5.8 The Off-line Pipe-line: Version 1

Version 1 of the PL initially carried out using the standard data reduction, with the advent of the on-line PL this code was easily removed to leave only the more computationally complex tasks. These are FITS file input/output, object detection, photometry, WCS determination and magnitude computation; each section is detailed below.

5.8.1 FITS File Input/Output

The FITS files data input/output is carried out by the same code as that outlined in the online PL, currently the code is duplicated but it is intended to include it in the PL software library, once the PL beta testing has occurred.

5.8.2 Object Detection

Object detection is also carried by the same code as that in the online PL. Currently the code is duplicated and operates with a considerable amount of redundant calculations. The removal of these calculations proves not to be a simplistic task due to the nature of the code. Re-coding of these routines will increase the PL throughput but not the quality of the operation.

5.8.3 Aperture Photometry

In practice the photometry (see Section 2.5) performed is aperture photometry. In principle “aperture photometry of digitized data is straightforward” (Eaton et al., 1999), the major problem with such a procedure is “making it robust enough to be used in an automated photometry package” (Shahbaz et al., 1994). What follows is a discussion of the scientific requirements of the aperture photometry software.

The purpose of aperture photometry is to measure the brightness of an object without including the possible contaminates from bias levels, sky, defects and other sources. Since some or all of these effects will be present in a finite size they must be accounted for.

An estimation of the local sky background can be obtained by generating an annulus around the object at a sufficient distance to ensure no stellar contribution. This however presents the problem of contaminating the sky estimation with additional objects. To overcome this the mode of the sky histogram within the aperture is taken, the mode being a maximum likelihood estimator ensuring that the most likely local sky value is obtained (Eaton et al., 1999). Once this value has been obtained it can be subtracted from all pixels representing the object. In the online PL detecting all the pixels of a source was done in a simplistic fashion because of speed considerations; all contiguous points 3 above the background were part of the object. The off-line PL however requires a more accurate answer and therefore a different approach is taken.

Determining the Aperture Size

“In obtaining digital photometry on CCD frames a decision has to be made as to whether to do a curve of growth analysis and attempt to correct a finite aperture to one of infinite radius, or simply to adopt some radius to which all photometry would be referred - if this is the case, what radius?” The latter method is what is done in practice for aperture photometry, with good results (Massey et al., 1989).

Determining the end point of a stellar profile from the sky background is difficult, a decision must be taken as to where to cut it off (Bessell, 2001). There are two boundary conditions to consider when evaluating what the optimum size aperture is. If the star is very bright its counts will be greater than the background (inclusive of sky counts, noise, etc.) everywhere on the detector. The optimum aperture size is therefore one which encompasses the entire CCD. The lower boundary is achieved by considering a star which is very faint, with the background counts being greater than the star’s (sky-limited). The optimum aperture size in this case is very small. At small radii however, where the signal-to-noise is best, the effect of seeing and telescope focus dominate the star profile, leading to inconsistent results from one frame to another (Massey et al., 1989).

However, the faint wings of a star’s point spread function (PSF) scale with the core of the PSF, which is the same regardless of brightness or position on the CCD (Kormendy, 1973). Therefore, selecting a fixed size aperture should merely exclude the same fraction of light, and the choice will not matter as long as the aperture is large enough to be insensitive to seeing, guiding, and focus variations (Massey et al., 1989). However using a large aperture increases the chances of contamination. Therefore it is neither practical nor necessary that the larger aperture contain the total flux of the star. As long as the same size aperture is used for all program and standard-star frames, the constant missing flux will be absorbed into the zeropoint of the derived transformation equations (Stetson, 1990). The aperture with the maximum signal-to-noise ratio will of course be different for stars of different apparent magnitude (Stetson, 1990).

The following derivation draws upon the notation and therefore model of work presented in Naylor (1998a). A generic representation of a PSF is P(x - x₀,y - y₀) where x,y are pixel positions and x₀,y₀ is the centre of the PSF as determined by centroiding. The integral of P over all area is set to be 1, therefore it can be seen that a star’s profile, its total counts T spread over its PSF, is TP(x - x₀,y - y₀). The flux at pixel (i,j) is therefore,

where the integral is over the area of the pixel (i,j) and the superscript on P is merely a reminder that the integral is over a given pixel. It is important to recognise the alternative interpretation of P_i,j^I, it is the fraction of light of the star in pixel (i,j). The integrals are summed relative to the constraint that:

(5.22)

where R is the aperture radius. The measured flux is then:

(5.23)

If the profile is well sampled i.e., the pixels are small compared to the PSF then the sum tends to an integral and the equation becomes:

(5.24)

For a given aperture the integral will be the same for all stars in the frame, and can therefore act as a multiplier to the total flux, thus the ratio of fluxes between two stars is independent of the aperture used (Naylor, 1998a) of course a standard star is required on the frame to obtain real values. As such the choice of aperture size need only be big enough to deal with guiding errors etc. Since the LT will have tracking of better than 0.2'' and a pixel is 0.135'' across, an aperture radius of 8 pixels is large enough to deal with guiding and small enough that contaminating stars should not be a problem. The extracted counts may then be converted to magnitudes using the equations presented in Section 4.1

5.8.4 World Canvas Construction

The world canvas is created by assuming the telescope pointing (see Section 2.2 and Table 2.1) is true and using the central pixel as the reference pixel for the co-ordinate transformation.

This has proved to be inadequate for the test data. The reason for this being that the pointing of the JKT (the origin of the test data) has, over time, become degraded and can be randomly up to 25'' from its true position. While the LT will have pointing accurate to < 2'', this is addressed in more detail in a later version of the PL.

5.8.5 Airmass curve creation

The airmass curves are created using algorithms presented in Section 2.5. However due to bad weather the photometricity of the test data changed throughout the night. Whilst during manual observation and reduction it is easy to flag bad observing periods it has proved more difficult to automate. Manual interaction to remove the flagged standards indicates good results. However removing the “bad” points autonomously is not a simple task, points can be randomly removed from the plot and goodness of fit tests run, yet there is no way of knowing if a better fit is generated because several good points have been removed.

5.8.6 Conclusion: Version 1

The infrastructure initiated by version 1 of the PL is its most important contribution to this work. Each pipe has been seen to work when run in an interactive manner (e.g., the manual removal of bad standards or the manual alignment of the WCS). However autonomous operation has proved more difficult.

Whilst the LT pointing should be accurate enough to enable rigorous fitting of a WCS through the pointing, the possibility exists that the pointing could become degraded, due to software or mechanical failures. The removal of points from an airmass curve is a common procedure. Observers who have noted cloud during periods of the night may quickly justify their removal of data. With no weather information available to the PL this task is considerably more difficult. These issues are addressed in future versions of the PL.