Large field-of-view

Additionally to the previously discussed issues, the large size of the field-of-view also intro-duces various difficulties.

Background variations

Images covering large field-of-view on the sky are supposed to have various background structures, such as thin cirrus clouds, or scattered light due to dusk, dawn or the proximity of the Moon or even interstellar clouds⁶. These background variations make impossible the derivation of a generic background level. Moreover the background level cannot be characterized by simple functions such as polynomials or splines since it has no any specific scale length. Because the lack of a well-defined background level, the source extraction algorithm is required to be purely topological (see also Sec. 2.4).

Vignetting, signal-to-noise level and effective gain

The large field-of-view can only be achieved by fast focal ratio optical designs. Such optical systems do not have negligible vignetting, i.e. the effective sensitivity of the whole system decreases at the corners of the image. In the case of HATNet optics, such vignetting can be as strong as 1 to 10. Namely, the total incoming flux at the corners of the image can be as small as the tenth of the flux at the center of the image. Although flat-field corrections eliminate this vignetting, the signal-to-noise ratio is unchanged. Since the latter is determined by the electron count, increasing the flux level reduces the effectivegain⁷at the corner of the images.

Since the expectations of the photometric quality (light curve scatter and/or signal-to-noise) highly depends on this specific gain value, the information about this yield of vignetting should be propagated through the whole photometric process.

Astrometry

Distortions due to the large field-of-view affects the astrometry and the source identification.

Such distortions can efficiently be quantified with polynomial functions. After the sources are identified, the optimal polynomial degree (the order of the fit) can easily be obtained by calculating the unbiased fit residuals. For a sample series of HATNet images we computed these fit residuals, as it is shown in Table 2.1. It can easily be seen that the residuals do not

6Although interstellar clouds are steady background structures, in the point of the analysis of a single image, these cause the same kind of features on the image.

7The gain is defined as the joint electron/ADU conversion ratio of the amplifier and the A/D converter.

A certain CCD camera may have a variable gain if the amplification level of the signal read from the detector can be varied before digitization.

Table 2.1: Typical astrometric residuals in the function of polynomial transformation order, for absolute and relative trans-formations. For absolute transformations the reference is an external catalog while for relative transformations, the reference is one of the frames.

Order Absolute Relative 1 0.841−0.859 0.117−0.132 2 0.795−0.804 0.049−0.061 3 0.255−0.260 0.048−0.061 4 0.252−0.259 0.038−0.053 5 0.086−0.096 0.038−0.053 6 0.085−0.096 0.038−0.053 7 0.085−0.095 0.038−0.053 8 0.085−0.095 0.038−0.053 9 0.085−0.095 0.038−0.053

decrease significantly after the 5−6th order if an external catalogue is used as a reference, while the optimal polynomial degree is around ∼ 3−4 if one of the images is used as a reference. The complex problem of the astrometry is discussed in Sec. 2.5 in more detail.

Variations in the profile shape parameters

Fast focal ratio optical instruments have significant comatic aberrations. The comatic aber-ration yields not only elongated stellar profiles but the elongation parameters (as well as the FWHMs themselves) vary across the image. As it was demonstrated, many steps of a com-plete photometric reduction depends on the profile sizes and shapes, the proper derivation of the shape variations is also a relevant issue.

Summary

In this section we have summarized various influences of image undersampling, crowdness and large field-of-view that directly or indirectly affects the quality of the photometry. Although each of the distinct effects can be well quantified, in practice all of these occur simultaneously.

The lack of a complete and consistent software solution that would be capable to overcome these and further related problems lead us to start the development of a program designed for these specific problems.

In the next section we review the most wide-spread software solutions in the field of astronomical photometric data reduction.

2.1. UNDERSAMPLED, CROWDED AND WIDE-FIELD IMAGES

Table 2.2: Comparison of some of the existing software solutions for astronomical image processing and data reduction. All of these software systems are available for the general public, however it does not mean automatically that the particular software is free or open source. This table focuses on the most wide-spread softwares, and we omit the “wrappers”, that otherwise allows the access of such programs from different environments (for instance, processing of astronomical images in IDL use IRAF as a back-end).

Pros Cons

IRAF¹

•Image Reduction and Analysis Facility. The most commonly recognized software for astro-nomical data reduction, with large literature and numerous references.

•IRAF supports the functionality of the package DAOPHOT², one of the most frequently used software solution for aperture photometry and PSF photometry with various fine-tune parame-ters.

•IRAF is a complete solution for image anal-ysis, no additional software is required if the general functionality and built-in algorithms of IRAF (up to instrumental photometry) are suf-ficient for our demands.

•Not an open source software. Although the higher level modules and tasks are implemented in the own programming language of IRAF, the back-end programs have non-published source code. Therefore, many of the tasks and jobs are done by a kind of “black box”, with no real assumption about its actual implementation.

•Old-style user interface. The primary user interface of IRAF follows the archaic designs and concepts from the eighties. Moreover, many options and parameters reflect the hardware conditions at that time (for instance, reading and writing data from/to tapes, assuming very small memory size in which the images do not fit and so on).

•Lack of functionality required by the proper processing of wide-field images. For instance, there is no particular effective implementation for astrometry or for light curve processing (such as transposing photomet-ric data to light curves and doing some sort of manipulation on the light curves, such as de-trending).

ISIS³.

•Image subtraction package. The first software solution employing image subtraction based pho-tometry.

•The program performs all of the necessary steps related to the image subtraction algorithm itself and the photometry as well.

•Fully open source software, comes with some shell scripts (written in C shell), that demon-strate the usage of the program, as well as these scripts intend to perform the whole process (in-cluding image registration, a fit for convolution kernel and photometry).

•Not a complete software solution in a wider context. Additional soft-ware is required for image calibration, source detection and identification and also for the manipulation of the photometric results.

•Although this piece of software has open source codebase, the algo-rithmic details and some tricks related to the photometry on subtracted images are not documented (i.e. neither in the reference scientific arti-cles nor in the program itself).

•The kernel basis used by ISIS is fixed. The built-in basis involves a set of functions that can easily and successfully be applied on images with wider stellar profiles, but not efficient on images with narrow and/or undersampled profiles.

•Some intermediate data are stored in blobs. Such blobs may contain useful information for further processing (such as the kernel solution itself), but the access to these blobs is highly inconvenient.

SExtractor⁴.

•Source-Extractor. Widely used software pack-age for extracting and classifying various kind of sources from astronomical images.

•Open source software.

•Ability to perform photometry on the detected sources.

•The primary goal of SExtractor was to be a package that focuses on source classification. Therefore, this package is not a complete solution for the general problem, it can be used only for certain steps of the whole data reduction.

•Photometry is also designed for extended sources.

1IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. See alsohttp://iraf.net/.

2 DAOPHOT is a standalone photometry package, written by Peter Stetson at the Dominion Astrophysical Observatory (Stetson, 1987).

3ISIS is available fromhttp://www2.iap.fr/users/alard/package.html with additional tutorials and documentation (Alard

& Lupton, 1998; Alard, 2000).

4SExtractor is available fromhttp://sextractor.sourceforge.net/, see also Bertin & Arnouts (1996).