Common Units and Numerical Scales

These tables collect the units and orders of magnitude most often needed for writing, estimates, and review. For the actual formulas, return to the first definition in the main text; when estimating, check units, scale, and validity range together.

Basic Constants and Astronomical Conversions

Quantity	Common value	Reminder
Speed of light	\(c=2.998\times10^8\,{\rm m\,s^{-1}}\)	Baseline light-travel time \(B/c\): \(1\,{\rm km}\) is about \(3.3\,\mu{\rm s}\), and \(1000\,{\rm km}\) is about \(3.3\,{\rm ms}\).
Planck constant	\(h=6.626\times10^{-34}\,{\rm J\,s}\)	Single-photon energy is \(E=h\nu=hc/\lambda\).
Boltzmann constant	\(k_{\rm B}=1.381\times10^{-23}\,{\rm J\,K^{-1}}\)	Needed for brightness temperature, Planck occupation number, and thermal noise.
Jansky	\(1\,{\rm Jy}=10^{-26}\,{\rm W\,m^{-2}\,Hz^{-1}}\)	AB magnitudes and photon-rate estimates often start from Jy.
Parsec	\(1\,{\rm pc}=3.086\times10^{16}\,{\rm m}\)	\(1\,{\rm AU}\) subtends \(1''\) at \(1\,{\rm pc}\).
Solar radius	\(R_\odot=6.96\times10^8\,{\rm m}\)	Useful for stellar angular diameters and binary scales.
Solar luminosity	\(L_\odot=3.83\times10^{26}\,{\rm W}\)	Often combined with \(F_{\rm bol}\), \(T_{\rm eff}\), and \(\theta\).

Angles, Wavelengths, and Baselines

Quantity	Common value	Main-text location
Angle conversions	\(1\,{\rm rad}=206265''\); \(1\,{\rm mas}=4.848\times10^{-9}\,{\rm rad}\); \(1\,\mu{\rm as}=4.848\times10^{-12}\,{\rm rad}\)	Chapters Mathematical and Physical Foundations and Spatial coherence and intensity interferometry.
Visible wavelengths	Blue-light intensity interferometry often uses \(400\)–\(450\,{\rm nm}\); broad-band imaging often uses \(500\)–\(800\,{\rm nm}\)	Chapters Spatial coherence and intensity interferometry and Observing design, error budgets, and feasibility calculations.
Diffraction scale	\(\lambda/B\) is about \(1\,{\rm mas}\) at \(500\,{\rm nm}\) and \(100\,{\rm m}\)	Hundred-meter arrays are well matched to bright-star angular diameters.
First-null scale	A \(1\,{\rm mas}\) uniform disk has its first null near \(100\,{\rm m}\) at \(416\,{\rm nm}\)	Chapter Spatial coherence and intensity interferometry, Eq. (94).
\(\mu{\rm as}\) structure	\(10\,\mu{\rm as}\) at \(500\,{\rm nm}\) corresponds to \(\lambda/\theta\sim10\,{\rm km}\)	Nearby supernovae, compact AGN structure, and future long-baseline cases.
Projected baseline	\(B_\perp\) changes with target elevation, hour angle, and array geometry	A fixed physical baseline is not a substitute for the full overnight \(u,v\) coverage.

Time, Frequency, and Coherence

Quantity	Common value	Main-text location
Frequency conversion	\(500\,{\rm nm}\) corresponds to \(6.0\times10^{14}\,{\rm Hz}\)	Optical bandwidths often require conversion between \(\Delta\lambda\) and \(\Delta\nu\).
Optical coherence time	A \(10\,{\rm nm}\)-class filter in the visible typically gives \(10^{-14}\)–\(10^{-13}\,{\rm s}\)	Chapter Mathematical and Physical Foundations, Eq. (17).
Correlation bin	Tabletop experiments can use ps–ns bins; astronomical intensity interferometry is often limited by electronic response and data rate	Chapters Data analysis for event tables and Teaching experiments and computational experiments.
Detector jitter	Good SPAD, PMT, and TDC systems can reach tens of ps to ns; system synchronization must be calibrated separately	Chapter Detectors, clocks, and event tables.
Dead time	SPAD dead time is often ns–\(\mu{\rm s}\); PMTs and electronics also have recovery times	Dead time creates negative correlations at short delays.
Afterpulsing	Probabilities can be \(10^{-4}\)–\(10^{-2}\)	Produces positive correlations at detector-specific delays.
Integration-time scaling	Pure statistical errors usually fall as \(T^{-1/2}\)	Once a systematic floor is reached, longer integration does not automatically improve the result.

