Visualization of optical gradient-index lens structure defects with refraction index radial distribution
The method of optical microscopy in determining the type and number of dislocations in materials has been used for years. In the production control of elements of optical and geodetic instruments, commercial domestic optical microscopes are widely used with up to 1500x magnification . Thus, for example, it was discovered that the operating parameters of T5E electronic theodolites and 2Ta5 and 3Ta5 tacheometers with the increase of thermomechanical stresses are reduced due to formation (generation) and dislocation movement in high-austenitic steels used to produce elastic suspensions of working bodies of geodetic instruments .
Heterogeneity of local areas of the glass structure as well as crystal dislocation constructional, constructional and functional materials, is defined by nano- and microbundle and anisotropy not only of the mechanical properties in various geometrical areas, but also of the optical-physical properties, especially in the miniaturization of optical elements, i. e. gradient-index lenses. The latter is most relevant in connection with the wide practical application of atomic resolution devices. The gradient-index lenses are made of transparent materials, imparting to them, through diffusion processes, a given law of refractive index distribution. Their name is derived from the English gradient-index (GRIN).
This paper attempts to decorate (visualize) micro- and mesodefects of the amorphous structure of the optical gradient-index lenses, typical samples nonlinear optics, which are major functional materials of optical engineering [3–8].
Widely used for transmission of information quartz-based optical fiber lightguides (OFL) can have technological and operational transverse structure mesodefects (Fig. 1). The main cause of a quartz glass structure defect is the slightest impurity of alkali metal oxides, actively interacting with the quartz glass base with the formation of the compounds readily soluble in water. As the experimental data obtained by different methods show, using meso- or microscopy or fractography analysis, the causes of defects are physical and mechanical factors. These include the applied stretching or bending external strains exceeding the value limit of proportionality, since the plasticity parameters of the quartz-based OFL are zero. In the case of a defect-free original OFL structure, the values of the tensile strength can reach 70 000 MPa, and in the presence of mesodefects the value of the tensile strength decreases by two orders of magnitude.
The lateral surface of the cylindrical optical gradient-index lenses with sintering of initial charge frit in an upright position is increasingly rough. Such roughness occurs due to difference in the softening temperature of local portions of glass, and motion of local areas with a predominance of the alkaline or acidic components caused by gravity. Alkaline components of local cross-sectional areas of samples have a lower softening point in comparison with acid base SiO2. This leads to the formation of protrusions and depressions on the lateral surface. The first attempt to determine the numerous parameters of the roughness of the gradient-index lens surface in accordance with ISO 4287:1997 on precision highly accurate measuring equipment is given in , and the form of various surface and subsurface defects of the structure of optical gradient-index lens is given in .
For the purpose of decorating the surface and subsurface micro- and mesostructural defects of the gradient-index lens structure, electrochemical analysis methods were applied. Modern fundamentals of electrochemistry, including applied solutions of electrolytes, thermodynamics and kinetic aspects of electrochemical reactions, substance transfer, analytical methods, applied aspects and corrosion can be found in . It is worth mentioning different types of heterogenic or galvanic corrosion, and in particular: the role of heterogeneity in a non-uniform corrosion and corrosion in the conditions of differential aeration. Dependence of the distribution on the diffusant concentration in low-temperature ion-exchange diffusion in the quartz-based cylindrical gradient-index lens cross-section with RI radial distribution has a linear character, decreasing from the sample surface to the center. Therefore, the experiments with differential aeration in specially selected electrolyte are of particular interest. The results of studies of local areas with grinded and polished flat spots with removed segment-shaped glass layer draws special attention.
All kinds of irregularities existing in the material cause the appearance of potentials difference between two phases (points) of the material. As a result, a galvanic pair emerges (element), which leads to uneven electrochemical heterogenic corrosion. Corrosion mechanism is indirect transfer of electrons from the reductant to the oxidant.
There are a large number of kinds of non-homogeneities or gradients of properties that determine corrosion. For the development of technology for the production of gradient-index lenses, such factors as temperature gradient, contact between two different materials are of particular attention; solution composition gradient and chemical or mineral material composition gradient, as well as the dissolved oxygen, i. e. differential aeration; zones of increased internal strains in the material from previous technological operations, e. g. from the parameters of sintering.
Galvanic corrosion is associated with the formation of a galvanic element upon contact of two different materials, submersed in corrosion and ion-conducting medium. Under these conditions, the material which becomes a negative pole, corrode, while oxygen recovery or water formation occurs on the material, a positive pole. In the formation of contact between materials with different values of electronegativity, corrosion of the more electronegative material is accelerated, and corrosion of the less electronegative material is discontinued.
