Method for designing phase-retrieval algorithms for Ronchi phase-shifting lateral-shearing interferometry

Wu, Feibin; Han, Jun; Tang, Feng

doi:10.1364/ao.58.003379

Cited by 20 publications

(7 citation statements)

References 25 publications

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“…The source grating modulates the intensity of the light source. According to the Van Cittert–Zernike theorem, 31 the interference between the odd diffraction orders by the Ronchi grating can be ignored, 23 , 24 and all odd diffraction orders interfere with the zeroth order; each diffraction order corresponds to the image of the pupil with a lateral shear. For shear in the x -direction, the interference patterns obtained by the charge-coupled diode (CCD) are written as 24 I(x,y)=A02+2∑mAm2+∑mcm(cos φm+cos φ−m),where m=1,3,5⋯; cm=2A0Amηm; A0 and Am represent the amplitudes of the zeroth and +mth orders, respectively; and ηm denotes the degrees of coherence between the +mth and zeroth orders.…”

Section: Interference Field Of the Double-grating Ronchi Lsimentioning

confidence: 99%

“… – 20 The impact of high diffraction orders can also be reduced using appropriate phase-retrieval algorithms, such as arbitrary phase shifts 21 and the calibration of relative errors in phase-shifting 22 . From this perspective, the 8-frame, 10-frame, and 13-frame algorithms 23 were designed to extract the shear phase between the +1st and zeroth orders in double-grating Ronchi LSI. However, they are still influenced by the interference between the −1st and higher orders (≥±9 orders).…”

Section: Introductionmentioning

confidence: 99%

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Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

Tang

et al. 2023

Opt. Eng.

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The accuracy of the shear-phase retrieval method is critical for accurate wavefront aberration measurements in double-grating Ronchi lateral shearing interferometry. Currently, the suppression of the interferences of unwanted diffractions generated by the Ronchi grating at the image plane is eliminated by adding more phase shifts, which increases the measurement time.Here, a stepped phase-shifting algorithm is proposed to suppress the unwanted diffractions and retrieve the shear phase between AE1st orders accurately with fewer phase shifts, and the measurement efficiency can be increased by 25% at least. The minimum number of phase shifts, which depends on the high diffraction orders existing in the interferograms, is analyzed. The proposed method was verified via numerical simulations and experiments. The wavefront measurement was validated via a comparison with the results of point-diffracted interferometry, and the root-mean-square difference was within 2.0 nm.

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Section: Interference Field Of the Double-grating Ronchi Lsimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

Tang

et al. 2023

Opt. Eng.

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“…At the detector, all odd diffraction orders interfere with the zeroth order. For shearing in x direction, the corresponding phase-shifted interferogram of the i-th frame obtained by the sCMOS can be written as: 5,8…”

Section: Ronchi Lateral Shearing Interferometrymentioning

confidence: 99%

“…To realize high-precision wavefront aberration measurement by Ronchi LSI, eliminating the impact of high diffraction orders in ROI is the prerequisite, which is mainly achieved by increasing the number of phase-shifting steps. Therefore, researchers proposed 8-frame, 10-frame, 13-frame, and (3N+1)-frame methods [6][7][8] to eliminate the effects of the first ±5, ±9, ±15, and all multi-diffraction orders, respectively. Among the existing methods, the 8-frame, 10-frame, and 13-frame methods cannot fully eliminate the errors of all diffraction orders, resulting in relatively large peak-to-valley (PV) and root-mean-square (RMS) values of the error wavefront at small shear rates.…”

Section: Introductionmentioning

confidence: 99%

Wavefront reconstruction for double-grating Ronchi lateral shearing interferometry with nonlinear optimization

Shi,

Liu,

Shao

et al. 2023

Optical Design and Testing XIII

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“…It offers the advantages of a shared optical path, eliminating the necessity for reference waves, and features a straightforward structure. This technology holds significant promise for enhancing wavefront measurement precision [6][7][8] .…”

Section: Introductionmentioning

confidence: 99%

Research on lateral-shear interferometry based on double checkerboard grating

Bai,

Liu,

2023

Optical Design and Testing XIII

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The grating lateral-shear interferometry has a wide range of applications in wavefront sensing. The lateral-shear interferometer based on Ronchi grating can be applied for high-precision wavefront aberration detection of lithography projection lenses, which is one of the critical issues to overcome lithography challenges. The conventional Ronchi shearing interferometer object grating consists of two sets of one-dimensional Ronchi grating lines perpendicular to each other in order to obtain wavefront information in two directions, namely X and Y. During the experiment, one set is moved into the optical path for phase shifting and measurement, then the other set of grating lines is repeatedly operated. To reduce the complexity of experimental operations, this paper proposes a lateral-shear interference system based on double checkerboard gratings. The object grating and image grating are both set as checkerboard grating, and the rotation angle of the checkerboard grating varies according to the optical system's shear rate, allowing each phase shift to obtain wavefront information in X and Y directions. Multiple uniform phase shifts are performed to extract ± 1 order diffraction wavefronts of X and Y directions. The shear wavefront of the optical system to be measured is calculated from the fourwave interference light field, then the original wavefront can be restored by differential Zernike. Through theoretical analysis and simulation, this double checkerboard system can achieve wave aberration measurement with the same accuracy as traditional Ronchi interferometers, improving the real-time performance of projection lenses wave aberration measurement, and providing more possibilities for subsequent structural improvements of Ronchi lateral-shear interferometer.

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Method for designing phase-retrieval algorithms for Ronchi phase-shifting lateral-shearing interferometry

Cited by 20 publications

References 25 publications

Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

Wavefront reconstruction for double-grating Ronchi lateral shearing interferometry with nonlinear optimization

Research on lateral-shear interferometry based on double checkerboard grating

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