Why does light pollution set the optimal sub-exposure?

Sky background light adds shot noise that grows with the square root of exposure time. Once that sky noise is several times the camera's fixed read noise, read noise becomes negligible. The brighter the sky, the faster it dominates, so light-polluted sites need shorter subs to be read-noise limited.

What does swamping the read noise mean?

It means exposing long enough that the random shot noise from the sky background is much larger than the camera's read noise, so stacking many subs gives nearly the same result as one long exposure. A common rule is to make sky-noise at least 3 to 5 times the read noise.

How is the optimal sub time calculated?

Set sky shot noise equal to a multiple of read noise: sqrt(sky_rate times t) = factor times read_noise. Solving gives t = (factor times read_noise) squared divided by sky_rate. A higher swamp factor or lower sky rate means longer subs.

Why not just take one very long exposure?

Long single exposures saturate bright stars, are ruined by satellites, planes, wind gusts, and guiding errors, and cannot be dithered. Many shorter subs that already swamp read noise give the same depth with far more flexibility, which is why the optimal sub is a minimum, not a target to exceed greatly.

How do I measure my sky background rate?

Take a short test sub, measure the median background level in ADU on an empty area, subtract the bias offset, multiply by the camera gain in electrons per ADU, and divide by the exposure time. That gives sky background electrons per pixel per second for that filter and sky.

What is the Astrophotography Light Pollution Exposure Calculator?

Enter sky background electron rate, camera read noise, and gain to find the minimum sub-exposure where sky-noise dominates read noise. For astrophotographers optimizing sub length in urban and suburban skies. It runs free in your browser on Gera Tools, with nothing uploaded.

Astrophotography Light Pollution Exposure Calculator

Name: Astrophotography Light Pollution Exposure Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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The most common astrophotography question from a light-polluted backyard is “how long should my subs be?” The answer is set by physics: expose just long enough that the noise from the sky background overwhelms your camera’s read noise, and no longer. This calculator finds that optimal sub-exposure from your sky rate and read noise.

How it works

Read noise is a fixed cost paid once per sub-exposure. Sky background contributes shot noise that grows as the square root of time. You want the sky shot noise to be several times the read noise so that read noise stops mattering:

sky_noise = sqrt(sky_rate * t)
goal:  sky_noise = factor * read_noise

Solving for the sub-exposure time:

t_optimal = (factor * read_noise)^2 / sky_rate

A “swamp factor” of 3 means sky noise is 3x read noise, which already pushes total read noise contribution to under 6% — a widely used target. Factor 5 is more conservative.

Why brighter skies want shorter subs

Because t is inversely proportional to the sky rate, doubling the sky brightness halves the optimal sub time. A Bortle 8 city sky might be read-noise limited in 30–60 seconds with a modern low-read-noise CMOS camera, while a dark Bortle 2 site needs several minutes.

Worked example

Suppose you have a CMOS camera with a read noise of 1.8 electrons at your chosen gain, and your sky background rate is 6 electrons per pixel per second (a typical broadband measurement for a Bortle 6 suburban site). With a swamp factor of 3:

t_optimal = (3 × 1.8)^2 / 6
          = 29.16 / 6
          ≈ 4.9 seconds

So roughly 5-second subs are already sky-noise dominated. With 60-second subs, the sky noise is overwhelming the read noise by a factor of 11 — there is no reason to push longer unless you are after very faint extended emission. In practice, 60-second subs (or even 30-second subs) are practical from this sky because they are well past the minimum threshold.

Now change the filter to a 3 nm Ha narrowband. A typical narrowband sky rate from the same Bortle 6 site might drop to 0.08 electrons per second — 75 times lower. The new optimal sub:

t_optimal = (3 × 1.8)^2 / 0.08
          ≈ 365 seconds (about 6 minutes)

This is why narrowband imaging from light-polluted sites can justify long subs: the sky contribution through a narrow filter is tiny, so read noise dominates until you expose for several minutes.

Measuring your own sky rate

To find the sky background rate for your specific camera, filter, and sky:

Take a test sub at a dark, empty patch of sky (no bright stars in frame).
Measure the median pixel value in ADU from an empty area.
Subtract the bias or dark offset from that value.
Multiply by your camera’s gain (electrons per ADU, from the published gain table).
Divide by the exposure time in seconds.

The result is your sky background rate in electrons per pixel per second for that filter and sky condition. Note that the rate changes with atmospheric transparency and the angular distance from the Moon, so measure for each session.

Tips

Modern cooled CMOS cameras have very low read noise (1–2 e-), so optimal subs are short and many — perfect for dodging satellites and dithering between frames. Treat the result as the minimum useful sub length; longer subs are fine as long as they do not saturate bright stars or run into tracking errors.