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In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of the Fresnel approximation is described. For diffraction by a focused wave, the general case is considered for both high numerical aperture and for finite values of the Fresnel number. One aim is to develop a theory based on the use of dimensionless optical coordinates that can help to determined the general behaviour and trends of different system parameters. An important phenomenon, the focal shift effect, is discussed as well. Explicit expressions are provided for focal shift and the peak intensity for different numerical apertures and Fresnel numbers. This is one application where the Rayleigh–Sommerfeld diffraction integrals provide inaccurate results. [ABSTRACT FROM AUTHOR]

The essential purpose of this research study is to analyze the relationship among information technology, precision agriculture, and sustainability. This research study is related to primary data analysis, which determines the research used specific questions related to the variables. The open-ended and closed-ended questions are used for gathering the data, and these questions fulfill from different participants who have knowledge about sustainability, information technology, and agriculture. For measuring the data, used smart PLS software and generated different informative results such as indicator correlation, R square, F square, discriminant validity, and composite Reliability. Also, that smart PLS Algorithm model in between independent and dependent variables. Information technology is the main independent variable, and precision agriculture, also sustainability are both dependent variables. The overall result found that information technology positively relates to precision agriculture. The significant and direct relation with sustainability and information technology are positively associated with each other. [ABSTRACT FROM AUTHOR]

This paper presents an off-axis differential method for the improvement of a femtosecond laser differential chromatic confocal probe having a dual-detector configuration. In the proposed off-axis differential method employing a pair of single-mode fiber detectors, a major modification is made to the conventional differential setup in such a way that the fiber detector in the reference detector is located at the focal plane of a collecting lens but with a certain amount of off-axis detector shift, while the fiber detector in the measurement detector is located on the rear focal plane without the off-axis detector shift; this setup is different from the conventional one where the difference between the two confocal detectors is provided by giving a defocus to one of the fiber detectors. The newly proposed off-axis differential method enables the differential chromatic confocal setup to obtain the normalized chromatic confocal output with a better signal-to-noise ratio and approaches a Z-directional measurement range of approximately 46 μm, as well as a measurement resolution of 20 nm, while simplifying the optical alignments in the differential chromatic confocal setup, as well as the signal processing through eliminating the complicated arithmetic operations in the determination of the peak wavelength. Numerical calculations based on a theoretical equation and experiments are carried out to verify the feasibility of the proposed off-axis differential method for the differential chromatic confocal probe with a mode-locked femtosecond laser source. [ABSTRACT FROM AUTHOR]

An intentional investigation on the thermal stability of a mode-locked femtosecond laser chromatic confocal probe, which is a critical issue for the probe to be applied for long-term displacement measurement or surface profile measurement requiring long-time scanning, is carried out. At first, the thermal instability of the first prototype measurement setup is evaluated in experiments where the existence of a considerably large thermal instability is confirmed. Then the possible reasons for the thermal instability of the measurement setup are analyzed quantitatively, such as the thermal instability of the refractive index of the confocal lens and the thermal expansion of mechanical jigs employed in the probe. It is verified that most of the thermal instability of the measurement setup is caused by the thermal expansion of mechanical jigs in the probe. For the improvement of the thermal stability of the probe, it is necessary to employ a low thermal expansion material for the mechanical jigs in the measurement setup and to shorten the optical path length of the laser beam. Based on the analysis result, a second prototype probe is newly designed and constructed. The improved thermal stability of the second prototype probe is verified through theoretical calculations and experiments. [ABSTRACT FROM AUTHOR]

A method is proposed to expand the Z-directional measurement range of a fiber-based dual-detector chromatic confocal probe with a mode-locked femtosecond laser source. In the dual-detector chromatic confocal probe, the Z-directional displacement of a measurement target is derived from the peak wavelength in the normalized intensity ratio from the two light intensities obtained by the two identical fiber detectors. In this paper, a new method utilizing the main-lobe and side-lobes of axial responses acquired from both the normalized intensity ratio Ia and the invert normalized intensity ratio In, which is the inverse of Ia, is proposed to obtain the seamless relationship between the peak wavelength and the Z-directional displacement of a measurement target. Theoretical calculations and experimental investigation are carried out to demonstrate the feasibility of the proposed measurement range expansion method. [ABSTRACT FROM AUTHOR]

In this paper, the problem to estimate the on-axis resolution in creating a desired field profile by radiation of an aperture A is addressed. The latter applies in both diffractive optics and antenna synthesis. This is because the 'aperture theory', A can schematize a source, for example, an antenna or a lens illuminated by an incident field radiating a significant field only on the same aperture. The analysis refers to a customary axicon geometry consisting of a circle aperture transverse to the observation domain. The aim was to find a resolution formula allowing to highlight the impact of aperture geometrical parameters for configurations that are below the Fresnel approximation. The results show that the aperture cannot approximate the target field with the same level of accuracy along with the observation domain. In particular, near the aperture, smaller details can be retrieved and as the distance increases this ability degrades. [ABSTRACT FROM AUTHOR]