Exposure Calculator
The Exposure Calculator is a tool inside the Equipment tab that helps astrophotographers determine the optimal sub-exposure length and total number of frames for a given night.
Where to find it
Equipment -> Exposure Calc
Inputs
| Field | Description | Default |
|---|---|---|
| Telescope | Select from your saved telescopes | - |
| Camera | Select from your saved cameras | - |
| Read noise (e⁻) | Auto-filled from camera profile if available | 4 e⁻ |
| Quantum efficiency (%) | Sensor QE; 60-75% covers most modern CMOS cameras | 65% |
| Total integration (h) | Planned session length | 3 h |
| Sky quality | Bortle class 1 (pristine) to 9 (inner city) | Bortle 5 |
Outputs
| Output | Meaning |
|---|---|
| Plate scale | Angular size of one pixel on the sky (arcsec/px) |
| Sky background | Estimated sky photon rate hitting each pixel (e⁻/px/s) |
| Recommended sub-exposure | Minimum exposure for sky-limited imaging |
| Number of subs | Subs needed to fill the requested total integration time |
Limitations
- QE is assumed flat across the spectral range. In practice, QE varies with wavelength. The formula uses V-band sky flux (matching the SQM meter passband), which gives the best absolute accuracy for broadband RGB imaging.
- Narrowband filters require different treatment: the sky background is much lower (fewer e⁻/px/s) through Ha/OIII/SII filters, so sub-exposures can and should be much longer. The calculator is primarily intended for broadband (L/RGB/OSC) imaging.
- Dark current is not included. For cooled cameras (−10 °C or colder), dark current is negligible. For uncooled or mildly cooled cameras add dark current to
B_skyif known. - Atmospheric extinction, light pollution gradients, and vignetting are not modelled.
Estimated minimum integration time
The Exposure Calculator sizes subs from a total integration the user supplies. The SkyTonight
advanced DSO filter “max estimated integration time” needs the opposite: a rough estimate of the
total integration a target needs. This is implemented in backend/equipment/exposure_math.py
(estimate_min_integration_hours) and is a deliberately rough planning heuristic, not a promise.
How the estimate is computed
Working in the sky-limited regime (which the sub-exposure length from Method guarantees), the per-pixel signal-to-noise ratio after a total integration time is
where and are the per-pixel photo-electron rates (e⁻/px/s) from the target’s mean surface brightness and from the sky, both computed with the same form used for in Method. Solving for to reach a chosen per-pixel SNR target:
- (per pixel, on the target’s mean surface brightness). This is a “detectable and processable” threshold, not “publication quality” - deep, clean images of faint targets need far more.
- The target’s mean surface brightness comes from the catalogue integrated magnitude spread over the
catalogue angular size (
skytonight_calculator._surface_brightness, then converted from mag/arcmin² to mag/arcsec²). This over-estimates the required time for objects with a bright core and faint outer halo (e.g. M31, M42) - the mean over the full catalogue extent is much fainter than the part you would actually expose for. - Sky brightness comes from the active location’s measured SQM if set, otherwise the Bortle -> SQM table in Method.
- Because and share the factor, aperture largely cancels: the estimate is driven by f-ratio, pixel size, sky brightness and target surface brightness - the well-known result that per-pixel SNR on extended sources depends on f-ratio, not aperture.
Limitations
- Broadband (L / RGB / OSC) only, exactly like the sub-exposure calculator - narrowband sky rates are far lower and the estimate does not model them.
- No QE-curve, atmospheric extinction, filter transmission, gradient or vignetting modelling.
- The mean-surface-brightness input skews the estimate long for centrally-concentrated targets.
- Treat the number as an order-of-magnitude planning aid (“minutes”, “a couple of hours”, “many nights”), not a target to hit.
Method
Plate scale
Sky background rate
The sky photon rate per pixel per second is computed from the observed sky surface brightness (SQM value derived from the Bortle class), the telescope aperture, and the plate scale:
Where:
- photons/m²/s/arcsec² - Vega zero-point flux, V-band
- - aperture in metres
- - in arcsec/px (so is arcsec²/px)
Bortle -> SQM mapping
| Bortle | SQM (mag/arcsec²) |
|---|---|
| 1 | 22.0 |
| 2 | 21.5 |
| 3 | 21.2 |
| 4 | 20.8 |
| 5 | 20.3 |
| 6 | 19.5 |
| 7 | 18.8 |
| 8 | 18.3 |
| 9 | 17.5 |
Optimal sub-exposure (5× criterion)
The recommended sub-exposure is chosen so that the sky background contributes 5 times more noise variance than the read noise:
This is the standard “sky-limited” criterion used in amateur astrophotography. Exposures shorter than this threshold are read-noise dominated; longer exposures don’t improve SNR per unit time.
Number of subs
Calibration
The formula was validated against published empirical measurements:
- ASI294MC Pro, f/7, 150 mm aperture, pixel = 4.63 µm, QE ≈ 75%, Bortle 5 (SQM 20.3)
- Expected sky background from real data: ~0.83 e⁻/px/s
- Formula result: ~1.0 e⁻/px/s - within the measurement uncertainty
Last updated 2026-11-13