The relativistic Doppler effect: when a zero frequency shift or a red shift exists for sources approaching the observer

It is shown without making use of Lorentz transformation that there exists a phenomenon of relativistic zero-frequency shift in Doppler effect for a plane wave in free space, observed in two inertial frames of relative motion, and the zero shift takes place at a maximum aberration of light. When it is applied to analysis of a moving point light source, two unconventional physical implications result: (1) a light source, when it is approaching (moving closer to) the observer, may cause a red shift; (2) a zero-frequency-shift observation does not necessarily mean that the light source is not moving closer, and in contrast, the light source may be moving closer to the observer at a high speed. This fundamental result of special relativity may provide an alternative way to experimentally examine the principle of relativity, and might have a significant application in astrophysics.Comment: (1) The words:"...for a plane wave in free space, observed in two inertial frames of relative motion,...the definitions of 'approaching' and 'receding' do not apply. When the zero-shift effect is applied to approximate analysis..." are added on p. 7. (2) "Reply to Comment by Sfarti" is added on p. 9. 7 figures, 9 page

Modeling the point-spread function in helium-ion lithography

We present here a hybrid approach to modeling helium-ion lithography that combines the power and ease-of-use of the Stopping and Range of Ions in Matter (SRIM) software with the results of recent work simulating secondary electron (SE) yield in helium-ion microscopy. This approach traces along SRIM-produced helium-ion trajectories, generating and simulating trajectories for SEs using a Monte Carlo method. We found, both through simulation and experiment, that the spatial distribution of energy deposition in a resist as a function of radial distance from beam incidence, i.e. the point spread function, is not simply a sum of Gauss functions.Semiconductor Research Corporation. Nanoscale Research InitiativeNational Science Foundation. Graduate Research Fellowship Progra