Light Amplitude Distribution Research Articles

Measurement error estimation and calibration for on-line detection phase variations in the laser-induced damage growth features of optical components.

The amplitude and phase distributions of reflection or transmission light are locally disturbed by damage regions. The damage state of optical components under successive laser irradiation can be evaluated according to the phase variation of a transmitted beam. The measurement accuracy of phase information related to the phase-unwrapping method is a critical factor for evaluating the damage state. This study analyzes and compares the performance of two important phase-unwrapping methods for detecting on-line large damage sites based on optimal modified lateral shearing interferometry. Meanwhile, the system stability and the measurement repeatability are also validated according to the retrieved phase pattern, which is beneficial to estimating the measurement accuracy. Experimental results of optical films are also presented and discussed to verify the feasibility of the estimation method utilized and the recommended phase-unwrapping method for on-line detection of the laser-induced damage growth features.

Comparative Characterization Study of a LaBr3(Ce) Scintillation Crystal in Two Surface Wrapping Scenarios: Absorptive and Reflective.

The properties of a 50 mm × 50 mm × 30 mm monolithic LaBr3:Ce scintillator crystal coupled to a position-sensitive multi-anode photomultiplier (PMT, Hamamatsu H9500), representing the absorbing detector of a Compton camera under study for online ion (proton) beam range verification in hadron therapy, was evaluated in combination with either absorptive or reflective crystal surface coating. This study covered an assessment of the energy and position-dependent energy resolution, exhibiting a factor of 2.5–3.5 improvement for the reflectively wrapped crystal at 662 keV. The spatial dependency was investigated using a collimated 137Cs source, showing a steep degradation of the energy resolution at the edges and corners of the absorptively wrapped crystal. Furthermore, the time resolution was determined to be 273 ps (FWHM) and 536 ps (FWHM) with reflective and absorptive coating, respectively, using a 60Co source. In contrast, the light spread function (LSF) of the light amplitude distribution on the PMT segments improved for the absorptively wrapped detector. Both wrapping modalities showed almost no differences in the energy-dependent photopeak detection efficiency.

Tunable hyperbolic apodizer

We unveil the use of two grey level masks for controlling continuously the attenuation of a spatial filter, which has an exponentially decreasing hyperbolic profile. We present analytical expressions that help to visualize the influence of our proposed grey level masks for reducing the side-lobes of a 1-D point spread function. Full Text: PDF References P. Jacquinot and B. Roizen-Dossier, "Apodisation," in Prog. Opt. 3, E. Wolf editor (North Holland, 1964) pp. 29-186. DirectLink C. W. McCutchen, "Generalized Aperture and the Three-Dimensional Diffraction Image", J. Opt. Soc. Am. 54, 240 (1964). CrossRef H. Arsenault and A. Boivin, "An Axial Form of the Sampling Theorem and its Application to Optical Diffraction", J. Appl. Phys. 38, 3988 (1967). CrossRef C. W. McCutchen, "Convolution relation within the three-dimensional diffraction image", J. Opt. Soc. Am. A 8, (1991). CrossRef J. E. A. Landgrave and L. R. Berriel-Valdos, "Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point", J. Opt. Soc. Am. A 14, 2962 (1997). CrossRef A.W. Lohmann, J. Ojeda-Casta-eda and P. Rodríguez-Montero, "Axial irradiance shaping with binary polar curves", Opt. Comm. 108, 42 (1994). CrossRef J. Ojeda-Castafieda, L. R. Berriel-Valdos, and E. Montes, "Bessel annular apodizers: imaging characteristics", Appl. Opt. 26, 2770 (1987). CrossRef J. Ojeda-Casta-eda, and A. Díaz, "High focal depth by quasibifocus", Appl. Opt. 27, 4163 (1988). CrossRef J. Ojeda-Casta-eda and L. R. Berriel-Valdos, "Arbitrarily high focal depth with finite apertures", Opt. Lett. 13, 183 (1988). CrossRef J. Ojeda-Casta-eda and L. R. Berriel-Valdos, "Zone plate for arbitrarily high focal depth", Appl. Opt. 29, 994 (1990). CrossRef J. Ojeda-Casta-eda, E. Yépez-Vidal and E. García-Almanza, "Optical processor arrays for controlling focal length or for tuning the depth of field", Phot. Lett. of Poland 2, 162 (2010). DirectLink Jorge Ojeda-Castaneda, Emmanuel Yépez-Vidal, Eloy García-Almanza, and Cristina M. Gómez-Sarabia, "Tunable axial bursts using annularly distributed phase masks", Phot. Lett. of Poland 4, 115 (2012). DirectLink Jorge Ojeda-Castaneda, Sergio Ledesma and Cristina M. Gómez-Sarabia, "Hyper Gaussian windows with fractional wavefronts", Phot. Lett. of Poland 5, 23 (2013). CrossRef W. W. Bell, Special functions for scientists and engineers (Van Nostrand, London, 1968)

