Testing Aspheric Surfaces Research Articles

Triple Complex Phase Computer-Generated Holograms for Aspherical Surface Testing in Extreme Ultraviolet Lithography

Triple Complex Phase Computer-Generated Holograms for Aspherical Surface Testing in Extreme Ultraviolet Lithography

Mixed compensation for the testing of large convex aspheres

Since the testing of convex mirrors often requires a compensator with a larger aperture than the mirror under test, this is undoubtedly a trade-off not worth pursuing. Moreover, for surfaces with higher levels of asphericity, it further escalates the challenges in testing. In this study, high-accuracy testing of large convex aspheric surfaces with rotary symmetry was achieved via a method that combines sub-aperture stitching and Computer-Generated Holograms (CGH) compensation testing. Applying the methodology outlined in this study, practical testing was conducted on a large-aperture convex aspheric mirror with a diameter of 538 mm. The outcomes demonstrated that the center testing data and the outer ring testing data were stitched by the stitching algorithm to obtain the surface error of the full-aperture. The results were compared to those of Luphoscan and compensation testing, with a residual Root Mean Square (RMS) less than λ/20 (λ = 632.8 nm). Finally, the error analysis of the entire testing process showed that the accuracy was better than λ/50. The results demonstrate that the method can achieve highly accurate test of large convex aspheric surfaces.

F/0.78 High Order Aspheric Surface Testing with Null Compensator and Mapping Distortion Correction

F/0.78 High Order Aspheric Surface Testing with Null Compensator and Mapping Distortion Correction

Analysis of the influence of simultaneous phase-shifting shearing interference polarizer

The aspheric surface testing system based on the shearing interference principle is used to better analyze how the installation and fabrication errors of linear polarizer affects the precision of the aspheric surface. The effects of the angle error of the linear polarizer and the phase-shifting error of the wave plate on the reconstruction of the aspheric surface are studied. Constructing the model of the Jones matrix with the error term system, the reconstruction surface and residual after the corresponding error system are obtained using the four-step phase-shifting and differential Zernike method. The polarizer array of an angle of θ was varied from ( θ − 1 deg ) to ( θ + 2 deg ) every 0.2 deg, and the changes of the fitting surface and the residual surface were simulated. The phase-shifting error of the simulated one-fourth wave plate was <λ / 300. Then, the change of the fitting surface and residual surface when these two errors exist at the same time were simulated. The simulation results show that the influence of the phase-shifting error of the wave plate on the fitting surface is much greater than the angle error of the polarizer array. When assembling the interference system, the phase-shifting error of the wave plate should be <λ / 300 when the light transmission angle error of the polarizer array is between −0.2 deg and 0.2 deg, which will ensure the testing precision of the aspheric surface testing system.

Simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer

A novel simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer (OSD) is proposed, it is an effective technological measure of aspherical surface measurement, to effectively solve the non-uniformity of light intensity and limited transmission order caused by the beam displacer device. The OSD system is formed by the adoption of two-crystal polarization parallel beam displacers (PBDs), which makes it achieve the orthogonal shearing in the x- and y-directions simultaneously. A quarter-wave plate (QWP) is used to generate the desired phase-shifting, and four beam lateral shearing interference waves are simply generated in OSD orthogonal directions without any bulky and complicated optical components. The phase maps of the aspherical surface can be instantly obtained using the spatial phase-shifting technique with a polarization pixelated mask (or called micro-polarization array: MPA) integrated into CCD. In this study, the proposed method was theoretically described and simulation results were analyzed. The simultaneous two-step phase-shifting lateral shearing interference fringes can be extracted in real-time with the MPA. The experiment results compared with the ZYGO interferometer were performed, and proved that the measurement error is not more than 2%. This interferometry has made it possible to improve the stability and feasibility of aspherical surface testing experiments.

