High-aperture low-coherence interferometer with a diffraction reference wave

A high-aperture low-coherence interferometer with a diffraction reference wave based on a tipped single-mode optical fiber was proposed and investigated. Due to the usage of the central least-aberrated region of the diffracted wavefront, the interferometer comprise record working aperture among known PDIs. The interferometer makes it possible to study samples with a reflectance that varies over a wide range. A demonstration of the use of this interferometer for high-precision measurements of a spherical mirror is presented. Sub-nanometer reproducibility of measurements in terms of the peak to valley (PV) parameter and sub-angstrom reproducibility in terms of the rms are demonstrated.

Point diffraction interferometer based on a silicon nitride waveguide spherical wave source

A point diffraction interferometer based on silicon nitride waveguide (WG-PDI), adopting a silicon nitride waveguide spherical wave source (WG-SWS) with Si substrate and SiO₂ cladding, is proposed for spherical surface testing. The WG-SWS is used to overcome the drawbacks of the existing spherical wave sources, which can generate high accuracy and high numerical aperture spherical reference wave. In this paper, the theory of the WG-PDI is described, and the possible errors introduced by the device are analyzed. In addition, the lateral deviation between the curvature center of the test wave and the curvature center of the reference wave cannot be eliminated in the reflected configuration of the pinhole diffraction interferometer. After analyzing the influence of the systematic error introduced by the lateral deviation, the semi-reflective film was coated on the output facet of the waveguide spherical wave source to realize point diffraction interference without lateral deviation. Finally, the surface error of a spherical surface was measured by WG-PDI. The experimental results agree well with those measured by the ZYGO interferometer.

One-shot phase retrieval method for interferometry using a hypercolumns convolutional neural network

In three dimensional profilometry, phase retrieval technique plays a key role in signal processing stage. Fringe images need to be transformed into phase information to obtain the measurement result. In this paper, a new phase retrieval method based on deep learning technique is proposed for interferometry. Different from conventional multi-step phase shift methods, phase information can be extracted from only a single frame of an interferogram by this method. Here, the phase retrieval task is regarded as a regression problem and a hypercolumns convolutional neural network is constructed to solve it. Firstly, functions and each component of the network model are introduced in details; Then, four different mathematical functions are adopted to generate the training dataset; training and validation strategies are also designed subsequently; Finally, optimization processing is performed to eliminate local data defects in initial results with the help of polynomial fitting. In addition, hardware platform based on point diffraction interferometer is fabricated to support this method. Concluded from the experiment section, the proposed method possesses a desirable performance in terms of phase retrieval, denoising and time efficiency.

Reference wave source based on silicon nitride waveguide in point diffraction interferometer

Reference wave source (RWS) is the key component of the point diffraction interferometer, which determines the quality of the reference wave. The silicon nitride waveguide RWS is proposed to efficiently overcome the drawbacks of the existing RWSs, aimed at providing a spherical reference wave with high numerical aperture (NA) and high accuracy. The waveguide RWS consists of the straight waveguide, the bend waveguide, and the Y-branch edge coupler. The straight waveguide determines the accuracy and the NA of the reference wave, whereas the latter two determine the light transmittance of the RWS. Simulation results show that the peak-to-valley (PV) and the rms of the deviation from an ideal spherical wave are 2.86×10^-4λ (λ=532nm) and 4.83×10^-5λ, respectively, and the maximum light transmittance could reach 24%. Experiment results show that the NA of the reference wave reaches up to 0.58, its spot has a good circular symmetry, and its intensity has Gaussian distribution. Although the light transmittance is only 0.2%, it is expected to improve with the development of experimental conditions and waveguide fabrication technology.

Full-field analysis of wavefront errors in point diffraction interferometer with misaligned Gaussian incidence

The precision and accuracy of profile measurement achieved by a point diffraction interferometer (PDI) is determined by a spherical diffraction reference wavefront whose quality is mainly controlled by the pinhole's alignment. In consideration of a Gaussian beam incidence, different diffraction wavefront errors stemming from misalignment of pinhole including lateral shift, defocus, and tilt are analyzed with the help of a proposed systematic model and a new evaluation criterion established under spherical coordinates. The full-field distributions of various diffraction wavefront errors are obtained through simulation. The predicted accuracy of an actual PDI makes a good agreement with the experiment results. The achieved results will be beneficial to the accuracy evaluation of a PDI before and after its design.

Precision optical path alignment system for point diffraction interferometer based on image information

In a point diffraction interferometer, the existence of alignment error between an objective convergent spot and a diffraction pinhole can lead to wavefront error and diffraction intensity reduction. Meanwhile, the contrast of the point diffraction interferograms probably decreases in this procedure. These changes will have significant influence on its inspection precision. A precise alignment system of an optical path for a point diffraction interferometer is proposed in this paper. First, diffraction theory is used to analyze the mathematical relationships of alignment error to diffraction wavefront error and numerical aperture and wavefront error to pinhole size. Then, according to the requirement, the scheme of an optical path alignment system is designed. In this stage, alignment images as well as intensities of a reflected and diffracted beam from the point diffraction plate will be acquired. In addition, an image processing algorithm for measuring alignment error is designed, and a mathematical model between quantities of measurement and control is constructed. Finally, implementation and experiment of this method are also introduced. Misalignment situations, including lateral translation, longitudinal defocus, and tilt error, are well eliminated, and the quality of interferograms is also improved. From the results, it can be concluded that the system is of desirable precision and efficiency.

