Subframe evaluation

December 08, 2012
Each photograph in this gallery is an integration (i.e. a Winsorized sigma clipped, dispersion normalized, mean combination) of multiple exposures (subframes). Individual subframes vary in quality. Factors affecting subframe quality include optical focus, guiding errors, astronomical seeing, sky transparency and sky glow. To help evaluate subframe quality, I wrote a script that measures several subframe quality related properties. Measurements include star profile full width and half maximum (FWHM), star profile eccentricity (elliptical distortion) and subframe signal to noise ratio (SNR) weight.
 
The measurements for each property are presented in a plot, like the one shown below. The plot's horizontal axis represents subframes in chronological exposure order. The plot's left hand vertical axis represents property values in natural units. The right hand vertical axis represents property values in sigma normalized units. Sigma values are normalized in mean absolute deviation units from the median.
 
blog 2012_12_08
 
The central horizontal dashed line in the plot corresponds to the median of the measurements across all subframes. The two horizontal dashed lines above and below the median line correspond to one mean absolute deviation unit from the median greater than and less than the median, respectively.
 
The points corresponding to subframes whose exposures occurred on the same night are joined with darker lines. In the plot above the exposures were made on 5 nights. I usually attempt 6 exposures per night of a particular target, each 40 minutes in duration, all within about 2.5 hours of the meridian to minimize atmospheric extinction.
 
The plot above shows the median star profile full width at half maximum (FWHM) estimate for each subframe in arcseconds. The FWHM is a well-known and standardized measurement of the size of a star as seen on the subframe. It is the normalized width of a functional fit to a star image, measured horizontally at half its maximum height. I use an elliptical Moffat function with a β parameter equal to 4 as the star profile model [1].
 
FWHM is a useful measure because it well characterizes both optical focus, guiding errors and astronomical seeing. Note that the FWHM of the first subframe is relatively high. This high FWHM was due to optical focus drift during the exposure as a result of a large change in ambient air temperature. This subframe was rejected due to its high FWHM.
 
blog 2012_12_08
 
The plot above shows the median star profile eccentricity estimate for each subframe. Eccentricity is a measure of star profile elliptical distortion. Given an elliptical star profile with major axis radius a and minor axis radius b where a is greater than or equal to b, eccentricity equals (1 - b^2 / a^2)^0.5. An elliptical distortion with an eccentricity less than about 0.42 is not perceptible to most people.
 
Eccentricity is a useful measure because it well characterizes both optical aberrations and guiding errors. In this example no subframe was rejected due to high eccentricity.
 
blog 2012_12_08
 
The plot above shows the signal to noise ratio weight (SNRWeight) estimate for each subframe. SNRWeight is defined as m^2 / n^2, where m is the mean absolute deviation from the median of the subframe and n is an estimate of the standard deviation of Gaussian noise for the subframe.
 
SNRWeight is a useful measure because it well characterizes a combination of factors that affect signal to noise ratio, including sky transparency, sky glow and camera noise. A subframe integration weighted by SNRWeight is an approximate maximum likelyhood estimator for pixel values that correspond to background limited targets, without requiring additional information such as optic and sensor parameters. In this example the fourth subframe was rejected due to relatively low SNRWeight. This low SNRWeight was due to the presense of high clouds that resulted in low sky transparency during the exposure.
 
SNRWeight is a relative correlate of signal to noise ratio. Its formulation assumes that the subframes represent exposures of the same target and that the subframes have similar background gradients.
 
[1] Moffat, "A Theoretical Investigation of Focal Stellar Images in the Photographic Emulsion and Application to Photographic Photometry",  Astronomy and Astrophysics, 3:455-461, 1969 December.

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