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Quantization noise ( A / Hz ) arises from the finite size of the quantization steps of the analog-to-digital converter (ADC). It is given by: I quantization = R G 2 N 12 fN (10.27)
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where R = range of the ADC (V) G = gain from detector to quantization ( ) N = number of bits for quantization (no units) fN = Nyquist frequency, which is half the sampling frequency (Hz) Quantization noise is of concern in photometric systems utilized for observing object views of high radiance, such as the sun.
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Dark noise is the electronic noise observed when no radiation reaches the detector. This noise depends on the type of detector and the electronic circuitry used. The values used in the case of an InSb detector are 1.5 10 14 A / Hz for each detector. As for the quantization noise,
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dark noise in SpectRx systems remains a negligible contributor to system noise.
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Jitter noise is noise caused by jitter during sampling of the interferogram. Sampling jitter is mainly due to ADC jitter, laser intensity fluctuations, and the noise from the electronics that trigger the ADC. Jitter noise can become troublesome at elevated scanning speeds. This is because at high speeds, a given jitter becomes non-negligible as compared to the sampling interval. Jitter noise is especially annoying because it is proportional to the measured signal; therefore, the SNR due to jitter cannot be improved by observing a warmer object view. Because of this, rapid scanning systems require carefully designed electronic circuits to trigger the ADC. The reader is referred to (RD1) for more details.
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Scanning instability noise can be attributed to scanning speed instabilities together with uneven spectrometer response and/or a delay mismatch between the ADC triggering and the IR signal. Mainly because of the analog filter response at high frequencies, the SpectRx spectroradiometer is operated with a non-zero slope gain. This is not a problem if the scanning speed that converts optical speeds to electrical speeds is constant. This is not the case, however, and some noise-equivalent current results from the peak amplitude of the speed variation and the analog filter slope. Filter slope noise is often a nonnegligible contributor to FTIR system noise. This is the main reason why analog filter design is carefully analyzed. Speed variations can also introduce noise if the ADC triggering circuitry is not perfectly synchronized with the IR signal. Because it has a larger bandwidth than the IR channel, the sampling laser fringe detection circuitry usually has a smaller associated delay. If this delay-mismatch is not corrected, the spectroradiometer will sample the interferogram with a constant negative time offset: t. This is not a problem if the scanning speed is constant, but as this is not the case, the uneven sampling resulting from the delay-mismatch and speed variations converts into a noise-equivalent current. Like jitter noise, these two sources of noise are of great concern, especially as they are proportional to the measured signal, so that the SNR due to these sources cannot be improved by observing warmer object views. Careful design of the analog filter cut-off frequency as well as delay-mismatch compensation is therefore applied.
Instrument Efficiency
The modulation efficiency of the interferometer depends on many factors, such as the imperfections of the beam-splitter, and the shear
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and tilt of the recombining wavefronts. Modulation due solely to the imperfections of the beam-splitter is given by: MBS ( ) = 4 rBS ( ) tBS ( ) where MBS = beam-splitter modulation rBS = beam-splitter reflectivity tBS = beam-splitter transmissivity Maximum beam-splitter modulation (i.e., MBS = 1) occurs when rBS and tBS are equal to 0.5. The typical interferometer modulation for input port A is 70 percent using five-second precision corner-cube retroreflectors. Better modulation can be expected with the use of one-second precision retroreflectors. It should be noted that the total energy is split between the two output ports. This factor is normally included in the instrument efficiency together with beam-splitter modulation and system transmission. = T ( ) MBS 2 (10.29) (10.28)
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