_{2024-01-28 @17:45} #book/the-deep-sky-imaging-primer #photography/dynamic-range #digital-garden # Dynamic Range (DR) We can think of the dynamic range (DR) as the ratio between the brightest signal and the dimmest signal. There are two contexts to DR, that of a sensor and a scene. > [!QUOTE] > ##### The Deep Sky Imaging Primer - Charles Bracken > *For a sensors theoretical dynamic range, the well capacity defines the maximum possible signal and the read noise defines the lowest distinguishable signal.* # DR (as dB) DR has two contexts and that is of a scene or a sensor. DR is often expressed in decibels (dB), a base-10 logarithmic unit. To convert a raw ratio to dB, the formula is ... $ dB=20\times \log_{10}\left(\frac{b}{d}\right) $ $ (b)\space brightest \space signal $ $ (d)\space dimmest \space signl $ The DR of a sensor determines how much of a scene's dynamic range you can capture in one exposure. For a sensor the above formula would translate to ... $ dB=20\times \log_{10}\left(\frac{w}{r}\right) $ $ (w)\space full \space well \space capacity $ $ (r)\space read \space noise $ # DR (as F-stops) We can also characterize dynamic range in terms of F-stops. This is a base-2 logarithmic scale: *an increase in one corresponds to a doubling of dynamic range*. So for a sensor this would be ... $ fstops=\log_{2}\left(\frac{w}{r}\right) $ $ (w)\space full \space well \space capacity $ $ (r)\space read \space noise $ Sometimes we may already have the dynamic range in terms of dB so we can just divide by 6.02 to convert to F-stops. $ fstops=\frac{dB}{6.02} $ # Trade Off (DR vs Gain) Modern day cameras (including most astronomical cameras) have adjustable gain settings which is controlled by the ISO. This allows the charge to be amplified before it hits the ADC on read out. Since well capacity is fixed, increasing gain reduces the dynamic range we can capture in a single exposure. # Scenerio Within a faint nebula sits a bright star. The nebula has a brightness of magnitude 14 per square arcsecond, while the star has a magnitude of 4 and covers approximately one sqaure arcsecond when viewed through an optical system. *How many decibels of dynamic range would a sensor need to have to capture this scene in a single exposure? How would I express this in terms of F-Stops so I could configure my camera correctly?* > [!HINT] > A 10 magnitude between brightest and dimmest (treating 5 magnitudes as $100:1$ difference) is a factor of $100x100 = 10,000:1$ range in our scene. $ dB=20\times \log_{10}\left(\frac{b}{d}\right) $ $ dB=20\times \log_{10}\left(\frac{10000}{1}\right)=80\space dB $ $ fstops=\log_{2}\left(\frac{w}{r}\right) $ $ fstops=\log_{2}\left(\frac{10000}{1}\right)=13.3\space stops $