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Physical phenomena are usually measured in terms of an amplitude-versus-time function, referred to as a time history record. The amplitude of the record may represent any physical quantity of interest. The time scale of record may represent any independent variable. Depends on the nature of phenomena, in some cases specific time history records of future measurement can be predicted with certain accuracy. However, many physical phenomena of engineering are not predictable, that is, each experiment produces

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a unique time history record which is not likely to be repeated and can not be accurately predicted in detail. Such data and physical phenomena are called random. In such cases, the resulting time history from a given experiment represents only one physical realization of what might have occurred. To fully understand the data, one should conceptually think in terms of all time history records that could have occurred. This collection of all time history records which might have been produced by the experiment is called the ensemble that defines a random process describing the phenomenon. Random process or random media’s properties are randomly distributed in time and space. In optics, random media has a distorting effect on the propagation of electromagnetic waves. This effect has been studied in various literatures in the past, however the effect of such a distortion on the image and characterization of the effect statistically is the subject of interest in this study.

In practice, the resolution achievable in an imaging system is limited by inherent aberrations from optical system and frequently medium through which the waves must propagate. In such a condition, the optical system may achieve actual resolutions that are far poorer than the theoretical diffraction limit. Classical optical and image analysis methods [17,121] are usually focused on the reconstruction of a true object image X and

recondition of characteristics and identification of parameters of an object from an observed image Y. In general, only a distorted image Y instead of an ideal image X

can be observed that can be represented by a distortion (random or deterministic) transformationY=hX. Formally, the distortion operator wis defined as a digital filter to be inversely applied to restore unknown ideal/true image X. Usually, the distortion

operator h does not have a physical meaning and it is an abstract mathematical operator

that does not represent statistical properties of the actual distortion process.

However, if an object is placed behind (or into) a thin film of a random medium (e.g. lubricant) and an object image obtained, the obtained object image will be distorted by the media acting as a distortion operator. In this case, quality of the distorted object image (DOI) will mainly depend on the quality (actual condition) of the lubricant. Taking into account complex optical processes accompanying propagation of the light through the random liquid medium [45], a transformation/distortion operator h gains a

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mathematical notation as an optical transfer function (OTF) that represents a transformation of the original object image (OOI) into DOI. In addition, h _{gains a}

physical meaning representing an optical ability of the lubricant to deliver an object image. The actual condition of the lubricant will be accountable for causing distortion, diffusion, blurring and other image quality degradation processes.

It is obvious that the distortion operator h can be only identified in a case when OOI X and DOI Y are known. In this case, this approach for an identification of the

distortion operator h can be applicable for identification of the actual optical properties

of the media (e.g. engine lubricant). An additional advantage of this approach is that the OOI X is already known and it is a deterministic object (X=const). Therefore, an evolution of the actual optical properties of the engine lubricant media represented by variations of the distortion operator h (h=var) can be fully described by the variations of the DOI Y (Y=var). In a general sense, by “removing” known properties of the OOI

X from the DOI Y, properties of the distortion operator can be obtained that will fully

characterize an actual condition of the engine lubricant. Another way to estimate an evolution of the actual condition of the lubricant during engine functioning is to compare the current DOI Y properties with the properties of known OOI X.

When DOI Y is acquired through the random liquid medium (e.g. lubricant), the

acquired image will contain a complex combination of original object and a liquid medium images. Therefore, the acquired image (which is the DOI) and its parameters become functionally depended on interrelated optical parameters of the object shape and media. In this case, statistical analysis of characteristics and parameters of the DOI Y

can be successfully applied to determine two outcomes – a) identify parameters that characterize only object and media and b) identify a functional interdependence of the known object parameters and unknown parameters of the lubricant as an image-distorting liquid medium. This is why two methodologies (object shape-based and statistical optical analysis) are necessary to be developed as an addition to each other in order to

measure and analyse two afore-mentioned types (outcomes) of the complex object-liquid image parameters. Object shape-based optical analysis methodology is targeted to analyze the parameters of an object image distorted by the lubricant, and statistical

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optical analysis methodology is focused on the identification of cross-correlation

characteristics (e.g. OTF) of mentioned above functional interdependence that represents the distorting effect. Figure 4.1 shows a generalized schematic of two proposed methodologies for optical analysis of contaminated lubricants.

Figure 4.1 Generalized schematic of optical analysis methodologies