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A technology for multivalued holographic measurement of a plane angle—a holographic prism, which serves as the basis for a device for calibrating the testing tools for navigational equipment under rolling— has been developed. The holographic prism is a miniature sample of photosensitive material, which contains a system of superimposed holographic gratings, and a laser the radiation of which passes through gratings to form a fan of diffracted beams. The fan in a prism based on a calcium fluoride (fluorite) crystal with color centers contained six out-of-plane beams radiating from a region with a hard-to-localize center. This fact hindered calibration of the measure and its application in the testing device. The use of photothermo-refractive glass as a material for preparing a sample and recording a system of holograms in it makes it possible to eliminate the drawbacks of fluorite-based prism. The number of holograms rises up to 21, the fan becomes in-plane, and its center is localized in a small region, with a size of several tenths of the sample thickness (1–2 mm). The fan beams are energetically homogeneous, and each can be identified when using the fan in a testing device.

Photothermal transformations of color centers in additively colored calcium fluoride crystals and in a colored crystal with a recorded hologram have been investigated. It is shown that the absorption spectrum of a colored crystal can be reconstructed within the entire transparency range of the matrix crystal by varying both factors affecting the sample—actinic radiation wavelength and temperature—as well as the duration of their effect. This possibility is important for the application of additively colored CaF2 crystals as a holographic medium.

A holographic method for measuring linear displacements based on the use of a highly stable volume scale hologram recorded in an additively colored calcium fluoride crystal with photochromic color centers is proposed and experimentally approved. The essence of this method lies in measuring and analyzing harmonic signals formed during linear displacement of crystal with a volume hologram in an external interference field. A physical model of the formation of harmonic signals in photodetectors when measuring displacements is considered, and a mathematical method for calculating linear displacements by plotting a Lissajous figure is substantiated. A laboratory breadboard of a device for measuring linear displacements in a range of 10 mm, limited by the aperture of crystal with a recorded 8.7-mm-thick hologram, is designed. When using a scale hologram with a period of 2.18 μm and a 632.8-nm He-Ne laser for reading this hologram, the error in measuring displacements by this method is 9 nm at a resolution of 3 nm.

When holograms are recorded on color centers in calcium fluoride crystals, these centers undergo spatial redistribution in the crystal bulk, which is accompanied by their transformation. The nature of this transformation has been investigated by optical spectroscopy and confocal scanning microscopy. It is shown that, under the recording conditions we used, the degree of center aggregation increases in both minima and maxima of the interference field in which the recording performed. The enhanced aggregation in field minima is caused by the increase in the concentration color centers, while the additional aggregation in maxima is determined by the specific conditions of hologram recording: the wavelength and power density of recording radiation and the crystal temperature.

A hologram recorded in a CaF2 crystal by modulating the concentration of simple centers (F, M, R, and N) and highly aggregated (mainly colloidal) color centers has been exposed to incoherent 365-nm light to a dose of about 4000 J/cm2 at a temperature of 80°C. As a result of this exposure, the color centers were almost completely transformed into quasi-colloidal centers. The hologram was retained, and its diffraction efficiency increased; the intensity and number of observed diffraction orders increased as well. Analysis of the angular dependences of the diffraction response made it possible to construct a spatial profile of the hologram, which turned out to be much narrower in comparison with the initial-hologram profile; both profiles differ from a sinusoidal one. The hologram’s stability to such a large exposure to incoherent light at an elevated temperature is related to the peculiar diffusion-drift mechanism of hologram recording on color centers in ionic crystals.

The conditions for the formation of a holographic prism of modification II (for which a beam of diffracted rays is induced by a reference laser beam in the plane oriented perpendicularly to the reference beam) are described. A sample of this prism is implemented experimentally, and its response to the signal (reference) beam is demonstrated. Two modifications of a holographic prism as a basis for solving metrological problems of storing and reproducing flat angles and transferring the angle size to gradable and/or calibrated angle-measuring tools are compared. Each modification is found to have advantages in particular fields; thus, none can be considered as unconditionally preferred. The final choice of a particular modification can be made only after detailed analysis of the devices on their basis.

The conditions for preparing photochromic CaF2 crystals, recording holograms with 532-nm radiation in them, and postexposure photothermal treatment of samples with holograms that provide the formation of holographic elements of significant thickness (about 1 cm) are considered. It is shown that the diffraction efficiency of volume holograms in such crystals in the case of reading out by radiation with wave-lengths of 532 and 632.8 nm can be as high as 10–15%. The role of the recording mechanism and the Borrmann effect in the fabrication of these holograms is demonstrated.

