• Chinese Optics Letters
  • Vol. 14, Issue 8, 081202 (2016)
Meng-Chang Hsieh1、*, Jiun-You Lin2, and Chia-Ou Chang1、3
Author Affiliations
  • 1Institute of Applied Mechanics, National Taiwan University, Taipei 10617, China
  • 2Department of Mechatronics Engineering, National Changhua University of Education, Changhua 500, China
  • 3College of Mechanical Engineering, Guangxi University, Nanning 530004, China
  • show less
    DOI: 10.3788/COL201614.081202 Cite this Article Set citation alerts
    Meng-Chang Hsieh, Jiun-You Lin, Chia-Ou Chang. Measurement of small wavelength shifts based on total internal reflection heterodyne interferometry[J]. Chinese Optics Letters, 2016, 14(8): 081202 Copy Citation Text show less

    Abstract

    This Letter presents a method of an optical sensor for measuring wavelength shifts. The system consists of a diffraction grating and a total internal reflection heterodyne interferometer. As a heterodyne light beam strikes a grating, the first-order diffraction beam is generated. The light penetrates into a total internal reflection prism at an angle larger than the critical angle. A wavelength variation will affect the diffractive angle of the first-order beam, thus inducing a phase difference variation of the light beam emerging from the total internal reflections inside the trapezoid prism. Both the experimental and theoretical results reveal that, for the first-order diffractive beam, the sensitivity and resolution levels are superior to 5°/nm and 0.006 nm, respectively, in the range of wavelength from 632 to 634 nm, and are superior to 3.1°/nm and 0.0095 nm in the range from 632 to 637 nm. For the theoretical simulation of the fourth-order diffractive beam, they are superior to 6.4 deg/nm and 0.0047 nm in the range from 632 to 637 nm.
    Eio=(eiωt/200eiωt/2)12(11)=12(eiωt/2eiωt/2).(1)

    View in Article

    θ+1=sin1(λΛ).(2)

    View in Article

    Er=122(1111)(100eiϕBS)(100eiϕG)12(eiωt/2eiωt/2)=14(eiωt/2+ei(ωt/2ϕBSϕG))(11),(3)

    View in Article

    Ir=14[1+cos(ωtϕBSϕG)],(4)

    View in Article

    Et=122(1111)(100eiδt)(100eiϕG)12(eiωt/2eiωt/2)=14(eiωt/2+ei(ωt/2δtϕG))(11),(5)

    View in Article

    It=14[1+cos(ωtδtϕG)],(6)

    View in Article

    δt=9×2tan1{[sin2[45°sin1(sinθi/np))](1/np)2]1/2tan[45°sin1(sinθi/np)]·sin[45°sin1(sinθi/np)]},(θi=θinitialΔθi=θinitialsin1(λ0+ΔλΛ)+sin1(λ0Λ)).(7)

    View in Article

    Δλ=(λδt(θi(λ)))Δδt.(8)

    View in Article

    Δλerr=|ΔδterrΔδt|Δλ,(9)

    View in Article

    θ+m=sin1(mλΛ).(10)

    View in Article

    Meng-Chang Hsieh, Jiun-You Lin, Chia-Ou Chang. Measurement of small wavelength shifts based on total internal reflection heterodyne interferometry[J]. Chinese Optics Letters, 2016, 14(8): 081202
    Download Citation