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 ±1st 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.
Laser Fizeau interferometers are widely used for surface form metrology for optics and silicon wafers. The reference beam and sample beam share a common optical path in Fizeau interferometer when measuring a non-tilted optical flat. However, in the process of measuring surface topography of a wafer, as the form of a wafer often deviates from an ideal flat, such as surface warping caused by the manufacturing process, the so-called retrace error may occur due to the violation of the common path condition. In this paper, we establish two ray tracing models that correspond to the home-built Fizeau interferometer in our lab, and find that the retrace error only occurs in the presence of optical aberrations in the interferometer. In addition, we study the effect of the variation of the wafer surface form on the retrace error by superposing different Zernike polynomials on the flat surface. Based on the simulation results, the tolerance for aberrations in the specific Fizeau interferometer is provided.
Magnification and distortion are two important parameters for high-precision imaging systems. Point diffraction interferometers (PDIs) can measure the magnification, distortion, and wavefront aberration of imaging systems with high precision. However, determining the precise pinhole alignment of the classical PDI is difficult. A new method for measurement of the magnification and distortion based on a dual-fiber point diffraction interferometer (DFPDI) is proposed. The end faces of two fibers are placed on the object plane of the optics under test and imaged to the image plane. The distance between the image points in the x and y directions are proportional to the Z2 and Z3 Zernike coefficients of the wavefront measurement result, respectively. The measurements of the image placement shift and precise alignment of the point diffraction pinhole are realized rapidly with high accuracy. The feasibility of the method is verified experimentally. The wavefront aberration, magnification, and distortion of a 5 × reduction lens with numerical aperture (NA) of 0.3 is measured jointly. The measurement uncertainties (3σ) of the magnification in the x and y directions and distortion are 756 ppm, 793 ppm, and 0.233 μm, respectively. Error analysis shows that the position error of the object- and image-plane stages is the main error source. An improved measurement scheme with a pinhole–pinhole pairs array in the object plane and a pinhole–window pairs array in the image plane is proposed. The influence of the position errors of the stages is eliminated with optimized measurement procedure. The DFPDI’s measurement repeatability (3σ) of the Z2 and Z3 coefficients is 0.65 and 0.33 nm, respectively, corresponding measurement uncertainties (3σ) of the magnification (in the x and y directions) and distortion can reach 1.88 ppm, 1.69 ppm, and 0.812 nm, respectively.
A new FFT wavefront reconstruction algorithm is proposed in this work, which can retrieve the test wavefront without spectrum leakage error. Since only part of the test wavefront interferes with its copy wavefront in the lateral shearing interferometer, the sizes of the sheared wavefronts are usually smaller than the test wavefront. To solve the issues introduced by the incompatible sizes of the sheared wavefronts, we used the measured information in the sheared wavefronts to compensate the missing parts based on the periodicity of the Fast Fourier Transform. This procedure can be applied under an arbitrary shear amount. Since no estimation is required during the extension, the accuracy of the reconstructed wavefront can be improved. We also provide an algorithm to estimate the lost information due to the illposed problem of reconstructing wavefront from the sheared interferometric data base on the proposed algorithm. The detail of the FFT processing and the sheared wavefront extension algorithm is given in this work. Some test is performed to evaluate the performance of the proposed algorithm. The test result shows that this algorithm is capable of reconstructing the test wavefront without introduces extra error. The estimation of the lost information based on our algorithm is convenient to be applied in the frequency. When the shear ratio is less than 25%, the estimation can always give a better result. The accuracy of the reconstructed wavefront is improved by up to 14.3% after estimation.
A calibration method of shear amount based on the optical layout of point source microscope (PSM) for lateral shearing interferometric (LSI) wavefront sensor is proposed. A simulation model of quadriwave LSI is introduced to analyze the influence of the window size of the spatial filter and the shear amount on the accuracy of the shearing wavefront feature extraction (SWFE) method. Simulation results show that the accuracy of the SWFE method deteriorates at small shear amounts. The proposed calibration method makes use of the optical layout of PSM to generate spot images of the point source at the detector plane of the sensor itself. The shear amount is calibrated by the relationship between the lateral distance of the spot images and the distribution of the diffraction orders of the grating. In the experiments, an SID4 wavefront sensor and a circular-aperture modified Hartmann mask LSI wavefront sensor are calibrated by the proposed method. A phase plate etched with patterns has been manufactured as the test specimen. The etching depth is characterized by the two wavefront sensors, and the testing results are compared with that by a commercial ZYGO® interferometer. The feasibility and accuracy of the proposed calibration method are validated. This calibration method provides an easily conducted approach for calibrating the shear amount of LSI wavefront sensor with high accuracy.
