consecutively adjusted in discrete steps, and a stack of two-dimensional images of different
sections are collected. Since the acquired images are blurred due to contributions outside the
focal plane during the image formation, a digital process-called deconvolution-is carried out
to remove the blurring and to reconstruct a corrected 3D image. Optical sectioning and the
deconvolution algorithms used in this work are briefly discussed as follows; additional details
can be found in the literature.60 61
3.2.1 Optical Sectioning
In essence, optical sectioning samples discrete planes from a continuous light signal in a
three-dimensional space. This sampling process must satisfy the Nyquist sampling theorem,6 63
which requires the sampling frequency to be greater than twice the input signal bandwidth in
order to assure perfect reconstruction of the original signal from the sampled version. In the
spatial domain, this requires a sampling interval to be less than half of the characteristic
dimension of the source signal.
A CCD camera is used to sample the discrete planes along the optical axis. The sampling
interval in the axial direction (Az) is defined by the spacing between two adjacent image
1.4An
acquisitions. The axial resolution of a microscope is defined by r = N where 2 is the light
NA
wavelength, n is the refractive index of media, and NA is the numerical aperture of the objective
lens.60 To meet the requirement of the Nyquist sampling theorem, then A I< i i.e.,
2
0.7An
Az <---
NA2 (3-1)
3.2.2 Convolution
The images acquired via optical sectioning are degraded for two reasons: optical blurring
and image degradation due to electronic noise. Optic blurring is due to the optical aberration of