Brendan M. Quine

GENSPECT: a line-by-line code with selectable interpolation error tolerance

Current line-by-line radiative transfer codes accelerate calculations by interpolating the line function where it varies slowly. This can increase calculation performance by a factor of 10 or more but causes a reduction in calculation accuracy. We present a new line-by-line algorithm that computes absorption coefficients to a specified percentage-error tolerance in a near minimal number of calculations. The algorithm employs a novel binary division of a calculations spectral interval, coupled with a pre-computed lookup table that predicts where it is appropriate to reduce the resolution of a particular line without exceeding the required error tolerance. Line contributions are computed piecewise across a cascaded series of grids which are then interpolated and summed to derive the absorption coefficient. The algorithm is coded in MATLAB as part of a toolbox of radiative transfer functions for the analysis of planetary atmospheres and laboratory experiments.

Determining star-image location: A new sub-pixel interpolation technique to process image centroids

We develop a theoretical methodology to estimate the location of star centroids in images recorded by CCD and active pixel sensors. The approach may be generalized to other applications were point-sources must be located with high accuracy. In contrast with other approaches, our technique is suitable for use with non-100% fill ratio sensors. The approach is applied experimentally to two camera systems employing sensors with fill-ratios of approximately 50%. We describe experimental approaches to implement the new paradigm and characterize centroid performance using laboratory targets and against real night-sky images. Applied to a conventional CCD camera, a centroid performance of 11.6 times the raw pixel resolution is achieved. Applied to a camera employing an active-pixel sensor a performance of 12.8 is demonstrated. The approach enables the rapid development of autonomous star-camera systems without the extensive characterizations required to derive polynomic fitting coefficients employed by traditional centroid algorithms.

Efficient algorithmic implementation of the Voigt/complex error function based on exponential series approximation

We show that a Fourier expansion of the exponential multiplier yields an exponential series that can compute high-accuracy values of the complex error function in a rapid algorithm. Numerical error analysis and computational test reveal that with essentially higher accuracy it is as fast as FFT-based Weideman’s algorithm at a regular size of the input array and considerably faster at an extended size of the input array. As this exponential series approximation is based only on elementary functions, the algorithm can be implemented utilizing freely available functions from the standard libraries of most programming languages. Due to its simplicity, rapidness, high-accuracy and coverage of the entire complex plane, the algorithm is efficient and practically convenient in numerical methods related to the spectral line broadening and other applications requiring errorfunction evaluation over extended input arrays.

A derivative-free implementation of the extended Kalman filter

A nonlinear estimation paradigm is developed to estimate the mean and covariance of a time-evolving state distribution. The approach represents uncertainty by an ensemble set of state vectors rather than by the traditional mean and covariance measures, avoiding the need for the calculation of matrix partial derivatives (Jacobian matrices). The paradigm is shown to be equivalent to the extended Kalman filter in a limiting case. Implementation of the new filtering approach is illustrated with a simple example and a step-by-step description. The paradigm is not significantly more computationally intensive than traditional filters and proves ideal for the rapid implementation of complex nonlinear system and observation models.

A rational approximation for efficient computation of the Voigt function in quantitative spectroscopy

We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by residue calculus. The computational test reveals that with only 16 summation terms this approximation provides average accuracy 10 14 over a wide domain of practical interest 0 0 and 1 < x <1.

Scanning the Earth's limb from a high-altitude balloon: The development and flight of a new balloon-based pointing system

Abstract The development and first flight of a new balloon-borne pointing system is discussed. The system is capable of pointing a platform of optical instruments at an inertial target from a pendulating platform suspended below a high-altitude balloon. It operates in both a traditional occultation-scan mode, to observe solar absorption, and a limb-scan mode, to make measurements of Earths limb. The system employs integrated sensors and high-level icon-based software (Labview). A microprocessor controller derives real-time estimates of gondola attitude, employing an extended Kalman filter to combine gyro, magnetometer, tilt-sensor, and shaft-encoder information. These estimates are used to develop control demands that point a platform of instruments in elevation and azimuth. The systems first flight was from Vanscoy, Saskatchewan, Canada, on 29 August 2000. Results of the systems performance during this mission are presented. In flight, the system demonstrated a pointing accuracy better than 0.1° (1σ) ...

Sampling by incomplete cosine expansion of the sinc function

A new sampling methodology based on an incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the incomplete cosine expansion we obtain a rational approximation of the complex error function that with the same number of the summation terms provides an accuracy exceeding the Weidemans approximation accuracy by several orders of the magnitude. Application of the expansion results in an integration consisting of elementary function terms only. Consequently, this approach can be advantageous for accurate and rapid computation.

High-accuracy approximation of the complex probability function by Fourier expansion of exponential multiplier

Abstract The real K ( x , y ) and imaginary L ( x , y ) parts of the complex probability function are approximated as rapidly convergent series, based on the Fourier expansion of the exponential multiplier. This approach provides rapid and accurate calculations of the Voigt and complex error functions in the most challenging Humlicek regions 3 and 4.

Calibration and in-orbit performance of the Argus 1000 spectrometer - the Canadian pollution monitor

Argus 1000 is a new generation miniature pollution-monitoring instrument to monitor greenhouse-gas emission from the space. Argus was launched on the CanX-2 micro-satellite April 28, 2008. Operating in the near infrared and in a nadir-viewing mode, Argus provides a capability for the monitoring of Earth-based sources and sinks of anthropogenic pollution. It has 136 near infrared channels in the spectral range of 0.9-1.7 µm with an instantaneous spatial resolution of 1.25 km. With a mass of just 228 g in flight-model configuration, the instrument is a demonstrator for a future micro-satellite network that can supply near-real time monitoring of pollution events in order to facilitate the detection of the sources causing climate change. In this Letter, we describe the instrument, the analysis concept behind Argus 1000 and its in-orbit performance. Recent spectral data taken over Ontario, Canada, are presented.

A review of one-way and two-way experiments to test the isotropy of the speed of light

As we approach the 125th anniversary of the Michelson–Morley experiment in 2012, we have reviewed experiments that test the isotropy of the speed of light. Previous measurements are categorized into one-way (single-trip) and two-way (round-trip averaged or over closed paths) approaches and the level of experimental verification that these experiments provide is discussed. The isotropy of the speed of light is one of the postulates of the special theory of relativity and, consequently, this phenomenon has been subject to considerable experimental scrutiny. Here, we have tabulated significant experiments performed since 1881 and attempt to indicate a direction for future investigation.