Abbe’s diffraction limit

Spatial resolution (SR) With wavelengths of light between 2.5 pm and 25 pm, Abbe s diffraction limit constrains mid-IR microspectroscopy to the observation of areas which are of similar size to the cellular compartments. While Abbe s criterion describes the principal limitation for the lateral spatial resolution (SR), many other factors restrict the practically achievable SR further. Furthermore, the choice of the size of the sample area to be measured depends on the problem and the type of biomedical samples. However, depending on the specific case, the maximum SR is often not required in MIR microspectroscopy. 

It has to be noted that, due to Abbe s diffraction limit, two objects cannot be individually observed which are separated by less than A/2. However, if there is only a single object within the resolution limit the position of it can be determined with much higher precision. For this one has to scan spatially over the object, measuring the spatial intensity distribution. The precision of determining the position, 5x, is then approximately given by... 

T.A. Klar et al., Fluorescence microscopy with diffraction resolution limit broken by stimulated emission. Proc. Natl. Acad. Sci. U.S.A 97, 8206-8210 (2000) T.A. Klar, E. Engel, S.W. Hell, Breaking Abbe s diffraction resolution limit in huorescence microscopy with stimulated emission depletion beams of various shapes. Phys. Rev. E 64, 066613, 1-9 (2001)... 

Eor optical microscopy, the most significant advantage of TERS is its high spatial resolution beyond the diffraction limit of light An optical field is spatially confined into a region several tens of nanometers in size at the tip of the metalUc probe [55, 56], On the other hand, according to Abbe s theory, the minimum size A that can be resolved by a conventional optical microscope is given by [57]... 

R /f is the numerical aperture (N.A.) and is marked on all objective lenses, together with the magnification. For example, a x25 objective with N.A. = 0.5 is expected to resolve detail of the order of 2X 1 m, ideally. Equation (2.1) has been derived by considering diffraction by a coherently illuminated periodic object. Rayleigh s well-known criterion of resolution, derived for a nonperiodic object incoherently illuminated, gives nearly the same limit of resolution as that determined from the Abbe approach and need not be considered here (see, e.g., Giancoli 1984). 

---