Nyquist sampling theorem in an image calculation with angular spectrum method restricts a propagation distance and a focal length of a lens. In order to avoid these restrictions, we studied suitable expressions for the image computations depending on their conditions. Additionally, a lateral scale in an observation plane can be magnified freely by using a scaled convolution in each expression.

Friedrich Paschen war von 190 1 bis I924 Abstract.full professor of physics d t the University of Tubingen There he worked on the three subject areas radiation law [determination of u and thus h by Walther Gerlach), w i e s formulae of line spectrd (Paschen series) and the Zseman effect (Passhen-Back-Effekt) A Rowland grating provided the necessary high resolution In particular the theoretical interpretation of the measured atomic spectrd in mdgnetic fields finally led, i n collaboration with Sommerfeld and his students. via the Lande factor to the de\elopment of quantum mechnics by Heisenberg dnd Jorddn Goudsmit was prompted to introduce the electron spin by the measurements of Back at Tubingen, and later the nuclear spin was founded through the hyperfine irructure Pauli tested his principle first with medsurement ' 11 Tubingen before publishing it

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We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and non-minimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then proceeding to BRST quantize this system. Our analysis includes the introduction of constant ghosts and associated auxiliary fields needed to gauge fix symmetries associated with zero modes. All fields introduced in the process of quantization can be integrated out explicitly, resulting in the prescriptions for computing scattering amplitudes that have appeared previously in the literature. The zero mode insertions in the path integral follow from the integration over the constant auxiliary fields.

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