6.3 Throughput and Sensitivity

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So far, we have given the formulae for count rates in terms of the sensitivity (S). If you would like to use the throughput (T) rather than the sensitivity, you can use the following conversion equations.

For imaging modes, the transformation between T and S is given by:

S_\lambda=\frac{T_\lambda A\lambda}{hc}= \frac{A_{\rm eff}\lambda}{hc}

where:

  • Sλ is the sensitivity at wavelength λ;
  • Tλ is the system throughput at λ;
  • A is the area of an unobstructed 2.4 meter telescope (i.e., 45,239 cm2);
  • h is Planck’s constant;
  • c is the velocity of light;
  • Aeff is the effective area given by Aeff = TλA.

For spectroscopic modes, the transformation equation can be written as:

S_\lambda=\frac{T_\lambda A\lambda d}{hc}= \frac{A_{\rm eff}\lambda d}{hc}

where:

  • d is the dispersion in Å/pix.

In the first two examples given at the end of this chapter, we specifically show how the calculations can be done both in terms of the sensitivity and the throughput.

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