In-Situ Evaluation of the Pitch of a Reflective-Type Scale Grating by Using a Mode-Locked Femtosecond Laser

Dong Wook Shin,Eberhard Manske,Wei Gao,Hiraku Matsukuma,Yindi Cai,Lue Quan,Yuki Shimizu

doi:10.3390/app11178028

Abstract

Major modifications are made to the setup and signal processing of the method of in-situ measurement of the pitch of a diffraction grating based on the angles of diffraction of the diffracted optical frequency comb laser emanated from the grating. In the method, the improvement of the uncertainty of in-situ pitch measurement can be expected since every mode in the diffracted optical frequency comb laser can be utilized. Instead of employing a Fabry-Pérot etalon for the separation of the neighboring modes in the group of the diffracted laser beams, the weight-of-mass method is introduced in the method to detect the light wavelength in the Littrow configuration. An attempt is also made to reduce the influence of the non-uniform spectrum of the optical comb laser employed in the setup through normalization operation. In addition, an optical alignment technique with the employment of a retroreflector is introduced for the precise alignment of optical components in the setup. Furthermore, a mathematical model of the pitch measurement by the proposed method is established, and theoretical analysis on the uncertainty of pitch measurement is carried out based on the guide to the expression of uncertainty in measurement (GUM).

Highlights

A diffraction grating, which has periodic fine pattern structures on its surface, is one of the most important optical components often employed in many scientific and industrial fields
For the improvement of the accuracy of pitch measurement of a diffraction grating based on the laser diffraction with an optical frequency comb laser source, major modifications have been made to the optical setup and signal processing
A mathematical model of the pitch measurement in the proposed method with the employment of the optical frequency comb laser has been established while considering misalignments of optical components in the setup

Summary

Introduction

A diffraction grating, which has periodic fine pattern structures on its surface, is one of the most important optical components often employed in many scientific and industrial fields. With the employment of a fiber detector and a spectrometer for the observation of the diffracted beams in the optical frequency domain, much more information can be obtained for the pitch evaluation based on laser diffraction. In the previous study by the authors [17], a Fabry-Pérot etalon with a high free-spectral range was employed to expand the mode-spacing of the optical frequency comb so that each mode in the group of the first-order diffracted beams could be distinguished This could reduce the information of the angles of diffraction of the diffracted beams, resulting in diminishing the benefit of the proposed concept. Methods for measurement of the grating pitch with diffracted laser beams are based on the light diffraction equation that can be expressed as follows [19]:. Sci. 2021, 11, x FOR PEER REVIEW Since the focal length F of the obΔjdec=tiFvteanlαens was known to be 31 mm, 8α ocfa(61n7) be evaSluinactedthbeyfodceatel cletinnggth∆Fd owfithethoebjbecetaimveplernosfilwera.s known to be 31 mm, α can be evaluated by detecting Δd with the beam profiler

Objective lens

40 Negative beams

Uncertainty Analysis

Conclusions