Charles J. Wetterer, Integrity Applications International / Pacific Defense Solutions, Paul F. Sydney, Integrity Applications International / Pacific Defense Solutions, Joseph D. Gerber, Applied Defense Solutions, Jacob Griesbach, Applied Defense Solutions
Keywords: In-Frame Photometry, Background Normalization, Poisson distributed noise
Abstract:
Photometric processing of non-resolved Electro-Optical (EO) images has commonly required the use of dark and flat calibration frames that are obtained to correct for charge coupled device (CCD) dark (thermal) noise and CCD quantum efficiency/optical path vignetting effects respectively. It is necessary to account/calibrate for these effects so that the brightness of objects of interest (e.g. stars or resident space objects (RSOs)) may be measured in a consistent manner across the CCD field of view. Detected objects typically require further calibration using aperture photometry to compensate for sky background (shot noise). For this, annuluses are measured around each detected object whose contained pixels are used to estimate an average background level that is subtracted from the detected pixel measurements.
In a new photometric calibration software tool developed for AFRL/RD, called Efficient Photometry In-Frame Calibration (EPIC), an automated background normalization technique is proposed that eliminates the requirement to capture dark and flat calibration images. The proposed technique simultaneously corrects for dark noise, shot noise, and CCD quantum efficiency/optical path vignetting effects. With this, a constant detection threshold may be applied for constant false alarm rate (CFAR) object detection without the need for aperture photometry corrections. The detected pixels may be simply summed (without further correction) for an accurate instrumental magnitude estimate.
The noise distribution associated with each pixel is assumed to be sampled from a Poisson distribution. Since Poisson distributed data closely resembles Gaussian data for parameterized means greater than 10, the data may be corrected by applying bias subtraction and standard-deviation division.
EPIC performs automated background normalization on rate-tracked satellite images using the following technique. A deck of approximately 50-100 images is combined by performing an independent median calculation along the deck dimension for each image pixel. Because the images are rate-tracked, moving objects (such as background stars) are quickly eliminated. Stationary RSO signatures are removed from the resultant median combined image using a local area median filter that smoothes over the RSO responses. The result is an estimate of the background noise bias. The calculated bias estimate image is subtracted from each deck image, which effectively removes noise bias.
A variance correction is applied to address spatially varying noise by dividing each pixel by the square-root of its measured variance. This technique essentially uses the sky background noise (assumed to be uniform over the telescope aperture) to normalize the CCD quantum efficiency/optical path vignetting effects. Poisson distributed random variables have, by definition, equal mean and variance, which eliminates the need to estimate the variance explicitly. Simply dividing each pixel by the square-root of the measured bias effectively normalizes the imagery. The result after the bias and variance corrections are applied is a statistically stationary noise background appropriate for CFAR detection.
Additional techniques to address time-varying noise backgrounds (caused by atmospheric turbulence, clouds, and stray light) and hot-pixel / cosmic-ray mitigation are also explored.
Date of Conference: September 15-18, 2015
Track: Poster