High-security communication by coherence modulation at the photon-counting level.

We show that key-specified interferometer path-length difference modulation (often referred to as coherence modulation), operating in the photon-counting regime with a broadband source, can provide a quantifiably high level of physics-guaranteed security for binary signal transmission. Each signal bit is associated with many photocounts, perhaps numbering in the thousands. Of great importance, the presence of an eavesdropper can be quickly detected. We first review the operation of key-specified coherence modulation at high light levels, illustrating by means of an example its lack of security against attack. We then show, using the same example, that, through the reduction of light intensities to photon-counting levels, a high level of security can be attained. A particular attack on the system is analyzed to demonstrate the quantifiability of the scheme's security, and various remaining research issues are discussed. A potential weakness of the scheme lies in a possible vulnerability to light amplification by an attacker.

Determination of flow orientation of an optically active turbulent field by means of a single beam.

The cross-flow orientation of an optically active turbulent field was determined by Fourier transforming the wander of a laser beam propagating in the ocean. A simple physical model for the measured effect is offered, and numerical simulations are performed. The simulations are in good agreement with measurements, validating the assumptions made in the model.

Time-average Fourier telescopy: a scheme for high-resolution imaging through horizontal-path turbulence.

The problem of high-resolution imaging through long horizontal-path ground-level turbulence has gone unsolved since it was first addressed many decades ago. In this paper I describe a method that shows promise for diffraction-limited imaging through ground-level turbulence with large (meters) apertures and at large (kilometers) distances. The key lies in collecting image data in the spatial frequency domain via the method of Fourier telescopy and taking suitable time averages of the magnitude and phase of the Fourier telescopy signal. The method requires active illumination of the target with laser light, and the time averages required will likely be over many tens of seconds if not tens of minutes or more. The scheme will thus not be suitable for time-varying scenes. The basic scheme is described, and principle challenges briefly discussed.

Projection-slice theorem: a compact notation.

The notation normally associated with the projection-slice theorem often presents difficulties for students of Fourier optics and digital image processing. Simple single-line forms of the theorem that are relatively easily interpreted can be obtained for n-dimensional functions by exploiting the convolution theorem and the rotation theorem of Fourier transform theory. The projection-slice theorem is presented in this form for two- and three-dimensional functions; generalization to higher dimensionality is briefly discussed.

Cross terms of the Wigner distribution function and aliasing in numerical simulations of paraxial optical systems.

Sampling a function periodically replicates its spectrum. As a bilinear function of the signal, the associated Wigner distribution function contains cross terms between the replicas. Often neglected, these cross terms affect numerical simulations of paraxial optical systems. We develop expressions for these cross terms and show their effect on an example calculation.

Lucky imaging and aperture synthesis with low-redundancy apertures.

Lucky imaging, used with some success in astronomical and even horizontal-path imaging, relies on fleeting conditions of the atmosphere that allow momentary improvements in image quality, at least in portions of an image. Aperture synthesis allows a larger aperture and, thus, a higher-resolution imaging system to be synthesized through the superposition of image spatial-frequency components gathered by cooperative combinations of smaller subapertures. A combination of lucky imaging and aperture synthesis strengthens both methods for obtaining improved images through the turbulent atmosphere. We realize the lucky imaging condition appropriate for aperture synthesis imaging for a pair of rectangular subapertures and demonstrate that this condition occurs when the signal energy associated with bandpass spatial-frequency components achieves its maximum value.

Closure phase and lucky imaging.

Since its introduction by Jennison in 1958, the closure-phase method for removing the effects of electrical path-length errors in radio astronomy and of atmospheric turbulence in optical astronomy has been based on the non-redundant-spacing triple interferometer. It is shown that through application of lucky imaging concepts it is possible to relax this condition, making closure-phase methods possible with redundantly spaced interferometer configurations and thereby widening their range of application. In particular, a quadruple-interferometer can, under lucky imaging conditions, be treated as though it were a triple interferometer. The slit-annulus aperture is investigated as a special case.

Fundamental diffraction limitations in a paraxial 4-f imaging system with coherent and incoherent illumination.

In the usual model of an imaging system, only the effects of the aperture stop are considered in determining diffraction-limited system performance. In fact, diffraction at other stops--those associated with different lens elements, for example--can also affect system performance and cause the imaging to be space variant, even in the absence of vignetting in the conventional ray optics sense. For the 4-f imaging system investigated in this paper, the severity of the space variance depends on the relative sizes of the two lens stops and the aperture stops. If the diameters of the lenses are equal, the aperture of the first lens has a greater effect on system performance than does that of the second.

Imaging systems based on the encoding of optical coherence functions.

An imaging scheme is described that is based on the transmission of image-forming information encoded within optical coherence functions. The scheme makes use of dynamic random-valued encoding-decoding masks placed in the input-output planes of any linear optical system. The mask transmittance functions are complex conjugates of each other, as opposed to a similar coherence encoding scheme proposed earlier by two of this paper's authors that used identical masks. [Rhodes and Welch, in Euro-American Workshop on Optoelectronic Information Processing, SPIE Critical Review Series (SPIE, 1999), Vol. CR74, p. 1]. General analyses of the two coherence encoding schemes are performed by using the more general mutual coherence function as opposed to the mutual intensity function used in the earlier scheme. The capabilities and limitations of both encoding schemes are discussed by using simple examples that combine the encoding-decoding masks with free-space propagation, passage through a four-f system, and a single-lens imaging system.

Nonuniform coherence sampling for fields produced by incoherent three-dimensional sources.

A nonuniform sampling scheme is described for measuring the mutual intensity of the wave field produced in a plane a distance z from a spatially incoherent, three-dimensional source object. Both uniform and nonuniform sampling are analyzed and discussed in detail, and comparisons of the two schemes are made. It is shown that nonuniform sampling requires fewer measurements than uniform sampling to specify the coherence function. Additionally, the smallest separation required between measurement points is larger for the nonuniform case.

Milliwatt-peak-power pulse characterization at 1.55 microm by wavelength-conversion frequency-resolved optical gating.

A novel wavelength-conversion configuration based on four-wave mixing in an optical fiber has been used to generate a frequency-resolved optical gating (FROG) trace identical to that obtained from second-harmonic generation (SHG). The use of an optical fiber waveguide permits enhanced measurement sensitivity compared with that of conventional SHG-FROG and has been used for complete characterization of 1-mW peak-power picosecond pulses at 1.55 microm from an unamplified semiconductor laser diode gain switched at 10 GHz.

Continuous radio-frequency tuning of an optoelectronic oscillator with dispersive feedback.

We describe and demonstrate a novel technique for continuously tuning the frequency of a dual-loop-configuration optoelectronic rf oscillator. The rf tunability is obtained from a tunable diode laser and dispersive optical fibers. Results are presented for three ranges of frequency, centered at 550 MHz, 3 GHz, and 9 GHz. The frequency can be tuned electrically with constant rf power within a range of 0.1-1.9 MHz, depending on the center oscillation frequency. The tuning range can be increased eightfold through the use of highly dispersive fibers.