The common way to combine HST images obtained using dithering is based on the Driz- zle algorithm by Fruchter and Hook (2002). This is mostly done using the software called MultiDrizzle(Koekemoer et al., 2003).
Drizzling is a forward method unlike typical interpolation methods. All pixels of the original input images are mapped into pixels in the subsampled output image. In map- ping the pixels it is necessary to take into account shifts and rotations between images, in addition to the optical distortion of the camera. The user can decide to shrink the pixels before creating the output image using the pixfrac parameter so as to avoid to convolve the image with the large pixel footprint of the camera. The shrunken pixels, also called drops, rain down upon the output image as shown in the left panel of Figure 3.8. The final size of the drop is, then, adjusted by the code to consider the geometric distortion introduced by the camera. The user is also allowed to specify the size of the output pixels using the pa- rameter scale. The flux in each input pixel is divided up into the output pixels with weights proportional to the area of overlap between the drop and each output pixel. The parameter
kernel permits to specify which kernel function should be used to distribute the flux onto
the separate output images. The options available are: • Square, the original classic drizzling kernel.
• Point, which forces each input pixel to contribute only to the single pixel which is the closest to the output position. This kernel is equivalent to a square one with pixf rac → 0 and it is very fast.
• Gaussian, which is a circular Gaussian with F W HM = pixf rac, measured in input pixels.
• Turbo, which is similar to the square kernel, but with the box always with the same shape and size on the output grid and always aligned with the x and y-axis. It can increase significantly the speed of the process.
• Tophat, with a circular top hat shape of width equal to pixfrac. Only output pixels within pixf rac/2 of the output position are affected.
• Lanczos3, which is a Lanczos style kernel extending 3 pixels from the center. The Lanczos kernel is a damped, bounded form of the sinc interpolator and is very effec- tive for resampling single images when scale = pixf rac = 1. It leads to less resolution loss than the other kernels, and also less correlated noise in outputs, but it is much slower. It should never be used for pixf rac 6= 1.0.
When the drop size is too small or the point kernel is used, it is possible that not all output pixels receive data from each of the input images. This could be dangerous especially if the number of frames combined is small. One should, therefore, choose a drop size that is small enough to avoid convolving the image with a too large input pixel footprint, and, at the same time, large enough to have signal in all the output pixels.
One of the drawbacks of the Drizzle algorithm is the fact that the output pixels in the final drizzled image are not independent of the others, causing the noise in the output image to be correlated to some degree. In particular, the noise in adjacent pixels will be correlated. This depends on splitting the power from a single input pixel between several output pixels. This effect needs to be quantified properly for estimating the statistical er- rors when drizzled images are analyzed using SExtractor (Bertin and Arnouts, 1996). This correlated noise implies an underestimation of the noise on larger scales in the output im- age. This is true for all the kernels, but one. In fact, the point kernel does not spread the
Figure 3.8: On the left panel it is shown how Drizzle maps the input pixels onto the output image. On the right panel there is a scheme of the distribution of noise from a single input pixel (a+b colored area) between neighboring pixels of the output image.
flux of one input pixel into several output pixels, but associates it only to one single output pixel, without introducing any correlated noise in the final product.
MultiDrizzlecarries out a series of completely automated steps:
• Static Mask. In this step it examines all the images to identify negative bad pixels, and to include them in the data-quality array.
• Sky Subtraction. It subtracts the sky from each input image.
• Driz Separate. It drizzles the input images onto separate, registered outputs using shifts computed from the headers.
• Median. It combines the separate drizzled images to create a median frame.
• Blot. It “blots” the median image back to each original input image. It performs the inverse operation of Drizzle, i.e. it converts an undistorted image back into the original distorted one. It is mostly used to identify the cosmic rays in the original image.
• Driz cr. It creates a derivative image using each blotted image and, then, it computes the cosmic ray masks.
• Driz Combine. On the basis of the cosmic ray masks previously created, it does the final drizzle combination.
The final output image created by MultiDrizzle is characterized by the suffix * drz.fits and is a multi-extension FITS file, unless specifying built=no, which determines the creation of separate output files. Each * drz.fits file contains the science image (SCI) in the first extension, the weight image (WHT) in the second, and the context image (CTX) in the third one.
The science (SCI) image is corrected for distortion and dither-combined, if applicable. The weight (WHT) image gives the relative weight of the output pixels. It can be considered an effective exposure time map, if final wht type = EXP. Otherwise, setting final wht type
= ERR the output weight image is in units of inverse variance, calculated using the er-
ror arrays existing from the beginning in the *flt.fits file. Finally, if final wht type=IVM, MultiDrizzlelooks for inverse variance files provided by the user. In this case the user have to create an input file, containing two file names per line, i.e., the name of the *flt.fits file and of the corresponding *ivm.fits file.
The context (CTX) image encodes information about which input image contributes to a specific output pixel.