Blue shades indicate the light cone collected by each objective; black arcs indicate the extent of the NA (full-aperture angle 2θ) of each objective; red lines represent the light rays with the highest incident angle; black dashed lines show the optical axis. The intermediate image at the focal space of O2 is magnified by 1.33 (equal to NA1/NA2) along both the lateral and axial directions to minimize the aberration of the intermediate image. The blue dashed line indicates the position of the coverslip where the air–water interface is. All the light passing though O2 is refracted at this interface and enters O3, with the exception of only a small portion of the light being cropped by the coverslip (left side between the blue and red dashed lines). The effective detection NA along the x'-axis is ~ 1.33 × 1.33 × sin (73.8°/2) ≈ 1.06. The effective NA along the y axis can be obtained straightforwardly, since light is not cropped along this direction. We have therefore NAy ~ 0.9 × 1.33 ≈ 1.20, e.g., NA2 multiplying the magnification of the intermediate image. The collection solid angle of the system can be estimated as ~ 3.34, calculated by subtracting the cropped light at the air–water interface from the solid angle of O2. Assuming isotropic fluorescence emission, the resulting collection efficiency is then ~ 28.2%, equivalent to that of a water-immersion objective of NA ≈ 1.17. As an alternative way of understanding the remote imaging module and the reason for the high detection NA, O3 can be also seen as an air objective with NA = 1 where the collection solid angle is 2π. All light transmitted by O2 can then be collected by O3, resulting a high collection efficiency.