Accurate calibration of geometrical error in reflective surface testing based on reverse Hartmann test

The deflectometry provides a powerful metrological technique enabling the high-precision testing of reflective surfaces with high dynamic range, such as aspheric and freeform surfaces. In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, the calibration of system geometry is required to achieve "null" testing. However, the system miscalibration can introduce a significant systematic error in the testing results. A general double-step calibration method, which is based on the low-order Zernike aberration optimization and high-order aberration separation, is proposed to separate and eliminate the geometrical error due to system miscalibration. Both the numerical simulation and experiments have been performed to validate the feasibility of the proposed calibration method. The proposed method provides a general way for the accurate calibration of system geometrical error, avoids the over-correction and is feasible for the testing of various complex freeform surfaces.

Characterization of the pinhole diffraction based on the waveguide effect in a point diffraction interferometer

The nearly ideal spherical wavefront generated by pinhole diffraction is the key factor determining the achievable accuracy in point diffraction interferometers (PDIs), as it is employed as the reference wavefront. A comprehensive characterization of the diffraction of a pinhole at the operating-wavelength scale that is normally adopted in PDI is given. The incident light is coupled into the pinhole, which functions as a cylindrical waveguide, and is diffracted in the end. The field in the pinhole is analyzed based on mode theory and the diffraction wave in the far field is derived from the field equivalence principle. The diffraction wave is characterized by the light transmittance, the polarization, and the wavefront aberration, which are all determined by the properties of the mode in the pinhole. The diameter of the pinhole should not be smaller than 0.6λ to make the transmittance sufficient. With a linearly polarized incident light, the diffraction wave is elliptically polarized, and the wavefront aberration is dominated by the astigmatic component. The method explicitly reveals the physical mechanism of pinhole diffraction. The analytic solutions are fast to compute, easy to analyze, and intuitively show the diffractive properties of the pinhole. The conclusions are significant for insight into the nature of pinhole diffraction and provide theoretical reference for analysis of numerical results and the design of PDI systems.

Generalized shift-rotation absolute measurement method for high-numerical-aperture spherical surfaces with global optimized wavefront reconstruction algorithm

In this paper, a generalized shift-rotation absolute measurement method is proposed to measure the absolute surface shape of high-numerical-aperture spherical surfaces. Based on the wavefront difference method, the high order misalignment aberrations can be removed from the measurements. Our generalized shift-rotation absolute measurement process only needs one rotational measurement position and one translational measurement position. A wavefront reconstruction method based on the self-adaptive differential evolution algorithm is proposed to calculate the Zernike polynomials coefficient a_i of the absolute surface shape W_test(x,y), the rotation angle Δθ, the translation δ_x along the x axis, and the translation δ_y along the y axis. The translation error and rotation error in other absolute measurement methods are avoided using our generalized shift-rotation absolute measurement method. Experimental absolute results of the test surface and reference surface are given and the difference of reference surface shapes between two testings in experiments is 0.12 nm root mean square.

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test

The deflectometry provides a feasible way for surface testing with a high dynamic range, and the calibration is a key issue in the testing. A computer-aided testing method based on reverse Hartmann test, a fringe-illumination deflectometry, is proposed for high-accuracy testing of reflective surfaces. The virtual "null" testing of surface error is achieved based on ray tracing of the modeled test system. Due to the off-axis configuration in the test system, it places ultra-high requirement on the calibration of system geometry. The system modeling error can introduce significant residual systematic error in the testing results, especially in the cases of convex surface and small working distance. A calibration method based on the computer-aided reverse optimization with iterative ray tracing is proposed for the high-accuracy testing of reflective surface. Both the computer simulation and experiments have been carried out to demonstrate the feasibility of the proposed measurement method, and good measurement accuracy has been achieved. The proposed method can achieve the measurement accuracy comparable to the interferometric method, even with the large system geometry calibration error, providing a feasible way to address the uncertainty on the calibration of system geometry.

Problems in the application of a null lens for precise measurements of aspheric mirrors

Problems in the application of a null lens for surface shape measurements of aspherical mirrors are discussed using the example of manufacturing an aspherical concave mirror for the beyond extreme ultraviolet nanolithographer. A method for allowing measurement of the surface shape of a sample under study and the aberration of a null lens simultaneously, and for evaluating measurement accuracy, is described. Using this method, we made a mirror with an aspheric surface of the 6th order (i.e., the maximum deviation from the best-fit sphere is 6.6 μm) with the parameters of the deviations from the designed surface PV=5.3  nm and RMS=0.8  nm. An approximation of the surface shape was carried out using Zernike polynomials {Z(n)(m)(r,φ),m+n≤36}. The physical limitations of this technique are analyzed. It is shown that for aspheric measurements to an Angstrom accuracy, one needs to have a null lens with errors of less than 1 nm. For accurate measurements, it is necessary to establish compliance with the coordinates on the sample and on the interferogram.

