# Python modules

The following Python modules are used in AsPyLib (v1.2.2):
- Pyfits
- Numpy
- Scipy
- Matplotlib
- Parallel Python
- vo.table

# Median calculation

Calculating median values for large amounts of data (such as for stacking CCD images) in reasonable times can be difficult. In AsPyLib we use a very efficient piece of C code written by N.Devillard (based on the Wirth method). See here for more information.

# Bspline interpolation

The code to perform the Bspline interpolation, used in AsPyLib for most geometrical transforms (translation, rotation, scaling) but also for photometry, is taken from P.Thevenaz.
The original code can be found at this link, with all the explanations on how to use it.

Some useful papers about Bsplines (the .pdf can be found with Google):
• P. Thévenaz, T. Blu, M. Unser, "Interpolation Revisited", IEEE Transactions on Medical Imaging, vol. 19, no. 7, pp. 739-758, July 2000.
• R. Seta, K. Okubo, N. Tagawa, "Digital image interpolation method using higher-order interpolating polynomials with compact finite-difference", proceedings of 2009 APSIPA annual summit and conference, Sapporo, Japan, Oct 4-7, 2009, pp406-409.
• J. Pan, "Image interpolation using spline curves", see here
• M. Unser, A. Aldroubi, M. Eden, "Fast B-spline transforms for continuous image representation and interpolation", IEEE trans. on pattern analysis and machine intelligence, vol.13, no.3, pp 277-285 (1991).

In the first paper ("Interpolation revisited") a performance comparison between many possible algorithms is presented. The cubic Bspline interpolation turns out to be very accurate. This paper also explains quite clearly that the Bspline functions are not interpolating kernels but are used as a basis for image representation. The Bspline interpolation kernels are given in the paper from M.Unser.

# Aperture photometry

Some important papers about aperture photometry:
• S.B. Howell, "Two-dimensional aperture photometry: Signal-to-noise ratio of point source observations and optimal data-extraction techniques", PASP, vol.101, pp616-622 (1989).
• H. Kjeldsen, S. Frandsen, "High-precision time-resolved CCD photometry", PASP, vol.104, pp 413-434 (1992).
• P. Ryan, "Scintillation reduction method for photometric measurements", PASP, vol.110, pp 1235-1248 (1998).

The Howell paper is quite famous, and describes the principle of aperture photometry. However the noise analysis may be a bit simple. The second paper ("High-precision...") gives a more in-depth analysis of all sources of noise and perturbations.

The paper from Ryan explains in detail what is scintillation noise and how it scales with wavelength, telescope aperture, etc.

# Softwares for photometric surveys

• E. Bertin, S. Arnouts, "Sextractor: software for source extraction", Astron. Astrophys. Suppl. Ser., vol.117, pp 393-404 (1996).
• E. Bertin, "Automatic astrometric and photometric calibration with SCAMP", see link here
• J. Irwin, M. Irwin, S. Aigrain, S. Hodgkin, L. Hebb, E. Moraux, "The Monitor project: data processing and lightcurve production", link on Arxiv (14 Dec 2006).
• N. Kaiser, G. Wilson, G. Luppino, H. Dahle, "A photometric study of the supercluster MS0302 with the UH8K CCD camera: image processing and object catalogs", link on arXiv (16 Jul 1999).
• D.L. Pollacco et al., "The WASP project and the SuperWASP cameras", link on arXiv (22 Aug 2006).
• Y. Damerdji, A. Klotz, M. Boer, "The Tarot suspected variable star catalog", The Astronomical Jourmal, vol.133, pp 1470-1477 (2007).

An interesting algorithm for astrometric reduction is described in the Kaiser paper. In particular, an efficient method is given to quickly find the scaling and rotation laws to match an image with a star catalog.

# Orbit calculations

• J. Meeus, "Calculs astronomiques à l'usage des amateurs", Société Astronomique de France, Paris, 1986.
• A.U. Landolt, K.L. Blondeau, "The calculation of heliocentric corrections", PASP, vol.84, pp 784-809 (1972).

# Lightcurve fitting

The principles of fitting a periodic lightcurve with Fourier series are explained (in French) at this link that describes the CourbRot software.