Phase-shifting Point Diffraction Interferometer Research Articles

System design and error correction of simultaneous phase-shifting point-diffraction interferometer for dynamic wavefront detection with 400 mm aperture.

In this paper, a simultaneous phase-shifting point-diffraction interferometer (SPS-PDI) at632.8nm is designed with the assistance of an off-axis parabolic mirror (OAPM), through which the dynamic wavefront with 400mm aperture can be detected. In the system, a polarization point-diffraction plate (P-PDP) is developed to modulate the polarization states of the reference light and the test light through a simultaneous phase-shifting system based on a chessboard phase grating and a retarder array, and four phase-shifting interferograms can be acquired to realize dynamic detection. Furthermore, the circular carrier squeezing interferometry (CCSI) is proposed to suppress the phase errors generated by position mismatch, intensity distortion, and phase-shift error. The detection result of the SPS-PDI is consistent with the 4D PhaseCam6000 dynamic interferometer. The difference of the peak-to-valley (PV) and root-mean-square (RMS) values are only 0.04λ and 0.008λ. Additionally, the capacity to detect dynamic wavefront is good.

Lensless phase-shifting point diffraction interferometer for spherical mirror measurement

We demonstrate a lensless phase-shifting point diffraction interferometer with a tiny pinhole to measure spherical mirror surface figures. The interferograms used to reconstruct the surface figure are formed without imaging optics. Fresnel diffraction calculations with a coordinate transformation are studied as a means of reconstruction method for wavefront amplitude and phase. The Radon transform is used to determine the distance from the tiny pinhole to the CCD target, which guarantees the accuracy of the diffraction calculations. Our lensless phase-shifting point diffraction interferometer not only retains the higher measurement precision by the ideal reference wavefront, but also overcome the fabrication and mounting limitation of the imaging optics. The simulations and experiments have validated the accuracy and feasibility of the spherical mirror measurement by proposed lensless phase-shifting point diffraction interferometer.

Circular carrier squeezing interferometry: Suppressing phase shift error in simultaneous phase-shifting point-diffraction interferometer

Circular carrier squeezing interferometry (CCSI) is proposed and applied to suppress phase shift error in simultaneous phase-shifting point-diffraction interferometer (SPSPDI). By introducing a defocus, four phase-shifting point-diffraction interferograms with circular carrier are acquired, and then converted into linear carrier interferograms by a coordinate transform. Rearranging the transformed interferograms into a spatial-temporal fringe (STF), so the error lobe will be separated from the phase lobe in the Fourier spectrum of the STF, and filtering the phase lobe to calculate the extended phase, when combined with the corresponding inverse coordinate transform, exactly retrieves the initial phase. Both simulations and experiments validate the ability of CCSI to suppress the ripple error generated by the phase shift error. Compared with carrier squeezing interferometry (CSI), CCSI is effective on some occasions in which a linear carrier is difficult to introduce, and with the added benefit of eliminating retrace error.

Design of a grating by a joint optimization method for a phase-shifting point diffraction interferometer

A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant. In order to measure the projection objective with a numerical aperture of 0.2, we present a joint optimization method of a pinhole and grating based on scalar diffraction and the finite difference time domain method. The grating constant and the film thickness are selected, and the duty cycle of the grating is optimized. The results show that in the grating processing the material chromium is adopted, the thickness is 200 nm, and the grating constant is 15 μm. When the duty cycle is 55%, the interference fringe contrast is the greatest. The feasibility of the design result is further verified by experiment.

Virtual pyramid wavefront sensor for phase unwrapping.

Noise affects wavefront reconstruction from wrapped phase data. A novel method of phase unwrapping is proposed with the help of a virtual pyramid wavefront sensor. The method was tested on noisy wrapped phase images obtained experimentally with a digital phase-shifting point diffraction interferometer. The virtuality of the pyramid wavefront sensor allows easy tuning of the pyramid apex angle and modulation amplitude. It is shown that an optimal modulation amplitude obtained by monitoring the Strehl ratio helps in achieving better accuracy. Through simulation studies and iterative estimation, it is shown that the virtual pyramid wavefront sensor is robust to random noise.

Phase unwrapping with a virtual Hartmann-Shack wavefront sensor.

The use of a spatial light modulator for implementing a digital phase-shifting (PS) point diffraction interferometer (PDI) allows tunability in fringe spacing and in achieving PS without the need for mechanically moving parts. However, a small amount of detector or scatter noise could affect the accuracy of wavefront sensing. Here, a novel method of wavefront reconstruction incorporating a virtual Hartmann-Shack (HS) wavefront sensor is proposed that allows easy tuning of several wavefront sensor parameters. The proposed method was tested and compared with a Fourier unwrapping method implemented on a digital PS PDI. The rewrapping of the Fourier reconstructed wavefronts resulted in phase maps that matched well the original wrapped phase and the performance was found to be more stable and accurate than conventional methods. Through simulation studies, the superiority of the proposed virtual HS phase unwrapping method is shown in comparison with the Fourier unwrapping method in the presence of noise. Further, combining the two methods could improve accuracy when the signal-to-noise ratio is sufficiently high.

