• Chinese Optics Letters
  • Vol. 21, Issue 1, 011102 (2023)
Wenxin Zhang1、2、*, Yuxiu Tao1, Yangkang Wu1, Fu Zhu1, Wenchao Cai1, Ning Liu1, Qiang Zhao1, and Ping Xue2
Author Affiliations
  • 1College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
  • 2State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter, Tsinghua University, Beijing 100084, China
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    DOI: 10.3788/COL202321.011102 Cite this Article Set citation alerts
    Wenxin Zhang, Yuxiu Tao, Yangkang Wu, Fu Zhu, Wenchao Cai, Ning Liu, Qiang Zhao, Ping Xue. Vibration measurement with frequency modulation single-pixel imaging[J]. Chinese Optics Letters, 2023, 21(1): 011102 Copy Citation Text show less

    Abstract

    Single-pixel imaging can reconstruct the image of the object when the light traveling from the object to the detector is scattered or distorted. Most single-pixel imaging methods only obtain distribution of transmittance or reflectivity of the object. Some methods can obtain extra information, such as color and polarization information. However, there is no method that can get the vibration information when the object is vibrating during the measurement. Vibration information is very important, because unexpected vibration often means the occurrence of abnormal conditions. In this Letter, we introduce a method to obtain vibration information with the frequency modulation single-pixel imaging method. This method uses a light source with a special pattern to illuminate the object and analyzes the frequency of the total light intensity signal transmitted or reflected by the object. Compared to other single-pixel imaging methods, frequency modulation single-pixel imaging can obtain vibration information and maintain high signal-to-noise ratio and has potential on finding out hidden facilities under construction or instruments in work.
    I(x,y,n)={1+cos[π(Xy+xX)n/XY]}/2;x[1,X],y[1,Y],n[1,2XY].

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    S(n)=t(x,y)×I(x,y,n)=t(x,y)×{1+cos[π(Xy+xX)n/XY]}/2,

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    t(p)=nS(n)cos(2πpn/2XY)=nx,yt(x,y)×{1+cos[π(Xy+xX)n/XY]}/2×cos(πpn/XY)x,yt(x,y)δ(p=Xy+xX)+const.

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    t(xv,yv,t)=t(xv,yv)×[1+Acos(2πft+ϕ)]/2.

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    S(n)=t(x,y)×I(x,y,n)=xs,yst(xs,ys)×{1+cos[π(Xys+xsX)n/XY]}/2+xv,yvt(xv,yv,t)×{1+cos[π(Xyv+xvX)n/XY]}/2=xs,yst(xs,ys)×{1+cos[π(Xys+xsX)n/XY]}/2+xv,yvt(xv,yv)×[1+Acos(2πft+ϕ)]/2×{1+cos[π(Xyv+xvX)n/XY]}/2,

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    t(p)=nS(n)cos(2πpn/2XY)=nxs,yst(xs,ys)×{1+cos[π(Xys+xsX)n/XY]}/2×cos(πpn/XY)+nxv,yv{t(xv,yv)×[1+Acos(2πft+ϕ)]/2×{1+cos[π(Xyv+xvX)n/XY]}/2}×cos(πpn/XY)xs,yst(xs,ys)δ(p=Xys+xsX)/2+const1+const2+xv,yv[At(xv,yv)δ(p=2fXYt/n)]/4+xv,yv[t(xv,yv)δ(p=Xyv+xvX)]/4+xv,yvAt(xv,yv)δ[p=2fXYt/n+(Xyv+xvX)]/8+xv,yvAt(xv,yv)δ[p=2fXYt/n(Xyv+xvX)]/8,

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    f(Xyv+xvX)/T>XY/T.

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    Wenxin Zhang, Yuxiu Tao, Yangkang Wu, Fu Zhu, Wenchao Cai, Ning Liu, Qiang Zhao, Ping Xue. Vibration measurement with frequency modulation single-pixel imaging[J]. Chinese Optics Letters, 2023, 21(1): 011102
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