• Chinese Optics Letters
  • Vol. 16, Issue 6, 061201 (2018)
Jie Miao1、2、*, Xuejie Zhang1, Zhan Li1、2, Zijian Cui1, Yanjia Zhang1, Dean Liu1, and Jianqiang Zhu1
Author Affiliations
  • 1Key Laboratory of High Power Laser and Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
  • 2University of Chinese Academy of Sciences, Beijing 100049, China
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    DOI: 10.3788/COL201816.061201 Cite this Article Set citation alerts
    Jie Miao, Xuejie Zhang, Zhan Li, Zijian Cui, Yanjia Zhang, Dean Liu, Jianqiang Zhu. Transmittance and phase measurement via self-calibrated balanced heterodyne detection[J]. Chinese Optics Letters, 2018, 16(6): 061201 Copy Citation Text show less

    Abstract

    It is rare for a conventional direct detection method to measure the transmittance uniformity of mirrors with rigorous standards, especially to meet the requirement of transmittance/reflectance and phase detection simultaneously. In this study, a new method of self-calibrated balanced heterodyne detection (SCBHD) is proposed. It can be self-calibrated by a two-channel structure to overcome the environmental effects in large optics scanning detection by employing highly accurate heterodyne interference. A typical transmittance measurement experiment was performed at 1053 nm wavelength via SCBHD. A standard deviation (SD) of 0.038% was achieved in the preliminary experiment. The experimental results prove to reduce the SD by approximately two orders of magnitude compared with the conventional direct detection method in the same condition. The proposed method was verified as being promising not only for its wider dynamic measurement range and its higher accuracy but also for its simultaneous transmittance and phase detection ability.
    ES=Eo(x,y,z)[k1k2]eiφ,ELO=Eo(x,y,z)[k3k4]eiϕ(t),(1)

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    I0=12(k22+k32)|Eo|2+k2k3|Eo|2cos(ϕ(t)π4φ),I180=12(k22+k32)|Eo|2k2k3|Eo|2cos(ϕ(t)π4φ),I90=12(k12+k42)|Eo|2k1k4|Eo|2sin(ϕ(t)π4φ),I270=12(k12+k42)|Eo|2+k1k4|Eo|2sin(ϕ(t)π4φ).(2)

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    IBcos=I0I180=2k2k3|Eo|2cos(ϕ(t)π4φ),IBsin=I270I90=2k1k4|Eo|2sin(ϕ(t)π4φ).(3)

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    ES=TEo(x,y,z)[k1k2]eiφ.(4)

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    IBcos=I0I180=2k2k3|Eo|2=2k2k3·αIR2,IBsin=I270I90=2k1k4|Eo|2=2k1k4·αIR2,IBcos=2k2k3T|Eo|2=2k2k3T·αIR2,IBsin=2k1k4T|Eo|2=2k1k4T·αIR2,(5)

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    T=IBcos2IBcos2=IBsin2IBsin2=IBcos·IBsinIBcos·IBsin.(6)

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    TC=IBcos2·IR2IBcos2·IR2=IBsin2·IR2IBsin2·IR2=IBcos·IBsin·IR2IBcos·IBsin·IR2.(7)

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    RC=IBcos·IBsin·IR2IBcos·IBsin·IR2·RL,(8)

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    S=T[100eiΔ].(9)

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    IBcos=I0I180=2k2k3T|Eo|2cos(ϕ(t)π4φΔ),IBsin=I270I90=2k1k4T|Eo|2sin(ϕ(t)π4φ).(10)

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    IBcos=K1α1α2cos(ϕ(t)π4φ),IBsin=K2α3α4sin(ϕ(t)π4φ),(11)

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    β0=|IBcos/IBsin|=k2k3·α1α2k1k4·α3α4.(12)

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    Δβn=βn/βn1.(13)

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    Tn+1=Tn+1Δβn.(14)

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    Jie Miao, Xuejie Zhang, Zhan Li, Zijian Cui, Yanjia Zhang, Dean Liu, Jianqiang Zhu. Transmittance and phase measurement via self-calibrated balanced heterodyne detection[J]. Chinese Optics Letters, 2018, 16(6): 061201
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