as much angular bandwidth as the lens being tested (and of course, is uniform over that angular sector). In other words, we only require a point source which is produced by a convergent (uniform) spherical wave whose half angle is greater than the edge angle of the lens. Due to intrinsic limited resolution of the imaging systems, measured PSFs are not free of uncertainty. In imaging, it is desired to suppress the side-lobes of the imaging beam by apodization techniques. In the case of transmission imaging systems with Gaussian beam distribution, the PSF is modeled by the following equation: where k-factor depends on the truncation ratio and level of the irradiance, NA is numerical aperture, c is the speed of light, f is the photon frequency of the imaging beam, Ir is the intensity of reference beam, a is an adjustment factor and is the radial position from the center of the beam on the corresponding z-plane. History and methods The diffraction theory of point spread functions was first studied by Airy in the nineteenth century. He developed an expression for the point spread function amplitude and intensity of a perfect instrument, free of aberrations (the so-called Airy disc). The theory of aberrated point spread functions close to the optimum focal plane was studied by Zernike and Nijboer in the 1930–40s. A central role in their analysis is played by Zernike's circle polynomials that allow an efficient representation of the aberrations of any optical system with rotational symmetry. Recent analytic results have made it possible to extend Nijboer and Zernike's approach for point spread function evaluation to a large volume around the optimum focal point. This extended Nijboer-Zernike (ENZ) theory allows studying the imperfect imaging of three-dimensional objects in confocal microscopy or astronomy under non-ideal imaging conditions. The ENZ-theory has also been applied to the characterization of optical instruments with respect to their aberration by measuring the through-focus intensity distribution and solving an appropriate inverse problem. Applications Microscopy In microscopy, experimental determination of PSF requires sub-resolution (point-like) radiating sources. Quantum dots and fluorescent beads are usually considered for this purpose. Theoretical models as described above, on the other hand, allow the detailed calculation of the PSF for various imaging conditions. The most compact diffraction limited shape of the PSF is usually preferred. However, by using appropriate optical elements (e.g., a spatial light modulator) the shape of the PSF can be