Study of the Explosive Bridge Film Using Laser Shaping Technology

Laser shaping technology and its applications have gained widespread attention in different fields. Using laser repair technology prolongs the service life of micro-explosive products and reduces the production cost, as well as enables the recycling of resources. Although most research mainly focuses on aspheric surface shaping and testing technology, only a few studies on repair technology for micro-explosive products using laser shaping have been reported. To promote the better application of laser shaping technology in the production and repair process of micro-explosive components, this work mainly studied the effect of laser shaping on the repair of an explosive bridge film to enhance the ignition performance and prevent damage. Different processes were used to repair the metal film using laser shaping and non-shaping, respectively. Furthermore, we investigated the similarities and differences of a laser-damaged film surface before and after shaping, and the influence of laser energy parameters on the microstructure and ignition properties of the repaired region. Additionally, we obtained a reasonable repair scheme by analyzing the temperature field variation from the simulation. The results show that the damage caused by the non-shaping and shaping lasers can be repaired using the heat flow and vaporization methods, respectively. By controlling the process parameters, the quality of repair can be improved and the production cost of the bridge film can be reduced.

Single-shot phase retrieval for aspheric surface testing based on the transport of intensity equation and a prism-mirror module

Transport of intensity equation (TIE) relates the longitudinal intensity derivative of propagating light wave to the transverse phase gradient. The phase is retrieved by measuring the intensity of propagating light wave at two or more longitudinally displaced planes by moving the detector and then solving the TIE. We present a single-shot transport of intensity equation-based phase retrieval using a prism-mirror based module to capture the two defocused intensity images simultaneously. The results obtained by single-shot transport of intensity equation-based phase retrieval have been compared with interferometry and profilometer-based measurements. We highlight an important aspect of the TIE-based approach that this formulation decouples the intensity and the unwrapped phase of the unknown field. Intensity and phase are individually low-bandwidth functions when compared to the complex field associated with the unknown wavefront. When compared to interferometry, the TIE-based approach therefore inherently has many reduced sampling requirements. For a given array sensor, TIE can therefore measure large phase deviations for which an interferometer would produce very high density fringes that are impossible to sample as per the Nyquist criterion. The prism-mirror module shown in this work is easy to fabricate, align, and can be easily integrated with an experimental setup. The applications of the proposed method for the wavefront measurement of spherical and aspheric lenses are demonstrated.

Testing of aspheric surface with low reflectivity using hybrid type computer-generated hologram (invited)

Testing of aspheric surface with low reflectivity using hybrid type computer-generated hologram (invited)

Automatic Aspheric Surface Testing Technology Based on Axial Movement of Knife-Edge Instrument

Automatic Aspheric Surface Testing Technology Based on Axial Movement of Knife-Edge Instrument

Non-null testing of the aspheric surface using a quadriwave lateral shearing interferometer

A non-null aspheric surface testing system using a quadriwave lateral shearing interferometer (QWLSI) based on the randomly encoded hybrid grating is proposed. The system uses a non-null lens to partially compensate for the longitude aberration of the aspheric surface, which is more versatile than the null configuration. QWLSI is a common-path and self-reference system and requires no reference surface. Compared with the conventional Twyman–Green interferometer (TGI), QWLSI has higher dynamic range, better antivibration ability, and higher stability. For a non-null testing system based on the QWLSI and TGI, the compensation ranges of different aspheric surfaces and the allowable range of aspheric axial positions are analyzed under the condition that the interference fringe satisfies the Nyquist sampling theorem. The iterative reverse optimization retrace error-correction algorithm based on the exact system modeling and the localization algorithm of aspheric axial position are discussed. Simulation results show that the root mean square value of the aspheric surface reconstruction residual is less than 1 / 200 λ , which indicates that the system has extremely high theoretical testing accuracy. In the experiment, the QWLSI non-null system and the autocollimation null method with a ZYGO interferometer agree with the testing results of the same aspheric surface, which demonstrates the feasibility and accuracy of the QWLSI aspheric non-null testing method.

Research on compensating stitching testing for convex aspherical surface

Aspherical optical elements bring much benefit to modern optical systems, due to its significant role in improving optical performance by compensating residual aberrations, and decreasing system’s weight. However, manufacturing aspherical surfaces in high accuracy is usually limited by the ability of surface metrology, especially for convex aspherical surfaces. In this paper, we propose a compensating stitching method combining computer generated hologram (CGH) compensating testing and stitching testing to achieve the full aperture map of convex aspherical surfaces. Firstly, we introduce our self-developed mathematical models in the compensating stitching method, including CGH design model, subapertures’ alignment model and stitching model. Then the performance of our proposed method is demonstrated with compensating stitching testing of an off-axis convex aspherical mirror with its aperture of 332mm×144mm. The experimental result shows that the convex aspherical surface can be tested in full aperture with our proposed method effectively, which demonstrates that our proposed surface testing method opens a new path for the testing of convex aspherical surfaces.

