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Applying the iterative stitching algorithm, we demonstrate the power of subaperture testing through experiments. Naturally the algorithm applies to flats, spherical or aspheric surfaces. We first apply it to a silicon carbide flat mirror with larger aperture than the interferometer's. The testing results help to obtain a high-precision mirror through five iterations of ion beam figuring. The second experiment is 37-subaperture testing of a large spherical mirror. Good consistence is observed between the stitching result and the full aperture test result using a Zygo interferometer. Finally we study the applicability of the algorithm to subaperture testing of a parabolic surface. The stitching result is consistent with the auto-collimation test result. Furthermore, the surface is tested with annular subapertures and also retrieved by our algorithm successfully.

Abstract: We present a method for optical wavefront measurement using phase retrieval with subaperture stitching method in situations where detected intensity patterns are undersampled or where the limit of aberrations is determined by the largest spot size overfilling the detector array. In this technique we use a smaller moving subaperture to produce a number of adequately sampled intensity patterns captured by the detector located near the focus plane. These patterns are then used to retrieve the full-aperture wavefront through an optimization phase retrieval algorithm. The relationship between the optimization parameters of moving subaperture and the support information is given. Then expressions for the gradient of an error metric with respect to the optimization parameters are presented. An experimental setup used to measure the reflected wavefront of a concave mirror by employing this method is arranged. The experimental results indicate that the phase retrieval results are in excellent agreement with that obtained with interferometer, which confirms the validity of this method. [Copyright &y& Elsevier]

Abstract: We present a method for calibrating the position error of phase retrieval with transverse translation diversity in optical wavefront in situation where the position error sharply influences algorithm precision. This method involves testifying that the essence of the position error in phase retrieval is the translation in frequency domain and the minimum of iterative error against position error reaches when there is no position error. Then the least square method is used for fitting the relationship between the iterative error and the assumed position error in polynomial function. The computer simulations used to prove the validity of this method are described. The results indicated that this method can calibrate the position error to approximately 1/500mm which nearly has no influence on the phase retrieval. [Copyright &y& Elsevier]

Abstract: Phase retrieval technology for off-axis ellipsoid surface measurement with a high dynamic range algorithm is proposed in this paper. A high dynamic range algorithm (HDRA) for phase retrieval is proposed. We proved the validity of it in simulation. Then the HDRA is used to measure an off-axis ellipsoid. The measurement setup was established and the HDRA was applied to retrieve the surface shape of the off-axis ellipsoid. The experimental results show that the phase retrieval results are good agreement with that obtained by interferometer, which confirms the validity of this method. [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]

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: In an ion-beam figuring (IBF) process, the desired material removal, which is specified to the contour algorithm to calculate dwell time, decides the calculated process time and the resulted residual surface figure error. Usually, an IBF process with more removal consumes a longer process time, although the resulted residual error is smaller, whereas an IBF process with less removal needs only a shorter process time, but the resulted residual error is greater. Therefore, in order to balance the process time and the residual error, an optimum removal should be determined. In this study, the characteristic relationship between the process time and the residual error on different specified removals is investigated first. The investigation shows that for smaller removals, the residual error decreases rapidly while the process time increases slowly, and for larger removals, the process time increases rapidly without much decrease in residual error. This characteristic makes the figure-prediction curve (process times vs. rediual errors (RMS)) often in the shape of the letter “L”. Therefore, the optimum removal can be determined at the corner of the curve. Finaly, experiments are performed to verify the proposed method. [Copyright &y& Elsevier]