Measurement of reduced radii, depths, and optical densities of pits using computer analysis of micrographs of CR-39 plates etched after irradiation with 12C ion beam

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Highlights

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    The simultaneous automatic analysis of all micrographs of etched plates in batch mode.

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    New parameters – the reduced radius and depth of etched pits of the etched pits of plastic detector.

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    Frequency distributions of etched pit parameters over water chamber depth.

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    The evolution of the averaged profiles of etched pits over water chamber depth.

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    Computer densitometry of micrographs in nanometer, micrometer and macrometer scales.

Abstract

This work is a further development of our method, published in 2018, for computer analysis of micrographs taken from a plastic detector CR-39, etched after irradiation with a beam of 12C ions of energy 216 MeV/amu in the radiobiological research chamber of the ITEP-TWAC accelerator-storage complex. The aim of this work is to study geometric and optical parameters of pits in the etched plastic. This study is based on a new concept of reduced radii, which are the radii of the cross-section of inclined conical micro- and nano-pits at the points of intersection of their longitudinal axes and the etching surface of the detector; formulas for their calculations are derived. One CR-39 plate was irradiated in a radiobiological chamber filled with air, and eight plates were exposed at different depths of the chamber filled with water (phantom). 275,070 images of etched pores were found and analyzed in the plates. Differential frequency distributions of the reduced radii and depths of the pits and their average values on the etched surfaces of the plates are obtained. Formulas for nanodensitometry, microdensitometry, and macrodensitometry of pit images on micrographs are deduced. The dependences of the differential distributions and averaged values of pits optical densities on the ions passed ranges in the water phantom are calculated. Pairwise fittings by linear functions of the mutual dependences of the averaged values from each other and from the specific energy losses of ions are performed. It is shown that the most accurate linear fit is for the optical density-pit depth relationship.

Introduction

The first detectors of charged particles and fast ions were photographic materials and specially created nuclear emulsions [1], [2], [3]. Physicists tried to establish relations between parameters of observable tracks in developed nuclear emulsions and parameters of ions creating these tracks – atomic number Z, atomic weight A, and energy E. It was especially important to establish relations between the track optical density and the parameters of fast heavy ions [4], [5].

The first method for visualizing latent ion tracks in non-photographic materials using the etching process was discovered in 1957 [6]. To date, a detailed mathematical apparatus for calculating the geometric parameters of etched pits in various solid materials has been developed and described in a large number of works [7], [8], [9], [10], [11]. These methods have been used, for example, to study fragmentation of nuclei and tracks of fast heavy ions in various materials. Furthermore, for the photoemulsion method, a scientific direction appeared, devoted to the relationship between the geometric parameters and optical density of the etched pits on the one hand and the ion parameters on the other hand [12], [13], [14], [15], [16].

The development of automatic methods for measuring the parameters of ion tracks in detectors began also in 1957 [17] and continued successfully later [18], [19]. Currently, these scientific areas are developing very rapidly, and there are a large number of publications devoted to them; for example, [20], [21], [22], [23]. Nevertheless, this work demonstrates the novel capabilities of specially developed new automatic computer methods.

The objectives of this work are as follows:

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    Development of mathematical methods and computer algorithms for analyzing the geometric shape and optical densities of pits etched in plastic CR-39 detectors located at different depths along the longitudinal axis of the 12C ion beam in the water phantom.

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    Searching for the frequency distributions on the parameters of pits found in the CR-39 at various depths of the water phantom.

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    Evaluation of the linearity of the relationship between the averaged values of the measured parameters of the etched pits in the CR-39 plastic and of the linearity of their dependences on the specific ion energy loss at different depths of the water phantom.

Section snippets

Description of the experiments

This work is a continuation of studies [24] in which plates of the CR-39 polymer detector were irradiated at the ITEP-TWAC accelerator-storage complex along the normal to their surfaces with a 12C beam with energies up to 216 MeV/amu. Two experiments were performed. The first was auxiliary with only one plate placed into the radiobiological research biochamber filled with air. The second experiment was the main one, in which two sets of three and five plates, placed in the same chamber filled

The shape of the inlets of etched pits

The ions of the beam enter the phantom along the normal to its window with some accuracy. In addition, there is some scattering of ions during passing through the water and the material of the detector plates. Consequently, some of the ions can enter the plates with deviations from the normal to the plate surfaces. Depending on the dip angle of ions, the latent tracks etching form pits with the contour lines of the inlet openings of various geometric shapes. If the accelerated ion enters the

Fit ellipses in the dark areas of micrograph

As described in [24], the set of pixel image points of each dark region found can be divided into two subsets — the interior points of the area Ri,j and the outer boundary points ℵi,j — forming a two-dimensional contour. The index i enumerates points along the horizontal (0X) direction, and the index j enumerates points along the vertical direction (0Y) of the micrograph. To recognize the shape of a dark region, it is sufficient to use only boundary points, for which the equation of the contour

Calculation of optical densities of the found dark regions of micrographs

Densitometry of pixel images of etched plastics can be divided into three modes – nanodensitometry, microdensitometry, and macrodensitometry. Nanodensitometry is the densitometry of an individual pit with an aperture of the objective of a computer densitometer equal to the image area of the pit. The computer operates in microdensitometry mode, when it calculates the optical density of several pits as if they were stacked side by side and the mathematical aperture is equal to the sum of the

Investigation of the linearity of the relationship between the found parameters of the pits

Three dependences < r(S)>, <L(S)>, and D(S), according to Fig. 8, Fig. 11, and Fig. 16, behave quite identically and all are similar to the specific ion energy loss (dE(S)/dS). Therefore, it is interesting to check how accurately linear functions can describe their dependence on each other and on the specific energy losses of ions (dE(S)/dS).

Let us consider two functions f(S) and χ(S). Suppose that there is a linear dependence between them and we denote the approximating function as fa(χ(S)),

Conclusion

A special computer method has been created for studying the parameters of etched pits and nanopits in plastic irradiated with a beam of accelerated 12C ions at various depths of the water biochamber, including the Bragg peak. For this, several new ideas were implemented.

The first idea, already published in [24] and effectively used in this work, is related to the simultaneous automatic analysis of all images from each surface of the plates in batch mode. Thus, all the calculations of this work

CRediT authorship contribution statement

V. Ditlov: Conceptualization, Methodology, Software, Formal analysis, Supervision. A. Bakhmutova: Methodology, Data curation. M. Kolyvanova: Software, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We are very grateful to professors A.A. Golubev and N.N. Kisilev for their very useful discussions of our research at seminars of their ITEP departments.

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