Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 124

Fig. 4.4 ( a ) A diffracting aperture represented here as a uniform disc (Courtesy Inria), and ( b )the
2-D Airy disk pattern after diffraction by the aperture (Adapted from Wikimedia Commons)
small circular aperture (Fig. 4.4 a), such as an objective lens in a microscope, it does
not produce a bright dot as a 2-D image, but rather a diffused circular disk, known
as Airy disk, surrounded by much fainter concentric circular rings (Fig. 4.4 b). This
Airy disk is the system's response to an impulse (here a Dirac source) signal and
it constitutes the best description of the imaging properties of the optical system
(here a microscope) [ 10 ]. This non-random spreading of a point light source, or
blurring, is a consequence of diffraction by a limited aperture (either the objective
or the condenser lens or both). An image whose resolution is thus constrained is
said to be “diffraction-limited” [ 32 ]. The experimental measurement of this barrier
by Abbe (Eq. 4.1 ), which was discussed in Sect. 4.1 , is exactly due to diffraction.
Effect of Pinhole Size. The size of the pinhole in a CLSM is calibrated against the
diffraction rings. The sizes of the pinholes are annotated by their back-projected 4
values in Airy units (AU). We define 1 AU=(1 . 22 λ ex ) / NA,where λ ex is the
excitation wavelength. As we reduce the pinhole size, the diffraction rings are
blocked out. At 1 AU, the pinhole has about the size of the central principal
maximum. From our experiments in [ 52 ], with a sample from the Arabidopsis
thaliana plant immersed in water, it was observed that, with sizes < 1 AU there
might be more contrast and less blur, but there are very few photons detected at the
PMT. This is on top of the low Quantum efficiency (QE) 5 of the PMTs (around 6 %).
While, images obtained with pinhole sizes > 3 AU have larger spot and more intense
signal (signal from the region of interest and out-of-focus signal), but loss in contrast
as well due to unwanted fluorescence. As far as the photon statistics are concerned,
one could even say that the microscope almost behaves like a wide-field because of
4 Back-projected diameter is the diameter of a pinhole in the object space. It is equal to the ratio
between the real physical diameter of the pinhole and the total magnification of the system.
5 Quantum efficiency for a photosensitive device measures the percentage of photons hitting the
photoreactive surface that will produce an electron-hole pair. It is an accurate measurement of the
device's electrical sensitivity to light.