Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 117

a b

Fig. 4.2 Comparison of the ray paths in ( a ) wide-field, and ( b ) confocal microscopes (Adapted
from Wikimedia Commons). The two schematics show the filter block consisting of the excitation
filter, emission filter and the dichroic mirror. In ( b ), the light from the in-focus plane reaches the
PMT while the emissions from the out-of-focus plane are blocked by the pinhole aperture

available molecules ( > 1 %) are activated and imaged. A two-dimensional (2-D)
Gaussian model is fitted to the detected intensities from each individual photo-
activated molecule. The image is built up slowly by summing the locations of
molecules imaged in successive activations. In wide-field SIM, the resolution is
improved by imposing and modulating a grid pattern in the illumination/excitation
light. A grid is projected onto the focus plane of the objective and then shifted
laterally with respect to the sample, and also oriented in three directions, 60 ◦ apart.
The sequence of images obtained, as a result of this lateral shifting and reorienting,
are de-interlaced in the Fourier space [ 32 ], and the inverse Fourier transform yields
the super-resolved reconstructed image in real space. We recommend the guide [ 66 ]
for the recent techniques in super-resolution microscopy (both near and far-field)
and also the article in [ 55 ].

4.1.2.4 Mathematical Context

The process of deblurring can be mathematically achieved by deconvolution.
Although deconvolution is discussed here in the context of microscopy, this
technique is neither new nor restricted to this field alone. Blur could be very
commonly encountered in almost all imaging applications such as satellite imaging,
remote sensing, and astronomical observations [ 16 ]. In general they fall under one
of the following three categories:

• Motion blurring caused due to a significant 'relative' motion between the

observed object and the imaging device;

• Interference by media. For example, in ground-based telescopes, when imaging

celestial objects, there can be image quality degradation due to atmospheric