Is There a Fundamental Limit to Spatial Resolution in Phase Microscopy? - Biomedical Optical Phase Microscopy and Nanoscopy - page 338

suggest that for a compact sample with volume d 3 , the resolution limit attainable by
deconvolution is such that the number of resolvable elements in the sample is less than half
m , i.e., δ xλd/D .

The above discussion assumes the ideal situation in which diffraction patterns of the object
can be accessed in every direction with the required dense angular sampling at intervals
λ / D in azimuth and elevation; an enormous task. The inevitable practicalities essentially

caused the limitation of resolution of the image shown in Figure 16.1 . However, the
analysis provides the tools for estimating achievable resolution under practical
circumstances. As a numerical example, we might take a coherent field of view of diameter
D 5 1000 (i.e., d/D 5 0.01).

Then, using 100 diffraction patterns of the object in distinctly different orientations, each
one recorded in a unit solid angle, one could theoretically obtain resolution of about 0.03

λ , diffracting off a sample whose extent is known to be d 5 10 λ

λ ,

which exceeds the Abbe's diffraction limit by an order of magnitude. Of course, here, we
have ignored the considerable computational effort required for each image, and the fact
that recording numerous diffraction patterns with high signal to noise might make the
process as slow as scanning, which we were trying to avoid!

16.7 Conclusions

Without the use of fluorescent markers, microscopic resolution is limited by the physics of
the diffraction process. However, this can be extended beyond the classical Abbe's limit.
Two proven methods of increasing resolution are SIM and reconstruction from sampling the
coherent diffraction pattern of an object. Both can create phase contrast. The former is
restricted to two-dimensional objects, while the latter requires the object to fill a known
small region of the field of view in order to make deconvolution possible in the presence of
noise.

Acknowledgments

I wish to thank Dr. E. Ribak for numerous comments on this manuscript.

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