Freeform Surface Testing Research Articles

Absolute testing of rotationally symmetric surfaces with computer-generated holograms.

Extremely high accuracy is demanded for optics working at very short wavelength. Interferometric testing of optical aspheres or freeform surfaces requires null optics, typically computer-generated holograms (CGHs), to balance the wave aberrations. The measurement uncertainty is primarily limited by the accuracy of the test wavefront, which is predominantly influenced by the CGH and the interferometer optics. Absolute testing is fundamental to achieving accuracy much higher than that of the test wavefront through error separation. This paper presents a method for absolute testing of rotationally symmetric surfaces with CGH null optics. The basic assumption is that the off-axis hologram fabricated by raster scanning beam writing has negligible error of rotationally symmetric component due to pattern error of the CGH. Consequently, the wavefront error contributed by the CGH and the transmission flat can be completely separated from the absolute surface shape by combining the N-position method and the shift-rotation method. A theoretical model for absolute testing is proposed under the assumption. Experimental cross test is then presented to validate the method with sub-nanometer uncertainty. The assumption is further confirmed by characterizing the fabrication error of the hologram structures using a white light interferometer. Finally, the effect of noise, translation error, rotation error and eccentricity of rotation on the absolute testing is analyzed.

Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching.

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than λ/30 (λ=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 λ (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

On-axis deflectometric system for freeform surface measurement.

We propose an on-axis deflectometric system for the accurate measurement of freeform surfaces with large slope ranges. A miniature plane mirror is attached on the illumination screen to fold the optical path and achieve the on-axis deflectometric testing. Due to the existence of the miniature folding mirror, the deep-learning method is applied to recover the missing surface data in a single measurement. Low sensitivity to the calibration error of system geometry and high testing accuracy can be achieved with the proposed system. The feasibility and accuracy of the proposed system have been validated. The system is low in cost and simple in configuration, and it provides a feasible way for the flexible and general testing of freeform surfaces, with a significant potential of the application in on-machine testing.

Design and error calibration of an on-axis deflectometric microscope system.

An on-axis deflectometric microscope system (ODMS) is proposed for the microscopic surface measurement with high accuracy and a large slope dynamic range. To reduce the geometry sensitivity, a beam splitter is employed to build the coaxial configuration among the illumination screen, camera, and tested sample, which facilitates the calibration of system geometrical parameters. Due to the small working distance, the system model miscalibration in the model-ray-tracing-based "null" testing could cause obvious geometrical aberrations. In this paper, the geometrical aberrations due to the system model miscalibration are analyzed, and the corresponding calibration method based on computer-aided reverse optimization is applied to achieve accurate measurement. In addition, the systematic error introduced by the system components in the ODMS are also discussed. Both the simulation and experiment have been carried out to demonstrate the feasibility and high accuracy of the proposed measurement method. The proposed system is compact in structure, large in measurable slope range, and high in spatial resolution, providing a viable metrological tool for the microscopic testing of various freeform surfaces, microstructural elements, and micro-devices.

Tilted Wave Fizeau Interferometer for flexible and robust asphere and freeform testing

Tilted Wave Interferometry (TWI) is a measurement technique for fast and flexible interferometric testing of aspheres and freeform surfaces. The first version of the tilted wave principle was implemented in a Twyman-Green type setup with separate reference arm, which is intrinsically susceptible to environmentally induced phase disturbances. In this contribution we present the TWI in a new robust common-path (Fizeau) configuration. The implementation of the Tilted Wave Fizeau Interferometer requires a new approach in illumination, calibration and evaluation. Measurements of two aspheres and a freeform surface show the flexibility and also the increased stability in both phase raw data and surface measurements, which leads to a reduced repeatability up to a factor of three. The novel configuration significantly relaxes the tolerances of the imaging optics used in the interferometer. We demonstrate this using simulations on calibration measurements, where we see an improvement of one order of magnitude compared to the classical Twyman-Green TWI approach and the capability to compensate higher order error contributions on the used optics.

