Photography of star fields
 

Point-like star images on photographs can only be obtained with a system that has a drive and guidance. Interesting results can be obtained by attaching a 35 mm camera, with its ordinary or telephoto lens, to a telescope mounting which has a drive. A series of photographs taken with increasing exposure times reveals that fainter and fainter stars are recorded. Photographs taken by this means provide material for star identification, determination of plate scale, etc but generally allow only qualitative measurements of stellar magnitudes. Colour film may be used giving a rough sense of the colour of the stars but black and white emulsions can also be used.
In order to be able to compare stellar magnitudes with some accuracy, the photographs need to be taken with a telescope camera, providing a reasonable plate scale. The sizes of the star images on the plate need to be measured in turn by using some kind of microscope with a graticule or adjustable cross-wire. Depending on the plate, the images may sometimes allow projection on to a screen for measurement. Note that for black and white films, the star images comprise a collection of blackened grains. Plot catalogued magnitudes against the measured diameter, the square root of the diameter and the logarithm of the diameter. See which of the following equations gives the best fit:

and determine the constants a and b. Having obtained the magnitude–diameter relationship for a particular plate, use it to see how closely determined magnitudes agree with catalogued values. (NB: Unless the equivalent wavelength of the sensitivity of the chosen plate is close to the one corresponding to the listed magnitudes values, it may be necessary to limit the range of stars investigated for a magnitude–diameter relationship to one spectral type.)
Any measured diameter of an image depends on the separation of two points that the observer considers to be the extremities of a circular package whose perimeter fades into the fog of the plate.
The criterion for deciding the extent of any image is, therefore, set by the individual observer. If magnitude–diameter relationships are obtained by different observers using the same plate and identical equipment, it is generally found that the constants a and b vary significantly from observer to observer. Once a relationship has been established by an observer using standard stars, it can be used only by that person for determining the magnitudes of other stars on the plate. Obviously, a set of magnitudes determined by various observers should agree, providing that they have used their own individual magnitude–diameter relationship.
As an alternative to performing magnitude determinations essentially following the principles used in professional astronomy, the measurement scheme might be modified in a way that perhaps makes the data reduction process easier. If the telescope aperture is fitted with a obscurator such as a pencil or a thick wire across a diameter then the stellar images are in the form of the diffraction pattern in the form of a line. The maximum strength of the record is at the image mid-point and tapers away into the fog at some distance along the line in both directions. The brighter the star, the longer is the perceived image. Thus, measurements of image lengths are related to the original brightnesses of the stars. It is a useful exercise to make an exposure of a star field and determine a magnitude/length calibration. From the scatter in the data providing the relationship, it is an easy matter to estimate the accuracy to which stellar magnitudes can be made with this diffraction arrangement.