Patent ID: 11921400
Assignee: BEIJING CHANGCHENG INSTITUTE OF METROLOGY & MEASUREMENT, AVIC
Field: Optics (Instruments)
Classification: CPC G  Y | IPC G

Claim 0:
1. A rotation speed measurement method, a measurement system used in the rotation speed measurement method comprising a femtosecond optical frequency comb, a laser beam expander, a polarization beam splitter, a quarter-wave plate, a first converging lens, a second converging lens, a first photodetector, a second photodetector, an electrical mixer, and a frequency counter; and the rotation speed measurement method comprising:
(S1) outputting, by the femtosecond optical frequency comb, a first laser; expanding, by the laser beam expander, the first laser into an emitting beam; allowing the emitting beam to pass through the polarization beam splitter, the quarter-wave plate, and the first converging lens sequentially, wherein an angle between a fast axis of the quarter-wave plate and a horizontal polarization direction of the polarization beam splitter is 45°; focusing, by the first converging lens, the emitting beam on a surface of a rotating object to be measured, and collecting scattered light from the surface of the rotating object to be measured; allowing the scattered light to pass through the quarter-wave plate, and to be reflected by the polarization beam splitter to the second converging lens; and focusing, by the second converging lens, the scattered light on the first photodetector;
(S2) outputting, by the femtosecond optical frequency comb, a second laser; receiving directly, by the second photodetector, the second laser; measuring, by the second photodetector, a repetition frequency fr of the femtosecond optical frequency comb; measuring, by the first photodetector, a repetition frequency fr′ of the femtosecond optical frequency comb after scattered by the rotating object to be measured; and inputting the repetition frequency fr and the repetition frequency fr′ to the electrical mixer, and measuring, by the frequency counter, a repetition frequency difference Δfr; and
(S3) calculating a rotation speed M of the rotating object to be measured according to the repetition frequency difference Δfr;
wherein the repetition frequency difference Δfr is directly proportional to the rotation speed M of the rotating object to be measured;
the femtosecond optical frequency comb comprises a plurality of longitudinal modes evenly spaced apart, and an electromagnetic field of the femtosecond optical frequency comb is expressed as formula (1):, E
       ⁡
       (
       t
       )
      
      =
      
       
        ∑
        
         n
         =
         
          -
          ∞
         
        
        
         +
         ∞
        
       
       
        
         A
         n
        
        ⁢
        
         e
         
          
           -
           i
          
          ⁢
          2
          ⁢
          
           π
           ⁡
           (
           
            
             n
             ⁢
             
              f
              r
             
            
            +
            
             f
             0
            
           
           )
          
          ⁢
          t
         
        
       
      
     
     ;
    
   
   
    
     (
     1
     )
    
   
  
 

wherein fr is the repetition frequency of the femtosecond optical frequency comb; f0 is a carrier-envelope offset frequency of the femtosecond optical frequency comb; the femtosecond optical frequency comb is superposition of a series of lasers with a frequency component of nfr+f0; An is a complex amplitude of a corresponding frequency component; when the femtosecond optical frequency comb is focused on the surface of the rotating object, individual frequency components of the femtosecond optical frequency comb will produce a doppler shift according to Doppler effect; and for a laser with a frequency off a doppler shift Δf is expressed as formula (2):, Δ
       ⁢
       f
      
      =
      
       
        2
        ⁢
        fv
        ⁢
          
        sin
        ⁢
          
        α
       
       c
      
     
     ;
    
   
   
    
     (
     2
     )
    
   
  
 

wherein v is a linear velocity at the surface of the rotating object to be measured; c is light speed; α is equal to half of a focused beam angle; and for a laser with a certain frequency, the doppler shift Δf is directly proportional to the linear velocity at the surface of the rotating object to be measured;
by substituting the formula (2) into the formula (1), an expression of the femtosecond optical frequency comb after being scattered by the rotating object to be measured is expressed as formula (3):, E
        ′
       
