We need a lens with high luminosity, characterized by the aperture
, the ratio of the focal length 
to the useful
lens diameter 
. The light energy received at a distance 
from a particle is proportional to the solid angle 
captured by the lens, see sketch. Decreasing the distance
is favourable, but there is an optimum, as y is limited by lens aperture
and the magnification condition 
(see sketch in fig.
5 right), where 
is the sensor length and 
the corresponding length on the field of view (see sketch in fig.
6 left). We make the approximation that the image
forms at a distance from the lens (which is strictly true
only for an object at infinity). Therefore
which depends only on the objective aperture 
, for a given
field of view and sensor.
For a given aperture, it is advantageous to use a large distance ,
providing less geometric distortion and a less critical focussing.
This is important for measurement in a volume, since the distance
to the camera is changing during the laser sheet scanning. Note that
a perfect focussing is not necessary advantageous. Some fuzziness
of the particle images indeed results in wider and smoother correlation
curves, which could lead to a better subpixel precision (although
we did not really test that).
We have plotted in fig. 6the visible field length
for our different lenses, with the two cameras, at viewing
distances 3 m. For other distances, the field varies of course in
proportion to the distance. The Pulnix(2.3)
camera has a sensor 6.7x9.6 mm, while the SMD(2.3)
has a sensor 14x14 mm, so the field is larger with the later. Objectives
with very large aperture (=0.9) are available only with diameter
1 inch, which is designed for a sensor up to 16 mm in diagonal. This
is all right for the Pulnix, but too small for the SMD2.3),
for which the corners of the field are darkened. However this drawback
is largely compensated by the higher luminosity for most part of the
image. Objectives for 24x36 photography (Sigma, Olympus or Nikon)
provide perfect image quality, but with lower luminosity.
Our best choice for large fields of view with the SMD2.3) camera is the Schneider 25 mm, which provides a field 2.5 x 2.5 m2 at distance 4 m. For smaller fields, the Nikon 35 mm or Olympus 50 mm provide images of excellent quality with still a good luminosity (aperture 1.4).
The deformation effects are small in air, except for the largest fields
of view, i.e. the smallest focal length, 17 mm or below. When we look
from air inside water, deformation is due to refraction at the interface.
A programme is available in the CIVproject package (see3)
to account for this deformation, by relating the 
coordinates
on the image to the physical positions, depending on
the lens and water depth below the free surface (assumed plane).
