Noise bandwidths

The NEP may be written in terms of the detector element active area, the number of detector pixels elements cormected for additive output the electronic noise bandwidth B and the detector element detectivity, D. Typically = 1, but may be increased for improved sensitivity with an attendant loss in resolution. 

Detectivity. Detector sensitivity (1,2) is expressed in terms of the minimum detectable signal power or noise equivalent power (NEP) given in units of watts or W. The reciprocal function when normalized for detector area, M, and noise bandwidth, is defined as detectivity, D, in units of /W. Thus,... 

The rms noise is measured in a noise bandwidth, The D is called D star lambda when the spectral band is limited to a given interval, and D blackbody when the total blackbody incident power density is used in the calculation. 

Under less restrictive noise/bandwidth considerations, one might drop the density to 6 points per resolution element at the risk of some minor noise aliasing. However, deconvolution by a factor of 3 would leave only two points per FWHM of a Gaussian spectrum-a number sufficient to characterize the spectrum, although display and measurement are difficult. 

These systems amplify and process the electrical signal from the detector and show it in a read-out form. The electrical noise bandwidth is usually determined by the system, which in turn influences the amount of noise of the signal and determines the response time of the system. 

First, what is the noise bandwidth (defined by the Integration time or time constant for each measurement) of each instrument Were the measurements made under similar conditions and, when using a method such as ICP-ES [12,13], does it make any difference ... 

P = constant coefficient which includes components due to the effective system noise bandwidth, the electronic charge, and gain fluctuations due to secondary electron emission. 

In high resistance circuits the noise bandwidth is limited by the time constant (t. ) of the source resistance (Rg) in parallel with the input resistance and the input capacitance (Cj) as shown in Fig. 1.5. The noise bandwidth is then given by the equation ... 

The expression for (S/N)s in the steady-state experiment is available in the literature (Ernst and Anderson, 1966). A singlescan, true slow passage experiment is assumed. It is also assumed that the balanced bridge is perfectly balanced and that Tj = T2. To reduce the noise bandwidth, a low-pass filter is used. The maximum S/N ratio is obtained with a linear matched filter and under conditions of partial saturation. 

The definitions of Wj and of Pj assume the amplified noise bandwidth Af is reduced to 1 Hz. For wider bandwidth Af the rms noise increases as (A Equation (3.10) represents the best performance attainable from a thermal detector. If all the incident radiation is absorbed by the detector, 17 = 1. 

Lower-speed ADC and lower-level processor It transmits a series of bursts of narrowband pulses where each burst is a sequence consisting of many pulses shifted in frequency from pulse to pulse with a fixed frequency step. Each received narrow-band pulse is phase detected and then combined into the large effective bandwidth (sequentially over many pulses). Therefore, the hardware requirement is less stringent relative to that of UWB-IR. The detector bandwidth is smaller, resulting in lower noise bandwidth and higher signal-to-noise (SN) ratio when compared with UWB-IR. 

Equivalent noise bandwidth The width of a rectangular filter that produces the same noise power at its output as an actual filter when subjected to a spectrally flat input noise signal. Real filters pass different noise power than implied by their nominalbandwidths because their skirts are notinfinitely sharp. 

The NEP formula (1.3) is convenient for predicting the minimum power a given system can detect, but it has some undesirable features. A good detector will have a small NEP, and detectors of different sizes and noise bandwidths will have different NEPs, so we cannot say in general what NEP a good detector should have unless we specify... 

Example of the Use ofD D is useful in predicting S/N for a given test environment Suppose that we had a detector of the same material as the one in the preceding example but with an area of 100 x 10 cm. If we used it with a circuit whose noise bandwidth was 200 Hz and an irradiance of 10 pW/cm, the resulting signal-to-noise ratio would be about 335 ... 

The noise bandwidth is common to noise expressions for both thermal and photon detectors - the faster the detector responds, the more noise we will see. We discuss noise bandwidth in more detail in Section 4.6.1. 

Noise (whether in amperes or volts) will always depend on a system noise bandwidth A/. Circuits that can respond to very high frequencies will exhibit more noise than circuits with limited bandwidths. The total noise power is proportional to the bandwidth, and the noise voltage is proportional to the square root of that bandwidth. The appropriate bandwidth for those calculations is called the noise-equivalent bandwidth, and we should report that bandwidth whenever we report noise. Equations 10.4a-c give the noise-equivalent bandwidths for three common situations. 

Boltzman constant temperature of the resistor (kelvin) resistance (ohms) noise bandwidth (hertz)... 

Later stages provide gain (while adding a negligible amount of noise) and are noise-bandwidth limiting. Chapters 6, 7 and 8 will discuss those functions that are unique to the IR business. 

To model this noise, imagine the capacitor being reset by shorting it with a resistor (with its associated Johnson noise) in an RC circuit. This is accurate, even though the resistance may be nearly zero. The noise bandwidth of the RC circuit is l/(4RQ, If we substitute that bandwidth into the Johnson noise formulas of Section 4.6.2, the resistance cancels out, yielding a simple expression for the variance of the voltage ... 

Required Data We need the noise N and the responsivity (or the change in IR input and the corresponding change in output). The noise and change in output must be in the same electrical units (voltage or current). The various NEX values differ only in the units we choose for the change of IR input photon irradiance for NEI, power for NEP, °C of scene temperature for NETD. D is a little different - for it we need the same information as for NEP, but we also need the detector area and noise bandwidth. 

Noise 2 det Af + (cxccss noisc Current) Substituting the noise bandwidth for an integrator ( A/ = — ) yields... 

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