Fig. 1. Schematic diagram of HEELR to make angle selection with an aperture. (a) The schematic of point-to-point imaging beamline with an aperture at the Fourier plane. (b) The angle distribution of incident electrons. (c1) and (c2) illustrate the electron angle distributions after target with different thicknesses and the corresponding position distributions at the Fourier plane. (d1) and (d2) are the electron angle distributions after penetrating the system with E/B field and the corresponding position distributions at the Fourier plane. The purple rectangular shadow indicates the aperture acceptance area

Fig. 2. The principle of areal density difference method to diagnose the areal density and E/B field. (a) The scattering angle distributions after the grille scattering target. Different color corresponds to different thicknesses (t₁ and t₂). (b) The surface plot with contour lines of T_r (t+t₁, θ) and T_r (t+t₂, θ). The intersection point of two contour lines with the same transmittance marks the solution (t, θ)

Fig. 3. Overall design of the dual degrees of freedom diagnostic. (a) The incident beams will be scattered by the scattering target before penetrating the real diagnosed target. (b) The front view (perpendicular to the beam bunches) of the scattering target, different color indicates different thickness

Fig. 4. (a) The wedge shape represents the hydrogen sample with gradient areal density. The color indicates the value of deflection angle from the E/B field and the coordinate system is as shown. (b) The ellipse shape aperture sets the upper limit of the angle acceptance as 1mrad. (c) The ring shape aperture which sets the angle acceptance as (1,2) mrad

Fig. 5. The analysis results when the angle acceptance of the ellipse shape aperture is 1 mrad

Fig. 6. The analysis results when the angle acceptance is set as from 1mrad to 2 mrad by a ring shape aperture