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Multilayer defects which reside on the top or inside the multilayer are one of the most critical concerns in the extreme ultraviolet lithography (EUVL) manufacturing process. We proposed the transport of intensity equation and partial least-square regression (TIE & PLSR) method to inspect the defect and reconstruct its geometric parameters: height and full width at half maximum (FWHM). The transport of intensity equation (TIE) is employed to retrieve the phase of the multilayer defect from the two scattering images, which collected at two adjacent propagation distances. Comparing the simulated ideal phase, the phase deformations caused by different top heights and widths of the defects are analyzed. The optical properties maximum, minimum and fitting Zernike coefficients are used to parameterize the phase deformation. Partial least-squares regression (PLSR) is applied to associate the optical properties of the phase deformation with the geometric parameters of the defects, and reconstruct geometric parameters of the measured defect from the established data library. The reconstruction error is less than 0.2% in simulation experiment.

Multi-beam interference will exist in the cavity of Fizeau interferometer due to the high reflectivity of test optics. The random phase shift error will be generated by some factors such as the environmental vibration, air turbulence, etc. Both these will cause phase retrieving error. We proposed a non-iterative approach called Carrier Squeezing Multi-beam Interferometry (CSMI) algorithm, which is based on the Carrier squeezing interferometry (CSI) technique to retrieve the phase distribution from multiple-beam interferograms with random phase shift errors. The intensity of multiple-beam interference was decomposed into fundamental wave and high-order harmonics, by using the Fourier series expansion. Multi-beam phase shifting interferograms with linear carrier were rearranged by row or column, to fuse one frame of spatial-temporal fringes. The lobe of the fundamental component related to the phase and the lobes of high-order harmonics and phase shift errors were separated in the frequency domain, so the correct phase was extracted by filtering out the fundamental component. Suppression of the influence from high-order harmonic components, as well as random phase shift error is validated by numerical simulations. Experiments were also executed by using the proposed CSMI algorithm for mirror with high reflection coefficient, showing its advantage comparing with normal phase retrieving algorithms.

A white-light microscopy interferometer was developed for measurement of the 3D profile and roughness.10X, 20X and 50X Mirau interference microscope objectives with the numerical aperture of 0.3, 0.4 and 0.55 were designed, manufactured and then provided as the accessories. Thickness deviation between beam splitter plate and reference mirror plate as well as the numerical aperture will both affect the contrast of interference fringe, according to optical modeling and image evaluation. The former would generate dispersion and then decrease the fringe contrast, while the latter would not produce dispersion separately but impact the amount of dispersion when thickness deviation exists, and their influence on fringe contrast was based on the expression of white-light interference intensity. Simulations for interference fringes from Mirau interference microscope objectives with different NA and thickness deviation were implemented, demonstrated that the fringe contrast will be falling with NA and thickness deviation increasing. A standard step with the nominal step value of 110 nm was used to calibrate the white-light microscopy interferometer, showing that less than1nm deviation can be reached.

A method for measuring the focal length of the lens and the radius of curvature of the spherical surface using wavefront difference method is proposed. Based on Fizeau interferometer, an experimental system for focal length measurements is set up to verify the principle. Based on the point diffraction interferometer, an experimental system for radius of curvature measurements is proposed to verify the proposed method. With the focal length testing system, both the positive and negative lens experimental results indicate that the measurement accuracy is less than 0.16%under normal experimental environment. With the radius of curvature testing system, the radius of curvature of spherical mirrors and the surface figure can be measured in a higher precision simultaneously. The experimental results indicate that the measurement accuracy is in the order of 10 -4 .

A 1.5mm focal length, F/4and F/3.75, miniature fisheye all spherical optical lens systems with 220 degree full field of view are designed in this paper, a brief discussion for a series of limiting factors is achieved, the performance evaluation is done by ZEMAX optical design and analysis software, which shows that the two designed fisheye lenses are perfect lateral color and axial chromatic aberration corrected, the maximum wavefront OPD at the full FOV is 0.6λ and 1.2λ, the RMS spot size is 3.75-3.9microns across the full FOV in both lens systems, and have diffraction encircled energy, as above 80% energy can be included in 4.8 μm radius circle. Finally, the modulation transfer function of these two designs produces a high-resolution projection with uniform in brightness over the entire range of field angles for security, monitoring, and tracking applications.

