Stokes profiles inversion techniques

Inversion techniques of the radiative transfer equation for polarized light are presented as one of the best current procedures to infer the vector magnetic field, as well as other quantities governing the physical state of the atmospheric layers that photons are coming from. Several characteristics of the various available inversion procedures are pointed out. They are mostly based on the diagnostic contents of the spectral lines as well as on the main hypotheses assumed in these procedures. In particular, the role of gradients in the atmospheric quantities is emphasized as of paramount importance in any diagnostic analysis and, hence, in any interpretation of inversion results.     

Numerical test of a newV-profile inversion technique

The diagnostic method proposed by Landi Degl'Innocenti and Landolfi (1982), based on the observation of circular polarization, has been generalized to derive the thermodynamic properties of unresolved magnetic elements in the solar atmosphere. The final aim is to derive the height dependence of several parameters of the flux tube atmosphere (such as temperature, magnetic field and velocity distributions, macroturbulence and filling factor). We have used a perturbation method based on the concept of response functions for the Stokes profiles introduced by Landi Degl'Innocenti and Landi Degl'Innocenti (1977). We present here the preliminary results of invertingV-profiles by an iterative standard least-squares technique, which allows to find the magnetic 1-D atmosphere consistent with simulated data.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

A fast technique for improved 3-dimensional mapping of the solar corona

To obtain improved maps of the coronal electron density distribution we have devised an iterative technique in which an approximation of the unknown distribution is successively modified to reduce discrepancies with the original data. With this technique we can now map the corona to a much finer resolution than shown in our previous papers, without greatly increasing the computational cost. The series representation of density may now contain more than 23 000 terms compared with previous limit of 128. This results in a fourfold increase in linear resolution, so that features about a tenth of a solar radius in width are now separated. The iteration algorithm can be adjusted to apply a mathematically optimal correction to a given approximation of the density. Although this correction minimizes noise levels, a cheaper version of the algorithm yields a better result.     

Atmospheric scattering effects on ground-based Fabry-Perot measurements of thermospheric winds: An inversion technique

The theoretical development of a technique to recover velocities measured with a Fabry-Perot interferometer in the presence of scattered light is presented. Simulations are carried out which show that the inversion is effective in recovering actual velocities, especially in instances when the observed brightness is dominated by scattered light.     

Modulation imaging based on a direct deconvolution technique

Image restoration from modulated intensities can be performed by directly solving the intensity modulation equation. This method of producing images does not rely on position sensitive detector. Computer simulation results for space low-energy-ray imaging show that images with fine angular resolution within a wide field of view can be obtained by simple collimated devices.     

Stokes II — A new polarimeter for solar observations

A Stokes polarimeter has been built at the High Altitude Observatory to obtain line profiles in both linear and circular polarization in solar spectral lines. These measurements are interpreted using the theory of radiative transfer in the presence of a magnetic field to obtain vector magnetic fields on the solar disk and using the theory of resonance scattering and the Hanle effect to obtain vector magnetic fields in prominences. The polarimeter operates on the Sacramento Peak Observatory 40 cm coronagraph. It is an extensively modified and improved version of an earlier instrument.Polarization modulation is achieved by two KD^*P Pockels cells at the coronagraph prime focus and demodulation is by a microprocessor. The instrument control and data handling is done by a minicomputer. Silicon photodiode 128 element line array detectors have replaced the two photomultipliers used on the earlier instrument. This gives a speed increase of a factor of 50.A polarization scrambler provides a chop to a reference beam of unpolarized light by time scrambling the polarization of the solar beam. This device improves sensitivity to polarizations less than 0.01%. The polarization measurements are photon noise limited in most cases. This noise is 0.1% for a typical three second observation which is about one gauss on the longitudinal field and 10 gauss on the transverse field.The National Center for Atmospheric Research is sponsored by The National Science Foundation.     

Research on the principle of space high-precision temperature control system of liquid crystals based Stokes polarimeter

The magnetic field is one of the most important parameters in solar physics,and a polarimeter is the key device to measure the solar magnetic field.Liquid crystals based Stokes polarimeter is a novel technology,and will be applied for magnetic field measurement in the first space-based solar observatory satellite developed by China,Advanced Space-based Solar Observatory.However,the liquid crystals based Stokes polarimeter in space is not a mature technology.Therefore,it is of great scientific significance to study the control method and characteristics of the device.The retardation produced by a liquid crystal variable retarder is sensitive to the temperature,and the retardation changes 0.09°per 0.10℃.The error in polarization measurement caused by this change is 0.016,which affects the accuracy of magnetic field measurement.In order to ensure the stability of its performance,this paper proposes a high-precision temperature control system for liquid crystals based Stokes polarimeter in space.In order to optimize the structure design and temperature control system,the temperature field of liquid crystals based Stokes polarimeter is analyzed by the finite element method,and the influence of light on the temperature field of the liquid crystal variable retarder is analyzed theoretically.By analyzing the principle of highprecision temperature measurement in space,a high-precision temperature measurement circuit based on integrated operational amplifier,programmable amplifier and 12 bit A/D is designed,and a high-precision space temperature control system is developed by applying the integral separation PI temperature control algorithm and PWM driving heating films.The experimental results show that the effect of temperature control is accurate and stable,whenever the liquid crystals based Stokes polarimeter is either in the air or vacuum.The temperature stability is within±0.0150℃,which demonstrates greatly improved stability for the liquid crystals based Stokes polarimeter.     