The shear ratio is an essential parameter of the lateral shearing interferometry system that affects dynamic range, signal-to-noise ratio, and accuracy. Some qualitative conclusions about the shear ratio’s influence can be found in existing reports, but no systematical analysis or quantified universal conclusion has been given. Using the sheared phase to reconstruct wavefront is the unique feature of the shearing interferometry, but it also affects the measurement accuracy significantly. The wavefront reconstruction methods can be divided into zonal and modal methods. We use the FFT reconstruction method and the least-square reconstruction method as the typical methods of modal and zonal methods to analyze the source of the reconstruction error and its relationship with the shear ratio. We conclude that the FFT reconstruction method and the least-square reconstruction method are equivalent to each other. The lost information during the shearing corresponds to some incalculable spectral values in the frequency domain and the pistons of different subgrids in the spatial domain. More spectral information will be lost if the shear ratio increased, which leads to more significant reconstruction errors. When the shear ratios are 1.6% and 6.3%, the corresponding relative reconstruction errors are about 1% and 1%, respectively. The error will be lower if the test wavefront can be represented by a limited amount of basis functions.
We propose a noncontact method for measuring the cone angle of an axicon. A microscanning stage moves the axicon being tested while a Fizeau interferometer is recording the scanning interferograms. The cone angle is measured accurately with the axial moving distance and the phase change calculated from interference fringe counting. Numerical analysis discusses the influence of standard deviation of the interference fringe count and the standard deviation of the scanning distance. Three methods for systematic error calibration are also proposed. This approach can measure both concave and convex axicons with a cone angle in the range of 96.4 deg to 170 deg. The measurable diameter of the axicon exceeds 100 mm. The spatial distribution of cone angle can be obtained with a resolution from 300 μm to 1 mm. The theoretical measurement accuracy is better than 10″ when the scanning distance is 1000 μm, and the positioning error is <10 nm. Experiments have been carried out to prove the feasibility of the proposed method, a 140-deg convex axicon is measured, and the measurement repeatability is ∼6 ″ .
A compact lateral shearing interferometer (LSI) based on circular Modified Hartmann Mask (cMHM) is proposed for the measurement of wavefront aberrations. A cMHM grating consists of a circular apertures amplitude grating and a phase chessboard grating. By choosing the radius of the circular aperture of the amplitude grating to be the first positive root of Bessel function, residual diffraction orders are suppressed. As a result, the diffraction field of cMHM is close to that of the ideal quadriwave lateral shearing interference which only contains ±1 orders in two orthogonal directions. An interferometer adopting cMHM as the diffraction element exhibits a diminished Talbot effect on the detection plane as those adopting the conventional Modified Hartmann Mask (MHM) grating or the improved Randomly Encoded Hybrid Grating (REHG). Compared with the REHG, the cMHM requires non-strict manufacturing process. Numerical simulations shows a better diffraction efficiency compared with that using the conventional MHM grating. In the experiments, the interferograms captured by the cMHM-LSI exhibit the same level of contrast as those by MHM-LSI.
A systematic error calibration method is presented to improve the measurement accuracy of lateral shearing interferometry (LSI). This method is used to remove the most significant errors: geometric optical path difference (OPD) and detector tilt error. Difference fronts in the 0° and 90° directions are used to reconstruct wavefront using difference Zernike polynomial fitting. And difference fronts in the 45° and 135° directions are also used to reconstruct wavefront. The coefficient differences between the reconstructed wavefront are generated from geometric OPD and detector tilt error. The relationship between Zernike coefficient differences and systematic parameters are presented based on shear matrix. Thus, the distance of diffracted light converging point (d) and detector tilt angle can be calculated from the coefficient difference. Based on the calculated d and detector tilt angle, the geometric OPD and detector-tilt induced systematic errors are removed and the measurement accuracy of LSI is improved.
The computation time of wavefront reconstruction is decreased by sampling the difference fronts in the present study. The wavefront can be reconstructed with high accuracy up to 64 Zernike terms with only 32×32 sampled pixels. Furthermore, the computational efficiency can be improved by a factor of more than 1000, and the measurement efficiency of lateral shearing interferometry is improved. The influence of the terms used to reconstruct the wavefront, the grid size of the test wavefront, the shear ratio, and the random noise on the reconstruction accuracy is analyzed and compared, when the difference fronts are sampled with different grid sizes. Numerical simulations and experiments show that the relative reconstruction error is <5% if the grid size of the sampled difference fronts is more than four times the radial order of difference Zernike polynomials with a reasonable noise level and shear ratio.
An efficient pixel-based mask optimization method via particle swarm optimization (PSO) algorithm for inverse lithography is proposed. Because of the simplicity of principles, the ease of implementation and the efficiency of convergence, PSO has been widely used in many fields. In this study, PSO is used to solve the inverse problem of mask optimization. The pixel-based mask patterns are transformed into frequency space using discrete cosine transformation and the frequency components are encoded into particles. The pattern fidelity is adopted as the fitness function to evaluate these particles. The mask optimization method is implemented by updating the velocities and positions of these particles. Simulation results show that the image fidelity has been efficiently improved after using the proposed method.