On the relationship between the size and surface coverage of starspots on magnetically active low-mass stars

We present a model that predicts the light curve amplitude distribution for an ensemble of low-mass magnetically active stars, under the assumptions that stellar spin axes are randomly orientated and that cool starspots have a characteristic scale length and are randomly distributed across the stellar surfaces. The model is compared with observational data for highly magnetically active M-dwarfs in the young cluster NGC 2516. We find that the best fitting starspot scale length is not constrained by these data alone, but requires assumptions about the overall starspot filling factor and starspot temperature. Assuming a spot coverage fraction of 0.4+/-0.1 and a starspot to unspotted photosphere temperature ratio of 0.7+/-0.05, as suggested by the inflated radii of these stars compared to evolutionary model predictions and by TiO band measurements on other active cool stars of earlier spectral type, the best-fitting starspot angular scale length is 3.5(+2)(-1) degrees, or a linear scale length of \sim 25000 km. This linear scale length is similar to large sunspot groups, but 2--5 times smaller than the starspots recently deduced on an active G-dwarf using eclipse mapping by a transiting exoplanet. However, the best-fitting spot scale length in the NGC 2516 M-dwarfs increases with the assumed spot temperature ratio and with the inverse square root of the assumed spot filling factor. Hence the light curve amplitude distribution might equally well be described by these larger spot scale lengths if the spot filling factors are <0.1 or the spot temperature ratio is >0.9.

Imaging the Gouy phase shift in photonic jets with a wavefront sensor

A wavefront sensor is used as a direct observation tool to image the Gouy phase shift in photonic nanojets created by micrometer-sized dielectric spheres. The amplitude and phase distributions of light are found in good agreement with a rigorous electromagnetic computation. Interestingly the observed phase shift when travelling through the photonic jet is a combination of the awaited π Gouy shift and a phase shift induced by the bead refraction. Such direct spatial phase shift observation using wavefront sensors would find applications in microscopy, diffractive optics, optical trapping, and point spread function engineering.

Wavefront sensor based on the Talbot effect with the precorrected holographic grating

A holographic wavefront sensor based on the Talbot effect is proposed. Optical wavefronts are measured by sampling the light amplitude distribution with a two-dimensional (2D) precorrected holographic grating. The factors that allow changing an angular measurement range and a spatial resolution of the sensor are discussed. A comparative analysis with the Shack-Hartmann sensor is illustrated with some experimental results.

Gouy phase anomaly in photonic nanojets

We investigate in real space amplitude and phase distributions of light in photonic nanojets emerging from micrometer-sized dielectric spheres with a high-resolution interference microscope. Strong localization of light and a Gouy phase anomaly are witnessed. We show that the phase advance of photonic nanojets significantly deviates from a plane wave due to the sudden transition from a converging to a diverging wave front. Understanding such phase anomalies and verifying the presence of photonic nanojets promises to pave the way to prospective applications that may exploit the ability to localize light in spatial domains smaller than the usual resolution limit.