Freeform complex surfaces with steep variations in local areas cannot be fitted by analytical functions with high accuracy in the whole aperture in optics. A framework with a combination of Zernike polynomials as base function with radial basis function method is presented to improve reconstruction accuracy for freeform complex surfaces with circular aperture. The algorithm of the framework is analyzed, and the performance of the method is investigated and verified by numerical experiments. The proposed method is accurate and highly adaptable, which could be applied in modern optical manufacturing and measurement.

There exists three variables in the radiative transfer equation based on dynamic energy conservation, including polar angle, azimuth angle and normalized penetrate depth. In order to solute this equation with double integral on polar angle and azimuth angle, the first step is to introduce proper method to isolate azimuthal dependency from polar angle. In this paper, we propose a novel phase matrix expansion with Zernike polynomials, which represents the probability of scattering events. The results show that it can provide a new improved strategy for the solution of radiative transfer equations in Discrete-Ordinate Method (DOM), which is different from commonly used Fourier series and Legendre polynomials expansion and we make conclusion that there are three principles for polynomials’ selection, including orthogonal performance, special theorem for polynomial derivation and triangle function generation.

Axicon surfaces are widely used in nowadays optical engineering, requiring accurate metrology for these highly aspheric surfaces. In this contribution, we present a complete approach to determine the shape deviation of axicons in an absolute manner. The setup is an interferometric null configuration using a computer generated hologram (CGH) as null optics. We demonstrate an absolute shifting method and the calibration issues connected with measuring the absolute cone angle. Experimental results are shown for the metrology of a 90° cone angle sample.

A portable phase-shifted interferometer with multiply usages is described. Several techniques are studied and used in this interferometer. In order to test an optical piece with obscuration or irregular edge, we study the seed-algorithm for wavefront reconstruction. For testing a corner cube reflector (CCR), we investigate the model to calculate its exit wavefront and angle error. To measure the figure of a convex or concave spherical surface, we develop a series of reference transmission spheres.

A combination of computer generated hologram (CGH) with a small liquid crystal display, phase-shifting detection, and Twyman-Green interferometer is used to test an aspheric. This method resolves the problem of real-time produce CGH. In the paper, a method of producing real-time computer generated hologram is proposed in which a small liquid crystal display is adopted as a recording material. The making principle of the real-time computer generated hologram is described. The experimental result is better.

A practical system is described to measure the retardation of wave plates with phase-shifted method. The tested wave plate is put in and the original angle between the axis of it and the analyzer is random, not 45 degree. For the measurement is made rapidly and automatically, a standard wave plate act as a compensator, the stepping motor is used to drive the analyzer to realize phase shifting and a grating encoder is used to measure its rotating angle. At the same time, while the beam comes out from the analyzer, the photoelectric detector gets its intensity, and then the signals is magnified, filtered and sent to computer through its serial port. The results show the system has the advantages of costing little time and high accuracy.

The optical quality and frequency response of an interferometer is influenced by its primary parts, for example its collimating input system, its reference lenses, its reference flat, its stop, etc. An interferometer is set up with optical design software to study the full view of influence by them in this paper. The data and curve is also given in this paper making sure the system error induced by them is less than 0.01λ (λis wavelength).

Reference lenses play an important role in test of spherical surfaces. In this condition, the ray reflected from the tested spherical surface goes the same way as that from the last surface of the reference lenses. If the two rays go different way, the focus of the reference lenses is not coincidence with its last surface’s curvature center, and system error is produced. The deviations between the focus and the curvature center of the last surface for a series of reference lenses are studied in this paper.

A torus is a kind of aspherical surface, different from quadratic rotary surface. It plays an important role in special optical systems. However, up to now there is no effective method to test its wavefront. In this paper, a method is proposed using long wavelength (10.6 micrometers ) IR interferometry to test a torus, whose curvature radii is different from submillimeter deducing to micrometer, the principle is also given. Then a example torus is tested in self-developed IR spherical interferometer. When this torus is placed in typical positions along the optical axis, some interferograms are shown. According to these interferograms the wavefront error and the difference of two radii can be obtained and shown in this paper.