New Methods of Manufacturing High-Aperture Computer-Generated Holograms for Reference Wavefront Shaping in Interferometry

Factors causing parasitic distortions of interferograms in control systems based on reference single-component high-aperture computer-generated holograms (CGHs), which are made on flat substrates and have a binary phase structure, are analyzed with respect to the problem of interferometric testing of spherical and aspherical surfaces with high angular apertures. The quality of such CGHs is improved using the methods, means, and writing materials (titanium and chromium films) suitable for direct laser writing of their diffraction structure, which provides the generation of interferograms with minimal parasitic distortions. In particular, it is proposed to modulate the local transmission coefficient of the CGH structure by applying duty cycle modulation to the diffraction zones in order to reduce the variations in contrast of the generated interferogram. Possibilities of the application of the thermochemical laser technology of writing on titanium and chromium films for manufacturing high-aperture holograms with the f-number $$f/1$$ and higher are discussed.

自准校正透镜位于共轭后点前的凹非球面检验

自准校正透镜位于共轭后点前的凹非球面检验

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

Fringe discretization and manufacturing analysis of a computer-generated hologram in a null test of the freeform surface.

A computer-generated hologram (CGH) is the core component for an aspheric surface test. According to fabrication demands, it is necessary to convert the designed CGH phase compensation function into the processed pattern, that is, the fringe discretization process. In this paper, we propose a new discretization method for a CGH in a test of the freeform surface, and realized the encoding of processed fringes by MATLAB software. Furthermore, we designed the experiment to verify the accuracy of the new discretization method and compared the calculation efficiency between the new algorithm and the reported algorithm. Finally, based on the testing requirement of a freeform mirror in a camera optical system, we completed the design, encoding, and fabrication of the CGH sample, and analyzed the influence of various errors on wavefront accuracy of the CGH.

Tool setting error compensation in large aspherical mirror grinding

Increasing competition and high accuracy make it necessary to optimize and evaluate the outcome of manufacturing processes. In tool grinding, models for the tool path and tool setting are of particular interest. In this article, to establish a valid general grinding model, an improved method for tool setting error compensation is proposed. We consequently developed models of tool path and tool setting, and verified the models by simulations. Lastly, the model is demonstrated through testing of a concave aspheric surface. The experiment results show that the introduced models are valid for grinding in aspherical mirror, since they are solely based on the geometry and process parameters, and hence are applicable for manufacturing process optimization.

Position error correction of large-aperture aspherical in-position measurement.

An improved mathematical model of aspherical in-position measurement calibration is proposed in this paper, including hardware and software methods. The hardware method is used in rough calibration, but it is not precise enough. Then, the software method is chosen to further reduce the error. Simulation experiments are performed to demonstrate the effectiveness of this improved approach. Lastly, the model is verified through the testing of a concave aspheric surface. The experiment results show that the measurement errors of mirror after data processing can be reduced about 2 μm.

Accurate testing of aspheric surfaces using the transport of intensity equation by properly selecting the defocusing distance.

In the last decade, the transport of intensity has been increasingly used in microscopy, wavefront sensing, and metrology. In this study, we verify by simulation and experiment the use of the transport of intensity equation (TIE) in the accurate testing of optical aspheric surfaces. Guided by simulation results and assuming that the experimental setup parameters and the conic constants are known, one can estimate an appropriate defocusing distance Δz that leads to an accurate solution of the TIE. In this paper, this method is verified through the construction of a non-nulled experiment for testing the 2D profile of an aspheric surface. The theoretical method and experimental results are compared to validate the results. Finally, to validate the TIE methodology, the phase distribution obtained by TIE is compared with the phase distribution obtained by a Shack-Hartmann sensor.

大口径离轴凸非球面的加工和检测

大口径离轴凸非球面的加工和检测

Optimization design of partially compensating lens for large aperture convex aspheric surface testing

Optimization design of partially compensating lens for large aperture convex aspheric surface testing