Annular Subaperture Stitching Research Articles

Optical form measurement employing a tiltable line scanning, low coherence interferometer for annular subaperture stitching interferometry

This contribution presents experimental and simulation results of a tiltable line scanning low coherence interferometer applied for form measurement of spherical and aspherical objects with a diameter of up to 300 mm. The region of interest is sampled by multiple annular subapertures that are realigned employing stitching algorithms based on Cartesian- and Zernike polynomial fittings. The paper addresses common challenges in the reduction and modeling of displacement errors associated with the motion of the interferometric sensor between subaperture measurements and compares the topography deviations of the experimental results with those simulated by a Monte Carlo based model.

Form deviations caused by lateral displacement errors in annular subaperture stitching interferometry

Annular subaperture stitching interferometry (ASSI) is a common approach for the measurement of aspherical surfaces. A common obstacle of ASSI is the occurrence of lateral displacement errors when the sensor or specimen is repositioned between the subaperture measurements. Our contribution focuses on modeling of the statistical displacement errors. A virtual experiment is presented simulating the propagation of the displacement errors through a cumulative and a global stitching algorithm to the retrieved surface form. For the considered experimental setup, the uncertainty in lateral position depends on the positioning uncertainties of the employed motion system and the uncertainty in the absolute distance measurement between the sensor and specimen. The lateral displacement uncertainty is determined experimentally employing a calibratable lateral grating. Thus, it is traceable to the SI unit of the length (meter). The experimental results show that the lateral displacement errors may be modeled by a normal distribution, and the results of the virtual experiment indicate that the statistical lateral displacement errors transfer linear through the stitching procedure and also cause a normal distributed topography error. This enables the assignment of an expanded uncertainty to each individual sample point employing the Zernike polynomial expression of the topography measurement.

Validation of simultaneous reverse optimization reconstruction algorithm in a practical circular subaperture stitching interferometer

We demonstrate the validity of the simultaneous reverse optimization reconstruction (SROR) algorithm in circular subaperture stitching interferometry (CSSI), which is previously proposed for non-null aspheric annular subaperture stitching interferometry (ASSI). The merits of the modified SROR algorithm in CSSI, such as auto retrace error correction, no need of overlap and even permission of missed coverage, are analyzed in detail in simulations and experiments. Meanwhile, a practical CSSI system is proposed for this demonstration. An optical wedge is employed to deflect the incident beam for subaperture scanning by its rotation and shift instead of the six-axis motion-control system. Also the reference path can provide variable Zernike defocus for each subaperture test, which would decrease the fringe density. Experiments validating the SROR algorithm in this CSSI is implemented with cross validation by testing of paraboloidal mirror, flat mirror and astigmatism mirror. It is an indispensable supplement in SROR application in general subaperture stitching interferometry.

高陡度保形光学非球面环形子孔径检测方法

高陡度保形光学非球面环形子孔径检测方法

环形子孔径拼接检测的中心偏移误差补偿

环形子孔径拼接检测的中心偏移误差补偿

Aspheric subaperture stitching based on system modeling

Instead of various mathematical stitching algorithms, an aspheric subaperture stitching interferometric method relying on modern computer modeling technique is presented. Based on our previously reported non-null annular subaperture stitching interferometry (NASSI), a simultaneous reverse optimizing reconstruction (SROR) method based on system modeling is proposed for full aperture figure error reconstruction. All the subaperture measurements are simulated simultaneously with a multi-configuration model in a ray tracing program. With the multi-configuration model, full aperture figure error would be extracted in form of Zernike polynomials from subapertures wavefront data by the SROR method. This method concurrently accomplishes subaperture retrace error and misalignment correction, requiring neither complex mathematical algorithms nor subaperture overlaps. Experiment results showing the validity of SROR method are presented.

Measurement for off-axis aspheric mirror using off-axis annular subaperture stitching interferometry: theory and applications

An off-axis annular subaperture stitching interferometry (OASSI) is presented to test off-axis aspheric surfaces. In view of this, the relationship between misalignment and wavefront aberration is deduced with a strict theoretical analysis. The analytic result shows that the relative misalignment errors between the interferometer and the off-axis mirror tested will lead to complex wavefront aberrations in the measurement result other than the ordinary terms of piston, tilts, and power. Based on the analytic result, a suitable off-axis stitching algorithm is developed for stitching the off-axis subaperture. Both the numerical simulations and preliminary experimental results prove the potential of the proposed approach for the measurement of off-axis aspheric surfaces. As far as we know, this is the first time that OASSI has been used to test the off-axis aspheric surface.

