## Diameter of Artificial Sources

We must carefully select a pinhole size in the artificial source so that it is smaller than the resolution of the instrument. On the other hand, it must be large enough to allow sufficient illumination to fill a defocused image with light. To calculate such a diameter, we extend the Airy disk radius to the distance of the pinhole. If that radius is chosen as the diameter of the source pinhole, we ensure that the source is no more than half of the angular extent of a point image.

This calculation is done for distances twice those in Table 5-2. The results are listed in Tables 5-3a and 5-3b. A quick glance at these tables shows some pinholes that will be extremely difficult to make or measure. It is certainly no easy task to make accurate sizes of pinholes only 0.07 mm (or about 0.003 inches) across. But these pinholes refer to unusual telescopesâ€” a 3-inch f/5, for example. Twenty times the focal length of a 3-inch f/5 is only 300 inches (7.6 m). It is relatively simple to use a pinhole 4 times as large (0.28 mm) and place it 4 times as far away (100 ft). The artificial source is still only a backyard away.

The pinhole can be punched in aluminum foil. To check the pinhole's size, expand it in a slide projector. Use a projection lens of known focal length and place the projector a measured distance from the screen. For

Table 5-3a Maximum diameters in millimeters for artificial sources

Focal Ratio

Table 5-3a Maximum diameters in millimeters for artificial sources

Focal Ratio

 4 5 6 8 10 15 D(in) D (mm) 2 . 4 61 0 07 0 07 0 08 0 11 0 . 13 0 20 3 76 0 09 0 07 0 08 0 11 0 . 13 0 20 4 . 25 108 0 12 0 08 0 08 0 11 0 . 13 0 20 6 152 0 17 0 11 0 08 0 11 0 13 0 20 8 203 0 23 0 14 0 10 0 11 0 . 13 0 20 10 254 0 28 0 18 0 13 0 11 0 13 0 20 12 . 5 318 0 35 0 23 0 16 0 11 0 . 13 0 20 14 356 0 40 0 25 0 18 0 11 0 . 13 0 20 16 406 0 45 0 29 0 20 0 11 0 13 0 20 17 . 5 445 0 49 0 32 0 22 0 12 0 . 13 0 20 20 508 0 56 0 36 0 25 0 14 0 13 0 20 24 610 0 68 0 43 0 30 0 17 0 13 0 20

Table 5-3b Maximum diameters in inches for artificial sources

 4 5 6 8 10 15 D(in) D(mm) 2 . 4 61 0 003 0 003 0 003 0 004 0 005 0 008 3 76 0 003 0 003 0 003 0 004 0 005 0 008 4 . 25 108 0 005 0 003 0 003 0 004 0 005 0 008 6 152 0 007 0 004 0 003 0 004 0 005 0 008 8 203 0 009 0 006 0 004 0 004 0 005 0 008 10 254 0 011 0 007 0 005 0 004 0 005 0 008 12 . 5 318 0 014 0 009 0 006 0 004 0 005 0 008 14 356 0 016 0 010 0 007 0 004 0 005 0 008 16 406 0 018 0 011 0 008 0 004 0 005 0 008 17 . 5 445 0 019 0 012 0 009 0 005 0 005 0 008 20 508 0 022 0 014 0 010 0 006 0 005 0 008 24 610 0 027 0 017 0 012 0 007 0 005 0 008

example, if a 75-mm projection lens is used and the projection distance is 5 meters, the magnification is about 5000/75 = 66 power. The 0.28 mm pinhole is expanded to 18.5 mm by projection (somewhere around 3/4 inch). A check of approximate roundness finishes the inspection. Be careful that you don't leave the foil illuminated longer than a few seconds in the projection gate. It's like an oven in there, and a great deal of energy is being dumped into the metal. If you allow too much heat into the aluminum, your slide mount may burst into flames.

You can effectively shrink a large pinhole down to a tiny one using another technique. If you have access to a good high-magnification microscope objective, you can image a large pinhole onto a small replica of itself. Here, place the large pinhole where the microscope's eyepiece normally sits (4 -6 inches from the threaded end of the objective). Shine light through the pinhole and then through the microscope objective, in a reverse direction to the way that microscopes customarily process light. The microscope objective is pointed at the distant telescope and the source appears to be floating a few millimeters in front of the objective. For example, if a 1-mm pinhole is placed 100 mm behind a 5-mm focal length microscope objective, the source appears to be diminished to about 0.05 mm. You can also use high-magnification oculars for this purpose (also used backwards), but microscope objectives are best.