The technique of automatic quantitative stellar spectral classification using stepwise linear regression

A new technique of three-dimensional automatic quantitative stellar spectral classification using stepwise linear regression analysis has been developed. The technique has been based on objective prism spectra of F-G-K stars having a dispersion of 166 Å mm^–1 at H. The investigation has been undertaken in the interests of a stellar statistical study of the galactic structure in the direction of the main meridional cross-section of the Galaxy.     

A chromospheric temperature inversion and its implications on millimeter brightness distribution

The brightness temperature curve of the quiet Sun at millimeter wavelengths suggests a possible inversion in the mid-millimeter range. Interpreting this as a result of an actual inversion in the chromospheric temperature structure, and example of a model chromoshere is presented whose calculated temperature curve exhibits such an inversion. This model is then tested for radial brightness distribution at millimeter wavelengths. Comparing the calculated distributions at 3.2 mm and 6 mm with eclipse measurements made with parabolic cylinders at 3.2 mm and 8.6 mm shows qualitative agreement, allowing for instrumental smoothing. It is conluded that a chromospheric temperature inversion, either actual or effective, could account for the inversion suggested by millimeter data and also the complex brightness distributions measured during eclipses with parabolic cylinders.     

Note on Lagrange's inversion formula

An inductive algorithm is proposed to solve Lagrange's implicit equation when its right hand member is a power series in the small parameter.     

A new inversion of solar rotational splitting data

The fine structure of the solar p-mode spectrum is used to obtain an estimate of the Sun's internal rotation rate, as a function of both latitude and depth, for fractional radii in the range 0.55 < r/R < 0.85. Because each piece of data is a weighted average of the rotation rate over an extended region of the solar interior and because the number of such measurements is finite, such an inversion unavoidably has limited resolution and suffers from other systematic errors. Accordingly, the results of the inversion presented here and other published inversions should be interpreted with this in mind. These problems are discussed in detail for the present inversion.Such systematic errors can be avoided by seeking not a functional form of the rotation rate but rather the values of suitably weighted averages of the rotation rate (or of functions derivable from it). Here it is shown that the value of a broad average over depth of the radial gradient of the solar rotation rate, concentrated in the convection zone, is consistent with the gradient being zero in this region but is apparently inconsistent with the picture of constant rotation on cylindrical surfaces aligned with the rotation axis. This result, which confirms the inference from the former type of inversion, is of importance for modelling the dynamics of the convection zone and also for dynamo models of the Sun's magnetic field.The National Center for Atmospheric Research is supported by the National Science Foundation.     

A note on the Hori-Lie perturbation technique

In this paper we describe how to avoid the introduction of Hori's pseudo time in general planetary theory in the case of two planets.     

A second note on Hori-Lie perturbation technique

In this second note we show how to avoid the introduction of Hori's pseudo-time in analytical planetary theory in the case of the eight principal planets of our solar system excluding Pluto.     

A note on the variational method of Stokes and DeMarcus for radiative transfer in planetary atmospheres

A generalized functional which yields the Milne integral equation on variation and whose extremum value is proportional to the reflectivity at arbitrary emergent angle is proposed. A similar functional exists for computing the transmissivity at arbitrary emergent angle. This work is a generalization of the variational method of Stokes and DeMarcus (1971, Icarus14, 307) based on the principle of reciprocity. In the special case of trial functions that are linear in the undetermined parameters, the calculation is greatly simplified. The computational value of our variational principle is demonstrated.     

Vacuum solution of a quadratic red-shift based correction in f(R) gravity

In the present paper, using action derivative with respect to Ricci scalar and its expansion relative to red-shift, to the second-order and consequently without needing dark energy, the history of cosmos expansion is reconstructed in vacuum. Then, employing supernova data, free parameters of the model which are the expansion coefficients, are calculated. It will be seen that if the free parameters of the model are zero, action of general relativity, which is a boundary mode of the gravity, is found. Also the cosmic age for this model in vacuum is calculated. Finally, it is attempted to reconstruct the reference action in terms of its Taylor expansion. Thus, it will be found that the reconstructed action and their actions definitely pass the Solar system tests.     

A fast wide-field telescope: Mechanical design

A mechanical design of a fast wide-field telescope with an entrance pupil that is 180 mm diameter, a focal length of 294 mm, and an angular field of view of 10° is described. Original construction solutions have been found for this type of system.     

A fast tracking mirror for adaptive optics

A piezo driven tilt mirror was developed and built as one component of an image motion compensation system for a solar telescope. The bandwidth of the mirror with a diameter of 60 mm is about 1 kHz with negligible phase shift between input signal and mirror response up to 900 Hz. The tilt range is 1.6 mrad. Special care was taken to maintain the surface quality of the mirror to better than /15 after fixing it to the substrate.