元智大學電機通訊學院 2016專題製作成果博覽會 Measurement of in-plane displacement by using a angle-rotated holographic grating Yu-Chian Lin, Yi-Cen Shi, Chia-Wei Chiang, Cheng-Chih Hsu* Department of Photonics Engineering, Yuan Ze University, 135, Yuan-Tung Road, Chung-Li, 32003 Taiwan (Tel : +886 3 4638800 Ext 7520 ; *E-mail: [email protected])

Abstract

Results

This paper proposed a method for displacement measuring that integrated with a wavelength-modulated heterodyne interferometer and a holographic diffraction grating. To rotate the grating with suitable angle can reduce the grating pitch and increase measurement sensitivity. The results indicated that the best sensitivity could be enhanced 0.34 % as the rotation angle of 5.

Methods AN(45 )

Fig. 2. Stability of the wavelengthmodulated heterodyne method and EOM-modulated heterodyne method.

D Lock-in Amplifier

PBS

M2

Fig. 3. Wavelength-modulated heterodyne method for measuring the phase retardation of quarter wave plate. Comparison of experimental and theoretical simulations

RS-232

M1

Laptop -1st

0 1 3 5

V(t)

+1st

Vb  V

Stage

HPI

2

Vb

Grating

i

HPI

Vb  V

2

t

Birefringent crystal Movement direction

OA l

mirror

Laser Diode P ( 45  ) Rotationstage

Fig. 1. The optical configuration of the proposed method.

Fig. 4. Effective grating pitch measurement.

The intensity detected by the photodetector :

I D  E 1s  E 1 p

2

 cost  k L1  L1    1   1 

The phase difference results from the stage movement:

 4S  4S    1  1   d cos i d eff

Therefore, the displacement S can be written as:

F × deff S= -4p

Fig. 5. Displacement measurement under various rotation angles of grating.

 The effective grating pitch decreased as the rotation angle of grating increased. The effective grating pitch decreased approximated of 7 nm as the rotation angle of grating at 5.  Figure 5 showed that the displacement measurement under various rotation angles of grating. It is clear that there were no significant difference compared to the result measured by the HP interferometer.

Conclusion  The results of Wavelength-modulated heterodyne method showed that the experimental results and the theoretical simulation had no significant difference.  The results showed that the effective grating pitch reducing approximated of 7 nm as rotation angle of 5.  The results also indicated that the displacement error could be enhanced about 0.34 %.

Acknowledgements The authors would like to thanks the National Science Council of the Republic of China for financially supporting this research under Contract MOST 105-2221-E-155-025.

主辦單位：元智大學電機通訊學院 協辦單位：元智大學電機工程學系 教育部獎勵大學教學卓越計畫補助 Sponsored by the Ministry of Education, Teaching Excellence Project