Image photometry: Photographic photometry
 
One of the purposes of recording a star field on a photographic plate is to allow determination of stellar brightness. The usual procedure is to place the photographic plate in the focal plane of the telescope so that in-focus images are produced. The spectral range may be limited by placing colour filters prior to the emulsion. Exposures may last from a few minutes to a few hours.
An inspection of any star field plate immediately reveals that the images vary in size and are in some way related to the brightnesses of the stars. It should be noted that the distribution of image

Figure 1. A typical magnitude–diameter calibration curve.
diameters does not reflect the distribution of the physical diameters of the stars. An inspection of the star images with a microscope reveals that any image is made up of a collection of blackened grains, the image being dense at its centre, becoming weaker at the edges. Simple measurements reveal that the sizes of the images are much greater than the Airy disc predicted by diffraction theory. There are two main reasons for this.
The first is caused by scattering within the emulsion of the plate. Any light falling on to the surface of an emulsion may be scattered by the grains before it is finally absorbed and this effect obviously spreads out the size of any pinpoint image. The second is caused by the seeing. During the exposure, any telescopic star image dances and wanders over the emulsion. The recorded image represents the blurred patch over which the image has been in motion and the distribution of the density within the image reflects the amount of time the star image has spent at particular positions during the exposure. When the observer looks at the image in the developed plate as a disc, the eye is effectively deciding the positions in the image where the plate threshold has been reached, i.e. positions where there has been just sufficient energy to cause perceptible blackening on the plate. No matter what mechanism is responsible for the image-spreading, it is obvious that more energy will be available to spread the image for bright stars. Consequently, the emulsion threshold will be achieved at greater distances from the centre point of the image according to the star’s brightness. Thus, the apparent size of the recorded image depends on the brightness of the star and on the length of the exposure. Without the image-spreading mechanisms, it would be very difficult to make assessments of the brightness of the star by an examination of a point-like image.
Determinations of stellar magnitudes can, therefore, be obtained by measuring the diameters of images recorded photographically, with some kind of microscope. Any measured diameter is converted to a magnitude by means of a calibration curve. This curve is first obtained by measuring the image diameters of the standard stars which have also been recorded on the plate. Over the useful range of the plate, a range usually allowing a coverage of the order of six magnitudes between the brightest and faintest stars, the relationship between magnitude and image diameter is approximately linear. A typical calibration curve as obtained by microscope measurements is illustrated in figure 1.
An improvement to the method is obtained by using a specially designed laboratory instrument known as an iris diaphragm photometer. This machine allows measurements of star images to be made accurately and quickly.
With this special instrument, the plate is held on a moveable carriage which may have provision for reading its position in terms of coordinates, X and Y . By means of a lamp and projection system, a small area of any selected part of a plate can be illuminated uniformly. The size of this circular patch is controlled by an iris diaphragm. After the beam has passed through the plate it is directed to a photomultiplier. A chopping system allows the strength of the beam to be compared with a standard beam which is obtained from the original lamp. The strength of the beam, after passing through the photographic plate, depends on the size of the diaphragm and the density distribution of the area of the plate which has been isolated by this aperture. When a star image has been adjusted by movement of the carriage to be at the centre of the aperture, a balance between the compared beams can be achieved by controlling the size of the diaphragm.
It should be obvious that an image produced by a bright star will be very dense at its centre and will have a comparatively large disc. In order to allow a certain amount of light through this image to provide the balance, the diaphragm must have a large diameter. At the balanced or null condition, the diameter of the diaphragm is read off a scale. A calibration curve must first be obtained, by using standard stars, before the magnitudes of other stars may be determined. The uncertainties of any determined magnitudes are typically ±0·05 mag but, in some cases, it is possible to improve on this.
The ease of working the photometer is improved in larger instruments when the part of the plate under investigation and the image of the diaphragm are projected on to a screen, allowing the star field to be identified quickly. The X, Y and diaphragm diameter scales may also be projected and an electronic record of these parameters may be available for automatic dispatch to a computer. Automatic reduction instruments, may have a facility for determining brightness values as well as positional coordinates.