A new systematic error calibration method in lateral shearing interferometry (LSI) is proposed for extreme ultraviolet
lithography. This method is used to remove the most significant errors: geometric optical path difference (OPD) and
detector tilt error. The difference fronts of 0th and ±1st order diffracted waves are used to reconstruct wavefront. The
Zernike coefficients of the reconstructed wavefront are used to calculate the distance among different diffracted light
converging points (d). The difference front of 0th and +1st order diffracted waves is mirrored and added to the difference
front of 0th and –1st order diffracted waves. The sum is used to calculate detector tilt angle. The geometric OPD and
detector-tilt induced systematic errors are removed based on the calculated d and detector tilt angle. Simulations show
that the root-mean-square (RMS) value of the residual systematic error is smaller than 0.1nm. The proposed method can
be used to accurately measure the aberration of EUV optics with large numerical aperture (NA 0.5) in LSI.
An in situ aberration measurement method using a phase-shift ring mask is proposed for a lithographic projection lens whose numerical aperture is below 0.8. In this method, two-dimensional phase-shift rings are designed as the measurement mask. A linear relationship model between the intensity distribution of the lateral aerial image and the aberrations is built by principal component analysis and multivariate linear regression analyses. Compared with the principal component analysis of the aerial images (AMAI-PCA) method, in which a binary mask and through-focus aerial images are used for aberration extraction, the aerial images of the phase-shift ring mask contain more useful information, providing the possibility to eliminate the crosstalk between different kinds of aberrations. Therefore, the accuracy of the aberration measurement is improved. Simulations with the lithography simulator Dr.LiTHO showed that the accuracy is improved by 15% and five more Zernike aberrations can be measured compared with the standard AMAI-PCA. Moreover, the proposed method requires less measured aerial images and is faster than the AMAI-PCA.
Nonflatness of stage mirror surface affects the position accuracy of the wafer stage in lithography tool. Precise surface flatness measurement is needed for the computer controlled polishing of stage mirror. A subaperture stitching system using a commercial 4-inch Fizeau interferometer was presented in this paper. Absolute test was used to calibrate the surface figure of the reference mirror with the accuracy better than λ/100 PV (λ = 632.8nm). Subaperture stitching was used to extend the measurement aperture larger than 450×50mm. Stitching measurements were carried out for stage mirrors during surface polishing. Comparison tests were also made with a 24-inch interferometer. The results show that the stitching system has the advantages of larger dynamic range, higher spatial resolution, and better measurement accuracy in local area.
An in situ aberration measurement method using a phase-shift ring mask is proposed for lithographic projection lenses.
Two dimensional (2D) phase-shift rings are designed as the measurement mask. A linear model between the aerial image
intensity distribution and the aberrations is built by principal component analysis and multivariate linear regression
analyses. Compared with the AMAI-PCA method, in which a binary mask and through-focus aerial images at are used
for aberration extraction, the aerial images of the phase-shift ring mask contain more useful information. This provides
the possibility to eliminate the crosstalk between different kinds of aberrations. Therefore, the accuracy of aberration
measurement is improved. Simulations with the lithography simulator Dr. LiTHO showed that the accuracy is improved
by 15% and 5 more Zernike aberrations can be measured compared with AMAI-PCA. Moreover, the speed of aberration
measurement is improved because less aerial images are required using the new 2D mask.
An in situ aberration measurement method using a two dimensional (2D) phase-shift ring mask has been proposed for
lithographic projection lenses, which is more accurate and faster than AMAI-PCA method. The defocus of the aerial
image of the 2D measurement mask is the main source of the measurement error of this method. In this paper, a defocus
measurement method for the aberration measurement method is proposed, in which the residual of the principal
component analysis process is used as the criterion. After the defocus is accurately measured, the most suitable linear
relationship model, which plays a very important role in the aberration measurement method, can be determined.
Simulations with the lithography simulator Dr. LiTHO demonstrated that the accuracy of the defocus measurement
method is approximately 1nm. The aberration measurement method can detect 12 Zernike aberrations (Z5~Z16) with
maximum systematic error of approximately 1mλ, when the suitable linear relationship model is used.
Simultaneous phase-shifting ellipsometry based on a grating beamsplitter is presented. In the corresponding setup, an orthogonal grating and analyzer array are used. The latter is composed of four separate analyzers arranged in a 2×2 grid, the polarization axes of which are set to 0, 45, 90, and 135 deg. A mask allows only four diffracted beams of the fist order, having the same optical intensities, to pass. Each beam is incident on one of the analyzers of the array. The intensities of the four beams are simultaneously detected by a quadrant detector. The ellipsometric parameters are obtained using the four intensity signals. The feasibility of simultaneous phase shifting ellipsometry is thus demonstrated.
A white light interferometer is developed to measure the distributed polarization coupling in high-birefringence polarization-maintaining fibers (PMFs). Usually the birefringence dispersion between two orthogonal eigenmodes of PMFs is neglected in such systems. Theoretical analysis and experimental results show that the birefringence dispersion becomes a nonnegligible factor in a long-fiber test. Significant broadening of interferograms and loss of longitudinal coherence are observed. The spatial resolution and measurement sensitivity of the system decrease correspondingly. Optimum spectrum width selection is presented for better spatial resolution and measurement range.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.