The present invention discloses a method to improve the 
image resolution of a 
microscope. This improvement is based on the mathematical 
processing of the 
complex field computed from the measurements with a 
microscope of the wave emitted or scattered by the specimen. This wave is, in a preferred embodiment, electromagnetic or optical for an 
optical microscope, but can be also of different kind like acoustical or matter 
waves. The disclosed invention makes use of the quantitative phase 
microscopy techniques known in the sate of the art or to be invented. In a preferred embodiment, the 
complex field provided by 
Digital Holographic Microscopy (DHM), but any kind of 
microscopy derived from quantitative phase 
microscopy: modified DIC, Shack-Hartmann 
wavefront analyzer or any analyzer derived from a similar principle, such as multi-level lateral shearing interferometers or common-path interferometers, or devices that convert stacks of intensity images (transport if intensity techniques: TIT) into quantitative 
phase image can be used, provided that they deliver a comprehensive measure of the complex scattered wavefield. The hereby-disclosed method delivers 
superresolution microscopic images of the specimen, i.e. images with a resolution beyond the Rayleigh limit of the 
microscope. It is shown that the limit of resolution with coherent illumination can be improved by a factor of 6 at least. It is taught that the 
gain in resolution arises from the mathematical digital 
processing of the phase as well as of the amplitude of the 
complex field scattered by the observed specimen. In a first embodiment, the invention teaches how the experimental observation of systematically occurring phase singularities in 
phase imaging of sub-Rayleigh distanced objects can be exploited to relate the locus of the phase singularities to the sub-Rayleigh distance of point sources, not resolved in usual 
diffraction limited microscopy. In a second, preferred embodiment, the disclosed method teaches how the 
image resolution is improved by complex 
deconvolution. Accessing the object's scattered complex field—containing the information coded in the phase—and deconvolving it with the reconstructed complex 
transfer function (CTF) is at the basis of the disclosed method. In a third, preferred embodiment, it is taught how the concept of “Synthetic Coherent 
Transfer Function” (SCTF), based on 
Debye scalar or Vector model includes experimental parameters of MO and how the experimental Amplitude 
Point Spread Functions (APSF) are used for the SCTF determination. It is also taught how to derive APSF from the measurement of the complex field scattered by a 
nanohole in a metallic film. In a fourth embodiment, the invention teaches how the limit of resolution can be extended to a limit of λ / 6 or smaller based angular scanning. In a fifth embodiment, the invention teaches how the presented method can generalized to a tomographic approach that ultimately results in super-resolved 3D 
refractive index reconstruction.