Spatial filtering

The first and last terms correspond to oscillating polarizations that emit light at twice the frequency of E and 2 respectively, and the other two terms correspond to sum- and difference-firequency mixing of the two frequencies. In general, experiments can be conducted in such a way as to strongly favour one non-linear process above the others. However, if this is not possible, steps can be taken to detect the ouqmt of a single process through the use of appropriate filters, spatial separation of the emitted beams and choice of detector. 

Spike filter / Spatial filter / Pre-monochromator Beam expander... 

At this point it is worth comparing the different techniques of contrast enliancements discussed so far. They represent spatial filtering teclmiques which mostly affect the zeroth order dark field microscopy, which eliminates the zeroth order, the Schlieren method (not discussed here), which suppresses the zerotii order and one side band and, finally, phase contrast microscopy, where the phase of the zeroth order is shifted by nil and its intensity is attenuated. 

Quadrupole mass spectrometers (mass filters) allow ions at each m/z value to pass through sequentially for example, ions at m/z 100, 101, 102 will pass one after the other through the quadrupole assembly so that first m/z 100 is transmitted, then m/z 101, then m/z 102 (or vice versa), and so on. Therefore, the ion collector (or detector) at the end of the quadrupole unit needs to cover only one point or focus in space (Figure 29.1a), and a complete mass spectrum is recorded over a period of time. The ions arrive at the collector sequentially, and ions are detected in a time domain, not in a spatial domain. 

Figure 9.22 illustrates how a CARS experiment might be carried out. In order to vary (vj — V2) in Equation (9.18) one laser wavenumber, Vj, is fixed and V2 is varied. Here, Vj is frequency-doubled Nd YAG laser radiation at 532 nm, and the V2 radiation is that of a dye laser which is pumped by the same Nd YAG laser. The two laser beams are focused with a lens L into the sample cell C making a small angle 2a with each other. The collimated CARS radiation emerges at an angle 3 a to the optic axis, is spatially filtered from Vj and V2... 

Direct interception refers to a sieve-type mechanism in which contaminants larger than the filter pore size are directly trapped by the filter. This sieve retention mechanism of particle arrest is the mechanism of choice and occurs owing to geometric or spatial restraint. This type of particle arrest is considered to be absolute, that is, it is independent of filtration conditions. 

The use of a laser beam expander as a spatial filter has also been found to be satisfactory 42). The beam expander consists of an interchangeable negative input lens and a positive output lens. Both the input and output lenses are designed for minimum spherical aberration. The expansion power may be varied by using a different input lens (Fig. 23.) The laser beam... 

After the preamplifier, the beam is expanded to 2 mm, collimated and imaged onto a 1 mm aperture, producing a flat-top intensity profile. A 3-element telescope relays the aperture plane to the amplifier with a collimated 0.5-mm diameter. The telescope contains a spatial filter pinhole. The nominal power levels are 3 mW into the preamp, 500 mW out of the preamp and 200 mW out of the aperture. A 6° angle of incidence bounce beam geometry is utilized in the amplifier cell. The "bounce" foofprinf overlaps with the 4 pump beam fibers, arranged in 2 time sefs of 13 kHz. The pump fibers have f 50-60% fransmission. The amplifier brings the power up to < 20 W at 26 kHz. 

One of the attractive features of single mode waveguides is their ability to filter the spatial field distribution. All the wavefront aberrations only result in a photometric fluctuation easy to monitor. It results in a very good calibration of the interferometric data as firstly demonstrated by FLUOR, as seen in Fig. 8 (Coude du Foresto et al., 1998). Nevertheless, care has to be taken to keep in mind that turbulence may have a spectral selectivity in the launching pro-... 

Figure 8. Calibration of the fringes contrasts by means of spatial filtering in monomode...

This first step makes necessary a correction of the atmosphere aberrations by means of an adaptive optics or at the minimum a tip tilt device. If the turbulence induces high aberrations the coupling efficiency is decreased by a factor VN where N is the number of spatial modes of the input beam. Note that tilt correction is also mandatory in a space mission as long as instabilities of the mission platform may induce pointing errors. Figure 10 (left) illustrates the spatial filtering operation. This function allows a very good calibration of... 

Figure 10. Left Monomode optical fibre acts as a spatial filter. The coupling efficiency is 1/N where N is the input beam number of modes. Right Using a wavefront corrector the coupling efficiency is significant and quite stable (K band CFHT/ GHANA) (Perrin et al., 2000).

Figure 18. ISTROG Interferometer. The high improvement on the accuracy of contrast measurements with such devices mainly results from the efficient spatial filtering and the spatial stability of the recombining assembly.

Hirose et al. [26] proposed a homodyne scheme to achieve the background-free detection of the fourth-order field. With pump irradiation in a transient grating configuration, the fourth-order field propagates in a direction different from that of the second-order field because of different phase match conditions. The fourth-order field is homodyned to make ffourth(td. 2 D) and spatially filtered from the second-order response hecond td, 2 D). 

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