# LENR verses Master Dark Frames

 Several times now several groups have discussed the relative effectiveness of long exposure noise reduction (LENR) and the use of master dark frames in dark correcting an image and there seems to be some question as to which one produces the best results. For those that just want a simple answer - master dark frames are better by a LARGE margin. There is simply no comparison between the two techniques. The slightly more complicated answer lies in the nature of noise. Noise is a random variation about some mean or true value. Because noise is a random signal, it cannot be subtracted from an image and dark subtraction actually increases the noise in an image although it greatly reduces the dark signal and improves image quality overall. Let's assume that we take an image that has an average level of 400. The photon noise in the image is, on average, the square root of 400 or 20. Now we subtract a dark frame that has an average noise level of 10 and we find that the resultant image has a noise level that is the RMS sum of 20 and 10. RMS is calculated by taking the square root of the sum of the squares of the individual noises. This gives us a total noise level of 22.4 and a signal of 400 for an SNR of 22.4 for each light frame taken. Now when we stack ten dark corrected light frames, the average level becomes 10*400 or 4000. The noise in each image RMS adds to give 70.7 for a total SNR of 4000/70.7 or 56.6. This is the case when LENR in camera is used when capturing each light frame. Now let's look at what happens if we take ten lights and ten darks, produce a master average of the ten darks and use this master to dark correct the lights. The noise in the average dark is the RMS addition of the individual darks divided by ten. The RMS sum of ten frames with a noise level of ten is 31.6. The average is this divided by 10 or 3.2 (rounded to one decimal place). Using this to dark correct the lights produces a noise that is the RMS sum of 20 and 3.2 or 20.3 per corrected light frame. Now once again stacking 10 such frames we get a signal of 4000 and a noise level of 64.2. This gives a final SNR of 4000/64.2 or 62.3. As we can see from the above discussion, using in camera LENR produces an image with a SNR of 56.6 while using a master dark produces an image with an SNR of 62.3. It is clear from this that creating a master dark will always be better than using in camera noise reduction to dark correct images. Below are two images made from six identical exposures, one image was darked corrected in camera while the other was made from images corrected by a master dark made from six dark frames. Image dark corrected in camera Image dark corrected with master dark 