Is There a Fundamental Limit to Spatial Resolution in Phase Microscopy? - Biomedical Optical Phase Microscopy and Nanoscopy - page 333

The concept of image retrieval from minimum data, in the presence of noise, is extremely
important in telescope imaging. Because astronomical fields are mainly black anyhow,
deconvolution with the known point spread function is very effective [19,20] . In terms of a
microscope image, biological objects satisfying the conditions are rare; however, it is
possible to isolate an object by using a field stop provided that the object is illuminated by
a much broader coherent beam so that the coherence within the field stop is complete and
therefore its diffraction pattern is well determined. In the work of Shapiro et al. [7] , the
support was derived iteratively rather than being known exactly a priori. Moreover, the
authors emphasize that since the object is small compared with the size D of the coherent
illuminating X-ray beam, the Fourier transform can be sampled on a fine lattice (at angular
intervals of λ / D ), which makes the reconstruction possible.

16.5 Structured Illumination Microscopy

The method of structured illumination, which can be applied to transmitted or reflected
light imaging, requires illuminating the object not with uniform light but with an
illumination pattern containing high spatial frequencies. The resulting image has a Fourier
transform, which is basically the transform of the required image convolved with that of the
illumination pattern. Because of the high spatial frequencies in the latter, similar high
frequencies in the object transform are transferred by the convolution operation to low
frequencies in the image transform and are therefore clearly represented. The image is then
reconstructed algorithmically from this transform. The effect is well known to us as the
moir´ effect, where two superimposed high-frequency gratings give rise to low-frequency
“beats” in the image ( Figure 16.2 ). This method is hinted at in Lukosz's [6] paper but was
developed by Ben-Levy and Pelac [21] for semiconductor wafer inspection and by
Heintzmann and Cremer [22] and Gustafsson [23] for microscopy. The usual
implementation is to use an illumination grating with spatial frequency k g close to the
resolution limit of the microscope, which we will call k m , approximately

/2NA
( Figure 16.3 ). Now you can see that information in the image with frequency 2 k m , normally
well outside the imaging capabilities of the microscope, provides a component at
(2 k m

λ

k g ) 5 k m when it is modulated by the grating frequency, and this is just at the
resolution limit of the microscope and can therefore contribute to the image. The resolution
limit has thus been increased by a factor of two . To carry this out isotropically for a general
two-dimensional image containing information at many spatial frequencies, it is necessary
to record a series of modulated images with the illumination grating at several angles and
each at least in three different phases. The process is shown in Figure 16.3 .

SIM has been developed for both bright-field and fluorescence imaging, although mainly
for the latter. This is because the modulation transfer function (MTF) for spatially
incoherent illumination, which is usually used for nonfluorescent microscopy to avoid
speckle, approaches zero at the resolution limit ( Figure 16.4 ). This can be overcome by