Limiting magnitude

The limiting magnitude is one of the mandatory header keywords in the Phase 3 archival standard and characterizes the depth of an observation. According to the ESO Phase 3 standard, it is defined as the magnitude of an unresolved source whose flux is 5 times the noise background, i.e. the magnitude of a point like source detected with S/N = 5.

In PyHDRL this is hdrl.func.Maglim.

Algorithm

The limiting magnitude of an image is determined as follows:

• The input image is convolved with a Gaussian kernel specified by fwhm (the FWHM of the kernel), kernel_size_x and kernel_size_y. To minimize border effects during convolution, the input image gets enlarged by a border depending on the kernel size. extend_method specifies the algorithm for out-of-bounds pixels: hdrl.func.Maglim.ImageExtendMethod.Nearest (nearest border pixel) or hdrl.func.Maglim.ImageExtendMethod.Mirror (mirror the image with respect to the border). Masked pixels are ignored in the convolution.

• Compute the mode of the convolved image (see the collapse mode method in the HDRL Pipeline Developer Manual).

• Consider all the non-masked pixels in the convolved image below the mode (valid pixels), and compute the noise as NOISE = 1.4826 * MAD(valid pixels) * c with c ≈ 1.6588967. If MAD = 0, then NOISE = STDDEV(valid pixels) * c.

• Compute the limiting magnitude as ABMAGLIM = -2.5 log10(5 * NOISE * 4πσ²) + ZPT with σ = FWHM / sqrt(4 ln(4)).

Compute

mode_param is a hdrl.func.Collapse (typically hdrl.func.Collapse.Mode(...)) or None. compute() takes a cpl.core.Image and returns a float.

mode_param = hdrl.func.Collapse.Mode(
    0.0, 0.0, 0.0, hdrl.func.Collapse.Method.Median, 0
)
maglim = hdrl.func.Maglim(
    zeropoint,
    fwhm,
    kernel_size_x,
    kernel_size_y,
    hdrl.func.Maglim.ImageExtendMethod.Mirror,
    mode_param,
)
limiting_magnitude = maglim.compute(image)