Apertures distance from detector

Fig. 1.23. The electron diffraction apparatus developed by Parks and coworkers includes an rf-ion trap, Faraday cup, and microchaimel plate detector (MCP) and is structured to maintain a cylindrical symmetry around the electron beam axis [147]. The cluster aggregation source emits an ion beam that is injected into the trap through an aperture in the ring electrode. The electron beam passes through a trapped ion cloud producing diffracted electrons indicated by the dashed hues. The primary beam enters the Faraday cup and the diffracted electrons strike the MCP producing a ring pattern on the phosphor screen. This screen is imaged by a CCD camera mounted external to the UHV chamber. The distance from the trapped ion cloud to the MCP is approximately 10.5 cm in this experiment...

The formulas described in Section 2.3.3 handle most of the cases of interest in a detector test lab, but occasionally more elaborate formulas are required. For example, we might have a large detector at a relatively small distance from a large irregular source. Another example is the circular or rectangular aperture off-axis from a small detector. 

Evidently, we cannot get all of the required background reduction with a cold shield alone, so we will need a spectral filter in conjunction with the cold shield. We pay a penalty for the use of the spectral filter the signal from the blackbody will be reduced. Assume that (like many labs) we have 500 and 800 K blackbodies with apertures that range from 0.050 to 0.500 in diameter, and that total distances from the blackbody aperture to the detector can be as small as 8 . We calculate the irradiance we can expect with three filters, each with a bandpass of 0.2pm, centered at 3, 4, and 5 pm, using two blackbody temperatures (500,800 K) and the two blackbody aperture extremes. Table 9.1 shows the irradiances that we can expect with the 12 different combinations. It also lists the signal-to-noise ratios that we will see, based on the expected NEI. From this table we can pick out the acceptable combinations. 

Verily the distance from the detector to the blackbody aperture. 

Set up a spreadsheet to contain all of your data. Provide unique cells for a distance offset, and two cells for each aperture diameter - one for the nominal value, and one for some assumed or apparent value. Let all calculations that require the detector-to-aperture distance use the nominal value plus your offset, and let all calculations that depend on aperture diameter use the assumed or apparent values. Start with an offset of zero and assumed diameters equal to the nominal values, and save the resulting graph of output versus irradiance and deviation from a straight line versus irradiance. Those are your baseline results. Examine them for any patterns. 

Fig. 4. Schematic drawing of the vacuum cell for parallelized IR analysis with adsorbed gases (top) and photograph of the cell (bottom). The light comes from the front, hits the top mirror, passes the cell and is reflected towards the detector by the bottom mirror which is turned away from the viewer. Upper left insert in the photo shows the distance element with the eight apertures in which the samples are placed (from ref. [22]).

The largest observable d-spacing of such a camera depends on the limits of diffuse scattering in the detector plane. This limit — L — can be approximately calculated from the size of the aperture slits (St), the distance of the detector plane from the guard slits (Lj) and the size of the focus (a) [4], In real space one can write ... 

The mathematical expression for a is derived as follows (Fig. 8.4). A plane source of area emitting Sq particles/(m s), isotropically, is located a distance d away from a detector with an aperture equal to A. Applying the definition given by Eq. 8.2 for the two differential areas dA and dAj and integrating, one obtains ... 

Consider the point isotropic source of strength Sg particles per second located a distance d away from the detector, as shown in Fig. 8.6. If one draws a sphere centered at the source position and having a radius greater than d, the number of particles/(m s) on the surface of the sphere is Sq/AvR. The particles that will hit the detector are those emitted within a cone defined by the location of the source and the detector aperture. If the lines that define this cone are extended up to the surface of the sphere, an area is defined there. 

Consider the geometry of Fig. 8.10 with a point isotropic source located a distance d away from a detector having a rectangular aperture with area equal to ab. The solid angle is given by ... 

Consider the geometry shown in Fig. 8.12. A disk source is located at a distance d above a detector having a rectangular aperture with an area equal to ab. It is assumed that the center of the source is directly above one comer of the aperture, as shown in Fig. 8.12. The more general case of the arbitrary position of the source is derived from the present example. 

If we are interested in the axial intensity of the beam as measured on a detector opposite the source aperture at a distance r which is large with respect to the aperture dimension, Eq. (5-12) is integrated over all values of V from zero to infinity after setting cos 0 = 1 and dQ = alr, where a is the area of the source aperture. The result is... 

The performance of the coded aperture mask is not limited by diffraction effects so that, in principal, there is not an intrinsic limitation to the angular resolution which may be achieved. From a technical point of view the limit is set by the distance between the mask and detector and hence the size of the spacecraft. The size of the pixels within the detection plane also provide another technical limitation to fine angular resolution. However, both mask distance and pixel size do have an indirect influence on the large-scale... 

---