Interferometric thickness assessment of optical flat by combining iterative analysis and wavelength tuning

Kim, Sung-Tae; Kim, Yangjin; Hibino, Kenichi; Sugita, Naohiko; Mitsuishi, Mamoru

doi:10.1016/j.ijleo.2022.169450

Cited by 3 publications

(1 citation statement)

References 34 publications

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“…In recent years, a variety of multi-surface phase-shifting methods have been developed based on the wavelength-shifting technique. By designing the roots of the equations to target different measurement performances, Kim et al designed window functions based on characteristic polynomials, which are capable of suppressing phase-shifting errors and can be insensitive to multiple reflected harmonic signals [6], [7]. Based on the least-squares fitting method, which is an effective method for solving the phase-shifting value and initial phase, Sun et al designed a parameterization algorithm for multicosine interferometric harmonic superposition signals, which is robust to nonlinear phase-shifting errors [8].…”

Section: Introductionmentioning

confidence: 99%

Error analysis and comparison of wavelength tuning phase shifting interferometry of transparent optical flats

Chang,

Gao,

2023

AOPC 2023: Optic Fiber Gyro

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Wavelength-tuning phase-shifting interferometry has advantages over conventional hardware phase-shifting for the simultaneous detection of all surfaces of the transparent parallel flats. The Fourier transform and its derivative methods can be used to characterize the signal based on the optical path difference and the phase-shifting value of the corresponding interferometric harmonic signals on each measured surface and to solve for the phase accordingly. Therefore, considering the influence of the sampling length and the choice of the window function in the Fourier transform on the measurement results, based on the established multi-surface interference model, an adequate simulation analysis is carried out, and the corresponding explanations and discussions are given subsequently. In practical measurements, the appropriate window function and sampling length should be selected according to the corresponding measurement conditions, so that reliable measurements can be guaranteed.

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Section: Introductionmentioning

confidence: 99%

Error analysis and comparison of wavelength tuning phase shifting interferometry of transparent optical flats

Chang,

Gao,

2023

AOPC 2023: Optic Fiber Gyro

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Assessment and verification of thickness homogeneity in mask blank by utilizing main harmonics of triple-surface interferometry

Kim,

Sugita

et al. 2024

Precision Engineering

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Wavelength-stepping algorithm for testing the thickness and front and back surfaces of optical plates with high signal-to-noise ratio

Servı́n¹,

Padilla²,

Паез³

et al. 2023

J. Opt. Soc. Am. A

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We propose a least-squares phase-stepping algorithm (LS-PSA) consisting of only 14 steps for high-quality optical plate testing. Optical plate testing produces an infinite number of simultaneous fringe patterns due to multiple reflections. However, because of the small reflection of common optical materials, only a few simultaneous fringes have amplitudes above the measuring noise. From these fringes, only the variations of the plate’s surfaces and thicknesses are of interest. To measure these plates, one must use wavelength stepping, which corresponds to phase stepping in standard digital interferometry. The designed PSA must phase demodulate a single fringe sequence and filter out the remaining temporal fringes. In the available literature, researchers have adapted PSAs to the dimensions of particular plates. As a consequence, there are as many PSAs published as different testing plate conditions. Moreover, these PSAs are designed with too many phase steps to provide detuning robustness well above the required level. Instead, we mathematically prove that a single 14-step LS-PSA can adapt to several testing setups. As is well known, this 14-step LS-PSA has a maximum signal-to-noise ratio and the highest harmonic rejection among any other 14-step PSA. Due to optical dispersion and experimental length measuring errors, the fringes may have a slight phase detuning. Using propagation error theory, we demonstrate that measuring distances with around 1% uncertainty produces a small and acceptable detuning error for the proposed 14-step LS-PSA.

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Interferometric thickness assessment of optical flat by combining iterative analysis and wavelength tuning

Cited by 3 publications

References 34 publications

Error analysis and comparison of wavelength tuning phase shifting interferometry of transparent optical flats

Error analysis and comparison of wavelength tuning phase shifting interferometry of transparent optical flats

Assessment and verification of thickness homogeneity in mask blank by utilizing main harmonics of triple-surface interferometry

Wavelength-stepping algorithm for testing the thickness and front and back surfaces of optical plates with high signal-to-noise ratio

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