlet of the exciter; a reflecting mirror is directly arranged in front of the phase modulation device; a grating is arranged on a left side of the reflecting mirror; the device further comprises two reflecting mirrors and three polarization beam splitting prisms, wherein the two reflecting mirrors are respectively a first reflecting mirror and a second reflecting mirror; the first reflecting mirror and the second reflecting mirror are arranged correspondingly up and down; the three polarization beam splitting prisms are respectively a first polarization beam splitting prism, a second polarization beam splitting prism, and a third polarization beam splitting prism, wherein the first polarization beam splitting prism and the second polarization beam splitting prism are located in one optical path; the first polarization beam splitting prism and the third polarization beam splitting prism are located in the other optical path; the three polarization beam splitting prisms are arranged at right angles; a first ¼ wave plate is arranged between the first polarization beam splitting prism and the second polarization beam splitting prism; a second ¼ wave plate is arranged between the first polarization beam splitting prism and the third polarization beam splitting prism; a first photoelectric detector and a second photoelectric detector are arranged on both sides of the second polarization beam splitting prism; and a third photoelectric detector and a fourth photoelectric detector are arranged on both sides of the third polarization beam splitting prism;
the phase modulation device is a spiral phase plate or a spatial light modulator;
a Dove prism is arranged between the grating and the second reflecting mirror;
the measurement method comprises the following steps that:
Step 1): emergent laser of the laser travels through a phase modulation device to generate a vortex beam; the vortex beam is reflected to a grating through a reflecting mirror and is diffracted to generate +m-order diffracted light and −m-order diffracted light; the laser emitted from the laser is converted into a Laguerre-Gaussian vortex beam carrying orbital angular momentum through a spatial light modulator, and the characteristics of the vortex beam are mainly characterized by a radial index n and an azimuth direction index l;
Step 2): the +m-order diffracted light enters a first polarization beam splitting prism after being reflected by the first reflecting mirror, and the −m-order diffracted light carries opposite topological charges after traveling through a Dove prism and then enters the first polarization beam splitting prism through a second reflecting mirror;
Step 3): light is divided into two beams through the first polarization beam splitting prism; in one light path, +m-order S light and −1-order P light travel through a first ¼ wave plate, and in the other light path, +m-order P light and −1-order S light travel through a second ¼ wave plate;
Step 4): the two paths of light respectively enter a second polarization beam splitting prism and a third polarization beam splitting prism again and then are divided into two beams again to respectively form circularly polarized light to interfere with each other, so as to generate four coherent patterns finally;
Step 5): when a grating displaces, the ±m-order diffracted light generates a phase difference Δϕ; at this moment, the phase change caused by a measured displacement amount corresponds to a rotation angle of an equally angular distributed interference pattern, and a rotation direction corresponds to a measured displacement direction; and the measured grating displacement can be demodulated from rotation angle information of the interference pattern;
Step 5) is as follows specifically:
vortex light field expressions with the azimuth direction indexes of l and −l are respectively abbreviated as:

El(r,θ)=Rl(r)exp(ilθ)

E−l(r,θ)=Rl(r)exp(−ilθ)

an electric field amplitude generated by the coherence of the vortex light fields is:

El(r,θ)+E−l(r,θ)=2Rl(r)cos(lθ)

when the grating displaces, the +m-order diffracted light and the −m-order diffracted light will generate a phase difference Δϕ due to a Doppler shift effect of diffracted light, and the expression thereof is:, Δ
   ⁢
   ϕ
  
  =
  
   4
   ⁢
   m
   ⁢
   π
   ⁢
   
    x
    p
   
  
 

wherein, x is the displacement that the grating displaces, and p is a grating pitch; the above formula shows that the grating displacement x can be solved by the phase difference Δϕ between the +m-order diffracted light and the −m-order diffracted light; at this moment, the electric field amplitude generated by the coherence of the two diffracted beams is:, E
        l
       
       (
       
        r
        ,
        θ
       
       )
      
      +
      
       
        E
        
         -
         l
        
       
       (
       
        r
        ,
        θ
       
       )
      
     
     =
     
     
      
       
        R
        l
       
       (
       r
       )
      
      ⁢
      
       {
       
        
         exp
         [
         
          i
          ⁡
          (
          
           
            l
            ⁢
            θ
           
           +
           
            Δ
            ⁢
            ϕ
           
          
          )
         
         ]
        
        +
        
         exp
         ⁡
         (
         
          
           -
           il
          
          ⁢
          θ
         
         )
        
       
       }
      
     
    
   
  
  
   
    
     =
     
     
      2
      ⁢
      
       
        R
        l
       
       (
       r
       )
      
      ⁢
      
       exp
       ⁡
       (
       
        i
        ⁢
        Δ
        ⁢
        ϕ
        /
        2
       
       )
      
      ⁢
      
       cos
       ⁡
       (
       
        
         l
         ⁢
         θ
        
        +
        
         Δ
         ⁢
         ϕ
         /
         2
        
       
       )
      
     
    
   
  
  
   
    
     =
     
     
      2
      ⁢
      
       
        R
        l
       
       (
       r
       )
      
      ⁢
      
       exp
       ⁡
       (
       
        i
        ⁢
        
         
          2
          ⁢
          m
          ⁢
          π
          ⁢
          x
         
         p
        
       
       )
      
      ⁢
      
       cos
       ⁡
       (
       
        
         l
         ⁢
         θ
        
        +
        
         
          2
          ⁢
          m
          ⁢
          π
          ⁢
          x
         
         p
        
       
       )
      
     
    
   
  
 

the phase change Δϕ caused by the measured displacement amount x corresponds to a rotation angle of an equally angular distributed interference pattern, and the rotation direction corresponds to the measured displacement direction; and in the vortex beam-excited precision grating displacement measurement method, the displacement p/m of the measured displacement corresponds to the rotation of a circle of an interference petal pattern, and then the rotation of 1° of the interference petal pattern corresponds to the measured displacement amount of p/360m.