Feature-based characterization and extraction of ripple errors over the large square aperture.

Freeform surfaces play an important role in modern optical systems with compactness and better performance. The fabrication tools tend to impart a structured signature on optical surfaces, called ripple errors, during the freeform surface manufacturing process. The description and extraction of ripple errors for freeform surface fabrication and testing have attracted extensive attention. In this paper, we develop a fast and accurate method to describe ripple errors for the large aperture based on Fourier model coupling. The polynomial expression is transformed into Fourier series form and surface errors are reconstructed by frequency feature extraction combining with the least square method. The high accuracy and efficiency of the proposed method for representing and filtering ripple errors consuming little computer memory are demonstrated using real experimental data. The proposed method offers a robust and powerful tool not only suitable for surface error characterization but also for image filtering and analysis.

Null-screen design for highly freeform surface testing.

A new alternative to calculate the null-screen for highly freeform or complex surfaces for any desired pattern to be observed on the detector is presented. To validate the proposed method, we used the Zernike polynomials to design complex surfaces with sagittas greater or equal to 40 mm, and peak to valley greater or equal to 30 mm, between the used surface and the best fit sphere. The freeform surfaces were fabricated using a 3D printer and a five-axis CNC machine. With the proposed method we can calculate the image that will be observed over the detector for any null-screen and any freeform surface that want to be analyzed. The results showed that the proposal works very well for extremely fast complex freeform surfaces (with slopes ≤ 80°), obtaining an error smaller than 0.66% in PV and 0.36% in rms in sagitta differences.

Interferometric measurement of freeform surfaces using irregular subaperture stitching

Irregular subaperture stitching interferometry (ISSI) is proposed for non-null optical freeform surface testing. Compared with circular and annular subapertures, irregular subapertures have a better performance in matching the locally resolvable interferograms due to the rotational asymmetry of freeform surfaces. A modified multi-aperture simultaneous reverse optimization reconstruction algorithm is employed for the subaperture stitching, allowing not only non-complementary subapertures but also no subaperture overlaps. Numerical simulations with error analyses display the accuracy of our method. Experiments showing the effectiveness of the ISSI are presented by testing a Φ20 mm biconic surface with cross-validation.

A flexible angle compensation method for freeform surface testing based on tip/tilt mirror

Freeform surfaces with large asphericity are generally difficult to test. We propose a novel interferometric method based on tip/tilt mirror (TTM) suitable for such surfaces. The incident ray directions are dynamically compensated in several dimensions by the TTM, to control the incident angles of the rays at locations where the local surface profile is steep. Therefore, the tilt angle depend on the local gradients of the tested surface. When the incident angles on all sub-zones are controlled, we can obtain a series of lower density interferograms based on which the surface profile can be determined. The compensating range in our method is analyzed, and the largest measurable slope is 2.8°based on 20-mrad tilt angle and 3.3 F-number. Besides, the influence of the compensating precision of the TTM is simulated, and the compensation error can be ignored when its precision is under 40 μrad. The precision and efficiency of this method were proved by a series of tests.

Point-cloud noncontact metrology of freeform optical surfaces.

In this paper, we demonstrate the development of a point-cloud metrology method for the noncontact, high resolution, high precision testing of freeform surfaces. The method leverages swept source optical coherence tomography together with a common-path setup in the sample arm configured to mitigate the axial jitter caused by scanning and environmental perturbations. The lateral x-y scanning field was also rigorously evaluated for the sampling step, linearity, straightness, and orthogonality. Based on the finely engineered system hardware, a comprehensive system model was developed capable of characterizing the vertical displacement sensitivity and lateral scanning noise. The model enables predicting the point-cloud surface-metrology uncertainty map of any freeform surface and guiding the selection of optimum experimental conditions. A system was then assembled and experimentally evaluated first with flat and spherical standards to demonstrate the measurement uncertainty. Results of measuring an Alvarez freeform surface with 400-µm peak-to-valley sag show 93 nm (< λ/14) precision and 128 nm (< λ/10) root-mean-square residual from the nominal shape. The high resolution measurements also reveal mid spatial frequency structures on the test part.

