High Spatial Frequency Errors Research Articles

Investigation on the smoothing of surface spatial frequency errors for borosilicate glass by heat-treatment

The mid-spatial frequency error and high-spatial frequency error on the optical glass component surface limit the development of high-power laser devices. By heat-treatment in wet atmosphere, the surface can be smoothed spontaneously under the action of capillary force, which is positive to improve the quality of optical components. In this paper, the finite element simulation model of the glass surface smoothing process is established based on the level-set method. The factors affecting the smoothing process, such as morphology wavelength and viscosity, are analyzed by simulation. A series of surface smoothing heat-treatment experiments for borosilicate glass were carried out to verify the effectiveness of improvement on surface quality through heat-treatment. Finally, the reasons for the discrepancy between theory and experiment are investigated through the simulation, and the effects of wavelength and the water content in the material are further investigated.

Laser energy absorption prediction of silicon substrate surface from a mid- and high-spatial frequency error.

Additional laser energy absorption of optical elements limits the further development of high-energy laser systems. In engineering, inexpensive and precise absorption test technology is essential. We attempt to predict energy absorption via surface spatial error value based on the roughness-induced absorption (RIA) theory. However, the absorption coefficients cannot match roughness values measured with an atomic force microscope or white light interferometer. We find three influencing factors and optimize the definition of RIA to spatial error-induced absorption (SEIA). SEIA is proportional to δ2 of a mid- and high-spatial frequency error in a certain frequency range. This range depends on laser diameter, wavelength, and coating. Excluding the absorption induced by fabrication defects, the total absorption can be classified into SEIA and background absorption (BGA). BGA is decided by material and process technology, which can be obtained by calculations. The sum of SEIA and BGA is predictable because both can be estimated. The substrate absorption of high-energy optics can be semi-quantificationally predicted. SEIA provides a new angle to research element-absorbed laser energy for high-power laser technologies.

Full aperture super-smooth polishing and surface topology evolution of the mandrels for X-ray optics used in eXTP mission

The X-ray focusing mirror used in enhanced X-ray Timing and Polarimetry(eXTP) mission are manufactured by the electroformed nickel replication process, and the machining accuracy of the mandrels are directly related to the focusing quality of the mirror. The optical performance of the focusing mirror is not only affected by the shape error, but also closely related to the mid and high-spatial frequency errors. In this research, the full-aperture polishing process of NiP die was investigated, and the evolution of surface waviness and the surface roughness under subsequent polishing processes were examined. The 7 × 4 h of full-aperture polishing experiment was conducted on the self-developed two-axis polishing machine with optical grade pitch as the polishing tool. The experimental results showed that the mid-spatial frequency error of the mandrel was effectively reduced and the root mean square value of the surface roughness was decreased to 0.266 nm, which meets the stringent requirements for the surface quality of mandrel in eXTP mission.

Fast, wide-field and distortion-free telescope with curved detectors for surveys at ultralow surface brightness.

We present the design of an all-reflective, bifolded Schmidt telescope aimed at surveys of extended astronomical objects with extremely low surface brightness. The design leads to a high image quality without any diffracting spider, a large aperture and field of view (FoV), and a small central obstruction that barely alters the point spread function (PSF). As an example, we design a high-quality, 36cm diameter, fast (f/2.5) telescope working in the visible with a large FoV (1.6°×2.6°). The telescope can operate with a curved detector (or with a flat detector with a field flattener) and a set of filters. The entrance mirror is anamorphic and replaces the classical Schmidt entrance corrector plate. We show that this anamorphic primary mirror can be manufactured through stress polishing, avoiding high spatial frequency errors, and testing with a simple interferometer scheme. This prototype is intended to serve as a fast-track scientific and technological pathfinder for the future space-based MESSIER mission.

Iterative wave-front reconstruction in the Fourier domain

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

Orthogonal experiment and analysis of power spectral density on process parameters of pitch tool polishing

Mid to high spatial frequency error (MSFR and HSFR) should be strictly controlled in modern optical systems. Pitch tool polishing (PTP) is an effective ultra-smoothing surface manufacturing method to control MSFR and HSFR. But it is difficult to control because it is affected by a lot of factors. The present paper describes the pitch tool polishing study based on eighteen well-planned orthogonal experiments (OA18 matrix). Five main process factors (abrasive particle size, slurry concentration, pad rotation speed, acidity and polishing time) in pitch tool polishing process were investigated. In this study, power spectral density (PSD) based on Fourier analysis of surface topography data obtained by white light interferometer was used as the results of orthogonal experiments instead of material removal rate and surface roughness. A normalization method of PSD was proposed as the range analysis rule. Three parts of spatial frequency bandwidth were selected and discussed. Acidity is the most important factor in part 1 and slurry concentration is the most significant one in part 2; while acidity is the least influenced one in part 3. The result in each part was explained by two-step material removal mechanism. At last, suggestions in low and high spatial frequency are given for pitch tool polishing.