       ⁢
       
        (
        t
        )
       
      
      =
      
       
        ∑
        
         n
         =
         
          -
          ∞
         
        
        
         +
         ∞
        
       
       
        
         B
         n
        
        ⁢
        
         e
         
          
           -
           i
          
          ⁢
          2
          ⁢
          
           π
           [
           
            
             n
             ⁢
             
              
               f
               r
              
              (
              
               1
               +
               
                
                 2
                 ⁢
                 v
                 ⁢
                   
                 sin
                 ⁢
                 
                   
                   
                 
                 ⁢
                 α
                
                c
               
              
              )
             
            
            +
            
             
              f
              0
             
             (
             
              1
              +
              
               
                2
                ⁢
                v
                ⁢
                  
                sin
                ⁢
                  
                α
               
               c
              
             
             )
            
           
           ]
          
          ⁢
          t
         
        
       
      
     
     ;
    
   
   
    
     (
     3
     )
    
   
  
 

Bn is a complex amplitude of a corresponding frequency component of the scattered light; as indicated by the formula (3), after being scattered by the rotating object to be measured, the repetition frequency of the femtosecond optical frequency comb changes, and the repetition frequency fr′ is expressed as formula (4):, f
       r
       ′
      
      =
      
       
        f
        r
       
       ⁢
       
        (
        
         1
         +
         
          
           2
           ⁢
           v
           ⁢
             
           sin
           ⁢
              
           α
          
          c
         
        
        )
       
      
     
     ;
    
   
   
    
     (
     4
     )
    
   
  
 

Doppler effect causes shift of the repetition frequency of the femtosecond optical frequency comb, and the repetition frequency difference Δfr is expressed as formula (5):, Δ
       ⁢
       
        f
        r
       
      
      =
      
       
        
         f
         r
         ′
        
        -
        
         f
         r
        
       
       =
       
        
         2
         ⁢
         v
         ⁢
         
          f
          r
         
         ⁢
           
         sin
         ⁢
           
         α
        
        c
       
      
     
     ;
    
   
   
    
     (
     5
     )
    
   
  
 

a relationship between the linear velocity and the rotation speed M is expressed as formula (6), wherein R is a radius of the rotating object to be measured, and the rotation speed M is in revolutions per second:

v=2πRM  (6);

the formula (6) is substituted into the formula (5) to obtain formula (7):, Δ
       ⁢
       
        f
        r
       
      
      =
      
       
        4
        ⁢
        π
        ⁢
        R
        ⁢
        M
        ⁢
        
         f
         r
        
        ⁢
          
        sin
        ⁢
          
        α
       
       c
      
     
     ;
    
   
   
    
     (
     7
     )
    
   
  
 

wherein the repetition frequency difference Δfr is directly proportional to the rotation speed M of the rotating object to be measured; and the formula (7) is converted into formula (8) to calculate the rotation speed M from the repetition frequency difference Δfr:, M
      =
      
       
        
         c
         ⁢
         Δ
         ⁢
         
          f
          r
         
        
        
         4
         ⁢
         π
         ⁢
         
          f
          r
         
         ⁢
           
         sin
         ⁢
           
         α
         ⁢
         R
        
       
       =
       
        κ
        ⁢
        
         
          Δ
          ⁢
          
           f
           r
          
         
         R
        
       
      
     
     ;
    
   
   
    
     (
     8
     )
    
   
  
 

wherein k is a scale factor, and expressed as follows:, κ
      =
      
       c
       
        4
        ⁢
        π
        ⁢
        
         f
         r
        
        ⁢
          
        sin
        ⁢
          
        α
       
      
     
     ;
    
   
   
    
     (
     9
     )
    
   
  
 

wherein the scale factor κ is calculated according to formula (9), or based on a slope of a curve of a rotation speed of a standard rotating object whose rotation speed is known versus the repetition frequency difference Δfr.