Poisson noise
Definition: Counting uncertainty that arises because independent photon arrivals fluctuate with variance approximately equal to the expected count.
Why it matters here: It establishes a fundamental noise floor even for a perfectly calibrated detector.
Relationships: For \(N\) detected electrons, \(\sigma\approx\sqrt{N}\); source, sky, and dark counting variances add in the SNR denominator.
Boundary / common confusion: Poisson noise is random scatter, not a removable calibration pattern.
sky background
Definition: Photons recorded from airglow, scattered light, unresolved sources, and other non-target illumination.
Why it matters here: Sky counts add noise inside the source aperture and can dominate a faint-source detection.
Relationships: The sky level is estimated from nearby pixels and contributes \(n_{pix}N_{sky}\) to the aperture variance.
Boundary / common confusion: Subtracting the estimated mean sky does not subtract its shot noise.
read noise
Definition: Random electronic uncertainty introduced when the detector charge is measured and digitized.
Why it matters here: It limits faint-source measurements and makes many very short exposures less efficient than fewer longer exposures.
Relationships: For an aperture of \(n_{pix}\) pixels, the variance contribution is \(n_{pix}R^2\), added in quadrature with photon-noise terms.
Boundary / common confusion: Read noise is not removed by bias subtraction; the mean bias pattern can be removed, but stochastic read noise remains.
dark current (SNR term)
Definition: The expected thermal-electron contribution per pixel over the science exposure, included as a variance source in the SNR calculation.
Why it matters here: It separates the uncertainty produced by thermal charge from the calibrated source and sky signals.
Relationships: For \(n_{pix}\) pixels, dark variance contributes \(n_{pix}N_{dark}\) when the counts are treated as Poisson.
Boundary / common confusion: This term is not the same as the residual mean after dark subtraction; the mean can be removed while its counting noise remains.
aperture
Definition: The chosen set of detector pixels whose background-subtracted counts are summed to measure a source.
Why it matters here: Aperture size controls the tradeoff between captured source flux and added sky/read noise.
Relationships: The SNR numerator grows with encircled source flux, while background and read-noise variance grow roughly with the number of included pixels.
Boundary / common confusion: A larger aperture is not automatically better and must not be confused with the telescope’s physical entrance aperture.
detection threshold
Definition: A stated signal-to-noise or false-alarm criterion used to decide whether a measured signal is distinguishable from noise.
Why it matters here: It turns “I can see something” into a reproducible statistical decision.
Relationships: A common convention is SNR near 5 for a secure isolated detection, but the false-positive rate also depends on how many locations or trials were searched.
Boundary / common confusion: A threshold is a convention tied to a noise model, not proof that the source is real under every systematic error.
shot noise
Definition: The Poisson fluctuation in the number of discrete photons or electrons counted during an exposure.
Why it matters here: It explains why relative precision improves only as the square root of the signal.
Relationships: For signal \(S\), the fractional shot-noise floor is approximately \(1/\sqrt{S}\).
Boundary / common confusion: Shot noise is not detector malfunction and cannot be calibrated away after the photons have been counted.