Segmented wave-front measurements by lateral shearing interferometry

Few cost-effective methods exist for measuring the wave front of mid- and long-wave infrared beams that span 3-5 and 8-12 μm, respectively. One obvious need within the infrared laser community is the ability to measure the degree of collimation of an infrared laser beam, e.g. that formed by a beam expanding telescope used with a CO₂ laser or a system of lenses used to collimate a Quantum Cascade Laser (QCL). An ideal approach for this type of metrology is the use of a lateral shearing interferometer (LSI). An LSI uses various methods to displace ("shear") a beam with respect to itself to create an interferogram that can subsequently be used for diagnosing the wavefront quality of the beam. Since this type of interferometer is of the common path variety, it is insensitive to vibration making it ideal for field applications, where vibration isolation may neither be possible nor practical. In this paper we present and demonstrate, through laboratory measurements and computer ray tracing simulations, a low-cost LSI using a single commercial off-the-shelf uncoated ZnSe window in conjunction with an infrared camera. This plane parallel plate LSI configuration was used to interactively collimate a LWIR beam and also provide quantitative transmitted wavefront error data using static fringe analysis software. We also present a self-contained review of the theory of lateral shearing interferometry, including the necessary design equations as applicable to this LSI configuration, to enable researchers to construct a similar beam diagnostic shearing interferometer from readily available components.

A modal phase-reconstruction method for wave-front analysis in lateral shearing interferometry is presented. Pseudo-Zernike polynomial functions describe the differential wave fronts and are related to a Zernike polynomial description of the original wave front. We show that this reconstruction is robust for shear ratios in the range 0.15-0.50. The error propagation properties of this differential Zernike polynomial matrix-inversion method are discussed on the basis of both analysis and simulation. It is concluded that the method allows wave-front analysis with an absolute inaccuracy of 2 mλ rms for diffraction-limited wave fronts and with 1% relative inaccuracy for more strongly aberrated wave fronts.

A lateral shearing interferometer has an advantage over previous wavefront measuring interferometers since it requires no reference. Therefore the lateral shearing interferometer can be a powerful solution to measure a freeform surface. It, however, has some issues to be resolved before it can be implemented. One of them is the orthogonality problem between two shearing directions in LSI. Previous wavefront reconstruction algorithms assume that the shearing directions are perfectly orthogonal to each other and lateral shear is obtained simultaneously in the sagittal and tangential directions. For practical LSI, however, there is no way to guarantee perfect orthogonality between two shearing directions. Motivated by this, we propose a new algorithm that is able to compensate the rotational inaccuracy. The mathematical model is derived in this paper. Computer simulations and experiments are also displayed to verify our algorithm.

With the development of new materials and ultra-precision processing technology, the sizes of measured objects increase, and the requirements for machining accuracy and surface quality become more exacting. The traditional measurement method based on reference datum is inadequate for measuring a high-precision object when the quality of the reference datum is approximately within the same order as that of the object. Self-referenced measurement techniques provide an effective means when the direct reference-based method cannot satisfy the required measurement or calibration accuracy. This paper discusses the reconstruction algorithms for self-referenced measurement and connects lateral shearing interferometry and multi-probe error separation. In lateral shearing interferometry, the reconstruction algorithms are generally categorized into modal or zonal methods. The multi-probe error separation techniques for straightness measurement are broadly divided into two-point and three-point methods. The common features of the lateral shearing interferometry method and the multi-probe error separation method are identified. We conclude that the reconstruction principle in lateral shearing interferometry is similar to the two-point method in error separation on the condition that no yaw error exists. This similarity may provide a basis or inspiration for the development of both classes of methods.

Lateral Shearing Interferometer (LSI), as a kind of self-interference technology, can achieve high-precision wavefront sensing and phase imaging. Quadriwave Lateral Shearing Interferometry (QWLSI) divides the wavefront into four transverse dislocated beams by a checkerboard phase grating. The lateral-shearing interferogram of the four waves occurs on the image plane, and then the test wavefront is reconstructed. The reconstruction precision is determined by the shear ratio, thus the variable shear ratio can meet the requirement of the different measurement accuracy. Here we proposed variable-ratio lateral-shearing interferometry with a vortex-splitting grating. Different from the checkerboard grating, topological charge is first encoded into grating and is then optimized to obtain two shear ratios in the same interference setup. The proposed variable-ratio lateral-shearing setup including of only an axial motion device is robust, effective and variable precision for wavefront sensing.

A lateral shearing interferometer has the orthogonality problem between two shearing directions. For practical LSI, it is hard to guarantee perfect orthogonality between two shearing directions. Motivated by this, we propose a new algorithm that can correct the rotational inaccuracy.

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.

