Photomultiplier Shot noise

Sources of error in the sample preparation should be recognized and interferences controlled. However, each analysis involves random (statistical) errors, and the whole error is the sum of cumulative errors at each stage of an analytical procedure. A number of effects contribute to the uncertainty of the final signal displayed on the readout system. In the measurement stage various sources of interference are fluctuations in radiation source signal, photomultiplier shot noise , electronic noise , flame fluctuations, nebuliza-tion and atomization noise , inaccuracies in the read-out system, and interelement interferences. 

Ideally, any procedure for signal enhancement should be preceded by a characterization of the noise and the deterministic part of the signal. Spectrum (a) in Fig. 40.18 is the power spectrum of white noise which contains all frequencies with approximately the same power. Examples of white noise are shot noise in photomultiplier tubes and thermal noise occurring in resistors. In spectrum (b), the power (and thus the magnitude of the Fourier coefficients) is inversely proportional to the frequency (amplitude 1/v). This type of noise is often called 1//... 

Our first chapter in this set [4] was an overview the next six examined the effects of noise when the noise was due to constant detector noise, and the last one on the list is the first of the chapters dealing with the effects of noise when the noise is due to detectors, such as photomultipliers, that are shot-noise-limited, so that the detector noise is Poisson-distributed and therefore the standard deviation of the noise equals the square root of the signal level. We continue along this line in the same manner we did previously by finding the proper expression to describe the relative error of the absorbance, which by virtue of Beer s law also describes the relative error of the concentration as determined by the spectrometric readings, and from that determine the... 

As was mentioned before, noise is a term used to describe any random output signal that has no relationship with the incoming signal (the incoming light). In photomultipliers, noise can be classified, depending on its origin, into three types dark current, shot noise, and Johnson noise. The differences between these three classes are explained next ... 

In the particular case of a photocathode, this fluctuation affects both the dark current it) as well as the illumination induced current (/lum)- In the absence of illumination, the only current generated in the photocathode is the dark current, and so the shot noise associated with it is Aif If the light-induced current, /lum. is smaller than the shot noise associated with the dark signal Ai,), then it will be not possible to distinguish any light-induced current. In these conditions, the incident light cannot be detected by the photomultiplier, as it is not possible to separate the noise and the signal. As a consequence, the shot noise associated with the dark current determines the minimum intensity that can be detected by a particular photomultiplier (or by a particular photocathode). This is clearly shown in the next example. 

This noise is due to the thermal motion of the carriers (electrons) in the different resistors used in the photomultiplier. In general, the signal uncertainty caused by this source of noise is much lower than those generated by both dark noise and shot noise. 

Dark noise in photomultipliers is caused by (1) leakage current across insulating supports (2) field emission from electrodes (3) thermal emission from the photocathode and dynodes (4) positive ion feedback to the photocathode and (5) fluorescence from dynodes and insulator supports. Careful design can eliminate all but item (3). Associated with the photocurrent from the photocathode is shot noise. There is also shot noise from secondary emission in the multiplier structure. 

It is possible to approach shot-noise-limited performance in many optical experiments. When light levels are low, photomultipliers serve as noise-free quantum amplifiers with a gain of 10 . For absorption measurements, detectors with the highest quantum efficiency and uniformity of response, such as end-on semitransparent photocathode styles, are better than the high gain, opaque photocathode, low dark count types that are used for luminescence measurements. If one needs to measure absorption with a precision of AA 10, then 10 photons need to be accumulated at each data point. At these light levels, the dark count usually may not contribute greatly to the S/N. However, in absorption... 

With phototubes and photomultiplier-type detectors (photoemissive detectors, ultraviolet to visible range), thermal noise becomes insignificant as compared to shot noise. Shot noise is the random fluctuation of the electron current from an electron-emitting surface (i.e., across a junction from cathode to anode), and in PM mbes that is amplified and becomes the noise-limiting fluctuation. In instruments with these detectors, the absolute error is not constant at all values of T, and the expressions for the spectrophotometric error become more complicated. It has been calculated that, for these cases, the minimal error should occur at 0.136 or A = 0.87. These instruments have a working range of about 0.1 to 1.5 A. 

When light strikes the photocathode of a photomultiplier, photoelectrons are continuously produced but the instantaneous rate of production shows a statistical fluctuation because the photons of incident light arrive at random. This fluctuation of photoelectron formation is the reason for the fluctuations known as shot noise. The root mean square fluctuation of the cathode current, A4, is given as... 

Thus, only about 1% of the photoelectrons is missed, which is inconsequential where the quantum efficiency or photon to electron conversion is at most 25%. If the photomultiplier is used in the analog mode, that is, at count rates much higher than the bandwidth, then the mean square shot noise at the output is increased by a noise factor, T =(5/( — 1) or 1.25 for our example. The expression for the output noise current is = IqVG iB with i = rjqP hv.ihQ photocathode current. 

More generally, the sum of aU noise contributions can be represented as a noise spectrum a conceptual example is included in Figure 14.1. The most noticeable feature of this curve is the steady increase in noise power as zero frequency is approached. This low-frequency noise (often called flicker noise) has several sources, e.g. the variation in dark current of a photomultiplier. At higher frequencies the spectrum flattens out into a reasonably constant background, known as the shot noise regime, associated with the quantum nature of events like photon or electron emission. Also shown are the specific contributions to the spectrum from other sources mentioned above. 

The lasers used in these experiments produce typical powers greater than 2mW. The detectors often are of nearly unity quantum efficiency. Thus, in one second, A< shot < 10 rad. Even with the decreased efficiency of photomultiplier tubes, and less light intensity in experiments which use many absorption lengths of vapor, one finds A< shot < 10 rad in an observation time (A ) = 1 sec. In practice, the noise in the measured angles often turns out to be larger than the shot noise limit, owing to a combination of mechanical and optical instabilities, and detector noise in some cases. In the most recent experiments, 10" rad can be resolved in less than 1 min of averaging time. 

The shot noise of the photocurrent (4.134) is amplified in a photomultiplier by the gain factor G. The rms noise voltage across the anode load resistor R is therefore... 

The advantages of Fourier transform spectrometry over the use of a scanning monochromator (often referred to as dispersive spectrometry) is fully valid only when the detector noise is independent of the power of the radiation incident on the detector. When the detector is photon shot-noise limited [as it generally is for a photomultiplier tube (PMT), and often is for other sensitive detectors used in the near-infrared, visible, and ultraviolet spectral regions], the noise level is proportional to the square root of the incident power. For a boxcar spectrum, this means that shot noise is proportional to the square root of the number of resolution elements in the spectrum, This disadvantage therefore precisely offsets Fellgett s advantage when continuous broadband sources are employed. It should also be... 

The output from the photomultiplier is fed to a discriminator amplifier that detects only electron bursts originating on the photocathode and in this way produce counting statistics which are limited only by shot noise. 

Q = 3 X 10 s. This is much larger than either the dark current of the photomultiplier (= 10 s ) or the shot noise due to random fluctuations in the photon counting... 

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