Measurement and calibration of interferometric imaging aberrations

Iterative correction method of a retrace error in interferometry

In interferometer measurements, the inconsistency of the optical range through which the reference and test lights pass introduces a retrace error in the phase measurement. In this study, we propose an iterative retrace error correction method in interferometry. A black-box model is established based on the linear and squared relationships between the retrace error and the tilt of the testing surface. The error correction phase is obtained using the least-squares method; thereafter, the global tilt is determined to iteratively correct the retrace error. The root mean square (RMS) of the residuals was > 3.2 × 10^-5λ, >6.4 × 10^-3λ, and >1.4 × 10^-3λ in the simulation, experimentally computed retrace error correction in the planar measurement, and spherical measurement, respectively, proving that the retrace error can be effectively corrected.

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

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.

Interferometer reference error suppression by the high-overlapping-density phase-stitching algorithm

The subaperture stitching interferometer is a flexible testing device that measures either high-numerical-aperture or large aperture optics without the requirement of additional auxiliary optics. In the measurement, the interferometer reference optics error can contaminate the stitched phase of the complete tested optics and reduce measurement accuracy. We propose high-overlapping-density subaperture stitching interferometry (HOD-SSI) to reduce the impact of reference optics errors on the stitched phase. The tested optics surface deformation phase is determined by averaging the multiple subaperture measurements taken at different rotational angles. Simulation and experiment show that HOD-SSI can effectively reduce the stitched phase errors due to the static reference optics errors.

Measurement improvement by high overlapping density subaperture stitching interferometry

The vibration-modulated subaperture stitching interferometer acquires the interferogram on the fly dynamically. With its highly improved measurement throughput, we applied the device for high overlapping density subaperture stitching interferometry to acquire hundreds of overlapping subapertures in a single phase stitching measurement. The averaging effect of the high overlapping density stitching interferometer is discussed. In the experiment, the proposed high overlapping density stitching interferometer is also proved to reduce measurement uncertainty and improve measurement quality effectively.

Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing

Calibration for misalignment aberrations is one of the challenges in non-null interferometric aspheric testing. The high-order misalignment aberrations are especially difficult to distinguish from the rest of the testing system. The traditional calibration method removing the first four terms from the Zernike coefficients of the test wavefront is obviously inaccurate. Computer-aided alignment is considered to be an effective method; however, it is less practical due to its dependency on mechanical or manual adjustment, as are other common methods. A practical and accurate calibration method based on system modeling is proposed in this paper for misalignment aberrations' removal. In this work, actual misalignments, which are calculated from five selected low-order aberrations of the test wavefront in the experiment, are simulated in the model to predict all misalignment aberrations by ray tracing. These aberrations then are removed by a simple wavefront data subtraction. The method depends on neither a precise adjusting mechanism nor a troublesome manual adjustment. Experimental results showing feasibility and repeatability of the proposed method are presented.

Novel compact dual-band LOROP camera with telecentricity

We report a new dual band compact oblique photography camera (LC11) that is the first to benefit from the incorporation of telecentricity. LC11 has a common front end F/6.6 telescope with 280 mm in aperture that forms its electro-optical (EO, F/7.5) and MWIR (F/5.6) modules. The design allows a substantial reduction in volume and weight due to i) the EO/MWIR compensator and relay lens groups arranged very close to the primary mirror (M1), and ii) light-weighted M1 and SiC main frame (MF) structure. Telecentricity of up to 2 and 0.2 degrees for the EO and MWIR modules, respectively, is achieved by balancing optical power among all lenses. The initial field test shows 0.32 ± 0.05 (EO)/0.20 ± 0.06 (MWIR) in measured MTF at 28 (EO) and 13 (MWIR) cycles/mm in target frequency, and an improved operability with a greater reduction in operational volume and mass than other existing LOROP cameras.

Generalized data reduction approach for aspheric testing in a non-null interferometer

Data reduction in non-null tests is difficult due to the presence of retrace error. We propose a simple yet effective data reduction approach for aspheric testing in a non-null interferometer. The new approach gives figure error of the aspheric by just subtracting the theoretical wavefront and first-order errors from the real wavefront obtained in the non-null interferometer. Precise prediction of the theoretical wavefront can be achieved by accurate calibration of the partial compensation system. The approach can be considered a generalization of the traditional data processing method in null tests, and errors that may affect its accuracy are discussed. A set of experiments have been carried out to demonstrate its validity and feasibility.

Diffraction effects for interferometric measurements due to imaging aberrations

Aspheric surfaces are often measured using interferometers with null correctors, either refractive or diffractive. The use of null correctors allows high accuracy in the measurement, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations couple with diffraction effects and limit the accuracy of the measurements, causing high frequency features in the surface under test to be filtered out and creating artifacts near boundaries, especially at edges. We provide a concise methodology for analyzing these effects using the astigmatic field curves to define the aberration, and showing how this couples with diffraction as represented by the Talbot effect and Fresnel edge diffraction. The resulting relationships are validated with both computer simulations and direct measurements from an interferometer with CGH null corrector.

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.

Absolute interferometric test of aspheres by use of twin computer-generated holograms

A complete absolute interferometric test of axially symmetric aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The aberrations of the spherical auxiliary wave are measured absolutely with either a spherical mirror or an absolute test for Fresnel zone plates. Thus the two types of aberration inherent in the CGH can be identified and separated from each other. The errors of the spherical wave can be transferred to those of the aspherical wave. Two different methods thatuse Twin-CGHs for absolute testing of aspheric surfaces are described. Test procedures are explained, equations are derived, and experimental results are presented. A mutual comparison of the two results and a comparison with the established N-position rotation test are given.

High-precision shape measurement by white-light interferometry with real-time scanner error correction

White-light interferometric techniques allow high-precision shape measurement of objects with discontinuous structures by detecting the peak of the coherence envelope. These techniques assume a specific change in the optical path difference (OPD) between the interfering beams; however, the scanning device effecting that change often introduces OPD errors that are carried over to the measurements. We present a technique for measuring OPD changes from the collected interference fringes during each measurement. Information about the scan is directly fed into the algorithm, which compensates for the errors, resulting in improved measurement accuracy. The method corrects not only the scanner errors but also slowly varying vibrations. In addition, this technique can be easily adapted to any existing low-coherence interferometer because no large data storage or postprocessing is required.