Standard Diffraction Theory Research Articles

Retinal image quality for multifocal lenses with on- and off-axis annular zones.

Multi-focal intra-ocular or contact lenses, intended to increase depth of focus, conventionally have annular zones of additional refractive power, generating wavefront rings of coaxial spherical surfaces. It is, however, possible to influence depth of focus by changing not only the curvature of the wavefront, i.e., refractive power, in the annulus, but also the tilt, i.e., circularly symmetrical linear radial deviation imposed on the spherical wavefront. Employing the example of a single annulus bifocal, retinal image light distributions in the two regimes are calculated, using standard diffraction theory. Four measures of retinal image quality in through-focus scans show that plus power additions and wavefront tilts operate almost interchangeably. In testing these lenses, attention needs to be paid to the detailed operating characteristics of measuring devices of the Shack-Hartmann type to ensure that their grain and precision is compatible with the framework of the analysis.

Breaking the diffraction barrier outside of the optical near-field with bright, collimated light from nanometric apertures.

The optical diffraction limit has been the dominant barrier to achieving higher optical resolution in the fields of microscopy, photolithography, and optical data storage. We present here an approach toward imaging below the diffraction barrier. Through the exposure of photosensitive films placed a finite and known distance away from nanoscale, zero-mode apertures in thin metallic films, we show convincing, physical evidence that the propagating component of light emerging from these apertures shows a very strong degree of collimation well past the maximum extent of the near-field (lambda(0)/4n-lambda(0)/2n). Up to at least 2.5 wavelengths away from the apertures, the transmitted light exhibits subdiffraction limit irradiance patterns. These unexpected results are not explained by standard diffraction theory or nanohole-based "beaming" rationalizations. This method overcomes the diffraction barrier and makes super-resolution fluorescence imaging practical.

Second harmonic generation from resonantly excited arrays of gold nanoparticles

We show that second harmonic generation from lithographically prepared arrays of symmetric gold nanorods can be increased by two orders of magnitude by choosing the nanoparticle size to be resonant with the 800-nm wavelength of the 50-fs pump laser. The angular variation of the second-harmonic yield, which is defined by the pitch of the nanorod array, can be predicted using standard diffraction theory. This in turn makes it possible to bound approximately the relative contributions of dipole and quadrupole oscillations to the total second-harmonic yield; the two contributions appear to be of similar magnitude. Resonant ultrafast irradiation also changes the nanorod morphology, apparently due to surface melting and refreezing. At higher fluence, the intensity dependence of the second-harmonic yield changes from quadratic to cubic, an indication that the reshaping influences the mechanism of second-harmonic generation.

Detection of subwavelength slit-width variation with irradiance measurements in the far field

We demonstrate that, under suitable conditions, subwavelength feature variations of an object can affect the corresponding far-field diffraction pattern in a measurable way. We present an experiment in which width variations of less than 1/100 of the wavelength are measured with a slit whose width is 100 times the wavelength. Integral and differential intensity measurements in the far field are fully consistent with standard diffraction theory even in the subwavelength variation regime. In particular, slit modulations of 6 nm with a wavelength of 670 nm are shown to follow theoretical calculations within the experimental sensitivity of ~10(-5) .

Spectrum-induced changes in diffraction of pulsed optical beams

Propagation of ultrashort optical pulses in a linear homogeneous medium is studied using the standard diffraction theory of electromagnetic fields. Diffraction pattern of a Gaussian beam consisting of such short pulses depends on the pulse shape. In general, the pulsed beam does not remain Gaussian on propagation and its spot size is enhanced. In the visible region, changes in the diffracted intensity become noticeable only for pulse widths below 10 fs and are larger for chirped pulses and for pulses whose spectrum has long tails. We also show that the diffraction characteristics of coherent but pulsed and CW but partially coherent Gaussian beams are identical if the two have identical optical spectra.

Imaging of trace species distributions by degenerate four-wave mixing: diffraction effects, spatial resolution, and image referencing

We describe the theory of imaging by degenerate four-wave mixing (DFWM) using a standard diffraction theory of imaging by coherent light. We demonstrate that, even with the phase-conjugating geometry, no aberration correction can be achieved by DFWM imaging. We demonstrate the coherent nature of DFWM image formation using spatially modulated signals generated in flame OH in the phase-conjugating geometry. The intensity distribution in the Fourier plane of a telecentric lens system is shown to be the spatial Fourier transform of the object distribution characteristic of coherent imaging. The brightness of the DFWM signals exceeds that of similar laser-induced fluorescence signals that can be discriminated by restricting the aperture of the imaging system while still allowing a spatial resolution of approximately 70 ?m. DFWM imaging with the forward-folded boxcars geometry is demonstrated and used in a simple referencing scheme to compensate for structure on the images imposed by nonuniformity of the laser beams employed. Images formed in NO are used to illustrate that structure on a scale of less than 100 ?m arising from beam inhomogeneity can be removed by this referencing technique.

Microscope resolution

When dealing with the topic of finite conjugate, point-source resolution in elementary discussions, we generally take one of two courses. Either we adopt the (somewhat unmotivated) standard Jenkins and White approach or else we try to derive the result on the basis of standard diffraction theory using the known result for the diffraction by a circular aperture. However, the Jenkins and White approach, while giving a believable resolution formula, implies a magnification formula which appears to be wrong. On the other hand, the diffraction approach gives the ’’correct’’ magnification formula but its resolution formula implies that infinite resolution is possible for finite wavelength light since the diffraction angle goes to zero for large apertures. It is shown that the key to a coherent presentation of this topic and the resolution of these difficulties is provided by the relatively obscure Abbe’s sine theorem.

On the Deduction of the Refractive Index Profile of a Stratified Atmosphere from Radio Field-Strength Measurements

A method developed by Macfarlane for the theoretical deduction of the refractive index profile of a horizontally stratified atmosphere from radio field-strength measurements was applied to several sets of radio field-strength data for which complementary measured refractive index profiles were available, for both standard and nonstandard meteorological conditions. The formal theoretical validity of Macfarlane's method was affirmed for the case of a linear M curve, dM/dH=3.6 units/100 feet, by application of the method to several theoretical radio field-strength profiles given by Standard Diffraction Theory. M curves were derived which were linear and possessed slopes within 3 per cent of the control slope of 3.6 M units/100 feet However, application of the method to the theoretical radio field-strength profiles of Standard Diffraction Theory revealed that in order to yield satisfactory refractive index data, a higher degree of accuracy was required of the radio field-strength data than one could expect to realize experimentally. The inherent sensitivity of the method to small, inevitable inaccuracies in the radio field-strength data makes it impossible to apply the method directly to experimental data. It is often possible, however, to approximate a radio field-strength profile, within the limits of experimental error, by an analytical curve or a combination of curves appropriately joined together.

Diffraction of High-Frequency Radio Waves around the Earth

This paper reports nonoptical height-gain measurements on a remarkably uniform desert link at frequencies of 25, 63, 170, 520, 1,000, 3,300, and 9,375 Mc using horizontal polarization. It has been shown that when the index of refraction of the atmosphere is a linear function of elevation, the problem of refraction and diffraction may be represented approximately by a problem in diffraction alone. Data taken under linear and slightly nonlinear index of refraction gradients are compared with fields predicted by standard diffraction theory. A mechanism other than diffraction is required to explain the higher-frequency fields observed under standard meteorological conditions.