Biomedical Engineering Reference
In-Depth Information
specimen is removed. The reference hologram could possibly be recorded by replacing the specimen
with a frequency doubler crystal. While this could compensate for most of the setup aberrations, it is
however very likely that such a nonlinear crystal will introduce other aberrations that will reverberate
in the reference hologram-corrected reconstructions.
See Colomb et al
.
(2006b) and Miccio et al
.
(2007) for more details on this technique.
9.5 image contrasts in Digital Holographic SHG imaging
Holography differs from most optical imaging techniques, in the sense that it does not produce images
of light intensity contrasts. Instead, holography encodes in an intensity contrast hologram both the
amplitude and the phase of an object wavefront. With classical holography, this leads to a 3D appear-
ance of the reconstructed images. In digital holography, amplitude and phase can be simultaneously
reconstructed in separate images of different contrast (Cuche et al
.
, 1999).
Holographic SHG imaging also makes possible retrieval of both second-harmonic amplitude and
phase and may thus provide similar image contrast. There is altogether one important difference
between holographic SHG imaging and bright-field digital holography: SHG images are background-
free, meaning that there is a signal (amplitude and phase) only where SHG occurs. In opposition, the
object wave in bright-field digital holography generally has intensity all over the field of view, even in
regions where there is no object. As a result, part of the light incident on the specimen is not diffracted
and reaches the detector unaltered. Yet not diffracted by the specimen, this light still interferes with the
reference wave and thus provides a support for the carrier frequency of the hologram fringes. This is
not the case with holographic SHG imaging and, as we have already seen, it has dramatic consequences,
notably making use of reference hologram correction impossible.
Here, we show how holography makes possible the retrieval of amplitude-, intensity-, and phase-contrast
images. For the following discussion, let us suppose that hologram reconstruction yields the wave ψ =
Ae
i
φ
.
9.5.1 Amplitude images
The amplitude contrast image is obtained by assigning
ψ
=
A
to a colormap. The amplitude contrast
image is proportional to the electric field distribution. An interesting observation is that, for a given
dynamic range, amplitude contrast provides a better sampling of weak signals than intensity contrast.
To illustrate this, let us consider an Airy disk amplitude object imaged with an ideal 8-bit detector
that fully exploits its given bit depth. Now, let us compare an image of the object amplitude retrieved
with a holographic method to one obtained by simple intensity-based imaging. For this comparison,
we suppose that the image is recorded in focus for both methods and that, since the detector is ideal, its
dynamic range scales from 0 and 255 in both cases.
Even then, weak signals are sampled differently by the two methods. On one hand, Figure 9.8a illus-
trates the square root (i.e., the amplitude) of the 8-bit intensity image recorded by our ideal detector. On
the other, Figure 9.8b illustrates the amplitude of the complex wavefront retrieved from the 8-bit digital
hologram. Looking at the profiles plotted in Figure 9.8c, one sees that both methods provide a similar
sampling of the central spot, but that holography provides a better sampling of the diffraction rings.
Indeed, more rings are visible in the holographic image. Furthermore, discrete intensity levels are seen
for the profile obtained with intensity-only imaging that are not observed on the profile obtained with
the holographic method, even though the hologram was discretized to the same bit depth. This is due to
the modulation introduced in the hologram by the interference fringes and to the image reconstruction
process. We note that it would have been even more advantageous, with such an ideal detector, to record
the hologram out of focus so that the intensity of the central region would spread over a larger surface,
therefore, reducing the dynamic range of the object wave.
In summary, because holography retrieves the amplitude of the object wave, it is more suited than
intensity-based imaging for detection of weak signals.
