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This paper presents an improved data processing method, which is referred to as the tracking intersection method, for a fibre-based dual-detector differential chromatic confocal probe with a mode-locked femtosecond laser source. In the dual-detector differential confocal system, two fibre detectors of an optical spectrum analyzer are employed to detect the spectra of the confocal signals. One of the fibre detectors, referred to as the measurement detector, is located at the confocal position of the confocal system, and the other fibre detector, referred to as the reference detector, is located at a position with a certain offset from the confocal position. In the tracking intersection method, the Z-directional displacement of a measurement object is derived from tracking the wavelength at the intersection point of the two fibre detector outputs. A new algorithm is proposed to generate a normalized output with a sharp peak at the intersection wavelength, from which the intersection wavelength can be detected with a high-sensitivity while the influence of the non-smooth spectral distribution of the femtosecond laser source can be removed. Compared with the previous tracking local minimum method, the new tracking intersection method is more robust to noises in the fibre detector outputs and consequently can realize better performance such as higher resolution and larger range in measurement of the displacement of the object. The advantages of the new method are demonstrated by simulation and experiment. [ABSTRACT FROM AUTHOR]

The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams. [ABSTRACT FROM AUTHOR]

The Fresnel diffraction of an aperture with a rough edge is studied in this paper. Circular and elliptical apertures with sinusoidal and random edges are chosen as examples to investigate the influence of the aperture edge on the diffraction. The numerical calculation results indicate intuitively the variations of the transverse and longitude diffraction intensity distributions with the edge parameters of the aperture. The data files of aperture models are obtained through the numerical calculations, and the aperture samples are obtained with the help of a liquid crystal light modulator (LCLM). Thus, the practical experiments of the diffractions of apertures with rough edges are carried out. The measured results are consistent with the calculated ones. The approximate analytic expressions of the diffraction by the modified aperture are deduced on the basis of the Fresnel diffraction theory and the statistic optics, and the reasonable explanations for the influence of edge parameters on the diffraction are given through the theoretical analysis. [ABSTRACT FROM AUTHOR]