A null lens moving back and forth relative to a point source can generate variable spherical aberration for flexible test of aspheres. Different from the previous methods, variable spherical aberration null theory was developed by us to optimize the null lens. The optimized null was a plano-convex singlet containing a high order even asphere. Its attractive advantages are the simple structure and the broad range of testable surfaces. Most concave prolate conic and near conic surfaces with k∙R value varying between 0 and about 70000mm and with smaller relative aperture than that determined by each k∙R value can be tested. The testable asphericity range is between 0 and about 230λ. Relations among these testable surfaces were revealed as different groups of equidistant surfaces. To explicitly show the ability of the null, the measurable surfaces range map that contains all parameters defining a conic surface was offered. A practical near-null test system using this null was established. Alignment, near-null data processing, and error sources are analyzed in detail. To verify the broad testable surfaces range, three surfaces with widely varying amounts of asphericity were tested. Cross tests were provided to verify the test system accuracy.

Near-null interferometry using an aspheric null lens generating a broad range of variable spherical aberration for flexible test of aspheres

A novel radius of the curvature measurement method for optical spherical surfaces using absolute interferometry is proposed A measurement setup is designed and built around a common-path Fizeau interferometer The cavity length (volume of air between reference and tested surfaces) can be measured by the absolute wavelength tuning interferometry An interconnection of data from three different tunable laser diodes (central wavelengths 780, 785 and 852 nm) allows us to measure the cavity length with uncertainty from tens to hundreds of nanometres Once the reference radius of curvature is known/measured/calibrated, the radius of surface under test can be computed applying the value of the cavity length The radius of curvature is measured directly in confocal position of the interferometer with relative precision of about 10 ppm Moreover, unlike standard radius measurement by interferometry, the uncertainty of the introduced method can be optimized by selecting a suitable transmission sphere In the paper, the method is described, tested, and verified by measuring several specimens featuring different radii of curvature The results are analysed and furthermore compared to other measurement device

Absolute interferometry for fast and precise radius measurement

Aspheric surface parameters, including vertex radius of curvature, conic constant, and high-order aspheric coefficients, decide the optical properties of aspheric surfaces. The measurement of aspheric surface parameter errors (SPEs) is a substantial issue for the fabrication of aspheric surfaces. Interferometry is a mature high-accuracy method in aspheric surface figure error measurement, but challenges still exist in the measurement of SPEs for high-order aspheric surfaces or convex aspheric surfaces. We propose an interferometric measurement method for high-order aspheric SPEs based on a virtual-real combination iterative algorithm (VRCIA). We also propose a recommended measurement system including a partial compensation interferometer to obtain the partial compensated wavefront and a laser differential confocal system to obtain the best compensation distance for calculating SPEs through the VRCIA. A high-order convex aspheric surface is measured to demonstrate the feasibility of the method. The relative accuracy of vertex radius of curvature error, conic constant error and fourth-order aspheric coefficient error can reach 0.025%, 0.095% and 3.02%, respectively.

Interferometric measurement of high-order aspheric surface parameter errors based on a virtual-real combination iterative algorithm

Surface parameters, such as vertex radius of curvature and conic constant, are used to describe the shape of an aspheric surface. Surface parameter errors (SPEs) are deviations affecting the optical characteristics of an aspheric surface. Precise measurement of SPEs is critical in the evaluation of optical surfaces. In this paper, a partial compensation interferometry measurement system for SPE of a conicoid surface is proposed based on the theory of slope asphericity and the best compensation distance. The system is developed to measure the SPE-caused best compensation distance change and SPE-caused surface shape change and then calculate the SPEs with the iteration algorithm for accuracy improvement. Experimental results indicate that the average relative measurement accuracy of the proposed system could be better than 0.02% for the vertex radius of curvature error and 2% for the conic constant error.

Partial compensation interferometry measurement system for parameter errors of conicoid surface.

Aspherical surfaces can provide significant benefits to a wide variety of optical systems, but manufacturing high-precision aspherical surfaces has historically been limited by the ability to measure them. Null testing has always been the ideal method in aspherical measurement. However, in many cases, it is hard to realize null testing for complex surfaces, especially for convex surfaces in complicated forms. In this paper, we propose a hybrid compensation method combining a spherical mirror and a computer generated hologram (CGH) to achieve the null testing of the convex aspherical surface. Firstly, we introduce our self-developed mathematical models in the hybrid compensation method, including optics alignment model, distortion correction model and spherical surface error removing model. Then the performance of our proposed method is analyzed by a null testing experiment of an off-axis convex ellipsoid mirror. The experimental result shows that the proposed method can accomplish the hybrid compensation testing of convex aspherical surfaces effectively, and it can also bring much to the application of our method in convex aspherical surface testing.

