Measurement and interpretation of the 3D amplitude point spread function of lenses and microscope objectives

The intensity point spread function (IPSF) is most often used to characterize optical imaging systems. For some imaging applications such as digital holographic microscopy the 3D amplitude point spread function (APSF) more completely describes an optical system such as lenses and microscope objectives. It provides necessary data both on the intensity (obtained by squaring the modulus of the complex amplitude) and phase behavior. The original approach that we have chosen was to measure and interpret the APSF by evaluating in amplitude and phase the image of a single emitting point (NSOM tip) with a digital holographic experimental set-up. In this way, besides the intensity information, expressed by the IPSF, we have access to the phase information, described by the PPSF (phase point spread function), which is directly extracted from the phase of the APSF. Different models (scalar, paraxial and vectorial), based on diffraction theory, have been applied to calculate the 3D APSF of an optical diffraction-limited system and the theoretical predictions obtained by each model for the same optical system were compared. Even if the vectorial model is preferable as the most complete model, including polarization information and being appropriate for high numerical apertures, it seems that a simpler scalar model gives also a correct idea on the 3D APSF of an optical system. The scalar and the vectorial models were further extended to include the effect of primary aberrations (spherical, coma and astigmatism) and could be also easily developed for higher order aberrations. The specific aberrations appearing when a microscope objective is used under non-standard conditions such as it is the case when immersion oil is used with coverslip parameters different from the standard ones, have been also considered in the frame of the vectorial theory. This kind of aberration is ubiquitous in each microscope objective and it was shown that significant APSF modifications appear even for very small variations of these parameters. All these developed APSF models, without and with aberrations, will serve as a sound basis to understand and to interpret further the experimental APSF measurements. An original experimental set-up, based on digital holography, was developed to measure the APSF. The method is relatively easy to implement and the acquisition and processing of data are very fast. With only one acquired hologram we have access to both IPSF and PPSF in a transverse xy plane and the extension to the 3D APSF is achieved by recording and processing the collected hologram stack obtained by a fast scan along the optical axis. The set-up was found stable enough to perform precision phase measurements and the reproducibility of the measurements was verified. A good agreement was found between the experimental data and the theoretical predictions, even when only a simple theoretical scalar model is applied. The phase measurements bring new information and, in some cases, t