Accurate calibration of geometrical error in reflective surface testing based on reverse Hartmann test.

The deflectometry provides a powerful metrological technique enabling the high-precision testing of reflective surfaces with high dynamic range, such as aspheric and freeform surfaces. In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, the calibration of system geometry is required to achieve "null" testing. However, the system miscalibration can introduce a significant systematic error in the testing results. A general double-step calibration method, which is based on the low-order Zernike aberration optimization and high-order aberration separation, is proposed to separate and eliminate the geometrical error due to system miscalibration. Both the numerical simulation and experiments have been performed to validate the feasibility of the proposed calibration method. The proposed method provides a general way for the accurate calibration of system geometrical error, avoids the over-correction and is feasible for the testing of various complex freeform surfaces.

Review of optical freeform surface representation technique and its application

Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform surface has been a fundamental and key research topic in recent years. Moreover, it has a close relationship with other aspects of the design, manufacturing, testing, and application of optical freeform surfaces. Improvements in freeform surface representation techniques will make a significant contribution to the further development of freeform optics. We present a detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences. Additionally, we analyze the future trends of optical freeform surface representation techniques.

Advances in the design of freeform systems for imaging and illumination applications

Freeform optical surfaces are getting increasingly popular in imaging and illumination systems. A review of recent advances in the optimization, surface description and testing of freeform surfaces is given. We compare the tools being developed for imaging as well as illumination systems and shown, that while the key problems are similar the current tools and methods are often specific for the application. In both fields we will give an impression about the current status and the main remaining problems associated with freeform systems. Moreover we present current research in the area of phase space optics and recent new methods for interferometric testing of freeform surfaces.

Fast and Flexible Non-Null Testing of Aspheres and Free-Form Surfaces with the Tilted-Wave-Interferometer

The Tilted-Wave-Interferometer (TWI) is a non-null, full-field interferometric measuring technique for aspheric and free-form surfaces with a new degree of flexibility. The interferometer uses a set of tilted wavefronts to locally compensate the deviation of the surface under test from its spherical form. Since it is a non-null technique, there is no need for costly compensation optics. The measurement data acquisition is highly parallelized, leading to a short measurement time in the region of few seconds, by simultaneously achieving a high lateral resolution. The unique combination of these characteristics makes the TWI a perfect candidate for the integration into the process chain of aspheric and free-form surface manufacturing.

Limits of diffractometric reconstruction of line gratings when using scalar diffraction theory

We study errors that occur in geometry and phase reconstruction when using scalar diffraction theory in line gratings with periods below 10 μm. The application of those gratings in so-called computer-generated holograms in high-precision interferometric testing of aspheres and free-form surfaces imposes high demands on the generated phase, leading to error budgets in the range of λ/100. Using rigorous simulations as references, we identify the limits where scalar diffraction theory fails to accurately describe grating geometries and identify the significant error mechanisms.

非球面光学元件的面形检测技术

In this paper,several aspheric testing methods for different fabrication steps and their new research progresses are introduced. Especially,we emphasis on the testing methods for precision polishing step,in which subaperture stitching interferometric testing and non-null partial compensating testing method are described in detail. Moreover,several combined interferometric testing methods which perform well in measuring large and steep aspherics are introduced. In addition,we provide a general description of free-form surface testing. The further development of aspheric surface testing methods is also prospected.

Interferometry using binary holograms without high order diffraction effects

We describe a technique for a phase-stepping interferometer based on programmable binary phase holograms, particularly useful for optical testing of aspheric or free-form surfaces. It is well-known that binary holograms can be used to generate reference surfaces for interferometry, but a major problem is that cross talk from higher diffraction orders and aliasing can reduce the fidelity of the system. Here, we propose a new encoding technique which improves the accuracy of the technique and demonstrate its implementation using a binary liquid crystal spatial light modulator.