Search

The general transformation properties of aberrations in cylindrically symmetric optical systems are described using matrix analysis. The aberrations in an optical system can change with any change in the position of the aperture stop, or when the system operates at new conjugates even if the relative positions of the refractive surfaces and their powers are fixed. Expanding the wavefront aberration function in terms of aberration coefficients allows the new aberration coefficients to be written as linear combinations of the old aberration coefficients for every order. A pattern is established by which higher-order aberration transformations can be calculated.

From an analysis of new hemoglobin solution transmission spectra at various oxygen saturations (SO2), path lengths, and pH, we find the determination of SO2 by using the classical oximetry technique to be poorly calibrated. We used this data set to develop a proposed method for SO2 determination based on the spectral shift of the hemoglobin transmission minimum between 475 and 510 nm. The method does not require accurate knowledge of hemoglobin extinction coefficients and is linear in relation to SO2 despite changes in path length, pH, or hemoglobin concentration.

Techniques for noninvasively measuring the oxygen saturation of blood in retinal arteries and veins are reported in the literature, but none have been sufficiently accurate and reliable for clinical use. Addressing the need for increased accuracy, we present a series of oximetric equations that explicitly consider the effects of backscattering by red blood cells and lateral diffusion of light in the ocular fundus. The equations are derived for the specific geometry of a scanning-beam retinal vessel oximeter; however, the results should also be applicable to photographic oximeters. We present in vitro and in vivo data that suggest the validity of these equations.

Refraction, reflection, and amplitude relations are derived that apply to polarization ray tracing in anisotropic, optically active media such as quartz. The constitutive relations for quartz are discussed. The refractive indices and polarization states associated with the two modes of propagation are derived as a function of wave direction. A procedure for refracting at any uniaxial or optically active interface is derived that computes both the ray direction and the wave direction. A method for computing the optical path length is given, and Fresnel transmission and reflection equations are derived from boundary conditions on the electromagnetic fields. These ray-tracing formulas apply to uniaxial, optically active media and therefore encompass uniaxial, non-optically active materials and isotropic, optically active materials.

Procedures for performing polarization ray tracing through birefringent media are presented in a form compatible with the standard methods of geometrical ray tracing. The birefringent materials treated include the following: anisotropic optically active materials such as quartz, non-optically active uniaxial materials such as calcite, and isotropic optically active materials such as mercury sulfide and organic liquids. Refraction and reflection algorithms are presented that compute both ray directions and wave directions. Methods for computing polarization modes, refractive indices, optical path lengths, and Fresnel transmission and reflection coefficients are also specified. A numerical example of these algorithms is given for analyzing the field of view of a quartz rotator.

We use ray-trace equations for uniaxial birefringent materials to derive third-order estimates for aberrations that are produced in imaging through uniaxial plates and horizontal-vertical (HV) depolarizers. An HV depolarizer is a spatial pseudodepolarizer; it converts a uniform input polarization state into a continuum of spatially varying polarization states in an output beam. An HV depolarizer consists of two birefringent wedges whose crystal axes are crossed at 90 degrees . The interface between the wedges is inclined, which leads to a spatially varying retardance that provides the spatial pseudodepolarization. In HV depolarizers, spherical aberration, astigmatism, and image doubling are the principal aberrations for on-axis objects. Only spherical aberration occurs in isotropic plates, while the presence of birefringent wedges introduces astigmatism and image doubling. It is shown that image separation is proportional tothe magnitude of the retardance variation. Image separation is independent of the thickness, wedge angle, and refractive indices that are used to achieve this variation. A computer program is used to perform an exact birefringent ray trace and produces spot diagrams that confirm the aberration estimates.

We consider the interaction of two 100% amplitude-modulated fields with a two-level system. The analysis includes a discussion of the stability of an amplitude-modulated laser field to the growth of subharmonic amplitude-modulated fields.

Through the use of modulation spectroscopy we have measured the absorption spectrum experienced by a weak probe beam in the presence of a saturating pump beam at two different wavelengths within the broad homogeneous absorption band of alexandrite. At 584 nm the absorption saturates at high pump intensities, and a hole (of width 612 Hz) appears at frequencies near that of the pump laser. However, at 457 nm the absorption demonstrates the inverse of normal saturation because of strong excited-state absorption, and an antihole appears at the pump frequency. These results are in good quantitative agreement with the predictions of a model that ascribes the origin of these spectral features to the temporal modulation of the ground-state population at the beat frequency between the pump and the probe beams. These population oscillations are treated properly within a rate-equation approximation in which the amplitude modulation of the total optical intensity caused by the beating of the pump and the probe beams is taken into account.

A theory is presented that describes a series of bichromatic states of an ideal homogeneously broadened laser. These states are produced when the laser is pumped far above threshold so that the intracavity field is strong enough to overcome damping and produce Rabi oscillations of the atomic inversion. The two-frequency laser field is amplitude modulated at a frequency that may be either the Rabi frequency or a subharmonic of it. The theoretical predictions are compared qualitatively with recent experimental results.

The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.