High-NA fiber point-diffraction interferometer for three-dimensional coordinate measurement

The numerical aperture (NA) and power of diffraction wave in point-diffraction interferometer (PDI) could significantly limit the measurement range of the system. A fiber point-diffraction interferometer with high NA is proposed for the measurement of absolute three-dimensional coordinates. Based on the single-mode fiber with submicron aperture, the diffraction wave with both high NA and high power is obtained, by which the achievable measurement range of the PDI can be extended. A double-iterative method based on Levenbery-Marquardt algorithm is proposed to determine the three-dimensional coordinates under measurement. Numerical simulation and comparison experiments have been carried out to demonstrate the accuracy and feasibility of the proposed PDI system, with both high measurement precision and nice repeatability achieved.

Roughness measurement and ion-beam polishing of super-smooth optical surfaces of fused quartz and optical ceramics

The main problems and the approach used by the authors for roughness metrology of super-smooth surfaces designed for diffraction-quality X-ray mirrors are discussed. The limitations of white light interferometry and the adequacy of the method of atomic force microscopy for surface roughness measurements in a wide range of spatial frequencies are shown and the results of the studies of the effect of etching by argon and xenon ions on the surface roughness of fused quartz and optical ceramics, Zerodur, ULE and Sitall, are given. Substrates of fused quartz and ULE with the roughness, satisfying the requirements of diffraction-quality optics intended for working in the spectral range below 10 nm, are made.

Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces

A point diffraction interferometer (PDI) with adjustable fringe contrast is presented for the high-precision testing of spherical surfaces. The polarizing components are employed in the PDI to transform the polarization states of the test and reference beams, and a good fringe contrast can be realized by adjusting the relative intensities of interfering waves. The proposed system is compact and simple in structure, and it provides a feasible way for high-precision testing of spherical surfaces with low reflectivity. The theory of the interferometer is introduced in detail, along with the properties of optical components employed in the system, numerical analysis of systematic error, and the corresponding calibration procedure. Compared with the testing results of the ZYGO interferometer, a high accuracy with RMS value about 0.0025λ is achieved with the proposed interferometer. Finally, the error consideration in the experiment is discussed.

Misalignment aberrations calibration in testing of high-numerical-aperture spherical surfaces

The calibration of misalignment aberrations is a key issue in the testing of high-numerical-aperture spherical surfaces, and it is hard to separate the high-order aberrations introduced by misalignment from the measured data. The traditional calibration method is still applicable in the case of only wavefront tilt, but no longer effective in the existence of defocus. A calibration technique based on the wavefront difference is proposed to calibrate the misalignment aberrations in the presence of wavefront defocus, and it can be carried out without foreknowledge of the spherical surface under test. With the wavefront difference method, the calibration needs two separate measurements to separate the high-order aberrations. Both the computer simulation and experiments with the ZYGO interferometer have been carried out to validate the proposed calibration technique, with the accuracies better than 0.0005λ RMS and 0.0010λ RMS achieved, respectively. The proposed calibration method provides a feasible way to lower the requirement on the adjustment in the measurement, while retaining good accuracy.

A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture

A new type of a reference spherical wave source (SWS) based on a single mode optical fiber with a narrowed down up to the submicrometer size exit aperture is proposed. It is intended for the precision point diffraction interferometers as a source of a reference wave. Systematic experimental errors which influence the measurement accuracy of the quality of the wave fronts generated by the SWSs are considered. Experimental data on wave front deformations are given. The combined root-mean-square (rms) wave deformation for a couple of the SWSs measured in a numerical aperture of NA=0.27 reaches the value of rms=0.36 nm that corresponds to rms=0.25 nm of a single SWS or about lambda2500 for the red He-Ne laser.

Wavefront error measurement of high-numerical-aperture optics with a Shack-Hartmann sensor and a point source

We developed a new, to the best of our knowledge, test method to measure the wavefront error of the high-NA optics that is used to read the information on the high-capacity optical data storage devices. The main components are a pinhole point source and a Shack-Hartmann sensor. A pinhole generates the high-NA reference spherical wave, and a Shack-Hartmann sensor constructs the wavefront error of the target optics. Due to simplicity of the setup, it is easy to use several different wavelengths without significant changes of the optical elements in the test setup. To reduce the systematic errors in the system, a simple calibration method was developed. In this manner, we could measure the wavefront error of the NA 0.9 objective with the repeatability of 0.003 lambda rms (lambda = 632.8 nm) and the accuracy of 0.01 lambda rms.