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The area of an optical element A = diameter of the optical element. D2 where D is the 4
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Wavelength in microns is converted from the wave number by = 10, 000 . Dfs The divergence of a telescope is approximated by = d where Dfs is the diameter of the field stop and d the focal length of the primary. The solid angle of a beam at the entrance of a telescope is Afs approximated by = 2 where Afs is the area of the field d stop and d the focal length of the primary. The relation between the solid angle and the divergence is = 2 1 cos . For small angles (e.g., in calculations related 2 to the FOV of telescopes), the following formula provides a good approximation: = 2 . 4 The diameter of an object at a distance d and subtended by a divergence is given by Ds = d . The throughput between two optical elements is given by = A , Aas being the area of the aperture stop, and , the solid angle or divergence, introduced by the field stop. We can approximate by taking the area of the field stop and dividing it by the square of the distance between both stops. The throughput is then expressed by = Afs Aas . d2 Converting radiance to irradiance is done by multiplying the radiance by the solid angle of the telescope. Converting irradiance to apparent intensity is done by multiplying the irradiance by the square of the distance between the point source and the primary of the telescope. Converting apparent intensity-to-intensity is done by correcting the apparent intensity with an atmospheric transmission spectrum computed by modeling software (Fast Code, Lowtran, Modtran, and others).
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Spectral information can be obtained using several technical methods. Most of them rely on the dispersion of light to achieve spectral separation. This can be done with a prism or a grating. In this case, the spectral distribution is transformed into a spatial distribution and requires a scanning mirror in one axis. Circular variable filter radiometers are also currently used, but spatial/spectral smearing effects add to the other drawbacks of this method. The fast Fourier transform (FFT) spectrometer does not rely on spatial dispersion, but rather on time dispersion of the spectral
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