A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Structural vibrations and hysteresis nonlinearities in piezoactuators have been fundamental limitations when using these actuators for high-speed precision-positioning applications. Positioning speed (bandwidth) is limited by structural vibrations, typically, to about one-tenth the fundamental vibrational frequency of the piezoprobe. Further, precision in positioning is limited by hysteresis nonlinearities, which can result in signie cant errors for large-range positioning applications. This paper shows that signie cant improvements in precision and bandwidth can be achieved by using an inversion-based approach to compensate for hysteresis and vibrations in the piezodynamics. Theapproach decouplestheinversion into 1 )inversion of thehysteresisnonlinearity and 2 )inversion ofthe structuraldynamics,toe ndaninputvoltageproe lethatachievesprecisiontracking ofa desiredpositiontrajectory. Theapproachisappliedtoapiezoactuator,andexperimentalresultsshowthatanorderofmagnitudeimprovement in positioning speed is achieved, while maintaining precision tracking of the desired position trajectory. I. Introduction P IEZOACTUATORS can achieve nanometer resolution positioning and are hence increasingly being used for ultraprecision positioning in aerospace applications, 1;2 vibration control, scanning probe microscopy for surface characterization, and nanofabrication. 3i5 Two major limitations of present positioning techniquesusing piezoactuatorsare 1 )lowoperating bandwidthdue to positioning errors caused by structural vibrations at high speeds and 2) low precision for relatively large-range displacements (due to errors caused by hysteresis nonlinearities ), resulting in restricted positioning range. This paper presents a method to improve both the accuracy and the speed of piezoactuators by using an inversionbased approach to e nd the voltage input to the piezoactuators that compensates for the hysteresis nonlinearities and the structural vibrations. This approach e rst decouples the system dynamics into two separate subsystems that model 1 ) the hysteresis nonlinearity

Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application

The tracking control accuracy of piezoceramic actuators is limited due to their inherent hysteresis nonlinearity. This paper presents a computer-based tracking control approach for a piezoceramic actuator based on incorporating a feedforward loop with a PID (proportional-integral-derivative) feedback controller. The hysteresis nonlinearity of the piezoceramic actuator is modeled in the feedforward loop by using the classical Preisach model. Experiments were performed on a stacked piezoceramic actuator for tracking sinusoidal waveforms with signal frequencies ranging from 0.1-20 Hz. A comparison was made between a feedforward control scheme, a regular PID feedback control scheme, and a PID feedback control scheme with hysteresis modeling in the feedforward loop. The results show that the tracking control performance is greatly improved by augmenting the feedback loop with a model of hysteresis in the feedforward loop. The maximum error in tracking a sinusoidal waveform is about half that obtained using a regular PID controller.

Tracking control of a piezoceramic actuator

Process gas discharged from a bypass pipe to a gas exhaust system can be prevented from diffusing back to the inside of a process chamber without having to install a dedicated vacuum pump at the downstream side of the bypass pipe. The substrate processing apparatus includes a process chamber accommodating a substrate, a gas supply system supplying process gas from a process gas source to the process chamber for processing the substrate, a gas exhaust system configured to exhaust the process chamber, two or more vacuum pumps installed in series at the gas exhaust system, and a bypass pipe connected between the gas supply system and the gas exhaust system. The most upstream one of the vacuum pumps is a mechanical booster pump, and the bypass pipe is connected between the mechanical booster pump and the rest vacuum pumps located at a downstream side of the mechanical booster pump.

Substrate Processing Apparatus

A wafer transport method includes the steps of preparing a semiconductor process equipment having a transport chamber and a process chamber. An interface means connects the transport chamber to the process chamber. A transport means transports a semiconductor wafer from the transport chamber to the process chamber by way of the interface means. The transport means mounting a substrate is inserted into a communicating corridor including a supply means and an exhaust means. The substrate is transported while performing the supply and exhaust by sequentially controlling a supply shutoff means, an exhaust shutoff means, and a communicating shutoff means according to the position of a conductance part formed of a gap between the transport means and the communicating corridor. Thus, the substrate is transported at a high throughput without contamination of the substrate while keeping the different atmospheric conditions for the transport chamber and the process chamber, thereby manufacturing a semiconductor device with high performance capabilities.