Calculation of the light pulse distributions induced by fast neutrons in organic scintillation detectors

We develop a fully analytic and self-contained description of the amplitude distribution of light pulses in an organic scintillation detector due to a monoenergetic source of fast neutrons. To this end, two classes of problems have to be handled. One is a formula for the light pulse amplitude distribution for the complete life history of neutrons slowing down in a mixture of hydrogen and carbon as a statistical average over all collision sequences that can occur, accounting also for neutron leakage. A complete solution is given in terms of a non-recursive convolution integral expansion with respect to the various possible collision histories. These latter are dependent on the collision probabilities of neutrons of a given energy. The second is the calculation of this collision probability from analytical expressions for the geometry of the detector, in the present case a right cylinder. This quantity was taken from Monte Carlo simulations in previous work. Recursive formulae are derived for the probabilities of arbitrary collision sequences, and quantitative results are given for up to five consecutive collisions of all combinations. These probabilities can be used to determine how to truncate the non-recursive expansion of the full light amplitude distribution in quantitative work. The calculational method serves to lend insight and understanding into the structure of the pulse height spectra, as well as it provides a computationally cheap method of generating a large number of such spectra for various detector compositions, sizes and neutron energies, for the development and test of new spectrum unfolding techniques.

Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: comment.

Landgrave and Berriel-Valdos presented axial and radial sampling expansions for three-dimensional light amplitude distribution around the Gaussian focal point. [J. Opt. Soc. Am. A 14, 2962 (1997)]. The expansions were obtained under the assumption that the pupil function was rotationally symmetric. We present a new derivation of the axial expansion that does not make use of arbitrary formal assumptions used by Landgrave and Berriel-Valdos and eliminates some faults of the derivation given by Arsenault and Boivin, who published this expansion in 1967 [J. Appl. Phys. 38, 3988 (1967)]. We also discuss generalizations of the axial expansion to the case of pupils that exhibit no symmetry with respect to the axis considered.

Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: reply to comment

The Comment by Kowalczyk [J. Opt. Soc. Am. A20, 2390 (2003)] on our paper on sampling expansions for three-dimensional light amplitude distributions in the vicinity of an axial image point [J. Opt. Soc. Am. A14, 2962 (1997)] presents a “new” derivation of the axial sampling expansion (ASE), pointing out some “faults” in our derivation and that of Arsenault Boivin [J. Appl. Phys.38, 3988 (1967)], a derivation of which we were not aware. Finally, it also summarizes work done in generalizing the ASE to the case of nonrotationally symmetric pupil functions. The purpose of this reply is to clarify some relevant issues concerning the derivation of this kind of expansion, since, judging from some ideas expressed in their Comment, we believe these issues were left insufficiently clear in our paper. In doing this, we derive some additional sampling expansions.

Amplitude and phase evolution of optical fields inside periodic photonic structures

Optical amplitude distributions of light inside periodic photonic structures are visualized with subwavelength resolution. In addition, using a phase-sensitive photon scanning tunneling microscope, we simultaneously map the phase evolution of light. Two different structures, which consist of a ridge waveguide containing periodic arrays of nanometer scale features, are investigated. We determine the wavelength dependence of the exponential decay rate inside the periodic arrays. Furthermore, various interference patterns are observed, which we interpret as interference between light reflected by the substrate and light inside the waveguide. The phase information obtained reveals scattering phenomena around the periodic array, which gives rise to phase jumps and phase singularities. Locally around the air rods, we observe an unexpected change in effective refractive index, a possible indication for anomalous dispersion resulting from the periodicity of the array.

A wavefront sensor based on the fractional Talbot effect

We propose a wavefront sensor based on the fractional Talbot effect. Optical wavefronts are measured by sampling the light amplitude distribution with a two-dimensional periodic phase grating. At certain fractions of the self-imaging distance, a reference wavefront generates an array of bright spots – the so-called Fresnel images of the grating. The local shifts in the Fresnel images that take place in the presence of wavefront aberrations can be related to the local wavefront slope. In an analysis of the angular and spatial resolution the variable measurement range and accuracy of this method is discussed. Finally some experimental results will illustrate this approach.