If you consider gradient-index lens sample, partially submerged in the electrolyte, then the concentration of dissolved oxygen in the upper layer of electrolyte is higher than in the lower one. In this case, we observe the process of differentiation aeration . True gradient-index lenses contain both alkaline and acidic phases of ordered stoichiometric structure with different values of electronic structure and local electronegativity. Thus, at the constant temperature (20 ± 2 °C), oxygen concentration gradient creates anode below the optical element workpiece and cathode at the top . The element formed under such conditions will tend to equalize the concentration of oxygen in the lower and upper parts of the solution. Corrosion occurs in the oxygen-depleted electrolyte. This experimentally shows that corrosion is an electrochemical reaction, wherein the electronic exchange is implemented on the various sections of the electrode, and not in chemical oxidation-reduction. In this case it is possible to say about the existence of corrosion porosity .
Microscopic and mesoscopic drop-shaped light round structure condensate-related defects are observed on polished working planes of the gradient-index lens samples exposed to long-term transportations under variable temperature and relative atmospheric humidity conditions after manufacturing. It is for this reason that the corrosion products together with the small dust particles form a halo surrounding water drop, and foreign particles are adhered at the periphery (Fig. 2). All these defects negatively affect the values of the transmittance ration in wavelength optical band and the scattering values of the working beams.
For the development and contrasting (decoration) of surface and near-surface defects of the structure of segregation origin , various compositions of electrolytes with the content of crushed yttrium and magnesium particles were selected in the presence of a massive silver platform-substrate on which the studied quartz-based gradient-index lens samples with radial RRI shape were placed (Fig. 3).
In this paper, we used yttrium of ItM‑1 grade of vacuum smelting in a copper water-cooled crystallizer with a mass of 440 g with a certificate purity of 99.945% by weight. The actual impurities for analysis were: gadolinium ≤0.005; terbium ≤0.01; dysprosium ≤0.005; holmium ≤0.005; iron ≤0.01; calcium ≤0.01 and copper ≤ 0.01% by weight.
Separation of the ingot was performed on a universal milling machine with a circular saw made of R18 steel, 1 mm thick, with a tool rotation speed 63 rpm, a longitudinal feed of less than 13 mm/min and a milling depth of less than 3 mm. Heating of the ingot during the separation operation was less than 60 °C, because there was a slight fusion of the surface protective wax layer. The chips were magnetized by a high-energy magnet of the intermetallic compound SmCo5. The final separating technological operation was the filing with a smooth file.
Yttrium in air rapidly forms three valence compounds and a chemical compound Y2( C2 O4 )3 · 9 H2 O . There is a rapid hydration of yttrium in the presence of water vapor. It has structural instability and high chemical activity, thermodynamic instability. Between the yttrium and silver, three chemical compounds of different stoichiometric correlation with hexagonal and body-centered cubic cells can be formed along four eutectic reactions. The normal electrode potential of silver is 0.7994 V. It easily combines with sulfur, forming a sulphide film. It is highly resistant to any type of water, ethyl and methyl alcohols of any concentration. In accordance with , the atomic radius of yttrium is 0.181 nm, electronegativity is 0.9, and the ionization potential is 6.38 eV.
In this paper, we used deformable magnesium of industrial purity, the chips from which were obtained by the above technology. In accordance with , the atomic radius of magnesium is 0.162 nm, electronegativity is 0.9, the ionization potential is 7.64 eV, and the crystal cell is hexagonal close-packed. In moist air, it is covered with a film Mg(OH)2, which does not protect against further oxidation. The initial chemical composition is 99.95% magnesium, impurities: less than 0.02% zinc; less than 0.001% of iron; less than 0.01% silicon and less than 0.001% aluminum.
High-purity yttrium and magnesium are chosen for the study due to large values of electronegativity, intensive corrosive destruction and transfer of the decomposition products into the composition of the working electrolyte. In the presence of water, yttrium and alcohol in the electrolyte, the following chemical compounds are possible: colorless oxide Y2 O3, light yellow hydrated oxide Y (OH)3, and oxalate colorless crystalline compound Y2 (C2 O4 ) · 9 H2 O (Table 1).
In an yttrium-based anhydrous electrolyte, single microscopic shiny formations are noted inside the surface of the gradient-index lens shells, by an order of magnitude smaller than the average size of the shells, similar to the emission of gases in the local bottom volumes of the shells. Simultaneously, sub-surface transverse mesodefects of both continuous rectilinear shape and zigzag structure under differential aeration conditions are seen on the flat spots of gradient-index lens.
Some mesodefects in certain areas acquire a branched form. When the distilled water is added to the electrolyte, bubbles with a diameter of 0.1 mm are formed, which in 7–10 minutes reach a diameter of 0.5 mm. Moreover, against the background of the perimeter of gradient-index lens, the number of bubbles is an order of magnitude larger in comparison with other local volumes of electrolyte (laser monochromatic illumination in conjunction with the standard changes the color and appearance of the bubbles). Such phenomena are observed within 120 hours of observation from the moment of adding distilled water to the electrolyte.
Fig. 5 shows the results of experimental studies of two samples of gradient-index lenses (equal geometric dimensions) exposed to low-temperature ion-exchange diffusion. The first sample stayed in the above electrolytes of different compositions for more than 2 000 hours, and the second was not electrochemically exposed.