Measurement of aspheric surface combining point diffraction interferometry and annular subaperture stitching

Point diffraction interferometry (PDI) combined with annular subaperture stitching is proposed for ultrahigh-accuracy measurements of aspheric surfaces. By adding an axial movement to the test optics in the PDI system, aspheric surfaces with large departures can be measured with high accuracy by stitching the annular measurement data of different axial positions. We examine the principle of PDI-based annular subaperture stitching and the stitching algorithm. Simulations and experiments demonstrate the feasibility and effectiveness of our proposed method. Our method retains the ultra-high accuracy of PDI while extending the vertical dynamic range of the interferometer, enabling nanometer or even subnanometer accuracy measurements of large-departure rotationally symmetric aspheric surfaces.

Non-null annular subaperture stitching interferometry for steep aspheric measurement.

A non-null annular subaperture stitching interferometry (NASSI), combining the subaperture stitching ideal and non-null test method, is proposed for steep aspheric testing. Compared with standard annular subaperture stitching interferometry (ASSI), a partial null lens (PNL) is employed as an alternative to the transmission sphere, to generate different aspherical wavefronts as the references. The coverage subaperture number would be reduced greatly for the better performance of aspherical wavefronts in matching the local slope of aspheric surfaces. In this way, relatively large overlapping areas can be obtained for adjustment errors correction while the error accumulation would be decreased. With the reverse optimization reconstruction (ROR) method for retrace error correction, the figure error of each subaperture can be retrieved accurately. Therefore, the testing accuracy and efficiency are thus increased. The dynamic test range is extended as well. A numerical simulation exhibits the comparison of the performance of the NASSI and standard ASSI, which demonstrates the high accuracy of the NASSI in testing steep aspheric. Experimental results of NASSI are shown to be in good agreement with those of the Zygo interferometer.

Measurement of aspheric surfaces using annular subaperture stitching interferometry based on an automatic positioning method: theory and application

A simple and effective automatic positioning method (APM) is proposed for the application of annular subaperture stitching interferometry in the stage of precision polishing. In the testing process, a series of optical path difference (OPD) data of subaperture are obtained since the interferometer is shifted relative to the tested aspheric surface. These OPD data are analyzed by the APM to get the key stitching parameters (e.g., aspheric departure) without a precision motion system. The basic principles of the APM are described. The performance of the method is simulated in some pertinent cases. Finally, we study the applicability of the proposed method to subaperture stitching tests of a hyperbolic mirror. The stitching results agree with the full-aperture test results. It demonstrates the validity and practicability of the proposed algorithm.

Measurement of aspheric surfaces using an improved annular subaperture stitching interferometry (IASSI)

An improved annular subaperture stitching interferometry (IASSI) is proposed for testing aspheric surfaces in the stage of precision polishing. It includes a reasonable stitching model and an automatic positioning operation. In the testing process, a series of optical path difference (OPD) data of annular subapertures is obtained as the interferometer is gradually shifted relative to the tested aspheric surface. Then these OPD data can be analyzed by the automatic positioning operation to get the key stitching parameters, and can be stitched together based on a reasonable mathematical model. To verify its validity, we study the applicability of the method to subaperture stitching tests of two conic aspheric surfaces. The stitching results agreed with the full-aperture test results.

Optimization stitching model for subaperture test of aspheric surfaces

Annular subaperture stitching interferometry (ASSI) is increasingly used for precision metrology of aspheric surfaces. The stitching model is a critical factor for stitching algorithms in ASSI. An optimized stitching model is proposed, which describes the alignment errors of adjacent subapertures based on an off-axis model and wave aberration theory. To keep the stitching errors from transmitting and accumulating, a simultaneous optimization algorithm is presented. The residual difference of overlapped regions of adjacent subapertures is utilized to evaluate the stitching accuracy. Finally, the comparative numerical simulations and experiments are carried out. It shows that the optimized stitching model has a better performance and validity.

Modified stitching algorithm for annular subaperture stitching interferometry for aspheric surfaces

In this paper, a modified stitching algorithm for annular subaperture stitching interferometry (ASSI) for aspheric surfaces is proposed. The mathematical model of adjustment error is deduced based on the wavefront aberration theory and rigid body movement; meanwhile, its basic principle and theory are introduced. The modified stitching algorithm is established based on the mathematical model and the simultaneous least-squares method, which keeps the error from transmitting and accumulating. So the adjustment error can be compensated efficiently. In addition, the standard deviation (SD) in the overlapped regions is used as the figure of merit to determine the stitching accuracy. Finally, simulations and experiments are given to verify the validity and rationality of the proposed algorithm. The results show that the introduced method is quite efficient.

环形子孔径拼接检测非球面中的数据处理和标定

环形子孔径拼接检测非球面中的数据处理和标定

环形子孔径拼接干涉检测非球面的建模与实验

环形子孔径拼接干涉检测非球面的建模与实验