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Entropy-Based Dark Frame Subtraction

Noise due to dark current is a serious limitation for taking long exposure time images with a CCD digital camera. Current solutions have serious drawbacks: interpolation of pixels with high dark current leads to smoothing effects or other artifacts – especially if a large number of pixels are corrupted. Due to the exponential temperature dependence of the dark current, dark frame subtraction works best for temperature controlled high end CCD imaging systems. On the physical level, two independent signals (charge generated by photons hitting the CCD and by the dark current) are added. Due to its random distribution, adding (or subtracting) the dark current noise signal increases the entropy of the resulting image. The entropy is minimal if the dark current signal is not present at all. A dark frame is a good representation of the dark current noise. As the generated dark current depends on the temperature equally for all pixels, a noisy image can be cleaned by the subtraction of a scaled dark frame. The scaling factor can be determined in an optimization step which tries to minimize the entropy of the cleaned image. We implemented a software system that effectively removes dark current noise even from highly corrupted images. The resulting images contain almost no visible artifacts since only the noise signal is removed. This extends the range of usable exposure times of digital cameras without temperature control systems by about one to two orders of magnitude.