Characterization techniques - Micromixers Fundamentals Design and Fabrication - page 298

Another important parameter of the microscope/camera system is the relation between the in-plane
spatial resolution d , magnification M , and the pixel size of the sensor d pixel . The in-plane spatial
resolution is limited by the diffraction effect [1] :

r

n
NA

2

d ¼ 1 : 22 M l 1 (8.12)

where n is the refraction index of the recording medium and NA and M are the numerical aperture and
the magnification of the microscope system, respectively. The required pixel size d pixel can be esti-
mated from the in-plane spatial resolution and the size of the sample (such as an particle) d p as

q

d 2 M 2 d P d pixel ¼ þ : (8.13)

If d [ Md p , the required pixel size is determined by diffraction. If d Md p , the required pixel size is

determined by the geometric sample size, d pixel z Md p .

Figure. 8.2 only depicts a simplified and ideal microscope system with ideal lenses. Real lenses
have problems with longitudinal chromatic aberration. This means different colors are focused at
different positions along the optical axis because the refractive index is a function of wavelength.
Modern microscopes have complex lens systems with achromatic droplets, which comprise a convex
crown glass lens next to a flint concave lens.
Because measurement of intensity distribution is important for quantitative characterization of
micromixers, the quality of the illuminating system is important for the microscope setup. The illu-
minating system of a research-grade microscope should fulfill three basic criteria:

It should allow maximum resolution and maximum contrast,

It should be simple and easy to adjust, and

It should have uniform illumination.

The most common illumination source of modern microscopes is laser. The laser light produces an
output beam that is both coherent and collimated, which is ideal for illumination purposes.

8.1.2 Two-dimensional fluorescence microscopy
One solution for problems associated with chromatic aberration is using chromatic illumination and
detection. Fluorescent microscopy is based on fluorescence, which is an optical phenomenon in cold
bodies. A molecule absorbs a photon and then emits another photon with a longer wavelength. The
energy difference between the absorbed and emitted photons is dissipated as heat. The absorbed
photon is commonly in the high-energy ultraviolet range, and the emitted light is in the visible range.
However, many fluorescent dyes or fluorophores have both excitation and emission wavelengths in the
visible range. The difference between the emission wavelength and the excitation wavelength is called
the Stokes shift.
In a fluorescence microscope, excitation and emission wavelengths have to be separated selectively
from other wavelengths using optical filters. Figure. 8.4 (a) shows the basic concept of a fluorescence
microscope system. Light from a source is directed to a filter cube through a condenser lens system.
Typical light sources for a fluorescence microscope system are high-pressure mercury lamps, xenon
lamps, halogen lamps, or lasers. A heat filter keeps infrared wavelengths out of the optical system to