Unambiguous coherence retrieval from intensity measurements

It is demonstrated that the members of different classes of two-dimensional fields that have the same intensity distributions everywhere in free space but different coherence properties can be identified by measuring the fields' intensities after passing the fields through an anamorphic optical system, such as a cylindrical lens. In this way the ambiguity in coherence determination from intensity measurements alone, present for the case of two-dimensional fields, is removed.     

Shaping the focal intensity distribution using spatial coherence

The intensity and the state of coherence are examined in the focal region of a converging, partially coherent wave field. In particular, Bessel-correlated fields are studied in detail. It is found that it is possible to change the intensity distribution and even to produce a local minimum of intensity at the geometrical focus by altering the coherence length. It is also shown that, even though the original field is partially coherent, in the focal region there are pairs of points at which the field is fully correlated and pairs of points at which the field is completely incoherent. The relevance of this work to applications such as optical trapping and beam shaping is discussed.     

Determining spatial modes of lasers with spatial coherence measurements

We explain a technique that extracts both the structure and the modal weights of spatial modes of lasers by analyzing the spatial coherence of the beam. This is the first time, to our knowledge, that an experimental method is being used to measure arbitrary forms of the spatial modes. We applied this method to an edge-emitting Fabry-Perot semiconductor laser with a stripe width of 5 mum and extracted fundamental and first-order lateral modes with relative power weights of 96.2% and 3.8%. There was a single transverse mode.     

Multifractality of laser beam spatial intensity in a turbulent medium

We present the results of a laser beam passing through a turbulent medium. First we measure the geometric parameters and the spatial coherence of the beam as a function of wind velocities. A multifractal detrended fluctuation analysis algorithm is applied to determine the multifractal scaling behavior of the intensity patterns. The measurements are fitted with models used in the analysis of river runoff records. We show the surprising result that the multifractality decreases when the spatial coherence of the laser is decreased. Universal scaling properties could be applied to the spatial characterization of a laser propagating in a turbulent medium or random medium.     

Measurement of the spatial coherence of light influenced by turbulence

To evaluate the Earth's surface with a sensor on a satellite, it is important for one to use a correction factor such as atmospheric turbulence. The spatial coherence of light influenced by turbulence was measured in the laboratory by use of a simulator equipped with a multiple reflection system. The turbulence was generated by changing the ambient temperatures from 32 to 48 degrees C. It was found that the spatial coherence of light that passed through the turbulent region decreased when the temperature increased. Double-slit interference fringes were analyzed by a photographic method. The visibility of the interference fringes is the degree of coherence.     

Separation and analysis of forward scattered power in laboratory measurements of light beam transmittance through a turbid medium

In laboratory measurements of the transmittance of a light beam through a diffusing medium (water plus latex spheres), a distinction between the attenuated beam power and the received forward scattered power was made possible by the use of a transmissometer whose receiver has a variable field of view. The dependence of the received scattered power on the FOV angle and on the medium optical depth was analyzed. The deduced separated contributions of first- and second-order scattering, as well as the total received scattered power, were compared to the results of calculations.     

Measuring the light beam intensity spectrum by prism coupling technique

A new method for measuring the intensity spectrum of a light beam is proposed, which is based on monitoring the angular dependence of the reflected radiation power in a thin-film structure by prism coupling technique.     

Path of a beam of light through an optical coating

A simple model for the path of a light beam through an optical coating is the path of a ray predicted by Snell's law. By determining the exit point of a beam for various types of coating, one finds that the simple model is a good approximation in the case of antireflection coatings, but not for coatings of other designs. An approximate method for determining the correct path of a beam through the coating is derived and the path is illustrated using a Gaussian incident beam and tracing the position of the peak field of the beam as it traverses the coating.     

Three-dimensional mapping of the light intensity transmitted through nanoapertures

A general method to map the 3D spatial distribution of light emerging from nanoscale apertures is presented that uses photolithographic techniques to create polymer replicas of the intensity distribution. The resulting features varied with aperture diameter and exposure time and showed good correlation with theory. This method provides direct visualization of the intensity distribution in close proximity to nanostructures and overcomes limitations imposed by physical probes where the contribution of the probe to the map requires deconvolution.     

Transverse mode analysis of a laser beam by near- and far-field intensity measurements

A quantitative measurement of laser-beam quality can be performed by determination of the presence of multiple transverse modes of the laser oscillator and by calculation of their power content. Along this line of argument, we discuss a new approach that, starting from near-field and far-field intensity measurements, can evaluate the complex excitation coefficients of the transverse modes in a laser beam. The exploitation of near-field measurements sharply improves the performances of the technique in those cases in which only far-field measurements are used. The validity of the method is confirmed by several accurate numerical simulations and by some experimental results relative to a multimode Q-switched Nd:YAG laser.     

