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This paper examines theoretically two different effects which are sometimes encountered in double probe measurements under continuum large-Debye-length conditions: (i) Electron emission due to the de-excitation of metastable atoms and molecules on the probe surface, and (ii) asymmetric double probe characteristics that result from number-density gradients on the plasma. Electron emission is shown to have little effect on the probe characteristics. A method of analysing asymmetric double probe characteristics is discussed.

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Buchdahl's aberration coefficients are normalized with respect to the numerical aperture and the field angle by the use of the normalized object-entrance pupil coordinates. The aberration Δ Y' in the Gaussian image plane is given by ΔY'/L = ρ3 I 3(cos θ, sin θ) + ρ2(-n 1tan α)I I 3(1+2cos 2θ, 2cos θsin θ) + ··· + ρ5 I 5(cos θ, sin θ) + ρ4(-n 1tan α)(I I 5'+I I 5cos 2θ, I I 5cos θsin θ) + ··· where (ρcos θ, ρsin θ) are the coordinates of a ray on the entrance pupil and tan α is used to specify the incident angle of the principal ray. The calculation formulae for the coefficients of both spherical and aspherical systems are rearranged for the convenience of using an electronic computer. Numerical examples for Tessar, Sonnar and Gauss types are given and compared with the results obtained by ray-tracing.