Characterizing and removing optical aberrations remains a key part of achieving ultimate resolution in EUV exposure tools. Common-path approaches such as lateral shearing interferometry (LSI) have had success at moderate numerical apertures (NA ≈ 0:3); however, these techniques run into several obstacles when applied at higher NA (NA > 0:4). Chief among these obstacles are systematic aberrations due to high incident angles on the diffraction grating and non-planar Talbot surfaces that create regions of low fringe contrast across the pupil. In this paper, we present strategies for addressing these obstacles to extend LSI to high numerical apertures. These strategies will be employed in the installation and alignment of the 0.5-NA SEMATECH Berkeley Microfield Exposure Tool (MET5).

Quadrowave lateral shearing interferometers (QWLSIs) have been widely used in many fields, such as optical testing, laser beam evaluation and biological imaging, because of their compactness and portability. However, when the QWLSI is used for optical testing of complex surfaces, such as in the early stage of processing, the surface distribution of the tested part is complex, and the high-frequency noise is severe, which leads to severe phase wrapping in the process of calculating the phase from the interference fringes. With the complex unwrapping algorithm, severe surface wire drawing phenomena can easily occur, and an accurate surface distribution cannot be obtained. In this paper, a double grating QWLSI is proposed. By using two QWLSI gratings with different periods to test the same measured surface, the dynamic range of the composite grating can be improved by 2~3 orders of magnitude compared with that of a single grating, and the spatial resolution remains unchanged. This method greatly simplifies the unwrapping process in the process of surface calculation and sometimes does not even require unwrapping. This method can help the QWLSI test optical components over a longer period of processing.

In-situ measurement and compensation of complex spatio-temporal couplings in ultra-intense lasers

Lateral shearing interferometry is widely applied in wavefront sensing, optical components testing, and defect inspection. The procedure of reconstructing the wavefront is the most specific difference between lateral shearing interferometry and other classical methods such as the Fizeau and Twyman interferometers. The speed and accuracy are two main features to evaluate the performance of one wavefront reconstruction method. In this work, optimized procedures for three typical wavefront reconstruction methods-the iterative FFT wavefront reconstruction method (FFT method), the partial differential least-squares method (LSQ method), and the difference Zernike polynomial fitting method (DZF method)-are designed. The calculation speeds of the three wavefront reconstruction methods are evaluated with different GPUs and CPUs. According to the test results, the DZF method is the fastest method both in the GPUs and CPUs. The shortest processing times of the DZF, FFT, and LSQ methods are 100, 449, and 494 ms, respectively, with the wavefront size of 1024×1024pixels. The calculation speeds of the FFT method and the LSQ method are similar in the CPUs, and the FFT method is faster in the GPUs. The relationship between the consumed time and the wavefront size is an exponential function in the CPUs and a power function in the GPUs. Generally speaking, GPUs' processing speeds are faster than CPUs'. But CPUs can be faster than GPUs when the test wavefront sizes are smaller than 64×64pixels. Besides, the differences between the consumed times of different CPUs are relatively smaller than those of the GPUs.

Transparent optical components, which are required for high-precision and high-performance, are made by a plastic injection molding method. This can cause inner defects to appear because of the difference in cooling rate and pressure. However, submicron inner defects, caused by the refractive index error, are extremely difficult to determine. Thus, digital holographic microscopy based on an optimal modified lateral shearing interferometer is proposed. This is to measure submicron defects in transparent objects, such as a defective microlens. In addition, the optimal lateral shearing distance is proposed to efficiently remove duplicate images. Optical experiments using the suggested lateral shearing interferometer are presented, and the experimental results with a test microlens confirm the feasibility of the proposed method.

Flexible lateral shearing interferometry based on polarization gratings for surface figure metrology

To test quality of the wavefronts number of arrangements are discussed in literature. Out of these the lateral shearing interferometers using diffracting elements are stable and simple devices. Lateral shear obtained by J.C. Waynt, rotation of two gratings by Hariharan et al and Rimmer and Waynt over come some of the drawbacks suffered by Ronchi interferometers. It has already been demonstrated that the two slightly displaced off axis zone plates acts exactly like a double frequency grating. This paper describes the holo-shear lens made on dichromatic gelatin for testing of off axis parabola. Joenathal et al investigate lateral shear interferometry with holo shear lens.

With the development of modern precision optical systems, optical detecting system requires the accuracy of wavefront aberration to arrive to sub-nanometer level. When the incident field with polarization information, the polarization information will have a significant impact on the accuracy of measurement results by interacting with polarization-sensitive optical components in the lateral shearing interferometer. We propose the integrated interferometer wavefront sensor (IIWS) system, which is based on the traditional lateral shearing interferometer. This wavefront is sheared by a two-dimension diffraction grating in our system, the two-dimension diffraction grating is the key element to analysis the metrology performance. When using a different grating period and shearing direction, the wavefront shearing and phase shifting with polarization information will produce different error, moreover the impact will vary in the different diffraction orders. In this paper, calculation is based on the finite difference time domain (FDTD) algorithm. When calculation of different polarization state distribution of the incident field, the interaction analysis of shearing phase shifted grating and incidence light play an important role in error analysis. Finally we can get the effect of polarization for grating performance.