Synthesis of a multiple-peak spatial degree of coherence for imaging through absorbing media

The synthesis of a multiple-peak spatial degree of coherence is demonstrated. This degree of coherence enables us to scan different sample points on different altitudes simultaneously and thus decreases the acquisition time. The multipeak degree of coherence is also used for imaging through an absorbing layer with different thicknesses or different indices of refraction along the layer. All our experiments are performed with a quasi-monochromatic light source. Therefore problems of dispersion and inhomogeneous absorption are avoided. Our experimental results are presented.     

Reconstruction of spatial, phase, and coherence properties of light

Image reconstruction of partially coherent light is interpreted as quantum-state reconstruction. An efficient method based on the maximum-likelihood estimation is proposed for acquiring information from blurred intensity measurements affected by noise. Connections with incoherent-image restoration are pointed out. The feasibility of the method is demonstrated numerically. Spatial and correlation details significantly below the diffraction limit are revealed in the reconstructed pattern.     

Fringing fields in a liquid crystal spatial light modulator for beam steering

Abstract

Phase modulating spatial light modulators (SLMs) can be used to alter the shape of a laser wavefront to achieve a deflection or change in the shape of a laser beam. This paper reports the results of characterization, simulation and optimization of a one-dimensional liquid crystal (LC) SLM. The device has a large ratio between LC layer thickness and pixel pitch that results in a fringing field between pixels. In effect, the applied phase patterns will be lowpass filtered and the loss of high frequency components limits, for instance, the usable steering range. A method is presented where intensity measurements in the far field are used to determine how the phase modulation at the SLM is distorted. The inhomogeneous optical anisotropy of the device was determined by modelling the liquid crystal director distribution within the electrode-pixel structure. Finite-difference time-domain (FDTD) simulations were used to calculate the light propagation through the LC. The simulated phase distortion was compared with the experimental results. A voltage compensation scheme to improve the diffraction efficiency was developed utilizing the measured and simulated results. It is demonstrated that a modification of the voltage patterns can give a better realization of high frequency components in the phase distribution and an increase in maximum steering angle by a factor two.     

Changes in the polarization and coherence of a random electromagnetic beam propagating through a misaligned optical system

On the basis of the generalized diffraction integral formula for misaligned optical systems in the spatial domain, an analytical propagation expression for the elements of the cross-spectral density matrix of a random electromagnetic beam passing through a misaligned optical system is derived. Some analyses are illustrated by numerical examples relating to changes in the spectral degree of polarization and in the spectral degree of coherence of an electromagnetic Gaussian-Schell-model beam propagating through such an optical system. We find that the degree of polarization in the neighboring areas of the focal plane is oscillating, and the effect of misalignment on coherence is not so evident as that on polarization.     

Effect of spatial coherence on knife-edge measurements of detector modulation transfer function

When an image of an edge object is used in the determination of the modulation transfer function of a detector array, the partial coherence of the illumination is often ignored. Although this approximation is valid in some cases, it may not be satisfactory, particularly for the small detector elements characteristic of present-day charge-coupled devices. Here we demonstrate the effect of partial coherence on edge-based modulation transfer function determination for various pixel sizes, degrees of coherence, and f-numbers of the test optics.     

Suppression of the zero-order diffracted beam from a pixelated spatial light modulator by phase compression

Phase compression is used to suppress the on-axis zero-order diffracted (ZOD) beam from a pixelated phase-only spatial light modulator (SLM) by a simple modification to the computer generated hologram (CGH) loaded onto the SLM. After CGH design, the phase of each SLM element is identically compressed by multiplying by a constant scale factor and rotated on the complex unit-circle to produce a cancellation beam that destructively interferes with the ZOD beam. Experiments achieved a factor of 3 reduction of the ZOD beam using two different liquid-crystal SLMs. Numerical simulation analyzed the reconstructed image quality and diffraction efficiency versus degree of phase compression and showed that phase compression resulted in little image degradation or power loss.     

Light intensity distributions of the Gaussian laser beam through an aperture team

Based on the propagating theory of the laser beam, the propagating characteristics of the Gaussian beam through an aperture team that comprises two apertures and a convergent lens, are studied. The approximate expressions for the field distribution are derived by the diffracted integral equation in detail under the condition of approximations. In comparison with the approximate expression and the precise expression, we know that there are the approximate same results for the two expressions if the radius of the second aperture is not too large. The numerical examples are given to confirm the correctness of our calculated results.     

Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Bessel function beams with a programmable spatial light modulator. We study the intensity patterns and the phase dependence of these nondiffracting beams. In addition, we examine interference effects caused by recording these patterns onto a binary spatial light modulator.