Cafer Ozkul

Application of the two-dimensional fractional-order Fourier transformation to particle field digital holography

We demonstrate that the fractional-order Fourier transformation is a suitable method to analyze the diffraction patterns of particle field holograms. This method permits reconstruction of in-line digital holograms beyond the Fraunhofer condition (d2/lambdaz approximately/= 10). We show that the diameter of spherical particles is measured with good accuracy. Simulation and experimental results are presented.

Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform

We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.

ENHANCEMENT OF WIRE DIAMETER MEASUREMENTS : COMPARISON BETWEEN FRAUNHOFER DIFFRACTION AND LORENZ-MIE THEORY

The Fraunhofer diffraction is compared with a numerical simulation based on the Lorenz-Mie theory to improve the performance of a laser diffraction instrument. This instrument, based on the analysis of diffraction fringes at the focal plane of a lens, is especially suitable for individual wire diameter measurements. We show that the error due to Fraunhofer approximation increases with an increase of the reflectivity and a decrease of the object diameter. Comparison with Lorenz-Mie theory enables us to correct these errors. For a given object, the laser diffraction instrument reproduces diameter measurements with a very small dispersion.

Application of two-dimensional wavelet transform to hologram analysis: visualization of glass fibers in a turbulent flame

In different fiberization processes, glass fibers are drawn out in a turbulent flame. High-speed in-line holography is applied to visualize glass fibers. However, the random spatial distribution of temperature in- duces strong local variations of the refraction index. Consequently, the reconstructed images are altered. The direct analysis of the diffraction patterns recorded by the holographic plate can offer an alternative solu- tion. The diffraction process can be interpreted as a convolution with a wavelet family of functions. The scale parameter a is related to the dis- tance between the object and the plane of observation. The 3-D location of a fiber element and its orientationu are estimated by searching for the parameters a and u, which yield a maximum modulus of the wavelet transform. The results are compared with those obtained from a conven- tional optical reconstruction. The application of the wavelet transform improves the SNR in the image and enables the 3-D fiber location to be determined more accurately (650 mm for the axial coordinate estima- tion).

Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements

Far-field diffraction patterns of a glass cylinder are spatially sampled with a photodiode array. Three photometric signal processing methods are discussed. The first one is based on the analysis of fringes in the central lobe. It can be used for diameter monitoring, but not for a wide range of diameter measurements. The second method consists of best-fitting between the theoretical model of the irradiance distribution in the central fringe and the corresponding experimental data. The accuracy of this method (±1 μm, in the range 10 to 50 μm) is improved by introducing the optical transfer function (OTF) of the photosensitive area into the calculation. The third method uses a reliable estimation of the intensity at the center and the half-width of the central fringe in order to resolve the inverse problem by Newtons method. This method can be used for realtime measurements but must be improved by statistical approaches.

On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field

We are dealing with the description of an optoelectronic instrument which does not necessarily need in-focus images for dimensional measurements. Assuming the point spread function (PSF) as Gaussian, spherical particle diameters are deduced from the image contrast and the cross-section areas of the defocused images. Here, a cross-section area is defined by the number of pixels whose grey level is inferior to the mid-point intensity. The instrument makes use of two CCD cameras with the same angle of view. The source is a double pulsed multimode laser diode. One of the CCD cameras is exposed to two pulses and the activation of the other is delayed for only recording the object field illuminated by the last pulse. Then the two video signals are subtracted. This operation increases the signal/noise ratio (SNR). The contrast of one image being inversed, not only the amplitude of the particle velocity but also its sign, can be determined.

Application of the photorefractive effect: particle image velocimetry from simultaneous recording of several light sheets and laser Doppler velocimetry with the Bessel beams

Two new applications of the photorefractive phenomenon to optical velocimetry are described. One of them concerns the laser Doppler velocimetry with photorefractive two-wave mixing. The second application is covered by the particle image velocimetry, where a photorefractive crystal volume and a set of light sheets are used, respectively, for sampling the flow field in depth instantaneously and for illuminating the fluid volume sealed by small particles.

Simultaneous particle size, 3D position, and velocity measurements from processing of defocused images recorded with two CCD cameras

Out of focus images recorded separately by two CCD cameras viewing the same object field are processed to measure simultaneously the size, 3-D position, and velocity of particles. The sign ambiguity of defocusing is removed by introducing a shift on the axial location of one camera with respect to the other and by using the ratio of the Fourier transforms of two defocused images. Particle sizing procedure includes mainly a calibration of the point spread function (PSF) of the optoelectronic setup for different amounts of defocusing and the measurement of both the contrast and the width at the intensity mid-point of defocused images.

Resonant behavior of the temporal response of the photorefractive InP:Fe under dc fields

The pump beam intensity dependent temporal response of the two-wave mixing in InP:Fe crystals under dc fields at stabilized temperature has been studied. We observed a resonant behaviour of the rise time of the photoinduced grating like the coherent amplification gain. Numerical solutions of the coupled field and material differential equations have been performed with a time dependent fringe modulation in the sample volume. The temporal evolution of the signal beam output intensity has been described taking into account the nonlinearity effect at large modulations. Preliminary theoretical and experimental results are in rather good agreement.