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Subaperture stitching test in combination of the reconfigurable optical null we proposed recently provides flexible solutions to various surfaces including convex aspheres and even aspheres of large aperture. However it is challenging for the stitching optimization to get the real surface error because the surface error is strongly coupled with misalignment-induced aberrations in near-null subaperture measurements. Aiming at this challenge, we first figure out the property of aberrations induced by misalignment of optical null or test surface. It shows that identical misalignment of the optical null introduces nearly identical aberrations to subapertures with different off-axis distances, while misalignment of the test surface introduces little aberrations to the central subaperture. The stitching algorithm is then proposed with focus on decoupling surface error and induced aberrations. The major step is to calibrate out the effect of misaligned near-null optics before stitching optimization by using the central subaperture measurement. We also present the through-the-back null test for the purpose of cross test. The axial distance is precisely monitored by a low coherence interferometer, which enables accurate determination of the spherical aberration component of surface error. Final experimental results show consistent spherical aberration obtained by stitching test and by the through-the-back null test. It is a big step towards instrumentation of subaperture stitching test for aspheres with rather big amount of misalignments in surface metrology practice. [ABSTRACT FROM AUTHOR]

With the research focus of subaperture stitching interferometry shifting from flat wavefronts to aspheric ones, a variety of algorithms for stitching optimization have been proposed. We try to category and compare the algorithms in this paper by their modeling of misalignment-induced subaperture aberrations which are of low orders. A simple way is to relate the aberrations to misalignment by linear approximation with small angle assumption. But it can not exactly model the induced aberrations of aspheres. In general, the induced aberrations can be fitted to free polynomials and then removed from subaperture measurements. However, it is at the risk of mixing up the surface error and the induced aberrations. The misalignment actually introduces different terms of aberrations with certain proportions. The interrelation is then determined through analytical modeling or ray tracing. The analytical model-based algorithm and the ray tracing-based algorithm both are tedious, aperture shape-related and surface type-specific. While the configuration space-based algorithm we proposed numerically calculates the surface height change under rigid body transformation, it is generally applicable to various surface types and different aperture shapes. Simulations and experiments are presented to compare the stitching results when different algorithms are applied to null cylindrical subapertures measured with a computer generated hologram. The configuration space-based algorithm shows superior flexibility and accuracy. [ABSTRACT FROM AUTHOR]

• Multi-scale measurement of DOEs based on stitching interference microscopy. • Inherited advantages of high resolution and high accuracy. • Extended lateral range of measurement to 10 mm scale via subaperture stitching. • Simultaneous correction of 6-dof scanning motion error for seamless data fusion. • Full aperture fabrication error map obtained with undercut effect verification. The development of diffractive optical elements (DOEs)enables fascinatingly compact design and chromatic aberration correction. Fabrication errors of DOEs include periodic pattern error, relief profile error and roughness which affect imaging quality and diffraction efficiency. Characterization of the DOE requires thus multi-scale measurement of the surface topography over the full aperture of 10 mm scale. This paper presents a method based on the white light interferometry in combination of subaperture stitching. Firstly, the principle of measurement and subaperture layout design is introduced. The measuring system is easily set up by integrating a scanning platform with the interference microscope. Subaperture stitching algorithm is developed based on the surface height change related to the scanning motion error. The slope of the relief profile is used to model the deviations of overlapping point pairs induced by lateral shift and rotation. Finally, the topography and fabrication error of a Fresnel lens surface are experimentally obtained and characterized over the full aperture through stitching of totally 67 subapertures. [ABSTRACT FROM AUTHOR]

Abstract: Subaperture stitching interferometry combined with a test plate is attractive for testing large convex aspheres, but the stitching algorithm is challenging because the aberrations induced by misaligned test surface or test plate are coupled with the surface figure. By relating the subaperture configuration to the overlapping deviations through ray trace and coordinate transformation, the subaperture misalignment is optimally recognized and corrected to give a minimal overlapping inconsistency in an iterative way. Allowing for misaligned test plate, we decompose the induced aberrations into three parts which are corrected by the stitching algorithm, removed in the form of the Zernike polynomials and left uncorrected as residuals. Finally we present simulation results of testing a convex aspheric mirror with a computer generated hologram which shows the algorithm successfully retrieves the surface figure with the test mirror or the hologram misaligned. [Copyright &y& Elsevier]

