Absolute radioassay of extended sources: an equivalent point-source coincidence-counting approach with application to the thyroid.

A general methodology is provided for the absolute assay of radioisotopes decaying with coincident photons in an extended source. In the determination of the source activity, the method requires neither the detailed consideration of the geometric and self-attenuation processes taking place between the source component points nor a knowledge of the distribution of activity across the source. It derives from the concept of the "equivalent point source," that is a fictitious point source whose activity would equal that measured for the actual extended source. It has been developed for an arbitrary number of coincident photon types displaying an arbitrary degree of mutual correlation, and for arbitrary detection geometry. A unifying formalism is developed for both point and extended sources and for single and dual detecting systems. It is found that in all cases the various instrumental and spectroscopic uncertainties appear within a composite parameter (herein called F factor) that can be determined by standard calibration procedures; this factor is in turn only weakly dependent on its own component parameters. New expressions and relationships are obtained that provide a greater physical insight into coincidence-counting methods.

Mie forward scattering: improved semiempirical approximation with application to particle size distribution inversion.

The approximations of Penndorf and Shifrin-Punina to the Mie solution at forward scattering angles are extended to smaller size parameter values. The present approximation, Eq. (7), is found to represent accurately the Mie result down to x ~ 0.5-1.0 for refractive index m = 1.33, and to x ~ 2.0 for much larger index values. The implications of this result are discussed relative to the reconstruction of particle size distributions utilizing the Shifrin-Fymat analytical inversion formula of forward scattered intensities.

Analytical inversions in remote sensing of particle size distributions. 3: Angular and spectral scattering in the Rayleigh-Gans-Born approximation for particles of various geometrical shapes.

Analytical inverse formulas are provided for reconstructing the size distribution of particulates whose scattering patterns can be adequately described by the Rayleigh-Gans-Born (or Shifrin) approximation. The formulas hold for arbitrary polarization states at incidence and scattering of light and for angular or spectral measurements. The particle shapes considered are spheres, spherical shells, thin disks (which may be randomly oriented), and thin rods. Circular cylinders and ellipsoids can also be encompassed by our formulas if these particles are described in terms of equivalent spheres having the same volume.

Analytical inversions in remote sensing of particle size distributions. 4:Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation.

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

Instrumentation optimization in fourier spectroscopy. 1: far infrared beam splitters.

Computations of the reflectivity, transmissivity, and efficiency properties for TE, TM, and T45 degrees waves of far ir beam splitters (BS) and of the polarizations induced at both reflection and transmission are described. Effects of variations in the state of polarization, orientation, pointing accuracy, and wavelength of the incident light, as well as variations in refractive index and thickness of the BS, are discussed. These results apply directly to Fourier interferometer-spectrometers. They can be used for optimizingthe performance of these instruments. They indicate, in particular, that some advantages may begained by the use of incident polarized light (angle of polarization smaller than about 45 degrees or negative elliptical polarization) or light of large incidence angle (larger than approximately 60 degrees ) or both. A novel method of inversion of experimental results to the end of determining the BS physical parameters is proposed. It makes use of the variations with incident light direction of the BS reflectivity, transmissivity, or efficiency curves.

Polarization effects in fourier spectroscopy. I: coherency matrix representation.

A general analytical method using the formalisms of polarization coherency and Jones's matrices is provided for the evaluation of all polarization effects in fourier spectroscopy. The method applies to any incident state of arbitrary (complete, random, or partial) polarization. Inversely, it may also be used for determining the intensity and state of polarization of the source of light. TE- and TM-mode reflectivity and transmissivity for beam splitters and the dependence of these quantities on the incident polarization are obtained. It is demonstrated that three different efficiencies for these optical components must be introduced. Interferometer efficiency expressions for the source beam and the detector beam are also derived and shown to be essentially different from the previous efficiencies. Polarization effects of beam splitters, reflectors, and their composite combinations (interferometers) are investigated in detail. General conditions for complete or restricted polarization compensation are derived. Theoretical SNR expressions for both the source beam and the detector beam are also obtained; these formulas specifically account for the incident state of polarization, the polarization effects of the interferometer, and make use of the exact expressions for the appropriate interferometer efficiency. In an Appendix, a brief comparison is made between some usual representations of the state of wave polarization.

Absorption profile of a planetary atmosphere: a proposal for a scattering independent determination.

