TL;DR: It is proved that in the general case, it is not possible to separate the sources without nonlinear distortion, and this work focuses on specific nonlinear mixtures known as post-nonlinear mixture, which are realistic models in many situations and emphasize interesting properties i.e., in such nonlinearmixtures, sources can be estimated with the same indeterminacies as in instantaneous linear mixtures.
Abstract: We address the problem of separation of mutually independent sources in nonlinear mixtures. First, we propose theoretical results and prove that in the general case, it is not possible to separate the sources without nonlinear distortion. Therefore, we focus our work on specific nonlinear mixtures known as post-nonlinear mixtures. These mixtures constituted by a linear instantaneous mixture (linear memoryless channel) followed by an unknown and invertible memoryless nonlinear distortion, are realistic models in many situations and emphasize interesting properties i.e., in such nonlinear mixtures, sources can be estimated with the same indeterminacies as in instantaneous linear mixtures. The separation structure of nonlinear mixtures is a two-stage system, namely, a nonlinear stage followed by a linear stage, the parameters of which are updated to minimize an output independence criterion expressed as a mutual information criterion. The minimization of this criterion requires knowledge or estimation of source densities or of their log-derivatives. A first algorithm based on a Gram-Charlier expansion of densities is proposed. Unfortunately, it fails for hard nonlinear mixtures. A second algorithm based on an adaptive estimation of the log-derivative of densities leads to very good performance, even with hard nonlinearities. Experiments are proposed to illustrate these results.
TL;DR: This paper reviews physiological measurements of cat striate cell responses, and concludes that both of the essential hypotheses of the linear/energy model are supported by the data.
Abstract: Simple cells in striate cortex have been depicted as rectified linear operators, and complex cells have been depicted as energy mechanisms (constructed from the squared sums of linear operator outputs). This paper discusses two essential hypotheses of the linear/energy model: (1) that a cell's selectivity is due to an underlying (spatiotemporal and binocular) linear stage; and (2) that a cell's firing rate depends on the squared output of the underlying linear stage. This paper reviews physiological measurements of cat striate cell responses, and concludes that both of these hypotheses are supported by the data.
TL;DR: In this article, a rotary motorized stage is used to selectively rotate the chuck and expose different areas of the workpiece to the beam, and a linear motor is used for selectively moving the rotary stage and thus exposing additional areas by operation of the linear stage.
Abstract: Apparatus for non-planar treatment of a workpiece utilizing exposure beam lithography includes a vacuum chamber, an exposure beam generator such as an electron beam generator disposed in the chamber for directing a beam towards a work location, a chuck disposed in the chamber for holding and positioning the workpiece at the work location, a rotary motorized stage disposed in the chamber and responsive to first control signals for selectively rotating the chuck, and thus the workpiece, to thereby expose different areas of the workpiece to the beam, and a linear motorized stage disposed in the chamber on which the rotary stage is mounted, said linear motor being responsive to second control signals for selectively moving the rotary stage and thus the chuck and workpiece in a linear direction which is generally parallel with the axis of rotation of the rotary stage. The workpiece is thus exposed over additional areas by operation of the linear stage. A controller supplies first and second control signals to the rotary stage and linear stage respectively to selectively effect the operation thereof.
TL;DR: In this paper, the pitch, yaw and roll errors of a commercial precision linear air-bearing stage actuated by a linear motor were measured by two different methods for assurance of reliability.
Abstract: This paper describes the measurement of straightness error motions (vertical straightness and horizontal straightness) and rotational error motions (pitch, yaw and roll) of a commercial precision linear air-bearing stage actuated by a linear motor. Each of the error motions was measured by two different methods for assurance of reliability. The stage was placed in the XY-plane and moved along the X-direction. The pitch error and yaw error, which were measured by an autocollimator and the angle measurement kit of a laser interferometer, were about 8.7 and 1.6 arc-s, respectively, over a travel of 150 mm with a moving speed of 10 mm/s. The roll error was measured by the autocollimator through scanning a flat mirror along the X-direction. The second method for roll error measurement was to scan two capacitance-type displacement probes along the flat surface placed in the XZ-plane. The two probes with their sensing axes in the Y-direction were aligned with a certain spacing along the Z-axis. The roll error can be obtained by dividing the difference of the outputs of the two probes by the spacing between the two probes. The roll error was measured to be approximately 11.8 arc-s over the 150 mm travel. The horizontal straightness error and the vertical straightness error (Y- and Z-straightness errors) were measured by using the straightness measurement kit of the laser interferometer. The second method for straightness measurement was to scan the flat surface with a capacitance-type displacement probe. The horizontal and vertical straightness errors of the stage over the 150 mm travel were measured to be approximately 207 and 660 nm, respectively.
TL;DR: In this paper, a collimated laser beam from a laser diode is projected onto a grating reflector mounted on the stage and the reflected 0th-order diffracted beam is received by an autocollimation unit, which consists of a collimator objective and a quadrant photodiode, for detecting the pitch and yaw errors.