Objective, beam stop and blade.

The objective must form an image of a given plane on the CCD sensor. The magnification $M$ must be selected in order that the required wavevector range $\left[q_{min},q_{max}\right]$ is inside the wavevector range the CCD sensor can measure: about $\left[2\times10^3\mathrm{m}^{-1},2\times10^5\mathrm{m}^{-1}\right]$. This means that:

$$\left[\frac{q_{min}}{M},\frac{q_{max}}{M}\right] \subseteq \left[2\times10^3\mathrm{m}^{-1},2\times10^5\mathrm{m}^{-1}\right]$$ (4.3)

Moreover, the numerical aperture of the lens must be enough to resolve details as small as the smallest wavelength involved, $2\pi/q_{max}$, or, equivalently, to collect light scattered at an angle $q_{max}/k$.

In our experiments, we used a 20X microscope objective for high magnification factors, and an achromatic, $10\mathrm{cm}$ focal length doublet for magnification factor around $1$. An achromatic doublet has also been tested for high magnification factors, since we do not require the high quality of a microscope objective, nor an extremely wide numerical aperture. Experiments proved no different performances of the doublet compared with the microscope objective, but it was more difficult to obtain the required magnification.

The objective lens must be placed so that it creates an image of a given plane on the CCD sensor. For ONFS and ENFS, the plane must be at a distance $z$ from the sample fulfilling Eq. (3.60). The best choice is:

$$z\approx 25 \frac{k}{q_{min}^2}$$ (4.4)

For SNFS:

$$z<\frac{kD}{2q_{max}}$$ (4.5)

For ONFS, the transmitted beam, focused by the objective, is stopped by an opaque or reflective element. In microscope objectives, the focal plane is inside, between two groups of lenses: we insert the beam stop through a hole. We tried three kinds of beam stops: a thin wire, a reflective wedge and an absorbing disc impressed by on a photographic film. The wire has a diameter of $70\mathrm{\mu m}$; it si stretched in the focal plane and is positioned by micrometric screws. It reflects the light inside the objective, and this could, in principle, increase the stray light. The photographic film we used are high contrast, black and white, $36\mathrm{mm}$ photographic films. The beam stop is circular, but the beam is not completely blocked, thus increasing the stray light. The wedge was obtained by a steel blade; the edge was kept parallel to the optic axis. The upper part, in the direction from which the light comes, was cut at $45^{\circ}$ and polished, in order to obtain a surface that reflects the main beam outside the lens mount, through a second hole. A section of the objective lens is shown in figure (4.6).

Figure 4.6: Section of the microscope objective and the beam stop.

This kind of beam stop is not symmetrical with respect to the optical axis. This could increase the difficulty to process the data. During the experiments, all the methods showed to be almost equivalent. Figure 4.7 shows the mount that holds the beam stop.

Figure 4.7: Picture of the microscope objective with the beam stop. The beam stop is glued to the blue rod, held by a mount with three micrometric screws, for the adjustment of the position in every direction.

For SNFS, a blade must be placed in the plane where the transmitted beam is focused. The blade must be extremely sharp: a razor blade is required. We mount it on a system with three micrometric screws, in order to accurately position it in the space. A picture of the Schlieren system is shown in Fig. 4.8.

Figure 4.8: A view of the Schlieren system. From the bottom, we see the cell, the focusing lens, the blade, held by a micrometric mount, the neutral filter and the CCD camera.

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