Responsivity at a specific wavelength

Equation 12.56 indicates that the response that would have been obtained on the master instrument is simply a linear combination of the responses obtained on the slave instrument. However, in spectroscopy, it is very unlikely that the response at a specific wavelength on the master instrument should depend on any responses on the slave instrument that are at wavelengths far from the specified wavelength. As a result, the PDS method imposes a structure on the F matrix such that only wavelengths on the slave instrument that are within a specified range of the target wavelength on the master instrument can be used for the transformation. 

We will deal with the integral of (2.15) by either an in-band approach, or by using relative spectral response data to determine an irradiance or exitance that is effective at a specific wavelength. The first method allows us to calculate the average in-band responsivity of the detector the second yields the responsivity at a specific wavelength. 

S.2 Effective Exitance at a Specie Wavelength, and Absolute Responsivity at a Specific Wavelength We do not normally know the absolute spectral response of a detector, but spectrometer tests can often provide the relative spectral responsivity of the detector Jl lA). Given 7i (A), the spectral exitance of the source, and the transmittance of any optical components in the path, we can calculate an equivalent monochromatic exitance (or irradiance) - the effective exitance (or irradiance) at some specific wavelength. We can combine this effective value with the measured broadband signal to determine the absolute responsivity at any desired wavelength. 

In other cases, we are required to determine the responsivity at a specific wavelength - for example, 3.65 pm. That can be done with broadband data, but it requires that we know the relative spectral response, and some mathematical manipulation - see Section 2.2.52. An easier way is to use a narrow-band spectral filter - 3.55-3.75 pm, for example. 

Spectral Content. The third complication has to do with our choice of handling the spectral content of our source and the spectral responsivity of the detectors. In Section 2.2, we discussed two ways of including the spectral response of our detector in the responsivity reporting average-in-band responsivity and reporting responsivity at a specific wavelength. These are based on in-band... 

We will use the spectral response of the detector for its own sake, and also to determine the absolute spectral responsivity at a specific wavelength Aq by using blackbody signal data and the effective irradiance at Aq. Calculation of responsivity from test data is described in Section 10.3.2. That calculation is trivial once the appropriate irradiance is determined, as described in Section 2.2.52 and the effective exitance of Equation 2.22. 

The Lambert-Beer law states that (i) doubling the concentration of the analyte doubles the absorbance at a specific wavelength and (ii) the contributions of the absorbing species are independent of each other. This is also sometimes abbreviated to linearity (i) and additivity (ii). A specific example is shown, taking Pb as the analyte, and Co as the only interferent. Assuming that the Lambert-Beer law holds in this case, then upon writing apb, aCo, bpb and bco for the temporal profiles and spectra of the analyte Pb and the interferent Co, respectively, the sensor response for the standard, Xpb, and mixture, X2, can be written as... 

Atoms that absorb in the UV-Vis range can be further classified as chromophores and auxochromes. Chromophore groups are responsible for the color of the compound and absorb radiation at a specific wavelength. Examples are given in Table 8.6. 

Variations Just as we can report the average responsivity in a given spectral band or at a specific wavelength, we can report the NEI or NEP as an in-band average, or at specific wavelength. See Section 10.3.2 and 2.2.52. Just be clear with your customer about what they really want and on the algorithms to be used. 

In one of the most common types of photodiodes used for time-resolved work, the p-i-n photodiode (see Figure 12.24), the depletion layer thickness (i for intrinsic) is fabricated to obtain this optimum performance. Manufacturers usually give full specification sheets detailing, active area, time/frequency response, responsivity amps/watt (AAV) at a given wavelength, dark current, depletion layer capacitance, and bias volts such that with minimal external electronics devices can be made operative. 

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