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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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10.5 The SpectRx FFT-NIR Technology Advantage
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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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information. This limits the number of moving components and provides a more reliable observation geometry. This is a further advantage that can be added to the three classic advantages of FFT spectrometry over dispersive spectrometry: Multiplexing all wavelengths fall on the detector at all times Throughput the aperture versus resolution limitation is reduced Wavelength accuracy the internal laser ensures stability in ppm levels In practical terms, the superiority of the FTIR spectroradiometer can be seen most clearly in its high spectral resolution and broadband capability. The throughput, and thus the sensitivity, of the SpectRx FT Spectroradiometer is superior to that of a dispersive spectroradiometer a tendency that increases as spectral resolution is increased. SpectRx FT spectroradiometer has inherent broadband capability. When no optical filtering is used, the spectral bandwidth of the instrument is the same as that of the detector used, for example 1 to 5.5 m in the case of an InSb detector. It is also important to note that there is no time penalty when acquiring a large bandwidth as opposed to a narrow one. Finally, the most useful characteristic of a SpectRx FFT spectroradiometer is its flexibility. The spectral resolution of the SpectRx FFT Spectroradiometer can be instantly changed by computer. Also, because of the complete separation of spectral information (performed in the time domain) and spatial information (performed in the spatial domain), the Field of View configuration of the instrument can be changed in the field, simply by changing telescope modules.
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