## Object's size estimation

based on photocounts distribution characteristics analysis

### Essence

In case of object location which is at hundreds kilometers from laser location system, scattered field intensity in optical detectors area is low. Radiation influence on photodetector result is current impulses forming at the output, which can be considered to be separate equivalent occurrences – photocounts.

Photocounts registration in time period probability distribution law depends on dimensions of object surface part which has been irradiated. Scattered intensity field number of degrees of freedom to a first approximation counted as quotient of coherent radiation area in detector aperture area to this detector area :

.

For most of real objects surface scattered radiation obey the Lambert law, therefore

,

where – is objects surface projection area on a perpendicular to vector of observations plane. Photocounts , depends on background radiation on photodetector effect. Photocounts

depends on objects surface scattered radiation on photodetector effect. If average counts less then average of photocounts, then.

To determine a kind of distribution and scattered field radiation number of degrees of freedom estimation on the basis of experimental observations, we must ascertain time interval start in which we register scattered impulse. If object location conditions are known, one can find radiation scatter type of object, which overall dimensions are known to, by obtained value. One also can get diffusing disk (flat model ) radius estimation, for which radiation scattered field statistic characteristics are equivalent to radiation field characteristics diffused by by the same

value. We must provide experimental photocount samples representativeness to determine value correctly. Necessary number of location cycles determine from radiation propagation conditions and required errors of object dimensions estimation.Experiments being carried out prove method efficiency. Radiation passed through rotating matted disk and replacement aperture with known diameter was detected by a photomultiplier tube. Fast AD converter and PC connected with it provided signal amplitude counts estimation, which are proportional to photocounts number, registered in observation time interval . After obtained signal amplitude counts estimations statistical treatment, registered photocounts distribution was counted and field radiation number of degrees of freedom was determined. Obtained number of degrees of freedom corresponds to object physical model dimensions.

Photocounts distribution obtained in experiments

### Evaluation of photocurrent

on the photomultiplier tube output modeling

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Signal evaluation analysis on the photodetector output is a perspective line of development of signal processing methods in impulse laser location. It can provide objects identification and ranging with high accuracy.

The most effective way of different processing methods potential possibilities analysis and the whole requirements to recording and transforming technical devices detection is simulation of their values on the photodetector output.

Photodetecting is a quantum-mechanical process: primary photoelectrons stream is a result of constant radiation influence on photodetector. Number of photoelectrons detected in time interval obeys the Poisson's law:

,

where – average number photoelectrons in time interval, – photodetector quantum efficiency, – quantum energy, – registered radiation energy:

,

where – radiation intensity in different points of photodetectors surface positioned by **r **radius-vector. Since is stochastic time function,

,

where – optical signal energy stochastic value . There is a relation of optical fields’ statistical characteristics and photoelectrons values, corresponded to them from semiclassical Mandel’s law:

,

It follows that distribution is not Poisson generally. Process on the photomultiplier tube output is a single-electron pulses superposition:

,

where – single-electron pulse amplitude, which is stochastic value due to multiplication factor fluctuation, – primary photoelectrons, formed in time moment , stochastic field value, – – impulse response function of dynode system and photomultiplier tube output on single-electron formation. Value is a time interval between single-electron forming and single-electron pulse maximum time.

Thus photomultiplier tube output current values modeling consists of number values of ,…, for stochastic value for all single-electrons pulses, detected in time interval, modeling.

Photocurrent pulses values in case of 5·10^{-9} s Gauss impulse registration.

Experiments done, show ranging error about 0,05 ... 0,1 m by current pulse envelope values registration in one location cycle on the photomultiplier tube output and its following analysis.

### References

- Себекин Ю.Н., Бурый Е.В., Загидуллин Р.Ш., "Оценка эффективности использования пачки импульсов в оптических локационных системах" // Алгоритмы обработки сигналов в радиоэлектронных устройствах: Сб. статей / Под ред. И.Б. Федорова. – М.: Изд.–во МГТУ, 1989.
- E.V. Buryi, Yu.L. Smirnova, "Effect of the quantum nature of detecting low-intensity radiation on the distance measurement error in pulsed laser ranging", QUANTUM ELECTRON, 2004, 34 (12).