Analysis of surface errors and subsurface damage in flexible grinding of optical fused silica

The surface errors and subsurface damage (SSD) formed during optical fused silica grinding processes have been investigated using the flexible grinding wheel (FGW). Surface errors, including low spatial frequency (LSF) errors, middle spatial frequency (MSF) errors, and high spatial frequency (HSF) errors, and SSD depths are measured. Compared with the rigid grinding wheel (RGW), it is found that the influences of grinding parameters on surface errors and SSD are the same in flexible grinding. However, LSF and HSF errors and SSD depths are obviously decreased and MSF errors are partly controlled. The grinding surface micrographs are also observed, and the surfaces after flexible grinding have less grinding scratches and surface defects. These results indicate that flexible grinding using FGW has high precision and elastic characteristics and can achieve good surface quality of optical fused silica.

Small Pitch Tool for Removing Middle Spatial Frequency Errors

More and more optical elements are needed in modern industry, which is reflected by both the bigger amount of requirement, and more complicated designed surface such as asphere and even free form surface. As a result, optical polishing using small tools on CNC machines is applied widely in the whole world, which has a lot of advantages such as fast speed, high accuracy, high flexibility and so on. But the small tool polishing can also cause in some problems. For example, the middle spatial frequency errors (MSFE) may be increased during the polishing. The reasons may consist of the following aspects: 1) the positional error of the workpiece; 2) the mistake of error data input; 3) the unexpected stop of the polishing process; 4) the stabilization of the slurry density during the process; 5) the temperature change of the contact area between the tool and the workpiece and so on. As is known, pitch is usually used in traditional optical manufacture, and it can reduce the middle and high spatial frequency errors in a large extent because of the different removal rate between the high points and low points on the optical surface. Therefore, the application of the combination of pitch and small tool is described in this paper in order to solve the MSFE problem, and we have got good polishing results of reducing the error from 2.155nm to 0.267nm by using the new pitch tool on the CNC machine after two runs.

Active optics methods for exoplanet direct imaging

Context. The next generation of exoplanet hunters will be targeting hot Jupiter-like exoplanets orbiting around nearby stars through direct imaging. The high contrast needed for such planet finders requires optical surfaces free of high spatial frequency ripples that might remain in the post-coronagraphic image as quasi-static speckles. Aims. We report results on the manufacturing of three supersmooth aspherical mirrors for the ESO/VLT-SPHERE instrument. The excellent optical quality obtained will allow the future planet hunter to increase the level of achievable contrast by a strong reduction of the noise level and residual quasi-static speckles on the image plane. Methods. The stress polishing method used on these mirrors is well suited to superpolishing aspheric components for astronomy. The main advantage of this technique is the very high optical quality obtained either on the form errors or on the high spatial frequency errors. Furthermore, the roughness can be decreased to a few angstroms, thanks to the classical polishing with a large pitch tool.Results. Interferograms obtained during polishing and in the final stage show the supersmooth quality of each mirror. Errors in the high spatial frequency range are lower than 4 nm rms WF, thereby avoiding the degradation of the post-coronagraphic image. A comparison of the power spectral density (PSD) obtained by stress polishing and the PSD of the VLT-UT3 primary mirror demonstrates that the contrast capabilities will not be limited by the aspherical mirrors.

Active Optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system

The manufacturing of toric mirrors for the Very Large Telescope-Spectro-Polarimetric High-Contrast Exoplanet Research instrument (SPHERE) is based on Active Optics and stress polishing. This figuring technique allows minimizing mid and high spatial frequency errors on an aspherical surface by using spherical polishing with full size tools. In order to reach the tight precision required, the manufacturing error budget is described to optimize each parameter. Analytical calculations based on elasticity theory and finite element analysis lead to the mechanical design of the Zerodur blank to be warped during the stress polishing phase. Results on the larger (366 mm diameter) toric mirror are evaluated by interferometry. We obtain, as expected, a toric surface within specification at low, middle, and high spatial frequencies ranges.

High-throughput high-density mapping and spectrum analysis of transistor gate length variations in SRAM circuits

High-throughput high-density mapping of gate length variations using static random-access memory (SRAM) as electronic test structures is reported. In the experiments, direct measurements of bit-line currents revealed the individual transistor gate length variations within every memory cell. With SRAM and its fast addressing circuits we can measure CD variations with measurement time as fast as 5 /spl mu/s per data point and spatial periodicities down to 6 /spl mu/m. Layout-dependent periodic errors were found to take up 30% to 90% of the total observed error variance, depending on the spatial frequency range and specific measurement grid used. Peaks in the error spectrum were found to be related to the periodicities existing in the circuit layout. Lithography simulations were done as efforts to identify the periodic error sources. It was found that proximity effects and pattern-dependent coma effects contributed to a large percentage of the high spatial frequency errors observed. By independent optical measurements of the poly mask, it was found that the CD error contributions from the mask are very small, and are negligible when compared to the stepper-lens-induced CD errors.

Zonal model of an adaptive mirror

An approximate model of an adaptive optic element is presented which works well for components having many actuators. This zonal model is used to gain insight into the general behavior of systems that correct for high spatial frequency errors. The model is derived from the method of least squares, and considers the nonshift invariant properties of adaptive mirrors. It may be implemented with Fourier transform techniques and is, therefore, easy to program. The relationship between the zonal model and the simpler bandpass filter model of Harvey and Callahan is discussed.