Biomedical Engineering Reference
In-Depth Information
imaging technique used, but rather to the imaged subject. When looking for a sensor for digital hologra-
phy, one must consider some other important specifications, like pixel pitch and total number of pixels.
One of the major problems of digital imaging in general is the shot noise. Shot noise is a type of noise
that occurs when the finite number of particles that carry energy is small enough to give rise to detect-
able statistical fluctuations in a measurement, according to Poisson statistical distribution. Shot noise is
independent of the quality of the electronic of a sensor and is only dependent on the number of photo-
generated charge carriers. To reduce its influence, one should work with the highest possible number
of photo-generated charge carriers. Critical for digital imaging is the (full) well capacity, that is, the
number of charge carriers a pixel can contain before it saturates.
As the collected SHG intensity is rather weak, there is an interest in having a camera multiplying elec-
trons before the readout is made. Electron multiplying CCD (EMCCD) and, possibly, intensified CCD
cameras, especially suited for any low-light-level application, thus appear ideal for holographic SHG.
For some specific applications, for example, fluorescence or nonlinear imaging, the operating tem-
perature of the sensor is important. When working with very weak signals, such as SHG, the thermally
generated dark noise can become quite important, compared to the intensity of the signal of interest.
Ideally, the detector would be cooled down to low temperature, in order to reduce thermal noise. A rule
of thumb states that the dark current reduces by half for every 9 K of temperature drop.
The bit depth is actually not very relevant for holography. We recall that Goodman's experiment
was carried out with a very low 3 bits depth, giving only eight quantized gray levels (Goodman and
Lawrence, 1967). In fact, Mills and Yamaguchi reported evidence that 4-bit quantization is enough to
provide a satisfactory visual image, and that not much difference could be seen for holograms recorded
with 6- or 8-bit quantization (Mills and Yamaguchi, 2005). Therefore, an 8-bit sensor is already enough
for digital holography.
More important is the total number of pixels which sets the speed of hologram reconstruction. As
most of the computation involves Fourier transforms, it is preferable (faster) to work with images having
dimensions N x and N y that are integer power of 2, for example, 512 × 512 pixels, although nothing pre-
vents the two dimensions to be different: the image can very well be rectangular. In any cases, the com-
puting time for digital reconstruction scales with the total number of pixels N = N x N y , so that holograms
with very high number of pixels might not be reconstructed live. In such cases, a stack of holograms can
still be recorded live at high speed, and reconstructed afterwards.
Finally, pixel pitch is a delicate specification. It must be large enough to have a high full well capacity,
but small enough to sample appropriately the hologram fringes. Because it is important that modula-
tions from both the off-axis angle (or the curvature mismatch, in the case of an in-line configuration)
and from the diffraction on the specimen produce interference fringes that can be sampled, the pixel
pitch imposes some limitations on the optical design of a digital holographic microscope. A tradeoff
therefore has to be found between separation power of undesired terms and noise level in the hologram.
We have found that 6.0-6.5 μm pixels, with full well capacity of 16-18 k photons, provide quite reason-
able noise levels and would not recommend going below that size limit. On the other hand, with typical
second-harmonic wavelengths in the visible spectrum (for instance 400 or 532 nm), pixel sizes larger
than 10-12 μm would not provide a good off-axis separation power, forcing one to either use advanced
scheme to retrieve the imaging term of interest or, ultimately, phase-shifting holography.
It would appear from the above discussion that scientific cameras designed for fluorescence imaging
are also good choices for holographic SHG imaging, assuming pixels are reasonably sized. One must
however make sure that the camera maximum frame rate and exposure time range are compatible with
high-speed image acquisition, one of the strengths of holographic SHG imaging.
9.3.2.3 Microscope objective
Requirements of holographic SHG imaging in terms of microscope objective are basically the same as
for scanning SHG microscopy. For one, the objective has to withstand high laser power, since most prac-
tical implementations of holographic SHG microscopes involve the ultrafast laser source going through
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