The specificity of additive coloring of CaF2 optical ceramic (formation of color centers in it and photothermochemical transformation of these centers in colored ceramic samples) has been considered. Under the same coloring conditions, this process occurs more slowly in ceramics rather than in crystals; at the same time, the limiting concentration of color centers that can be introduced into ceramics is much higher. The photothermochemical transformations of color centers in crystals and ceramics, which occur under illumination at different wavelengths and upon heating, have been studied. The specific features of introduction of color centers into ceramic and their transformation under illumination and heating are likely to be related to the mass twinning of ceramic grains.

The mechanism of the additive coloring of calcium fluoride crystals, both pure and doped with I- and III-group elements, has been investigated. The coloring rate and intensity and the dependences of these parameters on the experimental conditions, vapor mixture pressure, and temperature have been experimentally determined. It is shown that the concentration of anion vacancies/electrons that can be introduced into crystals is in the range of 1017–1018 cm−3; in crystals with a high concentration of rare earth ions, the limiting concentration can be an order of magnitude higher.

The specific features of recording a volume hologram in a photochromic reversible medium, which is characterized by simultaneous occurrence of hologram recording and relaxation, have been considered by the example of two ion crystals, i.e., cadmium fluoride with bistable gallium centers and calcium fluoride with color centers.

The kinetics of photoinduced absorption spectra of CdF2 crystals with bistable indium and gallium centers under femtosecond pulsed excitation has been experimentally investigated. Based on the example of indium ions, it is shown that the transmission band in the absorption spectrum of deep centers is formed for 0.8–1 ps, which significantly exceeds the photon absorption time. This process is interpreted as a result of displacement of indium ion from the initial interstitial position to a site of neighboring unit cell; the displacement velocity is estimated to be 200–250 m/s, a value close to the thermal velocity of this ion at room temperature. The times characteristic of the formation of free polarons as a result of the displacement of neighboring lattice ions have been experimentally estimated for the first time at a level of 0.8–1.2 ps. The capture times of free polarons by trivalent gallium and indium ions are estimated (5 and 10 ps, respectively), as well as the corresponding cross sections (2 × 10−16 and 8 × 10−16 cm2).

The study of the mechanism of additive coloring of calcium fluoride crystals, both pure and samarium-doped, demonstrates dynamical nature of processes that, in the course of coloring, tend to maintain equilibrium between Sm3+ and Sm2+ ions.

To determine the precise values of angles stored and reproduced by a new multivalued measure of plane angles, i.e., a holographic prism, it is expedient to use a procedure for collating two circular scales, one of which is determined by the prism upon its rotation on a rotary table, while the other is the device’s own scale. The two scales are considered to be equivalent. The collation procedure is discussed taking into account target (deviations of sought values of angles of both scales from their nominal values) and a number of nuisance parameters of the procedure. The scheme of the collation device is considered. The geometric model that determines sources of errors caused by design features of signal reading and recording devices of the holographic prism is analyzed.

The absorption spectra and holographic characteristics of a CaF2:Na crystal sample are measured at different wavelengths within the absorption band of colloidal centers, along with the same characteristics of the samples with holograms after their irradiation by incoherent UV light. Results of the study confirm the diffusion-and-drift mechanism of recording holograms on color centers in ionic crystals.

A new multivalued measure of plane angles is proposed, which is based on a highly stable system of superimposed holograms recorded in a photochromic material. Their mutual position forms a reference set of angles, which is stored by the measure and can be reproduced by a reference laser. The methods for fabricating a holographic measure (recording and reproducing holograms forming it) are discussed. One of two possible modifications of such a measure is implemented on the basis of calcium fluoride crystals with color centers. The technique for preparing this measure (holographic prism) and its properties are described. Based on this prism, one can develop a new generation of angle-measuring or -setting instruments that simultaneously satisfy two contradictory requirements, i.e., mobility and high discreteness and accuracy of angular measurements.

The differences in the optical spectra of CdF2:In semiconductors with bistable DX centers (concentrated (CdF2)0.9(InF3)0.1 solid solutions) and “standard” samples with a lower impurity concentration used to record holograms are discussed. In contrast to the standard samples, in which complete decay of two-electron DX states and transfer of electrons to shallow donor levels may occur at low temperatures, long-term irradiation of a (CdF2)0.9(InF3)0.1 solid solution by UV or visible light leads to decay of no more than 20% deep centers. The experimental data and estimates of the statistical distribution of electrons over energy levels in this crystal give the total electron concentration, neutral donor concentration, and concentration of deep two-electron centers to be ∼5 × 1018 cm−3, ∼9 × 1017 cm−3, and more than 1 × 1020 cm−3, respectively. These estimates show that the majority of impurity ions are located in clusters and can form only deep two-electron states in CdF2 crystals with a high indium content. In this case, In3+ ions in a limited concentration (In3+ (∼9 × 1017 cm−3) are statistically distributed in the “unperturbed” CdF2 lattice and, as in low-concentrated samples, form DX centers, which possess both shallow hydrogen-like and deep two-electron states.