# Hilbert Book Model Project/Perceptibility and Recognition at Low Dose Rate

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## Contents

# Perceptibility and Recognition at Low Dose Rate[edit]

#### Optical tract[edit]

With respect to the visual perception, the human optic tract closely resembles the visual tract of all vertebrates.

The evolution must have optimized the functionality of the visual tract of vertebrates for efficient operation under low light level conditions.

Hubel and Weisel discovered this. They got a Noble price for their work. The duo analyzed the optic tract of many types of vertebrates, including humans.

The sensitivity of the human eye covers a huge range. The visual tract implements several special measures that help to extend that range.

At high dose rates the pupil of the eye acts as a diaphragm that partly closes the lens, and in this way, it increases the sharpness of the picture on the retina. At such dose rates, the cones perform the detection job. The cones are sensitive to colors and offer a quick response. In unaided conditions, the rods take over at low dose rates, and they do not differentiate between colors. In contrast to the cones, the rods apply a significant integration time. This integration diminishes the effects of quantum noise that becomes noticeable at low dose rates.

The sequence of optimizations does not stop at the retina. In the trajectory from the retina to the fourth cortex of the brain, several dedicated decision centers decode the received image by applying masks that trigger on special aspects of the image. For example, a dedicated mask can decide whether the local part of the image is an edge, in which direction this edge orients and in which direction the edge moves. Other masks can discern circular spots. Via such masks, the image encodes before the information reaches the fourth cortex.

Somewhere in the trajectory, the information of the right eye crosses the information that contains in the left eye. The difference is used to construct three-dimensional vision.

Quantum noise can easily disturb the delicate encoding process. That is why the decision centers do not pass their information when its signal to noise ratio is below a given level. The physical and mental condition of the observer influences that level. At low dose rates, this signal to noise ratio barrier prevents a psychotic view. The higher levels of the brain thus do not receive a copy of the image that the retina detected. Instead, that part of the brain receives a set of quite trustworthy encoded image data that together with already stored data, will decipher in an associative way. Obviously for a part other parts of the brain act in a similar noise blocking way.

The evolution of the vertebrates must have installed this delicate visual data processing subsystem in a period in which these vertebrates lived in rather dim circumstances, where the visual perception of low dose rate images was of vital importance.

This explanation indicates that the signal to noise ratio in the image that arrives at the eyes pupil has a significant influence on the perceptibility of the low dose image. At high dose rates, the signal to noise ratio hardly plays a role. In those conditions, the role of the spatial blur is far more important.

It is easy to measure the signal to noise ratio in the visual channel by applying a DC meter and an RMS meter. However, at very low dose rates, the damping of both meters might pose problems.

What quickly becomes apparent is the relation between the signal to noise ratio and the number of the quanta that participate in the signal. The measured relation is typical for stochastic quantum generation processes that classify as Poisson processes.

It is also easy to comprehend that when the signal spreads over a spatial region, the number of quantal that participate per surface unit is diminishing. Thus, spatial blur has two influences. It lowers the local signal, and on the other hand, it increases the integration surface. Lowering the signal decreases the number of quanta. Enlarging the integration surface will increase the number of involved quanta. Thus, these two effects partly compensate each other. An optimum perceptibility condition exists that maximizes the signal to noise ratio in the visual trajectory.

##### Optical Transfer Function[edit]

The Point Spread Function causes the blur. This function represents a spatially varying binomial process that attenuates the efficiency of the original Poisson process. This result creates a new Poisson process that features a spatially varying efficiency.

Several components in the imaging chain may contribute to the Point Spread Function such that the effective Point Spread Function equals the convolution of the Point Spread Functions of the components. Mathematically it can be shown that for linear image processors the Optical Transfer Functions form an easier applicable characteristic than the Point Spread Functions because the Fourier transform that converts the Point Spread Function into the Optical Transfer Function converts the convolutions into simple multiplications.

Several factors influence the Optical Transfer Function. Examples are the color distribution, the angular distribution, and the phase homogeneity of the impinging radiation. Also, veiling glare may hamper the imaging quality.

#### Image intensification[edit]

Human night vision and the perceptibility under other low dose rate conditions can be improved by applying image intensifier devices.

##### Detective Quantum Efficiency[edit]

The fact that the signal to noise ratio appears to be a deciding factor in the perception process has led to a second way of characterizing the relevant influences. The Detective Quantum Efficiency (DQE) characterizes the efficiency of the usage of the available quanta. It compares the actual situation with the hypothetical situation in which all generated quanta would serve in the information channel. Again, the measured signal noise ratio compares to the ideal situation in which the stochastic generator is a Poisson process, and no binomial processes will attenuate that primary Poisson process. However the binomial process that is implemented by the point spread function will still be considered to be part of the overall Poisson process that generates the impinging quanta. These facts mean that blurring and temporal integration must play no role in the determination of the DQE and the analyzed device will be compared to quantum detectors that will capture all available quanta. It also means that the intensification processes will be considered as if they do not add extra relative variance to the signal. The application of micro-channel plates will certainly add extra relative variation. This effect will be accounted as a deterioration of the detection efficiency and not as a change of the stochastic process from a Poisson process to a more exponential process. Mathematically this is an odd procedure, but it is a valid approach when the measurements are used to evaluate perceptibility objectively.

### Mechanisms[edit]

The fact that the Optical Transfer Function in combination with the Detective Quantum Efficiency can provide the objective qualification of perceptibility at low dose rates, indicates that a Poisson process that couples to a binomial process, governs the generation of the quanta, where a spatial Point Spread Function implements the binomial process.

The mechanisms that ensure dynamical coherence appear to apply stochastic processes whose signal to noise ratio is proportional to the square root of the number of generated quanta.

Quite probably the quantum generation process belongs to the category of inhomogeneous spatial Poisson point processes.

### Particle imaging[edit]

The hop landing location generating mechanisms apply stochastic processes, which own a characteristic function. This ensures that the mechanism delivers a coherent hop landing location swarm that moves as a single object. The hop landing location swarm that represents the elementary particles already represents a kind of point spread function. The Fourier transform of this point spread functions represent a characteristic function. Other imaging components feature spatial point spread functions that also implement binomial processes. The Fourier transforms of these point spread functions represent optical transfer functions. Multiplication of the characteristic function and the OTFs results in a function that characterizes the quality of the optical imaging process.

The characteristic function of the stochastic process that controls the generation of the location of higher level modules also ensures that the module moves as a single object. In this way, this stochastic process plays an essential role in the binding and the internal movement of the elementary modules.