Digital phase-shifting point diffraction interferometer

A digital phase-shifting (PS) point diffraction interferometer is demonstrated with a transmitting liquid crystal spatial light modulator. This novel wavefront sensor allows tunability in the choice of pinhole size and eliminates the need for mechanically moving parts to achieve PS. It is shown that this wavefront sensor is capable of sensing Zernike aberrations introduced with a deformable mirror. The results obtained are compared with those of a commercial Hartmann-Shack wavefront sensor.

Calibration method to characterize the accuracy of phase-shifting point diffraction interferometer

Characterization of measurement accuracy of the phase-shifting point diffraction interferometer (PS∕PDI) is usually performed by two-pinhole null test. In this procedure, the geometrical coma and detector tilt astigmatism systematic errors are almost one or two magnitude higher than the desired accuracy of PS∕PDI. These errors must be accurately removed from the null test result to achieve high accuracy. Published calibration methods, which can remove the geometrical coma error successfully, have some limitations in calibrating the astigmatism error. In this paper, we propose a method to simultaneously calibrate the geometrical coma and detector tilt astigmatism errors in PS∕PDI null test. Based on the measurement results obtained from two pinhole pairs in orthogonal directions, the method utilizes the orthogonal and rotational symmetry properties of Zernike polynomials over unit circle to calculate the systematic errors introduced in null test of PS∕PDI. The experiment using PS∕PDI operated at visible light is performed to verify the method. The results show that the method is effective in isolating the systematic errors of PS∕PDI and the measurement accuracy of the calibrated PS∕PDI is 0.0088λ rms (λ = 632.8 nm).

相移点衍射干涉仪的高精度对准

相移点衍射干涉仪的高精度对准

Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers

A phase-shifting point diffraction interferometer (PS/PDI) with two optical fibers has been developed. This system consists of high numerical aperture optics and it forms an interferogram on a CCD without using imaging optics. The positions of the fiber cores were determined by an iterative method for analyzing interferograms. The surface figure of a test mirror was obtained from the measured amplitude and phase by digital holography. The surface figure of a spherical concave mirror was measured at two different axial orientations of the mirror. The difference between the two results had a peak-to-valley value of 2 nm and a root-mean-square (rms) value of 0.85 nm. When the moiré pattern, which is main cause for the difference, is eliminated, the measurement accuracy has an rms=0.15 nm. This procedure can also be used to measure aspherical mirrors. The measurement accuracy when measuring an aspherical mirror is expected to be the same as that when measuring a spherical mirror.

Numerical reconstruction of wavefront in phase‐shifting point diffraction interferometer by digital holography

AbstractA phase‐shifting point diffraction interferometer (PS/PDI) is applied for absolute surface figure measurement for large aperture optics. The intensity and phase distributions of measurement wavefront containing the surface figure profile are measured on the projection plane. The phase map gives the surface figure of the mirror. However, the wavefront reflected by the test mirror changes itself while propagating due to the surface figure of the mirror and the position of the point light source. The wavefront is different from the surface figure on the projection plane. For absolute surface profiling, the wavefront on the mirror has to be reconstructed from the measurement results. To reconstruct the wavefront digital holography has been studied. We have developed the numerical reconstruction method by using the Helmholtz–Kirchhoff formula. Spherical concave mirror measurements have been simulated to verify the availability. Ideal spherical mirror measurements, aspherical mirror measurements and a spherical mirror measurement in which the point light source was slightly displaced were simulated. As a result, the phase map on the projection plane did not fit the surface figure. It was also revealed that the light intensity distribution causes changes in the wavefront. In contrast, the reconstructed phase map on the mirror gave the real surface figure. For precise reconstruction the number of sampling on the projection plane must be increased. Copyright © 2008 John Wiley & Sons, Ltd.

Measurement Accuracy in Phase-Shifting Point Diffraction Interferometer with Two Optical Fibers

A phase-shifting point diffraction interferometer (PS/PDI) with point sources of two single mode optical fibers has been developed, which will be appropriate for the surface figure measurement of large aperture optics on a sub-nanometer scale. To reduce the measurement error factors, a fiber optic plate (FOP) is used as a projection plane for interference pattern. Errors caused by imperfection of optical alignment, such as position of point sources and tilt of FOP, are minimized by analyzing the measured phase data with an original method. Measurement accuracy in the PS/ PDI is estimated with the interference pattern produced by the two optical fiber sources. If inhomogeneity of the FOP and a systematic error of the PS/PDI are eliminated, the measurement accuracy of the present system is estimated to be less than 4nm P-V and 0.7nm rms, respectively, at a measurement wavelength of 632.8 nm.

Phase-shifting point-diffraction interferometer developed by using the electro-optic effect in ferroelectric crystals

A novel and simple phase-shifting point-diffraction interferometer using a z-cut lithium niobate wafer is proposed. The pinhole is realized by an optical lithography process, aluminum deposition, and subsequent lift-off on the surface of the wafer. The phase shifting is obtained by inducing the electro-optic effect along the z crystal axis. We demonstrate experimentally the possibility of retrieving an aberrated wavefront.