Wafer transport method

Aiming at large-area phase-contrast x-ray imaging, a separated-type x-ray interferometer system was designed and developed to produce 25×20 mm interference patterns. The skew-symmetric optical system was adopted because of the feasibility of alignment. The rotation between the separated crystal blocks was controlled within a drift of 0.06 nrad using a feedback positioning system. This interferometer generated a 25×15 mm interference pattern with 0.07 nm synchrotron x-rays. A slice of a rabbit’s kidney was observed, and its tubular structure could be revealed in a measured phase map.

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Operation of a separated-type x-ray interferometer for phase-contrast x-ray imaging

A high-precision, numerically controlled, diamond cutting machine has been developed for fabrication of asymmetrical aspheric mirrors, such as toroidal mirrors used in SOR optics. In this machine, a work-piece is securely fixed to a machine base, and its side face is cut by a flying single-point diamond tool. A tool spindle is laid on an X-Y slide, and its position is numerically controlled by using a laser interferometer. It is possible to fabricate a cylindrical surface by having the spindle-axis rotate slightly about an axis perpendicular to the X-Y slide. Furthermore, while the spindle is rotating, cutting-depth can be dynamically controlled by utilizing a piezo-actuator fixed to the diamond tool. The cutting-depth control is synchronized to the current rotation angle of the spindle, and cutting-depth data are numerically programmed as function of X-Y slide position. A suitable combination of these programmable figure parameters allows fabrication of asymmetrical aspheric mirrors. In order to achieve high figure accuracy, accurate straight motion is required with the X-Y slide. Therefore, straightness error compensation control is adopted, which incorporates a ZERODURE straightedge of 1m length and three optical-fiber gap sensors. The machine accepts a work-piece with maximum dimensions of 600mm length and 100mm width. A figure accuracy of 0.1 μm and surface roughness of 0.03μmRmax have been achieved.

Development Of A Precision Diamond Cutting Machine For Fabrication Of Asymmetrical Aspheric Mirrors

A technique and exposure apparatus measures, with a high degree of accuracy, figure and placement errors of individual optical elements constituting optics embedded inside of an exposure apparatus or the like, with the optics kept in an embedded state as they are. The system measures the distribution of wavefront distortions in the optics while changing the positions of a light source and an image point inside an exposure field of the optics being observed. Optimal displacements of reflective surfaces constituting the optics are then found by calculation based on the measured distribution of wave-front distortions. Finally, the positions of the reflective surfaces are corrected in accordance with the calculated optimal displacements. The positions of the reflective surfaces are corrected by individually controlling displacements output by a plurality of actuators attached to each reflective surface and by mechanically modifying appropriate portions of the reflective surfaces.

Methods for measuring optical system, and method and apparatus for exposure using said measuring method

Large-area (25 × 20 mm) phase-contrast X-ray imaging was attained by using a skew-symmetric two-crystal X-ray interferometer. The sub-nrad angular control required to operate the X-ray interferometer was achieved with a sleeve bearing and a feedback-positioning system. As a demonstration, measurements of a phase map of a rat's liver and a phase-contrast tomographic three-dimensional image of a piece of a rabbit's liver were performed at the Photon Factory using 0.07 nm synchrotron radiation X-rays.

Eiichi Seya

Papers

Wafer transport method

Operation of a separated-type x-ray interferometer for phase-contrast x-ray imaging

Development Of A Precision Diamond Cutting Machine For Fabrication Of Asymmetrical Aspheric Mirrors

Methods for measuring optical system, and method and apparatus for exposure using said measuring method

Large-area phase-contrast X-ray imaging using a two-crystal X-ray interferometer