Spectroscopic trading rules andNumerical filtersNumerical filtersOct 28 2008CHEM 5161• Photon Shot Noise (limiting mostly in the UV/vis/NIR)• Detector Noise (now limiting in the mid-IR and far-IR)– Dark Current Noise– Read Out Noise• Digitization noise • Interference Noise (e.g. power supply)• Flicker Noise (e.g. fluctuation noise)Digitization Noise• Caused by a limitation in the dynamic range of the ADCrange of the ADC• 16-bit ADC Ù 20–215Ù 32768An issue with FTS (Fourier Transform•An issue with FTS (Fourier Transform Spectrometers)S/ 0 001•S/N ≥ 0.0015• FTS built until themid 90s are digitization noisedigitization noise limitedSampling TheorySampling Theory• Most detectors: analogue outputCdiildi•Computers: digital devices⇒ Analogue-to-digital converters (ADC)⇒ Requirement: No information is lost in the samplingNo information is lost in the sampling process !•Sampling Theory:pg yA continuous time signal can be completely recovered from its digital representation if the original analogue signal is band-limited, and if the sampling frequency employed forand if the sampling frequency employed for digitization is at least twice the highest frequency present in the analogue signal.Spectroscopic trading rules•Spectral resolution, Signal intensity andSpectral resolution, Signal intensity andSignal to Noise are coupled quantities.•constant throughput:•constant throughput:Δν ↓ 2 = S/N ↓ 2S/N ↑ 2Ùt ↑ 4t tS/N ↑ 2 Ùt ↑ 4 to compensate• variable throughput:Δν ↓ 2 = S/N ↓ 4S/N ↑ 4 Ù t ↑ 16 to compensateConvolution (running average)(gg)Filters vary by the relative weights that are being assigned in the convolution process.• running average {1,1,1,1,1}/5• triangular smoothing {1,2,3,2,1}/9• Savitzky Golay (window width=5, polynomial order=2, repetition=1) {-3,12,17,12,-3}/35• Filtering in the frequency domain (Fourier filters, electronic filters)The ideal numerical filter •Requirements:Requirements:– Zero phase shiftNo undesirable side effects such as–No undesirable side effects, such as• Multiple peaks if only one is present•Overshoots or undershoots in response to an impulseOvershoots or undershoots in response to an impulse• Filter response function ≤ 1 (all points, repeated uses)Low pass filtersNumerical filters in IGORNumerical filters in IGORmake/o/n=256 mynoise = gnoise(1)k / / 256 i * 0 01make/o/n=256 t_series = p * 0.01make/o/n=256 signal = 0signal[5,10] = 10signal[15 20] = 10signal[15,20] = 10signal[25,30] = 10signal[50,100] = 10signal[150 200]=10signal[150,200] 10make/o/n=256 signal2 = signal +