Wavefront sensor using the Talbot effect

A method for measuring optical wavefronts is proposed by properly sampling the light amplitude distribution with a two-dimensional periodic mask. At the Talbot planes, where a reference wavefront (spherical or plane) would originate replicas of the aperture, distortions of the resulting selfimages take place. These intensity patterns are detected and processed for obtaining the required wavefront information. The approach is illustrated with some experimental results.

Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point

Two sampling expansions are derived, from which the three-dimensional (3-D) field amplitude distribution in the vicinity of an axial image point can be recovered entirely from a 1-D set of amplitude samples. In the first of these expansions, the sampling points are regularly spaced along the system optical axis, whereas in the second these points lie along one radius in a plane perpendicular to this axis. The expansions are derived with a scalar diffraction theory by using the paraxial and classical approximations. Apart from leading to very efficient computational schemes, both expansions are shown to provide a good basis for analyzing the structure of this kind of diffraction pattern, and knowledge of this structure can be applied in turn to the solution of pupil synthesis problems.

Diffraction theory of optimized low-resolution Fresnel encoded lenses

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

Fractional Fourier optics

There exists a fractional Fourier-transform relation between the amplitude distributions of light on two spherical surfaces of given radii and separation. The propagation of light can be viewed as a process of continual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through fractional transforms of increasing order. This result allows us to pose the fractional Fourier transform as a tool for analyzing and describing optical systems composed of an arbitrary sequence of thin lenses and sections of free space and to arrive at a general class of fractional Fourier-transforming systems with variable input and output scale factors.

Approximate scaling relationships of light diffraction by apertures with complicated shapes

Numerical and analytical simulations of Fraunhofer diffraction by oddly shaped apertures and exponential light amplitudes show that within an accuracy of 20-40%, the dependencies of the normalized encircled energy epsilon on ?, the fraction of the energy transmitted by the aperture within a given polar angle ? are similar in shape when ? is normalized by lambda/rho. Here rho is the size parameter of the aperture geometry (its shape and size) and of the light-amplitude profile. For a small ?, rho = rho(l,eff) = (Sigma(eff)/pi)((1/2)) depends on the effective aperture area Sigma(eff), which is calculated through the axial light intensity. For a large ?, rho = rho(2,eff) = 2Sigma(eff)/Rho(eff) depends on Sigma(eff) and the corresponding perimeter Rho(eff). In the case of a uniform light-amplitude distribution the normalization of rho(1) and rho(2) corresponds to the well-known expansion of epsilon(?) for small and large ?.

Signal processing using surface acousto-optic interaction in LiNbO3

Abstract Signal processing functions such as convolution, correlation, and Fourier Transformation have been obtained in realtime using the efficient diffraction of laser light from acoustic surface waves progagating on LiNbO3. Different device configurations and detection schemes are discussed. Results are presented for the usual delay-line transducer configuration, as well as for an improved scheme which eliminates the problem of the reflection signal which is associated with this configuration. A discussion is given indicating the extension of the acousto-optical convolver to the generation of ambiguity functions and the correlation of a light amplitude distribution with an acoustic signal.

Optical data processing and filtering systems

Optical systems, which inherently possess two degrees of freedom rather than the single degree of freedom available in a single electronic channel, appear to offer some advantages over their electronic counterparts for certain applications. Coherent optical systems have the added property that one may easily obtain many successive two-dimensional Fourier transforms of any given light amplitude distribution, or, by use of astigmatic optics, one-dimensional transforms can be obtained. Therefore, most linear operations of an integral transform nature are easily implemented. The optical implementation of integral transforms which are of importance to communication theory is discussed; the general problems of optical filter synthesis and multichannel computation and data processing are introduced, followed by a discussion of potential applications. Astigmatic systems, which permit multichannel operation in lieu of two-dimensional processing, are treated as a special case of general two-dimensional processors. Complex input functions are discussed with relation to their role in coherent optical systems.