Fast vectorial calculation of the volumetric focused field distribution by using a three-dimensional Fourier transform.

We show that the volumetric field distribution in the focal region of a high numerical aperture focusing system can be efficiently calculated with a three-dimensional Fourier transform. In addition to focusing in a single medium, the method is able to calculate the more complex case of focusing through a planar interface between two media of mismatched refractive indices. The use of the chirp z-transform in our numerical implementation of the method allows us to perform fast calculations of the three-dimensional focused field distribution with good accuracy.

Ambiguity of optical coherence tomography measurements due to rough surface scattering.

Optical coherence tomography (OCT) images are frequently interpreted in terms of layers (for example, of tissue) with the boundary defined by a change in refractive index. Real boundaries are rough compared with the wavelength of light, and in this paper we show that this roughness has to be taken into account in interpreting the images. We give an example of the same OCT image obtained from two quite different objects, one smooth compared to the optical wavelength, and the other rough.

Direct calculation of a three-dimensional diffracted field.

We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens-Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.

Application of orbital angular momentum to simultaneous determination of tilt and lateral displacement of a misaligned laser beam.

We present an analysis of the combined effects of tilt and lateral displacement on the orbital angular momentum spectrum of a laser beam. Our theory explains the symmetries and properties of the spectrum under the influence of misalignments. We apply the theory to establish a reliable and efficient method for determining and subsequently eliminating tilt and lateral displacement. An improved technique for obtaining the orbital angular momentum spectrum employing Laguerre-Gaussian modes is proposed. Finally, a numerical experiment is carried out to verify the method.

Pupil matching of Zernike aberrations.

The measurement of the wavefront at the exit pupil of an optical system is a reliable method to investigate its imaging performance. It is sometimes necessary to compare the measurement obtained with a wavefront sensor to some known aberration function, which is for example given by a simulation or a gold standard measurement technique such as interferometry. For accurate measurement systems, the residual after direct subtraction of the two wavefronts is often partly due to a mismatch between coordinate systems. We present in this paper a method that uses the Zernike expansion of wavefronts to numerically cancel such small alignment errors. We use this algorithm to quantify the accuracy of a custom-built Shack-Hartmann wavefront sensor in the measurement of known aberration functions.

Task Performance in Astronomical Adaptive Optics.

In objective or task-based assessment of image quality, figures of merit are defined by the performance of some specific observer on some task of scientific interest. This methodology is well established in medical imaging but is just beginning to be applied in astronomy. In this paper we survey the theory needed to understand the performance of ideal or ideal-linear (Hotelling) observers on detection tasks with adaptive-optical data. The theory is illustrated by discussing its application to detection of exoplanets from a sequence of short-exposure images.

Laboratory MCAO Test-Bed for Developing Wavefront Sensing Concepts.

An experimental optical bench test-bed for developing new wavefront sensing concepts for Multi-Conjugate Adaptive Optics (MCAO) systems is described. The main objective is to resolve imaging problems associated with wavefront sensing of the atmospheric turbulence for future MCAO systems on Extremely Large Telescopes (ELTs). The test-bed incorporates five reference sources, two deformable mirrors (DMs) and atmospheric phase screens to simulate a scaled version of a 10-m adaptive telescope operating at the K band. A recently proposed compact tomographic wavefront sensor is employed for star-oriented DMs control in the MCAO system. The MCAO test-bed is used to verify the feasibility of the wavefront sensing concept utilizing a field lenslet array for multi-pupil imaging on a single detector. First experimental results of MCAO correction with the proposed tomographic wavefront sensor are presented and compared to the theoretical prediction based on the characteristics of the phase screens, actuator density of the DMs and the guide star configuration.

Experimental light-scattering measurements from large-scale composite randomly rough surfaces.

We present experimental measurements of the angular distribution of light scattered from large-scale composite randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with microlithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the diffusely scattered light is strongly depolarized and that its pattern is rather different for each large-scale surface profile. Enhanced backscattering is also observed.

Effects of retinal scattering in the ocular double-pass process.

