Is There a Fundamental Limit to Spatial Resolution in Phase Microscopy? - Biomedical Optical Phase Microscopy and Nanoscopy - page 329

CHAPTER 16
Is There a Fundamental Limit to Spatial
Resolution in Phase Microscopy?

Stephen G. Lipson
Physics Department, Technion-Israel Institute of Technology, Haifa and Department of Physics and
Optical Engineering, Ort-Braude College, Karmiel, Israel

Editor: Zeev Zalevsky

16.1 Introduction

Abbe's well-known criterion for spatial resolution in incoherent imaging, /2NA, has

been the benchmark for all discussions of resolution since its publication in 1873. The term
“super-resolution” was coined in 1952 by Toraldo di Francia [1] who showed, theoretically,
that there is actually no resolution limit to imaging because a point spread function with
arbitrarily small diameter can be created by means of an appropriately designed phase
mask. This idea has recently been rediscovered and given the name “super-oscillation” by
Berry and Popescu [2] because the phase of the light in the central spot changes spatially at
a rate larger than k 0 5 2

δx 5 λ

. What is clear from Toraldo di Francia's papers is that the light
utilization is very poor, an overwhelming part of the light being diffracted into bright outer
rings of the point spread function; however, within a certain dark field of view, bounded by
the bright rings, super-resolution can be achieved. This method was first used to improve
resolution in a confocal microscope by Hegedus and Sarafis [3] , where the outer bright
rings of the point spread function could be obstructed by the light collection aperture.
Improvement of resolution of a two-point image using this technique was demonstrated by
Leiserson and Lipson [4] , and in principle their method shows that phase images could also
be created the same way. More recent work on resolution enhancement using coded
apertures is reviewed by Willett et al. [5] .

π / λ

The relationship between field of view and resolution had already been emphasized in 1966
by Lukosz [6] , who showed for a general imaging system that the real limitation is the
number of degrees of freedom in the image or the space-bandwidth product . Thus, when an
object is known to occupy a limited region of the field of view, an optical system can be