The method of determining the transmittance ratio is based on comparing the directional flux of radiation incident on the object and the flow that has passed through it. Monochromator MDR‑206 was used as a radiation source. Radiation was projected on a gradient-index lens through a diaphragm. The diaphragm was located directly in front of the gradient-index lens, and the gradient-index lens itself was located in front of the photodetector.
The spectral transmission of gradient-index lenses was monitored in the wavelength range 400–1100 nm. The spectral transmission of gradient-index lenses was determined as the ratio of the radiation flux that passed through the gradient-index lens (signal) and without it (100%).
The curves of the transmittance ratios (τλ) in the red (394 nm) – orange (425 nm) spectral range for both samples are between 0.45 and 0.80. Apparently, this testifies to the low transmissive capacity due to the segregation transverse defects in the gradient-index lens of the glass heterophase structure with the above geometric dimensions (400–425 nm). The latter assumption coincides with the experimental results of electron microscopic analysis of the quartz-based gradient-index lens .
With an increase in the wavelength of the visible range of the spectrum of more than 425 nm, inadequate changes in the values of τλ occur for the investigated samples. At a wavelength of 450 nm, the transmittance ratio τλ of the sample that was exposed to electrolytes is 0.92, and for the second sample, τλ is 0.88. This difference can be explained from the point of view of the laws of material science by the violation of the stoichiometric relationships of surface and near-surface excess phases of segregation origin in sample No. 1c by transferring to the electrolyte volume. Reducing the transmittance ratio of the second sample in the wavelength range 650–50 nm to τλ = 0.88 may indicate the presence of surface and subsurface segregation mesodefects of larger geometric sizes, which also agrees with the results of electron microscopy analysis .
Excess phases seem to be concentrated (segregated) on the transverse segregation mezodefections of the structure and refer to readily soluble alkaline chemical elements such as potassium, sodium, calcium, magnesium, etc. Such a significant difference in the values of transmittance ratios, as well as thermal coefficients of linear expansion of local micro- and nanoscale samples, is preserved up to the IR spectral region up to 950 nm (see Fig. 5), and then is kept at a level of 0.94–0.95 to a wavelength of 1 150–1 200 nm.
Thus, the presence of interfaces (or coherence violation) between the excess micro- and mesodimensional phases and quartz matrix reduces the transmittance ratio of working beams in the wavelength range of 394–1200 nm, most significantly in the range of 400–950 nm.
Since the composition of optical gradient-index lenses includes numerous acid and alkaline starting components in the form of oxides of chemical elements, the main factor that determines and controls the flow in the structure of all possible chemical reactions are not only binary, ternary, but also more multicomponent equilibrium phase state diagrams containing eutectic, eutectoid, and other chemical reactions . They inevitably lead to micro- and meso-segregation heterogeneities of local sections of the structure.
The first experimental studies of the roughness parameters (27 parameters) of the surface of domestic quartz-based gradient-index lenses are encouraged by the extremely high sensitivity of the geometric characteristics of the material surface to changes in the external environment. The research was conducted on precision equipment by Taylor Hobson. First, the surface of the samples was subjected to inspection. Then the gradient-index lenses were exposed for a long time (up to 2000 hours) in electrolytes and their surface was inspected once again. Measurements of the roughness parameters were carried out both with respect to the initial lateral cylindrical surface of the samples, and over the grinded and polished flat segmented flat spot . The overwhelming majority of parameters of roughness strongly reacts to the intensive chemical reactions occurring both on the lateral surface of gradient-index lenses and on flat spots with a depth of 0.4–0.5 mm .
The values of roughness parameters change by an order of magnitude after chemical reactions in the atmosphere of electrolytes: the "steepness" of the lateral cylindrical surface, after exposure to electrolytes increases a hundredfold; R3z, the average arithmetic value of the third heights of profile irregularities, decreases by eight times; parameter R3y decreases by a factor of nine. The values of the following roughness parameters of the lateral cylindrical surface of gradient-index lens decrease by two or more times: Ra; Rp; Rda; Rg; Rv; Rt; Rdg; Rz; Rc; Rz(DIN); Rdc; Rvo and RPc, which, apparently, indicates the multiphase structure of the optical material of the studied gradient-index lenses.
Thus, the decoration of defects in the structure of optical gradient-index lenses under conditions of electrolytic aeration and elecrocrochemical processes followed by a joint precision measurement of twenty-seven parameters of roughness of the lateral cylindrical surface of gradient-index lenses with RI radial and axial forms seems to be a very promising scientific basis for creating a methodology for studying the relationships of individual parameters of the surface roughness properties of gradient-index lens. The technique will make it possible to develop recommendations on the reduction of technological segregation deformation-shear defects (flaws) in the structure of domestic quartz-based gradient-index lens. It is possible to reduce the number of defects at the stage of the thermal sintering process of the initial charge-frit. To correct the geometric parameters and the mineral composition of the initial powder glass materials, one must use the form of equilibrium phase diagrams of the state of the components. These actions will lead to an increase in the transmittance ratio of laser radiation in a given spectral range of wavelengths, a decrease in the scattering of light, and the improvement of other optical-physical parameters of optical gradient-index lenses.