Astronomy CCD Calculator — Quick Exposure & SNR Estimator

Simple Astronomy CCD Calculator: Predict Star Signal, Noise & Histogram

Understanding how a CCD camera will capture stars lets you plan exposures, avoid wasted observing time, and produce cleaner images. This guide shows a straightforward CCD calculator workflow you can use to predict star signal, estimate noise and signal-to-noise ratio (SNR), and anticipate a simple histogram shape for your exposure.

1) What you need (inputs)

• Telescope aperture (D) — diameter in mm or inches.
• Camera pixel size (p) — microns.
• Quantum efficiency (QE) — fraction (e.g., 0.6 for 60%).
• System throughput (Tsys) — fraction for optics + filters + atmosphere (typical 0.3–0.6).
• Star magnitude (m) — visual magnitude of target star.
• Exposure time (t) — seconds.
• Gain — e−/ADU.
• Read noise (RN) — electrons RMS per pixel.
• Dark current (Id) — e−/pixel/sec (temperature-dependent).
• Seeing FWHM — arcseconds (to distribute star light over pixels).
• Plate scale — arcseconds/pixel (can be computed from focal length and pixel size).

2) Core calculations

Assume a zero-magnitude star delivers a known photon flux at the top of the atmosphere. For a simple practical calculator use this scaled approach:

• Photon flux for m = 0 star at telescope aperture:
  • Use a reference constant K ≈ 1.1×10^6 photons/s/cm^2 in V-band (approximate).
• Effective collecting area A = π (D/2)^2 (convert D to cm).
• Photons collected per second from star: Photons/s = K × 10^(−0.4 m) × A × Tsys
• Electrons detected per second: e−/s = Photons/s × QE
• Total star electrons in exposure: S = e−/s × t

3) Star profile and pixels

• Compute plate scale if you don’t have it: Plate scale (arcsec/pixel) ≈ 206.265 × (pixel_size_microns / focal_length_mm)
• Convert seeing FWHM (arcsec) to pixels: FWHM_px = FWHM_arcsec / plate_scale
• Approximate fraction of star flux in central pixel using Gaussian PSF: Peak fraction ≈ 1 / (2π (σ_px)^2), with σ_px = FWHM_px / 2.355. For practical purposes, total flux S will be spread over Npix ≈ π (FWHM_px/2)^2 pixels (area within FWHM).

4) Noise budget (per aperture)

Compute noise sources for the aperture that contains the star (use Npix from above):

• Photon (shot) noise from star: N_star = sqrt(S)
• Sky background: measure or estimate sky surface brightness B (mag/arcsec^2). Convert to e−/pixel/sec using same flux scaling, plate scale, QE and Tsys; then total sky electrons per pixel = B_e_per_s_pixel × t. Total sky in aperture = sky_pixel_e × Npix. Sky noise: N_sky = sqrt(sky_total).
• Dark noise: Dark_total = Id × t × Npix; N_dark = sqrt(Dark_total).
• Read noise: N_RN = RN × sqrt(Npix).

Total noise: N_total = sqrt(N_star^2 + N_sky^2 + N_dark^2 + N_RN^2).

SNR = S / N_total

5) Histogram preview (qualitative)

• Peak ADU level for star core: Peak_electrons ≈ S × peak_fraction (from section 3).
  Peak_ADU = Peak_electrons / gain.
• Background ADU = sky_e_per_pixel_total / gain.
• Histogram features:
  • A narrow peak at background ADU (sky + bias) whose width ~ sqrt(sky + RN^2/gain^2).
  • A high-ADU tail from stars; bright star cores form distinct counts above background.
  • If Peak_ADU approaches full well / ADC max, expect clipping on the right; avoid saturation.

6) Practical example (assumed values)

• D = 200 mm, QE = 0.6, Tsys = 0.5, m = 10, t = 60 s, pixel = 4.8 μm, focal_length = 1000 mm, RN = 8 e−, e−/s/pix, gain = 1.0 e−/ADU, seeing =