Optical Diffraction Tomography (ODT) allows a three-dimensional quantitative
imaging of the absorbtivity and refractive index of a specimen (Lauer,
2002). The fields diffracted by the object are measured from a number
of angles of incidence of a parallel laser beam. The object is reconstructed
from this plurality of field measurements. Reconstruction uses linear
Fourier transform algorithms in which case resolution is improved by a
factor of 2 as compared to holography or standard microscopy (Lauer, 2002).
In certain cases resolution can be further enhanced using iterative inversion
algorithms (Belkebir et al., 2003). These algorithms used amplitude
and phase data on the diffracted field in order to reconstruct the object.
The most straightforward method to record both the phase and amplitude
of the scattered wave is phase shifting holography. However, when successive
illumination beams of different directions are used, it is not possible
to control the phase of these beams. So, far Lauer successfully used phase
shifting holography by an accurate compensation of the non control phase
shift. But the setup of that experiment was very sophisticated.
The aim of this study is to build a non complex ODT experimental setup
in order to acquire the amplitude and the phase of the diffracted field.
These results could be used by iterative inversion algorithms team to
validate that method.
A transmission setup equipped with a Michelson interferometer is built
as shown in Fig. 1. A coherent beam is generated by
a polarized HeNe laser and split, by beamsplitter A into an illumination
beam and a reference beam. This illumination beam is a plane wave illuminating
the sample. It is phase modulated by an electro-optical phase modulator.
The reference wave is a plane wave Eref = Aref
exp j (Î”Ï†) superimposed to the information carrying wave by
beamsplitter B. The information carrying wave is the diffracted field
of the sample.
|| Diagram of the setup
|| Intensity Ird of the interference between
the diffracted field and the reference field at angle 6Â°
||Intensity Iri of the interference between
the non diffracted field and the reference field at angle 0Â°
With one photodetector placed on a moving arm, the intensity Ird
(Fig. 2) of the interference between the diffracted
field and the reference field at different angles is measured.
With the second photodetector, the intensity Iri (Fig.
3) of the interference between the two arms of the Michelson interferometer
With both signals Ird and Iri, the phase Ï†
of the diffracted field of the sample is determined.
RESULTS AND DISCUSSION
The sample is illuminated using the beam only in the normal direction.
With both signals the phase Ï† of the diffracted field is determined
as shown in Fig. 4.
A number of directions of the illuminating wave are used and the corresponding
intensities of interference are measured. Following this the corresponding
phases of the diffracted field are shown in Fig. 5.
|| Phase of the diffracted field
|| Normalised intensity of the diffracted field
From this experiment, it can be concluded that the setup used is easy
to build. It proves resistant to vibrations. Few optics element used in
the setup. By acquiring the signal, it is possible to control the phase
of whether illuminating beam. The measurement made and the phase obtained
lead to the expected outcome that is the effectiveness of this setup.