On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography

The point spread function is widely used to characterize the three-dimensional imaging capabilities of an optical system. Usually, attention is paid only to the intensity point spread function, whereas the phase point spread function is most often neglected because the phase information is not retrieved in noninterferometric imaging systems. However, phase point spread functions are needed to evaluate phase-sensitive imaging systems and we believe that phase data can play an essential role in the full aberrations' characterization. In this paper, standard diffraction models have been used for the computation of the complex amplitude point spread function. In particular, the Debye vectorial model has been used to compute the amplitude point spread function of ×63/0.85 and ×100/1.3 microscope objectives, exemplifying the phase point spread function specific for each polarization component of the electromagnetic field. The effect of aberrations on the phase point spread function is then analyzed for a microscope objective used under nondesigned conditions, by developing the Gibson model (Gibson & Lanni, 1991), modified to compute the three-dimensional amplitude point spread function in amplitude and phase. The results have revealed a novel anomalous phase behaviour in the presence of spherical aberration, providing access to the quantification of the aberrations. This work mainly proposes a method to measure the complex three-dimensional amplitude point spread function of an optical imaging system. The approach consists in measuring and interpreting the amplitude point spread function by evaluating in amplitude and phase the image of a single emitting point, a 60-nm-diameter tip of a Near Field Scanning Optical Microscopy fibre, with an original digital holographic experimental setup. A single hologram gives access to the transverse amplitude point spread function. The three-dimensional amplitude point spread function is obtained by performing an axial scan of the Near Field Scanning Optical Microscopy fibre. The phase measurements accuracy is equivalent to λ/60 when the measurement is performed in air. The method capability is demonstrated on an Achroplan ×20 microscope objective with 0.4 numerical aperture. A more complete study on a ×100 microscope objective with 1.3 numerical aperture is also presented, in which measurements performed with our setup are compared with the prediction of an analytical aberrations model.