New Projection Exposure Using a Double-line Matrix of Optical Fibers in Place of a Reticle

Abstract

One of the continuing challenges in cosmology has been to determine the largescale space-time metric from observations with a minimum of assumptions -without, for instance, assuming that the universe is almost Friedmann-Lemaître-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lemaître-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate y is null (light-like) and measured down the past light cone of the observer.In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution -i.e. our procedure is not restricted to our past light cone -and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. We also compare the two approaches with regard to determining the cosmological constant Λ. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations. Smoothed data functions enable us to include properties that data must have within the model.

Electrochemical printing: software reconfigurable electrochemical microfabrication

“…These flexible fabrication techniques aim to avoid hardware-based optical mask sets employed in photolithography. Several approaches substitute reconfigurable computer-controlled illumination systems [1][2][3][4][5] to selectively expose regions of a photoresist, while others employ laser-prototyped adhesivebacked masks to dictate where material is subsequently deposited [6]. Other flexible fabrication methods such as soft lithography [7] and Microfabrica's EFAB [8] use lithographic techniques to create a master 'stamp', or series of masks, which can be used and reused to control material deposition and/or removal.…”

Optical-Fiber-Matrix Exposure Using Light-Emitting-Diode Sources

“…For this reason, we previously proposed a new optical projection lithography method using an optical-fiber matrix. 1) In the proposed matrix-exposure method, optical fibers arrayed in a line matrix or a double-line matrix are used in place of reticles. The light supply to each fiber is controlled in accordance with the pattern shapes required, and a wafer or an exposed substrate is relatively scanned to the fiber matrix and the projection lens.…”

“…In the previous prototype of our optical-fiber matrixexposure system, mechanical shutters driven by solenoids were used for switching the exposure light. 1) However, some of the solenoid shutters soon broke down, and the reliability was not adequate for practical use. Therefore, in this study, as a countermeasure, light-emitting diodes (LEDs) are fixed at the entrance of each fiber as exposure sources, and the light supply to each fiber is controlled without using mechanical shutters but by switching the LEDs.…”