CCD equation
Definition: Ccd equation denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: The standard CCD signal-to-noise equation (Merline & Howell 1995 form) is SNR = S / √[S + n_pix(B + D t + σ_read²)], where B is the sky-background electron count (over the same exposure time and aperture) and n_pix is the number of pixels summed.
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with signal-to-noise ratio (SNR) to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...
signal-to-noise ratio (SNR)
Definition: Signal-to-noise ratio (snr) denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: A realistic worked scenario for this course -- an 18th-magnitude star observed with the Keck aperture, a representative 60% end-to-end system throughput, and a representative modern CCD -- requires only about 0 seconds of integration to reach signal-to-noise ratio 100, while the same...
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with CCD equation, sky background to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...
sky background
Definition: Sky background denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: The standard CCD signal-to-noise equation (Merline & Howell 1995 form) is SNR = S / √[S + n_pix(B + D t + σ_read²)], where B is the sky-background electron count (over the same exposure time and aperture) and n_pix is the number of pixels summed.
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with signal-to-noise ratio (SNR), background-limited to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...
background-limited
Definition: Background-limited denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: At short exposure times, the read-noise term σ_read² dominates the denominator and SNR grows roughly linearly with exposure time (read-noise-limited regime); at long exposure times, the S and B terms dominate and SNR grows only as √t (background- or source-limited regime) -- the crossover...
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with sky background, read-noise-limited to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...
read-noise-limited
Definition: Read-noise-limited denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: At short exposure times, the read-noise term σ_read² dominates the denominator and SNR grows roughly linearly with exposure time (read-noise-limited regime); at long exposure times, the S and B terms dominate and SNR grows only as √t (background- or source-limited regime) -- the crossover...
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with background-limited, exposure time calculator (ETC) to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...
exposure time calculator (ETC)
Definition: Exposure time calculator (etc) denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Every major observatory (Keck, Gemini, ESO/VLT, HST, JWST) publishes an online exposure-time calculator implementing the same underlying CCD equation used in this lecture, confirmed by comparing this course’s computed SNR values against the published forms of these tools’ documentation.
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with read-noise-limited, system throughput to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...
system throughput
Definition: System throughput denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: The total signal from a point source in an aperture is S = (photon flux) × (collecting area) × (system throughput) × (detector QE) × (exposure time); the total noise combines this same source’s own shot noise with sky-background shot noise, dark-current shot noise, and read noise in...
Why it matters here: Lectures 04-05 established how a detector generates signal and noise separately; this lecture combines every one of those terms into the single equation every observer actually uses to plan a real observation -- the same equation implemented, in more elaborate form, inside every professional observatory’s online exposure-time...
Relationships: It is used with exposure time calculator (ETC) to interpret the lecture model. The quantitative connection is the working relation \(\mathrm{SNR} = \dfrac{S}{\sqrt{S + n_{\rm pix}\left(B + Dt + \sigma_{\rm read}^{2}\right)}}\).
Boundary or common confusion: Assuming doubling the exposure time always doubles the signal-to-noise ratio. That linear scaling holds only in the read-noise-limited regime; once shot noise from the source or sky dominates, SNR grows only as √t, so quadrupling the exposure time is needed to double the SNR -- a distinction that changes an observing proposal’s time request by a large...