“…In order to elaborately generate multiple focal spots which has independent controllability in the focal plane, it is necessary to appropriately partition the incident beam and then apply different phase modulations. Here, we utilize the vector diffraction integral theory, of which the general focus formula can be expressed as 36 , 37 where, A = − kf /(2 π ), A 1 ( θ , ϕ ) is the amplitude of the incident beam, A 2 ( θ , ϕ ) is a 3 × 3 matrix related to the structure of objective, Δ α ( θ , ϕ ) is the phase distribution of the incident beam, p x , p y and p z is a matrix unit vector about the polarization of incidence light, θ is the converge angle given by sin θ = rNA /( Rn t ), NA is the numerical aperture of the objective, n t is the refractive index of the immersion medium, k is the wave number, ( r , ϕ ) and are the cylindrical coordinates in the pupil and focal planes, respectively.…”