Page 43 - Handbook of Properties of Textile and Technical Fibres

24 Handbook of Properties of Textile and Technical Fibres

field. The depth of field is the maximum vertical separation that can exist between two
2
objects that are in focus and is approximately 0:5 ðNAÞ mm where NA is called the
numerical aperture and will be defined in the following paragraphs.
Whatever the resolution of the image sensors, i.e., the number of photodiodes and
their size relative to the image projected onto the chip’s surface by the lens, the reso-
lution limitation comes from the light itself. For years, generations of scientists have
indeed thought they would never get a better resolution than that formulated in
1873 by Ernst Abbe. The wavelength of visible light is indeed around half a micron
and before the discoveries of the 2000s it was difficult to resolve objects in this size
range (Gustafsson, 2000). Ernst Abbe was the first to quantify the resolution limit
of optical microscopy, an instrumental technique invented in the 16th century and
widely used at the end of the 19th century in the field of life sciences. His analysis
makes it possible to calculate the maximum resolution of an optical microscope,
imposed by the diffraction phenomenon, as a function of the wavelength of the light
used. According to Ernst Abbe, in the case of an immersion microscope lens with
circular aperture and direct axis illumination, the resolving power is given by
l
RP ¼ (2.5)
NA

where l is the wavelength of the light. The numerical aperture expression,
NA ¼ n sin a, takes into account the refractive index of the surrounding observation
medium n and the half-aperture angle a. The use of water-immersion lens (n ¼ 1:33)
or oil-immersion lens (n z 1:5) thus improves the resolving power achieved with air
(n ¼ 1). Using an oblique illumination, the resolving power becomes
l
RP ¼ (2.6)
2NA
which is the classical Abbe’s formula. An empirical and a more familiar formulation
was proposed by Lord Rayleigh at the same time:

l
RP ¼ 1:22 (2.7)
2NA
Manual fiber-to-fiber analysis can be tedious using optical microscopy; so if it is the
fiber population distribution which is sought, some automated techniques can be used.
Most of these methods consist in spreading cut fiber snippets onto a glass slide.
Sequential digital images are then captured and more or less sophisticated image anal-
ysis algorithms are applied to automatically measure diameters. Today, most of the
particle shaped analyzers based on image analysis technology can be used. In 1991,
the optical fiber diameter analyzer instrument (Baxter et al., 1992) was made available
by Cottonscope Pty Ltd, which provides a robust, repeatable, and accurate method
dedicated to obtaining the diameters of fibers. This instrument has been combined
with a subpixel software algorithm to enhance the resolution and this allows fast mea-
surements up to 40,000 fibers/min (Brims and Hwang, 2015).