The validity of double-pass wave-front measurements in the eye is reviewed analytically and computationally. A mathematical description of the scalar optical field in the exit pupil plane after an ocular double-pass process is presented. With the help of this description, the relationship between the phase information losses and the statistical properties of retinal scattering is demonstrated.

Astronomical adaptive optics in parameter space.

We present a general, undiscretized formulation of astronomical adaptive optics that encompasses arbitrary guide star sources and deformable mirror configurations. It is shown that wave-front measurements can be represented as samples of an integral transform of the turbulence perturbation and also that the desired information for adaptive correction is a subset of this transformed space. Some properties of this space are explored, and their implications for adaptive optics are discussed.

Hybrid curvature and gradient wave-front sensor.

A new wave-front sensor for adaptive optics that gives signals for the curvature and the two gradient components of the wave front simultaneously is proposed. The sensor uses quad cells placed at the foci of an array of astigmatic lenslets, giving three intensity-normalized differential signals. The parameters of a single subdetector are optimized to maximize the curvature signal. The performance of such a sensor designed for a membrane curvature mirror is analyzed. The good match between sensor and mirror is exhibited by an almost diagonal response matrix between the mirror actuator controls and the curvature signals.

Single-pass measurements of the wave-front aberrations of the human eye by use of retinal lipofuscin autofluorescence.

We describe a technique for making single-pass measurements of the wave-front aberration of the eye. The technique utilizes the natural fluorescence of the retina that is produced by lipofuscin to form an incoherent pointlike source for conventional Shack-Hartmann sensing.

Low-order adaptive deformable mirror.

We report the main parameters of a nine-electrode bimorph piezoelectric adaptive mirror designed to correct low-order aberrations. We describe measurements of the control coefficients for defocus, astigmatism, pure coma, and spherical aberration of this mirror and the temperature stability of its profile. The performance of a simple adaptive optical system for imaging through laboratory-generated turbulence is investigated. This low-order device is suitable for small (<1-m-diameter) telescopes and for nonastronomical applications of adaptive optics.

Algebraic reconstruction of a small-scale wave front.

We show that a small-scale wave front can be reconstructed by an algebraic procedure from its intensity distribution in the focal plane, except for the ambiguities of the piston phase and the point-symmetrical solution of the complex conjugate. Details of the reconstruction procedure for a 3 x 3 wave front are presented, and the effectiveness of this procedure for a contaminated case is shown by computer simulation. A method for overcoming the ambiguity problem resulting from the point-symmetrical solution is also suggested.

Linnik microscope imaging of integrated circuit structures.

Experimental one-dimensional intensity and phase images of thick (>200 nm) oxide lines on silicon are presented together with profiles predicted from the waveguide model. Experimental results were obtained with a purpose-built Linnik interference microscope that makes use of phase-shifting interferometry for interferogram analysis. Profiles have been obtained for both TE and TM polarizations for a wide range of focal positions and in both bright-field [type 1(a)] scanning and confocal modes of microscope operation. The results show extremely good agreement despite several simplifying assumptions incorporated into the theoretical model to reduce computing times.

Measurements of the four-point coherence function by the use of the coherence enhancement phenomenon.

We present laboratory results for measurements of the four-point coherence function of a spherical wave in the region of coherence enhancement after backscattering through turbulence. Experimental results are compared with the theoretical predictions. We conclude that the shape of the four-point coherence function in our experiment depends on the value of the inner scale of turbulence.

Depth-resolved holographic imaging through scattering media by photorefraction.

A depth-resolved near-infrared imaging system has been demonstrated for recording three-dimensional images of objects embedded in diffuse media. Time-gated holographic imaging employing rhodium-doped barium titanate as the recording medium is used to acquire whole depth-resolved two-dimensional images in 1 s. Millimeter depth resolution has been achieved with a transverse resolution of ~ 30 microm.

Investigation of the temporal spread of an ultrashort light pulse on transmission through a highly scattering medium.

An experimental and theoretical investigation of the temporal spread of an ultrashort light pulse on transmission through a highly scattering medium has been made. For the strongly diffuse light, the transmitted pulse may be described by a universal function whose duration can be directly related to the width of the sample. For sufficiently scattering samples, experimental data and the diffusion approximation indicate that the output pulse duration scales with the square root of the sample width.