Experimental study on hybrid compensation testing of an off-axis convex ellipsoid surface.

Vertex radius of curvature (VROC) is an important shape parameter used to determine the properties of an optical aspheric surface. Precise measurement of VROC error is critical for manufacturing and aligning optical aspheric surfaces. This paper introduces VROC error measurement of aspheric surface by using slope asphericity with partial compensation interferometry. VROC error and the decoupled surface figure error (SFE) can be simultaneously measured. Experimental results indicate that the method exhibits relative measurement accuracy of 0.01% when the nominal VROC is 889 mm, and the decoupled SFE error is λ/10 of the peak-to-valley value.

Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry.

Measurement of aspheric and freeform surfaces remains challenging due to the various shapes of the surface under test (SUT), especially when the SUT has a large aperture and strong deviation from the spherical surface. This paper proposes a two-step carrier-wave stitching method to enlarge the measurement bandwidth of a digital Moire interferometry. Then, measurements of aspheric and freeform surfaces with a standard spherical interferometer without a phase-shifting mechanism are demonstrated. Experimental results with a root-mean-square repeatability of better than 1/200λ present good consistency to UA3P contact measurement results. Further simulation results with different residual wavefronts confirm measurement accuracies of peak-to-valley value of 10−3λ. The method is effective for large residual wavefronts and thus has potential for flexible measurement of aspheric and freeform surfaces.

Two-step carrier-wave stitching method for aspheric and freeform surface measurement with a standard spherical interferometer.

The invention discloses a digital moire fringe phase extraction method combining wavelet analysis and low pass filtering and belongs to the optical measurement and image processing technology field. The method is characterized by using actual interference graph and phase-shift virtual interference graph moire synthesis to generate a phase shift moire composite graph, and using low pass filtering and combining a phase shift interferometry to extract a preliminary result of a moire fringe phase; according to a virtual interference wavefront acquired by a virtual interferometer, combining a filtering radius of a filter to determine a distribution center and a range of a low pass filtering error in the preliminary result of the moire fringe phase; after a low pass filtering error range and the center are positioned, carrying out wavelet decomposition on the preliminary result containing the low pass filtering error; and according to the positioned error center and the range, processing a wavelet coefficient so that the filtering error can be removed, according to an approximation coefficient and a processed wavelet coefficient, carrying out reconstruction and acquiring the moire fringe phase where the low pass filtering error is removed, which means that a measurement range of digital moire interference measurement is expanded.

Digital moire fringe phase extraction method combining wavelet analysis and low pass filtering

The invention relates to a digital Moire fringe phase extraction method based on nonlinear optimization, belonging to the technical field of optical measurement and image processing. According to the method, a Moire synthesis light intensity distribution graph mathematical model is established, a fringe phase is used as an optimization variable, with actual Moire synthesis graph light intensity distribution as an optimization target, phase continuity is taken as a boundary condition, through nonlinear optimization calculation, the light intensity distribution of the mathematical model is equal to the light intensity distribution of an actual Moire synthesis graph, and the fringe phase at that time is the Moire fringe phase of the actual Moire synthesis graph. According to the method, the Moire fringe phase can be obtained without low pass filtering, a filtering error in a spectrum aliasing condition can be avoided, and a phase measurement precision is improved.

Digital Moire fringe phase extraction method based on nonlinear optimization

Digital Moiré based transient interferometry (DMTI) is an effective non-contact testing methods for optical surfaces. In DMTI system, only one frame of real interferogram is experimentally captured for the transient measurement of the surface under test (SUT). When combined with partial compensation interferometry (PCI), DMTI is especially appropriate for the measurement of aspheres with large apertures, large asphericity or different surface parameters. Residual wavefront is allowed in PCI, so the same partial compensator can be applied to the detection of multiple SUTs. Excessive residual wavefront aberration results in spectrum aliasing, and the dynamic range of DMTI is limited. In order to solve this problem, a method based on wavelet transform is proposed to extract phase from the fringe pattern with spectrum aliasing. Results of simulation demonstrate the validity of this method. The dynamic range of Digital Moiré technology is effectively expanded, which makes DMTI prospective in surface figure error measurement for intelligent fabrication of aspheric surfaces.

Yifeng Tan

Papers

Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry.

Two-step carrier-wave stitching method for aspheric and freeform surface measurement with a standard spherical interferometer.

Digital moire fringe phase extraction method combining wavelet analysis and low pass filtering

Digital Moire fringe phase extraction method based on nonlinear optimization

Digital Moiré based transient interferometry and its application in optical surface measurement