may be defined as the product of the illuminance, I (radiation energy /s/ m2, weighted by the visual sensitivity function) incident on the emulsion surface, and its duration t (sec). Thus, in photometric units:
where W is the radiant power in watts per Å at wavelength and V is the (photopic) visual sensitivity function normalised to unity at its maximum.
Note that the photometric definition covers only that part of the spectrum which produces a visual response in the standard observer, conventionally taken to be the region from 400 to 700nm. At the peak sensitivity of the standard observer (555nm) 1 lumen is defined as equivalent to 1/683 watt.
Since photographic emulsions can extend well outside the range of visible light, the energy incident on the emulsion may be expressed directly in radiometric units of:
An informal convention used in astronomical photography is to express exposures in terms of photons per 1000 and several examples of practical emulsion sensitivities expressed in this way are given in section 7.12.
is the logarithm of the ratio of light incident upon a developed emulsion to that transmitted by it.
where T is the transmittance of the developed image and O is the opacitance.
Image Density is the localised photographic blackening due to exposure and is conventionally expressed as the density of the image above the uniform background density of the support and chemical fog.
The numerical value of density varies according to the geometrical characteristics of the measuring instrument. Most densities in scientific photography are now reported in terms of the American National Standards Institute (ANSI) PH2.18-1959 (Diffuse density - see Altman 1977).
is the slope of the density versus log exposure curve (also known as the characteristic or H and D curve). It is normally specified at a given density or as the slope of the straight-line part of the curve which usually corresponds to the maximum slope.
Values of for some astronomical emulsions are given in Table 7.1.
can be defined as the reciprocal of the exposure required to produce a given density above gross fog.
The approximate sensitivities of some emulsions used in astronomy are given in Table 7.2
RMS Granularity () allows the objective classification of negative materials in terms of their apparent graininess The statistical distribution of many measurements of density ( D) made through a small aperture is an indication of the noise inherent in the photographic record and can be completely defined by its standard deviation () expressed in units of the variable D.
Industry standards for granularity ( i.e. those quoted in Kodak 1973, 1987) are measured through a 48m aperture at a density of 1.0 with an optical system of numerical aperture 0.25 (= f/2.0). The actual values obtained in this way are multiplied by 1000 to give large whole numbers. Values of rms granularity and photographic contrast for a variety of emulsions of astronomical interest are given in Table 7.1.
RMS Granularity x 1000 (48 um aperture ) and contrast
some Eastman Kodak
Values for are from the manufacturer's literature and were derived from exposures made under a variety of conditions. D = 1hr daylight exposure, 1MR = 1 min exposure to tungsen light + Wratten 25 filter (roughly equivalent to Schott RG 610 filter).
Granularity Constant ( G) is a measure of granularity substantially independent of the area ( A) of the measuring aperture (Selwyn 1935) and can be expressed as:
is a concept which is useful in evaluating the efficiency of various kinds of detectors (Rose 1946, Jones 1958)
When applied to photography, the concept embodies the three key parameters contrast (), sensitivity ( S) and granularity ( G), and can be used to determine the values of these at which the emulsion operates at optimum efficiency.
where G (= ) and refer to the same exposure level per unit image area. If A is in m, E will be in photons /. A well-hypersensitsed IIIa J emulsion might have a peak DQE, over a narrow range of exposure, of about 4%.
is often more appropriate than DQE for assessing the usefulness of photographic materials in astronomy (Davies et al 1968, Furenlid 1978)
The determination of has been greatly simplified by the publication of tables of versus density for a range of emulsions used in astronomy (Furenlid 1978). These are listed in Table 7.2.
ANSI Diffuse density D (above gross fog) and rms granularity measured with a slit of area 1000 um2.
a) unprocessed 25 - 30 um
b) processed 15 - 20 um (dense image areas are thickest)
The limiting photographic magnitude obtainable depends on a number of factors including night sky brightness, seeing, plate scale, photographic granularity and contrast. An empirical formula for estimating M has been given by Blanco (1975).
where S is the seeing in arc seconds and F the focal length of the telescope in meters. The factor P depends upon the emulsion used and its hypersensitisation. Blanco gives:
P = 1.2 for nitrogen baked IIIa J/GG 385 filter
P = 0.3 for nitrogen baked IIa O/GG 385 filter
For the AAT prime focus in 1 arc sec seeing this formula gives:
M for IIIa J = 24.8 (typical exposure
70 - 90 min)
M for IIa O = 23.9 (typical exposure 25 min)
For the AAT at the F/8 Cassegrain focus in 1 arc second seeing:
M for IIIa J = 25.7 (typical exposure
M for IIa O = 24.8 (typical exposure 2.5 hours)
These values seem about half a magnitude too generous to me (DFM)
This table (overleaf) lists the flux required over a 20 minute exposure to give a developed density of 0.6 (ANSI diffuse), expressed in terms of photons per 1000 at the given wavelength. These values are approximate since sensitivity can vary markedly from batch to batch and with various types of hypersensitisation. (See Smith 1980 for experimental details and filter specifications)