Polarization phase-shifting point-diffraction interferometer

A new instrument, the polarization phase-shifting point-diffraction interferometer, has been developed by use of a birefringent pinhole plate. The interferometer uses polarization to separate the test and reference beams, interfering what begin as orthogonal polarization states. The instrument is compact, simple to align, and vibration insensitive and can phase shift without moving parts or separate reference optics. The theory of the interferometer is presented, along with properties and fabrication techniques for the birefringent pinhole plate and a new model used to determine the quality of the reference wavefront from the pinhole as a function of pinhole size and test optic aberrations. The performance of the interferometer is also presented, along with a detailed error analysis and experimental results.

光ファイバからの点光源回折球面波を計測の絶対基準とした位相シフト光干渉計の開発

This paper describes a novel phase-shifting point diffraction interferometer (PS-PDI) that employs 2 fiber-optic point sources, as a tool for measuring surfaces for SOR and EUV mirrors with sub-nanometer accuracy using visible light optics. In conventional interferometry, the figure accuracy of the reference surface determines the measurement accuracy. We therefore need an absolute reference surface with sub-nanometer accuracy. One of the qualified surfraces is a spherical wavefront which comes from point light source. The proposed PS-PDI system uses 2 single-mode optical fibers as point light sources. The system is applied to the measurement of a commercial spherical concave mirror with 500 mm in radius of curvature and 30 mm in diameter. The repeatability of measurement for the mirror is estimated to be about 3 nm in peak-to-valley value at the wavelength of 632.8 nm in He-Ne laser.

Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function.

The estimation accuracy of a point-diffraction interferometer is examined with two phase-shifting schemes: spatial and temporal. Under the assumption of plane- or spherical-wave propagation through isotropic turbulence that can be accurately represented as a series of thin phase screens, results that are valid for any scintillation regime are obtained by use of the invariance with a propagation of the mutual coherence function. It is established that the estimation accuracy of the spatial phase-shifting point-diffraction interferometer is invariant with scintillation. Upper and lower bounds on the perfor mance of the temporal phase-shifting point-diffraction interferometer are developed. Wave optical simulation results are presented that validate the analytic predictions for the two phase-shifting schemes. The results and techniques presented can be used to assess the appropriate phase-shifting scheme given finite resources, such as a limited number of pixels in a detector array or a restricted detector frame rate.

Fourier transform interferometer alignment method.

A rapid and convenient method has been developed to facilitate the alignment of the image-plane components of point-diffraction interferometers, including the phase-shifting point-diffraction interferometer. In real time, the Fourier transform of the detected image is used to calculate a pseudoimage of the electric field in the image plane of the test optic where thecritical alignment o f variousoptical components is performed. Reconstruction of the pseudoimage is similar to off-axis, Fourier transform holography. Intermediate steps in the alignment procedure are described. Fine alignment is aided by the introduction and optimization of a global-contrast parameter that is easily calculated from the Fourier transform. Additional applications include the alignment of image-plane apertures in general optical systems, the rapid identification of patterned image-plane alignment marks, and the probing of important image-plane field properties.

Proposal of at-wavelength PDI for EUVL optics alignment by using a compact undulator

At-wavelength phase-shifting point diffraction interferometer (PDI) is a technique to measure wavefront error of EUV lithography optics. While they use radiation from undulators in medium size electron storage rings with further wavelength purification by monochrometers, we propose to use direct radiation from a compact undulator. We carried out an experiment at NewSUBARU and found that rather broad band radiation is applicable to this PDI, which is attributed to the wavelength dependency of grating diffraction. We designed an undulator with a periodic length of 2.9 cm, periodic number of 150 and magnetic field of 4.4 kG to be installed in a small storage ring. Applying a beam line conversion efficiency of 200, the exposure time to take one PDI picture for future EUVL optics was estimated to be 2.4 s with proper margin.

At-wavelength characterization of the extreme ultraviolet Engineering Test Stand Set-2 optic

At-wavelength interferometric characterization of a new 4×-reduction lithographic-quality extreme ultraviolet (EUV) optical system is described. This state-of-the-art projection optic was fabricated for installation in the EUV lithography Engineering Test Stand (ETS) and is referred to as the ETS Set-2 optic. EUV characterization of the Set-2 optic is performed using the EUV phase-shifting point diffraction interferometer (PS/PDI) installed on an undulator beamline at Lawrence Berkeley National Laboratory’s Advanced Light Source. This is the same interferometer previously used for the at-wavelength characterization and alignment of the ETS Set-1 optic. In addition to the PS/PDI-based full-field wave front characterization, we also present wave front measurements performed with lateral shearing interferometry, the chromatic dependence of the wave front error, and the system-level pupil-dependent spectral-bandpass characteristics of the optic; the latter two properties are only measurable using at-wavelength interferometry.

Extreme-ultraviolet lensless Fourier-transform holography

We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed.