Astronomy Principles and Practice Fourth Edition.pdf

The telescope and the collected energy 241
which are separated by an angle, θ. For convenience, one star has been placed on the optic axis of the
telescope. Rays which pass through the centre of the system (chief rays) are not deviated. Thus, it can
be seen from figure 16.2 that the separation, s, of the two images in the focal plane is given by
s = F tan θ.
As θ is normally very small, this can be re-written as
s = Fθ (16.2)
where θ is expressed in radians. In order to be able to examine images in detail, their physical size or
separation must be large and this can be achieved by using a telescope of long focus.
The correspondence between an angle and its representation in the focal plane is known as the
plate scale of the telescope. By considering equation (16.2), it is obvious that the plate scale is given
by
dθ
ds = 1 F .
It is usual practice, however, to express the place scale in units of arc seconds mm −1 and, in this
case, the plate scale is given by
dθ 206 265
= (16.3)
ds F
where F and s are expressed in mm and θ in seconds of arc, the numerical term corresponding to the
number of arc seconds in a radian.
16.3 The telescope and the collected energy
16.3.1 Stellar brightness
When any object such as a star can be considered as a point source, to all intents and purposes its
telescope image can also be considered as a point, no matter how large a telescope is used. All the
collected radiation is concentrated into this image. The larger the telescope, the greater is the amount
of collected radiation for detection. Thus, the apparent brightness of a star is increased according to
the collection area or the square of the diameter of the collector.
In allowing detection and measurement of faint stars, the role of the telescope may be summarized
as being that of a flux collector.
Although stellar brightness measurements are usually expressed on a magnitude scale, they result
from observations of the amount of energy collected by a telescope within some defined spectral
interval over a certain integration time. A stellar brightness may be put on absolute scale and be
described in terms of the flux, , or the energy received per unit area per unit wavelength interval per
unit time. A measure of the star’s brightness might be expressed in units of W m −2 Å −1 .
Estimation of the strength of any recorded signal and determination of the signal-to-noise ratio of
any measurement is normally performed in terms of the number of photons arriving at the detector. In
the first instance, the calculations involve determination of the number of photons passing through the
telescope collector and this can be done by remembering that the energy associated with each photon
is given by E = hν or E = hc/λ (see sections 4.4.2 and 15.5.1). Thus, the number of photons at the
telescope aperture may be written as
N T = π 4 D2 × t
∫ λ1
λ 2
λ λ
dλ (16.4)
hc
where λ 1 and λ 2 are the cut-on and cut-off points for the spectral range of the measurements and t is
the integration time of the measurement.