Is There a Fundamental Limit to Spatial Resolution in Phase Microscopy? - Biomedical Optical Phase Microscopy and Nanoscopy - page 331

therefore either two orders were within the aperture, in which case the object period could
be resolved, or only one, in which case it could not be. However, if the object is a finite
grating, the orders are not delta-functions, and even if the center of an order is outside the
aperture, its sidebands may be within the aperture and can allow resolution, although with
less accuracy. If the shape of the object envelope is known, mathematical techniques can be
used to improve this accuracy. Such techniques can be described as deconvolution, which
will be discussed later. We can take this to the extreme in near-field scanning optical
microscopy (NSOM) [12] , where the instantaneous field of view (the illuminated spot) is
much smaller than so that the diffraction order picture is not relevant. Some radiation is

always received by the detector, and the image is built up sequentially. However,
knowledge of the position of the imaged point is lost in the diffraction but is known from
the scanning mechanism. As a result, scanning microscopy is not diffraction limited.

λ

16.3 Parallel Full-Field Linear Imaging

From the point of view of spatial resolution, phase imaging is not different from intensity
imaging. This has been demonstrated by an interferometric NSOM, in which the detector
receives light simultaneously from the near-field probe and reference beam, and a phase-
dependent interference signal is recorded [13] . However, the question to be addressed here
refers to resolution limitations in linear imaging when the whole field is recorded by an
imaging device. This is important generally for observing dynamic processes or in industry
where point scanning methods are too slow for high throughput. Two main directions have
been explored for linear super-resolution: image reconstruction from coherent diffraction
patterns and structured illumination microscopy (SIM) using incoherent illumination.

16.4 Reconstruction from Diffraction Patterns

The basis of this method is like X-ray diffraction: the diffraction pattern of an object is
recorded, using a coherent incident beam, and the structure is determined by inverse Fourier
transformation. Its use for X-ray imaging by nonperiodic objects was first suggested in
1998 by Sayre et al. [14] . It is important to recall that if the diffraction pattern is not
centro-symmetric, the object must include nontrivial phase information. The phase
problem—that only the diffracted amplitudes are observed and not the phases—which
seemed to be an obstacle to such microscopy is solved algorithmically by applying
constraints to the object and finding by iterative techniques an object which fits both the
constraints and the observed diffraction pattern [11,15] . In crystallography, the constraints
of the unit cell properties and non-negativity of electron density are used [16] , while in
optics, the bounding shape of the object may be defined [7,8] . In these experiments, the
object fills a small region of the coherently illuminated field of view so that the diffraction
pattern is over-sampled [17] , and both amplitude and phase information about the object