Optimum Exposures Calculator

Astrophotography can seem like a fair bit of guess-work. In general the process of capturing images involves doing so at a certain exposure length and multiple times for the same target, using the same filter. The idea here being to combine the images captured during calibration in order to reduce the pronunciation of noise and increase the pronunciation of signal, i.e. to increase the Signal-to-Noise Ratio (SNR) of your target. Guessing how much time to spend on a target however can be hard to do. 

There has been a good amount of mathematical analysis done on this problem by astrophotographers over the years. John Smith sparked off a good analysis, suggesting as a conclusion that one should calculate his/her exposure time required to overwhelm the CCD camera's readout noise with light pollution noise and aim to capture 2N+1 exposures of half this exposure time (where N is the number of exposures needed to reach a certain SNR). Though this seemed like a good idea, Charles Anstey was later motivated on making some adjustments to this theory based on his own empirical results. Charles noted that John's method was recommending extremely short exposures that were not giving the CCD sensor enough time to acquire faint signal from targets. A mathematical development followed that aimed to adjust this and come up with an updated theory. The end result was an equation that was a function of both ideal exposure time and total imaging time (number of exposures). Unfortunately this meant that you needed to make an assumption on one to work out the other. There were also some red flags in terms of quantities with unknown units and the final equation being dimensionally inconsistent. 

Thankfully Steve Cannistra had made his own mathematical framework that was more closed-ended. Approaching the problem by determining an asymptotic SNR (theoretical maximum you can reach given photon noise contribution overwhelming the CCD camera's readout noise), Steve derived a simple equation to give one's optimum exposure time. There was however no framework for the optimum number of exposures needed. In general, if you capture too few exposures, you end up with lower SNR than desired. If you capture too many exposures, you are wasting time because of diminishing returns during stacking. There is no real set number of exposures one must capture as the more, the better (with diminishing returns). However, empirical work on increasing SNR boost of a stack of calibrated images over a single calibrated image has been done by Kayron Mercieca in order to determine how with dithered images, Kappa-Sigma Clipping in DeepSkyStacker (a common robust, statistically-weighted combination method) behaves with increasing number of images in the stack. The user may then determine how far they wish to improve a single image's SNR by stacking numerous (typically between 50% and 150% improvement is recommended) and the calculator determines about how many exposures are required for such an improvement. The assumption however goes that the user is dithering between images (very important!) and is using robust, statistically-weighted combination methods such as Kappa-Sigma Clipping in DeepSkyStacker

This calculator has been created based on the aforementioned mathematical framework. Credit for the theoretical maximum SNR framework used goes to Steve Cannistra and to Kayron Mercieca for the empirical work on SNR boost during stacking with Kappa-Sigma Clipping. You will need a program capable of opening Microsoft Excel XLSX spreadsheets in order to use the calculator. Please click the button to download. Some instructions for using this calculator are provided below. 

Current Version: 2.2

Date of Release: 17 / 09 / 2014

Instructions for Use