“…Then we calculate the emissivities projected on to the sky I(θ j , ψ j ) and direction n B (θ j , ψ j ) of the emission spot (θ j , ψ j ) on each open field line of each ring in the magnetic frame. We also take the aberration effect into account, and use the Lorentz transformation matrix to transform the emission direction n B (θ j , ψ j ) to the direction n ν (φ j , ζ j ) in the lab frame (observer frame), where φ j = arctan(n ν,y /n ν,x ) is the emission spot's rotation phase with respect to the pulsar rotation axis, and ζ j = arccos(n ν,z / n ν,x 2 + n ν,y 2 + n ν,z 2 ) is the viewing angle for a distant, non-rotating observer (see details for aberration effect in Lee et al 2010). We also add the phase shift δφ ret = −r n cos(θ μ,j − θ j ), the first order of equation (33) in Gangadhara (2005), caused by the retardation effect to φ j , where r n = r/R LC is the emission radius in units of the light cylinder radius and θ μ,j is the half opening angle of the emission beam at the emission spot (θ j , ψ j ).…”