Detector four-quadrant

Figure 2 shows the brief principle of a laser-detected FFM. A sample is put on a piezoelectrical tube (PZT), which scans X, Y plane and controls the feedback of Z axis. The laser beam from a diode is focused on the mirror of the free end of a cantilever with lens, and the reflected beam falls on the center of a position-sensitive detector (PSD), a four-quadrant photodiode. When the sample contacts with the tip and relatively moves under the control of a computer, the reflected beam deflects and changes the position on the PSD due to the twist and deflection of the cantilever caused by the changes of surface roughness, friction force, and adhesive force between the sample and the tip. The extension and re-... 

There is a corresponding relationship between the lateral voltage (Vi) of four quadrant position detectors and the torsional angle. So can be obtained from Vy. 

Transverse moving head of four-quadrant position detectors (Fig. 2), precise measuring lateral displacement which corresponds to lateral voltage F/ when it varies at the linear range of 10 V, thus we can compute the rotated angle a of the reflection ray ... 

Then, the corresponding relationship between lateral voltage of the four-quadrant position detectors (F/) and the torsional angle of the cantilever ( di). Thus we can obtain the variation of torsional angle 0i through reading the variation of lateral voltage (F ) from the front panel. 

Note Vj is the lateral voltage of the detector with four quadrants before scanning Vn is the lateral voltage of the detector with four quadrants while scanning and V /jt-V /s is the difference between the lateral output voltages of the detector with four quadrants. 

We established the coordinate system and plotted the curves using the Z-voltage of the piezoelectric ceramic as the X axis and the lateral voltage of the detector with four quadrants (V/s, Vii and Vn - Vi ) as the Y axis, as shown in Fig. 6. We fit linearly the varieties of the lateral voltages in the detector with four quadrants to the varieties of the... 

As long as there is at least uniaxial symmetry and the fiber axis is in the detector plane, the scattering pattern can be split into four quadrants which should carry each identical information. This means that there is some harmony in the scattering pattern, from which missing data can be reconstructed13. 

In wide field microscopy, spatial information of the entire image is acquired simultaneously thus providing comparatively short acquisition times compared with scanning microscopy implementations. Combining TCSPC with wide field microscopy is not straightforward. However, a four quadrant anode multichannel plate (MCP) has been used for time- and space-correlated SPC experiments [25, 26]. This detector has excellent timing properties that make it very suitable for FLIM. Unfortunately, it can be operated only at low count-rates ( 105-106 Hz) therefore, it requires comparatively long acquisition times (minutes). 

Nal(Tl) crystals. The sample to be counted is mounted between Mylar sheets on a 1/4-inch thick X 5-inch diameter plastic ring. This system is presently used with a four quadrant, multiplexed, 4096-channel, multidimensional analyzer. The multidimensional y spectrum in coincidence with the proportional counter events is recorded in one quadrant, and the anticoincident multidimensional y spectrum is recorded in another quadrant thus, no data are lost. The various background y spectra obtained with this detector assembly are compared in Figure 12. The y-y coinci-... 

Fig. 5. a Schematic representation of the SFM set-up using the optical beam deflection method, b When the tip interacts with the sample surface, the cantilever exhibits deflection perpendicular to the surface as well as torsion parallel to the surface plane. The normal force Fn and the lateral force FL corresponds to the force components which cause the deflection and torsion, respectively. Both responses are monitored simultaneously by the laser beam which is focused on the back side of the cantilever and reflected into a four-quadrant position sensitive detector (PSD)... 

A modification of the basic block detector has been made such that each PM tube straddles over four quadrants of four different blocks (Fig. 2.4). The technique of quadrant sharing permits the use of larger PM tubes and reduces the total number of PM tubes used in the PET system. This design improves the spatial resolution relative to the basic design, but has the disadvantage of increasing the dead time. 

Figure 2.4. Block detector illustrating the quadrant sharing of PM tubes, (a) PM tubes assigned in four quadrants separately, (b) Each PM tube shares four quadrants of four block detectors and improves the spatial resolution. (Reprinted with the permission of The Cleveland Clinic Center for Medical Art Photography 2009. All Rights Reserved).

As shown in Figure 1, a standard AFM tip has a sharpness (i.e., tip radius) of a few nanometers and is fabricated at the free end of a microcantilever. When the AFM tip is close to a surface or in mechanical contact, forces acting on the tip translate into a mechanical deflection of the cantilever, which is detected optically using a laser beam that reflects off the back side of the cantilever (Figure 2). A position-sensitive detector (PSD) in the form of a four-quadrant diode then converts the vertical and horizontal beam deflections into voltage signals, which are continuously recorded. 

Deflection detection schemes have been developed that use self-sensing piezoresistive cantilevers [104] or optical interferometry [105, 106]. But in nearly all practical systems cantilever deflection is measured with an optical lever system [107], as shown in Fig. 3.22. A small spot of laser light is reflected from the back of the cantilever and the reflected light is directed to an adjustable mirror. This in turn reflects the light onto a position-sensitive detector, a four-quadrant photo diode, shown schematically in Fig. 3.23. 

Figure 3.23. Schematic of the four-quadrant detector used in optical lever detection AFM.

Figure 2 shows a schematic of a typical AFM instrument that consists of a cantilever-mounted tip, a Piezoelectric scanner, four position-sensitive photo detectors, a laser diode and a control unit. The process of operation of an AFM is relatively simple. The beam from the laser is directed against the back of the cantilever beam onto the quadrants of the photo detector. As the tip is moved across a sample, this causes the cantilever beam to bend or be twisted in manner that is proportional to the interaction force. This bending or twisting of the cantilever causes the position of the laser on the photo detector to be altered. The deflection of the cantilever beam can then be converted into a 3D topographical image of the sample surface (Gaboriaud and Dufrene, 2007 Kuznetsova et al., 2007 Lim et al., 2006). 

Now the substrate does not have to be electrically conducting, because what is measured in the Z-direction is the change in the natural vibrations of the cantilever caused by van der Waals forces between it and the surface. The Z-movements of the cantilever are monitored by a visible laser, whose beam is reflected by the mirror on the back of the cantilever and measured by four semiconductor photoelectric detectors arranged in a quadrant to monitor the laser reflection and thus the sample position (Fig. 11.43). 

---