Poisson noise

In future improvements in technology may mean that that read noise no longer is the dominant noise source, and Poisson noise arising from the quantum nature of light is in fact the limiting factor. In this case the variance of the centroid noise is equal to. 

It is instructive to put equation 47-32 into similar form as equation 47-94 - for Poisson noise by replacing Es with TEr ... 

Thus, in the constant-noise case the absorbance noise is again proportional to the N/S ratio, although this is clearer now than it was in the earlier chapter there, however, we were interested in making a different comparison. The comparison of interest here, of course, is the way the noise varies as T varies, which is immediately seen by comparing the expressions in the radicals in equations 47-94 - for Poisson noise and 47-96. 

We present the variation of absorbance noise for the two cases (equations 47-94 - for Poisson noise and 47-96, corresponding to the Poisson noise and constant noise cases) in Figure 47-18. While both curves diverge to infinity as the transmittance —0 (and the absorbance - oo), the situation for constant detector noise clearly does so more rapidly, at all transmittance levels. 

Equation 48-105 is the closest we can come to the form of equation 42-37, so compare the functions describing the relative precision for the constant-noise case to that of the Poisson-noise case. 

So let us begin our analysis. As we did for the analysis of shot (Poisson) noise [8], we start with equation 52-17, wherein we had derived the expression for variance of the transmittance without having introduced any special assumptions except that the noise was small compared to the signal, and that is where we begin our analysis here as well. For the derivation of this equation, we refer the reader to [2], So, for the case of noise proportional to the signal level, but small compared to the signal level we have... 

To further appreciate the indistinguishability of these functions, we show the error bounds of a, assuming that the data came from an SPC instrument. Clearly, Poisson noise always greatly exceeds the differences exceptfor D3. For 104peak counts in SPC data, differentiation between any of these functions is impossible except perhaps for D3. Noise hides the differences. While we have selected only a small set of possible exponentials, clearly there is a continuum of possible lifetimes and preexponential factors that would be similarly indistinguishable. 

Figure 4.10. Differences between Eqs. (4.10) from the single Gaussian distribution of Eq. (4,S) with R = 0.25, 1 is D -Dg. 2 is Dj-Dg, and 3 is D3-DG. D4--DG is so close to zero thai it does not even show up on this plot. The curves labeled "Poisson Noise" represent one standard deviation SPC decay data. All functions, if over] aid, are essentially indistinguishable. (Adapted from Ref. 55.)...

Table V. Exponent of Dependence of SNR, MDC, and MAT on Three Instrumental Variables for Signal-Limited and Background-Limited Detection Cases in the Poisson Noise Limit...

Fig, 9 Simulated SIMS volume the 3-D image in Fig. 7 has been degraded with Poisson noise noisy 3-D image (left) one representative z slice (right). 

With the partition functions Qr, Qs, and ArH < / r, one therefore obtains a relative difference X / [R] in the equilibrium concentration of 4 x 10 or for a mole R (Na = 6.02 x 10 molecules/mol) a difference of approximately 2.4 x 10 molecules. This minimal difference vanishes in the statistical noise (the square root of Na corresponding to 8 x 10 molecules for Poisson noise for one mole), and one can ask whether the small value of 2( / [R] or of Ap E in biochemistry can play a role at normal temperatures. We shall return to this point and see that this remains an open question [13]. 

In a coded aperture camera without a fully-coded FOV or with a random pattern, such as the WXM, coding noise is common throughout the FOV. Coding noise introduces extra crosstalk between two or more point sources, on top of the Poisson noise. However, if there is only one source in the... 

In a coded mask experiment implementing a mechanical collimator, the off-axis sensitivity is dependent on how accurately the coUimator induced spatial modulation can be taken into account, that is, how good is the spatial oversampling of the detector cell defined by the collimator pitch. The aim is to select, in the deconvolution process, only the subset of each ceU which is actually exposed to a given direction, hereby obtaining a significant Poisson noise reduction. 

Figure 4.4. Compaiison of two intoisity decays, on a linear (UfO and logarithmic scale irighi). The error bars te esenf Poisson noise on the photon counts. The decay functions were described in Ref. 3.

Poisson noise in the difference d file. However, if the background level is large, it is necessary to consider the in eased noise level in the difference data file. 

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