Photon Rates, Magnitudes, and Backgrounds

Quantity	Common value	Main-text location
AB-magnitude flux	AB zero point and photon-rate estimates are given in Chapter Mathematical and Physical Foundations, Eqs. (42) and (41)	A proposal should state bandwidth, efficiency, collecting area, and background together.
Magnitude change	If a target is fainter by \(1\,{\rm mag}\), the photon rate falls by about \(10^{-0.4}\simeq0.40\)	Chapters Observing design, error budgets, and feasibility calculations and From white paper to research plan.
Telescope area	An ideal \(D=12\,{\rm m}\) aperture has geometric area about \(113\,{\rm m^2}\); the effective area must also include throughput and obscuration	Cherenkov-telescope optics, filters, and detector QE all enter.
Background dilution	If the target flux fraction is \(f\), the second-order correlation excess is approximately suppressed by \(f^2\)	Chapter Mathematical and Physical Foundations, Eq. (19).
Narrow-line observations	A narrower line gives a longer coherence time, but total photon number and filter leakage may worsen	Be-star disks, maser/laser candidates, and BLR cases should all report line/continuum separation.
Night sky	Varies with Moon phase, zenith angle, filter, and field stop	A dark-field background is not valid for every target position.

Instruments and Data Volume

Quantity	Common value	Main-text location
Single-stream sampled data rate	\(\Delta t=4\,{\rm ns}\), \(16\) bits, and one channel give about \(4\,{\rm Gb\,s^{-1}}\)	Chapter Detectors, clocks, and event tables, Eq. (102).
Multichannel expansion	64 spectral channels push the same example to about \(256\,{\rm Gb\,s^{-1}}\) per telescope	Requires real-time correlation, compression, or on-chip accumulation.
Number of baselines	4 telescopes give 6 baselines; 60 telescopes give 1770 baselines	Chapter Spatial coherence and intensity interferometry, Eq. (99).
Calibrator stars	Should be close to the target in sky position, color, and brightness, with known angular diameter	Chapter Observing design, error budgets, and feasibility calculations.
Quality slicing	Split by transparency, target elevation, background rate, dead time, and channel state	Reporting wall-clock time alone is not enough to reproduce an experiment.
Systematic floor	A correlation-amplitude floor of \(10^{-5}\)–\(10^{-4}\) can dominate many SII targets	Chapter Common pitfalls.

Astrophysical Orders of Magnitude

Quantity	Common value	Main-text location
Bright-star angular diameters	Nearby bright stars are often \(0.2\)–\(5\,{\rm mas}\)	Chapters Stars as quantum light sources and First-generation quantum-astronomy science cases.
Early Type Ia velocities	Photospheric velocities are often \(8000\)–\(15000\,{\rm km\,s^{-1}}\)	Chapters Explosions, transients, and multi-messenger quantum astronomy and Teaching experiments and computational experiments.
Nearby supernova angular radius	At \(20\,{\rm Mpc}\), \(v=10^4\,{\rm km\,s^{-1}}\), and 15 days, the angular radius is a few \(\mu{\rm as}\)	Kilometer to ten-kilometer baselines are needed for substantial information.
Crab period	About \(33\,{\rm ms}\)	Phase-resolved photon statistics require absolute timing.
AGN broad-line region	Reverberation delays are often days to months, while angular scales are usually very small	Combine reverberation, angular displacement, and model priors.
CMB temperature	\(2.725\,{\rm K}\)	Chapter Quantum questions in cosmology; optical photon statistics cannot be transferred directly.