Possibility to Construct a Machine for Primality Testing of Numbers

Like the optical prism to break white light up into its constituent spectral colors, the machine to show a prime as a single spectrum is proposed. From the theoretical analysis, it can be shown that the machine to recognize the prime number as a single spectrum can be realized by using the correlation function of Riemann zeta function. Moreover, this method can be used for a factorization of the integer consisted of two primes.

Multi-Layer Counter-Pressure Injection Molding for Thick-Walled Optical Lens

In precision optical applications, plastics thick-walled optical lenses are increasing. Dimensional stability and optical performance are the critical issues that should be addressed for plastic thick-walled lenses. A novel multi-layer counter-pressure injection molding process is proposed in this study. The experimental prism mold with moveable pistons was developed to investigate the effects of layering methods, counter-pressure and their combination on thick-walled optical lenses. The experimental results reveal that counter-pressure injection molding is effective in improving shrinkage, transmittance and refractive index of the thick-walled optical prism. Counter-pressure of the piston provided lower melt velocity and shorter flow path of melt to improve polymer molecules orientation, and also offered continuous holding pressure during the filling stage to eliminate defects such as shrinkage or short shots. The combination of counter-pressure and multi-layer injection molding technology further improved the dimension stability and optical performance of the thick-walled optical lens. Much thinner layers than the final wall thickness of prism ensures shrinkage reduction during the cooling stages. A thick-walled optical prism was fabricated successfully upon applying a multi-layer counter-pressure injection molding process.

Design and Testing of a Compact Optical Prism Module for Multi-Degree-of-Freedom Grating Interferometry Application

In this research, a key optical component for multi-degree-of-freedom (MDOF) surface encoder was designed, fabricated and evaluated. In a MDOF grating interferometry system, there are four diffraction beams from a two-axis scale grating and reference grating, respectively. For further modulation, these beams will propagate more than 100 mm, which makes paralleling these beams necessary. In previous research, collimation lens, separate prisms and a home fabricated diffraction device by combining four separate one-axis line gratings in a glass substrate have been demonstrated. However, large power loss and assembly complicity makes these techniques less competitive. For solving this problem, this research proposed a new lens module, which is an improved type prism, quadrangular frustum pyramid (QFP) prism. The prism is designed in such a way that these four reflected beams from the grating are symmetrically incident into the prism through the upper surface, total reflected on the inner sides of the prism, and then parallel getting through the bottom surface. A prism that allows an incident beam diameter of 1 mm and four paralleling beams with a 10 mm distance between the two diffraction beams along one direction was designed, fabricated and tested. Testing results based on an entire grating interferometry system verified that the proposal in this research is greatly effective in beam paralleling in terms of less power loss and high paralleling and greatly reduces the assembly complicity, which will eventually be beneficial for grating interferometry application.

Измерение показателя экстинкции диэлектрических пленок на основе спектроскопии нарушенного полного внутреннего отражения

Various methods of measuring the coefficient of light attenuation in optical coatings are considered. It is shown that the dimensionless extinction index of a coating made of a weakly absorbing film-forming material can be measured using a special attachment based on a parallelepiped-shaped optical prism. Parameters of the proposed attachment are calculated so that it could be arranged inside standard spectrophotometers.