Optimal Measurement Of Rotation Doppler Frequency Shifts Based On Rotational Symmetry

Since the photon orbital angular momentum was discovered in the 90s of last century,more and more researches have been done on the beam carrying orbital angular momentum.In recent decades,the related research is attracting more and more people's attention,and has penetrated into many fields,such as micro manipulation technology,etc..Especially in the field of quantum,such as quantum entanglement,quantum communication and so on,there are many related researches and potential applications.In this paper,we study the phenomenon of the the rotating Doppler effect which is related to orbital angular momentum.On the basis of digital spiral imaging theory,we use the special rule of the orbital angular momentum spectrum of the reflected light beam scattered from a symmetry object,and then devise an optimal method to measure the rotational speed of the object by the Doppler frequency shift.In this paper,we focus on the symmetry of the rotating object,and use the characteristic of the orbital angular momentum spectrum to get the best signal quickly and efficiently.In the experiment,we use the spatial light modulator,a precision instrument,with the holographic gratings according to different symmetry objects to simulate the objects.Our method can not only save lots of detection time,but also take into account the accuracy of the results,which has a very important role in promoting the application of the measurement of the rotational speed on the basis of the Doppler effect in the field of remote sensing and astronomy.In this thesis,we first review the background knowledge of the research.We introduce the basic knowledge and background of photon orbital angular momentum,and the vortex beams carrying orbital angular momentum containing the Laguerre-Gaussian beam;and then we introduce the concept of the rotational Doppler effect related to the photon orbital angular momentum after the introduction of the classical Doppler effect-the linear Doppler effect.And in the end of this part,we introduce the mechanism of the rotational Doppler effect:the value of the rotational frequency shift is equal to the product of the orbital angular momentum quantum number and the speed.In the second part of the thesis,we introduce the theoretical derivation of this method.For the general introduction of the research,we introduce the two scenarios involved:(1)when the incident light is Gauss beam,we detect the superposition of the orbital angular momentum;(2)when the superposition state is the state of the incident light,we detect the component that the orbital angular momentum is zero.The theoretical derivation results of both scenarios have verified the correctness of our project.And we can get the speed through analyzing the frequency spectrum of the signal.Then,the theory of digital spiral imaging is introduced.Starting from the symmetry of the object,we grasp the relationship between the symmetry of the object and the orbital angular momentum components of the reflected light.On the above theoretical basis,we put forward the optimization scheme for the rotating object with N fold symmetry:without touching it,you can quickly calculate the accurate speed if you directly probe the ±N superposition of the reflected light.Next,we introduce our experiments and results.In our experiment,we detect the speed of the object with three fold symmetry and the speed of the object with ten fold symmetry.For the three fold symmetric object,with clover as the representative,the speed error measured is 0.72%;the error about the ten fold symmetric object is 0.704%.The experimental results agree well with the simulated results,which shows that the optimization scheme is reasonable.The last part is the sum and prospect.