Sub-exposure length, from the formula.

The idea

Every sub-exposure pays a fixed read-noise cost when the sensor is read out, however long it lasts. The sky adds its own noise, growing with time. Make the sub long enough and the sky noise swamps the read noise, and longer subs gain you almost nothing. The SharpCap formula puts a number on that: sub length = C × RN² ÷ LPR, where RN is read noise in electrons, LPR is the light pollution (sky background) rate in electrons per pixel per second, and C is how much extra noise you accept. The thread’s author states the rate must be in electrons per pixel per second, and a later reply confirms read noise is dimensionless in the formula and the rate is per second.

What the constant means

In the thread, the author says that 10% gives a C of about 10, 5% gives about 20, and so on. Here is the arithmetic behind it, which is this page’s own working. At sub length t = C × RN² ÷ LPR the sky contributes LPR × t = C × RN² electrons of noise variance, and the read noise adds RN² more. So read noise adds 1 ÷ C to the variance: 10% at C = 10 and 5% at C = 20. In terms of standard deviation, which is what you see as grain, the rise is √(1 + 1 ÷ C) − 1, about 4.9% and 2.5%. Either way, going from C = 10 to C = 20 doubles the sub length and halves the extra variance, a poor trade if clouds, satellites or guiding errors cost you whole subs.

Finding the sky background

If you know the rate directly, enter it. Otherwise take a test sub and read the median of a patch of empty sky, subtract the bias offset, and multiply by the camera’s gain in electrons per ADU. That is the electrons per pixel in the test sub, and dividing by the test sub length gives the rate. Use the camera’s native ADU values and the matching gain figure. If a 12-bit camera reports 16-bit scaled values, divide them by 16 before using a gain published per native ADU.

What this does not cover

A bright star can saturate before the formula’s sub length, so check the histogram. Mount tracking and polar alignment can set a lower limit than the formula does; the polar alignment calculator covers that. And the answer is for broadband, not for narrowband filters, where the sky rate is far lower and so the formula gives much longer subs.

Worked example

These are illustrative numbers, not a specific camera. Read noise 1.5 e-, sky background 0.8 e-/pixel/s. At C = 10: 10 × 2.25 ÷ 0.8 = 28.1 seconds. In that time the sky puts about 22.5 electrons in each pixel, ten times the read noise variance of 2.25, so read noise adds 10% to the variance (4.9% to the noise). At C = 20 the sub is 56.3 seconds. From a test sub instead: a 30 second frame with a median of 600 ADU, an offset of 100 ADU and a gain of 0.25 e-/ADU holds (600 − 100) × 0.25 = 125 electrons, a rate of 4.17 e-/pixel/s, which gives 10 × 2.25 ÷ 4.17 = 5.4 seconds for the same camera under a much brighter sky.