Dual-wavelength Fourier ptychographic microscopy for topographic measurement.

Topographic measurements of micro- or nanostructures are essential in cutting-edge scientific disciplines such as optical communications, metrology, and structural biology. Despite the advances in surface metrology, measuring micron-scale steps with wide field of view (FOV) and high-resolution remains difficult. This study demonstrates a dual-wavelength Fourier ptychographic microscopy for high-resolution topographic measurement across a wide FOV using an aperture scanning structure. This structure enables the capture of a three-dimensional (3D) sample's scattered field with two different wavelength lasers, thus allowing the axial measurement range growing from nano- to micro-scale with enhanced lateral resolution. To suppress the unavoidable noises and artifacts caused by temporal coherence, system vibration, etc., a total variation (TV) regularization algorithm is introduced for phase retrieval. A blazed grating with micron-scale steps is used as the sample to validate the performance of our method. The agreement between the high-resolution reconstructed topography with our method and that with atomic force microscopy verified the effectiveness. Meanwhile, numerical simulations suggest that the method has the potential to characterize samples with high aspect-ratio steps.

Single-test Ritchey-Common interferometry.

The Ritchey-Common test is widely adopted to measure large optical flats. The traditional Ritchey-Common test eliminates the defocus error with multiple tests by changing the position of the mirrors, which suffers from cumbersome steps, poor repeatability, coupled system error, extra mirror deformation, and potential overturning. The above problems increase the test time, decrease the reliability and accuracy, increase the test cost, and threaten manufacturing safety. We propose a single-test Ritchey-Common interferometry to avoid the obligatory position change in the traditional method. A sub-aperture of test flat is directly measured by a small-aperture interferometer before the test, which is easy to implement, to replace the extra system wavefront measurement in different positions. The defocus is calculated in sub-aperture at exactly the same position as the full-field measurement without the position change, then the surface form under test can be obtained with accurate optical path modeling. Measurement experiments for 100 mm and 2050 mm aperture flats were performed to demonstrate the feasibility of this method. Compared with a direct test in a standard Zygo interferometer, the peak to valley (PV) and root mean square (RMS) errors were 0.0889 λ and 0.0126 λ (λ=632.8 nm), respectively, which reaches the upper limit of accuracy of the interferometer. To the best of our knowledge, this is the first proposal of the Ritchey-Common test that can eliminate the defocus error and realize high accuracy measurement in a single test. Our work paves the way for reliable and practical optical metrology for large optical flats.

Interferometric measurement of the radius of curvature based on axial displacement from a confocal position and corresponding defocus wavefront.

The radius of curvature (R) is a fundamental parameter of spherical optical surfaces. The measurement range of the widely adopted traditional interferometric method is limited by the length of the precision linear guide rail carrying the measured surface from the cat's eye to the confocal position, and the test result is vulnerable to airflow and vibration in the test environment. An interferometric method is proposed for the radius measurement of spherical surfaces based on a small axial moving distance and the corresponding defocus wavefront to eliminate the dependence on a long guide rail and extend the measuring range. To eliminate the influence of the test environment and calculate the R, a defocus transform algorithm is proposed to instantaneously measure the defocus wavefront from a single interferogram. Numerical simulations theoretically demonstrate that there is no limit to the measurement range of this method because only a short distance of the measured mirror must be moved. A spherical mirror with a radius of curvature of 101.6087 mm is experimentally tested, and the relative measurement error is 0.037%. This method can achieve high accuracy for optical shops and greatly increase the measurement range of the interferometric method without additional equipment.