Abstract: Stitching test of large optical flats is still quite challenging. In this paper, aiming to reduce the 2nd order error accumulation effect, separation of the reference surface error from the subaperture measurements is proposed in stitching of large flats. The reference error is decomposed into power and astigmatism, residual Zernike polynomial surface and high frequency component, which are estimated or calibrated, respectively. The error separation procedure is then incorporated into the subaperture stitching algorithm. Finally experiments are presented to show the effect of error reductions in stitching test of a 600mm-aperture flat, with reference surface separated and verified by the factory report of the transmission flat. [Copyright &y& Elsevier]

Null test is preferred for measuring surface error of aspheres. However for large convex aspheres, it is challenging to fabricate larger null optics. Subaperture stitching is hence introduced but requires different null optics for subapertures of different off-axis distances. It gets easier by using replaceable computer generated holograms (CGHs). In this paper, a convex high-order even asphere is taken as an example and multiple CGHs are designed for null test of different subapertures. The same transmission flat and tilt carrier are used to facilitate alignment of CGHs. Disturbance orders of diffraction are confirmed to be separated by the tilt carrier without ghost interference. A configuration-based stitching algorithm is applied to successfully retrieve the full aperture surface error. The CGH substrate error is calibrated out before stitching optimization by measuring its transmitted wavefront with a high precision reference flat. Finally, the stitching result is verified by through-the-back null test of the same asphere. • Measurement of large convex aspheres with null subaperture stitching. • Different subaperture aberrations compensated by replaceable multiple CGHs. • Tilt carrier designed for separation of disturbance orders of diffraction. • CGH substrate error calibrated out before stitching optimization. • Experimental cross test of an even asphere with through-the-back test. [ABSTRACT FROM AUTHOR]

Large aperture acylinders are typical optical elements in synchrotron radiation systems and laser shaping devices. The manufacture of such ultra-precision optical elements requires ultra-precision measurement of the surface figure. The use of computer-generated hologram (CGH) customized for the acylindrical surface can only achieve a "one-to-one" test. Limited by the aperture of CGH, it also cannot meet the requirements for large aperture acylinders. In order to realize flexible test of large aperture acylinders with mild aspherical departure, a method of surface figure reconstruction for subaperture measurements under near-null test is proposed. It is based on ray tracing and rigid body transformation. By using a general CGH for cylindrical surface, near-null test for various acylindrical surfaces can be realized. Subaperture stitching test can overcome the problem of the limited CGH aperture which cannot meet the requirement of large aperture acylinders. Finally an elliptical cylindrical mirror with an aperture of 240mm (sagittal) × 350mm (tangential) is measured. And the cross test is realized by using a customized CGH to verify the validity and precision of the proposed method. [ABSTRACT FROM AUTHOR]

• Solve the problem of microstructure measurement on large-area curved substrates. • Propose a method of interferometric microscope combined with sub-aperture stitching. • Designed a dedicated platform for scanning along the sub-aperture space trajectory. • The topography measurement of the spiral groove on the hemisphere is completed. • Extended FOV with high resolution achieved by stitching 21 sub-images. Hemispherical bearings fabricated with helical grooves on the working surface show improved aerodynamic performance which depends to a large extent on the machining accuracy of the grooves. Topography measurement of the entire groove from macro to micro scale is thus important to evaluate the bearing performance. White light interference microscopy is widely used in topography measurement. However, subaperture stitching is necessary to extend the field of view (FOV) for large area measurement but limited to planar surfaces. This paper presents a method of interference microscopy combined with subaperture stitching. The long groove is divided into a series of subapertures with overlapping regions. Each subaperture meets the requirement of FOV and measurable slope limit of the microscope. We show that the helical curve is approximately located on a geodesic circle of the hemisphere. Accordingly a special fixture is designed with a rotary table to rotate the groove around the axis perpendicular to the geodesic circle. A four-axis scanning platform is integrated with the interference microscope. Based on the principle of minimal deviations in overlapping regions, six-degree-of-freedom motion error introduced in subaperture scanning is simultaneously corrected through an iterative stitching algorithm. It is experimentally verified by measuring a real part with helical grooves etched on a hemisphere bearing rotor. Complete high-resolution topography of the entire groove is reconstructed and the stitching map shows no overlap sliding effect, which is instructive for assessment of the machining error and further evaluation of the bearing performance. [ABSTRACT FROM AUTHOR]