The use of scattering theory to infer atmospheric optical parameters requires the separation of absorption and scattering. It is demonstrated that a gradient flux relation exists that would provide the absorption (altitude) profile independently of scattering and irrespective of the state of polarization of the light field. The relation is derived for an atmosphere of plane-parallel or spherical geometry and for broad (continuum) and narrow (spectral line) frequency bands. The results are shown to hold, in particular, for the polarizations induced by both Rayleigh and Mie scattering in the field. Experimental setups are proposed for each of the cases considered of atmospheric geometry and frequency bandwidth. A final discussion considers the relevance of the present determination of the atmospheric absorption profile to the related problems of aerosol relative concentration, interpretation of radiometric and spectrometric data formed in the presence of scattering, clouds morphology, and radiative heat budget of the atmosphere.

Interferometric spectropolarimetry: alternate experimental methods.

Three alternate methods of obtaining spectra of the intensity and state of polarization of light are proposed. The methods make use of a two-beam amplitude division interferometer using the technique of Fourier spectroscopy. They can be applied to either emerging beam, source beam, or detector beam r to both. They do not require the presence of polarizers in the arms of the instrument. In one method (Method 2) a single analyzer is used in front of the detector with three successive orientations of its transmission axis azimuth (0 degrees , 45 degrees , 90 degrees ). In another method (Method 3) a (linear) polarizer assuming the same set of orientations is placed in the incident beam. A third method (Method 4), a hybrid of the former two methods, makes use of both a polarizer and an analyzer in the locations indicated. The latter method presents itself three alternate possibilities. Method 2 permits the determination of all four Stokes parameters of polarization, whereas Methods 3 and 4 cannot yield the ellipticity parameter. All methods require the recording of three interferograms. However, two interferograms can provide the intensity and degree of polarization in any of the methods described. The theory of our earlier method (Method 1, Fymat and Abhyankar, 1970) is also established more rigorously concerning the proposed interferometric arrangements, the applicability of the method to the source beam, and the possibility of deriving the orientation of the plane of polarization and the ellipticity from a single interferogram.

Jones's Matrix Representation of Optical Instruments. I: Beam Splitters.

A general method is provided for constructing Jones's reflection and transmission matrices of any beam splitter. Derivations are presented for the various known configurations. The method uses Abelès's matrices and pays special consideration to the different expressions of Jones's matrices relative to the various beams in an interferometric arrangement. The reversibility of the beam splitter in its action on the amplitude or phase, or both, of an incident light is studied. It is finally suggested that, even for an asymmetric beam splitter configuration, the symmetry of the interferogram can still be preserved by adjusting the thickness of the beam splitter in a prescribed manner.

Jones's Matrix Representation of Optical Instruments. 2: Fourier Interferometers (Spectrometers and Spectropolarimeters).

Our method of matrix synthesis of optical components and instruments is applied to the derivation of Jones's matrices appropriate for fourier interferometers (spectrometers and spectropolarimeters). These matrices are obtained for both the source beam and the detector beam. In the course of synthesis, Jones's matrices of the various reflectors (plane mirrors; retroreflectors: roofed mirror, trihedral and prism cube corner, cat's eye) used by these interferometers are also obtained.

An interferometric approach to the measurement of optical polarization.

After discussing the desirability of determining the variation of polarization with frequency in planetary spectra, the possibility of measuring the intensity and state of polarization of optical radiation by means of the high resolution Fourier spectroscopic method is discussed. In the proposed experimental arrangement a two-beam interferometer is used with a polarizer in each beam. After recombination the emergent radiation is analyzed with a linear polarizer. It is shown that the interferograms obtained in this way contain information about the four Stokes parameters of the incident radiation. The polarizers introduce an asymmetry in the interferograms requiring full (exponential) transforms for retrieval of the desired data. The effects of the finite range of path difference and the variation of its zero point with frequency are considered, and evaluation of the corresponding phase error with a proper choice of the polarizer settings is discussed. The formalism also takes into account the residual polarization introduced by the beam splitter, and the differential transmission of the two beams. Generally, three independent interferograms are needed for determining the phase error and the four Stokes parameters. Some simple arrangements are described in which the two beams are either both linearly or both circularly polarized. It is hoped that instruments based on the principle described here will be built by workers in the field.