Biomedical Engineering Reference
In-Depth Information
shifts have to be controlled with high precision, since the algorithm is based on the hypothesis that each
hologram is in phase quadrature with the previous.
Today, there exist many other phase-shifting algorithms to retrieve the amplitude and phase of the
object wavefront. Some require as few as three holograms when the phase shifts between the holograms
can be very precisely controlled, others require more holograms but no a priori knowledge of the phase
shifts between them. See Kreis (2005) for more information.
9.4.2.3 comparison between Phase-Shifting and off-Axis Methods
The major advantage of off-axis separation of zero-order and twin image terms is that it can be performed
from a single hologram. This makes off-axis digital holography more suitable than its phase-shifting
counterpart for real-time imaging. It also allows off-axis digital holography to excel in conditions where
phase-shifting digital holography is simply impossible to use: for example, in high vibration environ-
ments, such as moving vehicles like a space satellite, as well as for specimens moving or changing shape
at very high speed.
On the other side, phase-shifting holography uses the entire spatial bandwidth of the digital sensor
and thus produces sharper images, whereas off-axis holography, because it oversamples the optical fre-
quency content, does not look as sharp. This does not mean that off-axis holography suffers from a loss
of resolution. Most off-axis holographic microscopy setup have, anyway, diffraction-limited resolution,
determined by the microscope objective's numerical aperture. Rather, it means that this diffraction-
limited resolution corresponds to many pixels in the image, hence the loss of sharpness.
9.4.3 Aberration correction
The term optical aberration describes the nonideal behavior of imaging system that leads to distortion of
the produced image. To set ideas in context, the optical aberrations we are referring to are of the mono-
chromatic type, since digital holography generally uses monochromatic light sources. Every optical ele-
ment in a setup is a potential source of monochromatic aberrations and each can have a unique effect,
or signature, on the wavefront. Obviously, the more optical elements there are, the more complicated to
characterize may become the resulting optical aberrations.
Digital holography is a very powerful imaging technique, for it retrieves both the amplitude and the
phase of the object wavefront. As such, it is particularly adapted to characterize and correct for optical
aberrations. Indeed, the phase retrieved by digital holography is nothing but the simple addition of these
contributions:
1. The absolute phase shift introduced by the specimen
2. The tilt aberration due to the off-axis geometry
3. The curvature mismatch between
o
and
r
4. Any other aberration induced by the optical elements of the setup
Methods exist to identify nonspecimen-related contributions to the retrieved phase, and to com-
pensate them. In this section, we briefly present two different methods to numerically correct for opti-
cal aberrations in a digital holographic setup, namely the numerical parametric lens and the reference
hologram correction.
9.4.3.1 numerical Parametric Lens
This method is based on the assumption that any optical aberration can be decomposed in a series of lin-
early independent coefficients in a given polynomial base. This polynomial base can be, for instance, the
Zernicke polynomials or the standard polynomials of
x
and
y
, the lateral coordinates in the hologram
plane. For the sake of simplicity, only the latter will be treated here.
Let us suppose that the phase change introduced in the wavefront by the sum of all optical aberrations
can be expressed as
