Deconvolution and Denoising for Confocal Microscopy - Modeling in Computational Biology and Biomedicine - page 118

turbulence. This can be also the case for microscopes when the specimen medium
is turbid;

• Out-of-focus blur where part of the object is not in focus.

The mathematical description of each of the above cases is different principally
because the underlying physical phenomenon causing the deterioration are different.
In fluorescence microscopy, we often deal with the out-of-focus blur. The difference
between this and the other categories is that in fluorescence microscopy the blurring
phenomenon is in 3-D (i.e., both radial and axial).
In order to solve this image processing problem, it is necessary to break it down
into the following three sub-problems:

• A forward problem (also called direct problem), where knowing the object and

the observation mechanism, we establish a mathematical description of the object
observed. This model will be a compromise between exact description of the
observed physical phenomenon and a simple one for processing;

• An instrumentation problem, in which a complete description of the imaging

properties of the instrument must be acquired and modeled;

• An inverse problem, where the object must be estimated from the preceding

models and the data.

The above three sub-problems are unique for the optics and the imaging sensor used.
We will discuss these sub-problems in this chapter, with respect to fluorescence
microscopy, although not necessarily in the above order.

4.1.3 Bettering the Resolution

Better resolution is often a desired feature to inspect the specimen in detail.
However, the quality of the image produced and its resolution depend on the lens, its
Numerical aperture (NA), 3 and the wavelength of excitation light ( λ ). Ernst Abbe is
credited with showing that light, with a wavelength of λ , when traveling through a
lens of NA, will make a spot of radius governed by the following law:

d = 0 . 61 λ
NA

.

(4.1)

Most commercial microscope objective lenses in the range of 40 ×

magnification, have an effective working NA of about 1 . 4 (in immersion oil
medium). In such a case, the resolution limit, from Eq. ( 4.1 ), is a little less than

× to 100

3 The numerical aperture of a lens measures its maximum light collection angle. It can be calculated
as NA = n sin α ,where n is the refractive index of the imaging medium between the objective
lens and the coverglass, and α is the maximum semi-angle subtended by the incident light cone
accepted by the lens.