Guides to astrophotography math

What back focus is, why reducers and flatteners need an exact sensor distance, published values for real telescopes, and how to add up a spacer chain.

The geometry behind 2·arctan(d/2f), how large the small-angle error gets, why imaging area is pixels × pitch, and why crop factor is a framing convention.

What arcseconds per pixel mean physically, how 206.265 falls out of s = Fθ and the radian, and how pixel size, focal length, binning and Bayer filters change it.

Thin-lens formulas for reducers (R = 1 − d/f) and Barlows (M = 1 + d/|f|), why spacing changes the factor, designed back focus, and what a faster f-ratio buys.

Dawes' 4.56″ rule and the Rayleigh criterion 1.22 λ/D, worked for real apertures, and why atmospheric seeing sets the limit for long exposures.

John Bortle's nine sky classes from 2001 with their naked-eye limiting magnitudes, where the published copies disagree, and how sky brightness enters imaging plans.

How ADC bit depth, full well and system gain in e-/ADU decide where a CMOS astro camera saturates, what unity gain is, and how binning affects read noise.

How guide-camera image scale compares with your imaging scale, what PHD2's documentation says about arcseconds and RMS, sub-pixel centroids, and the 1:4 rule.

How a Bayer color filter array splits the pixels, what that does to the image scale of each color, and what a mono camera with filters changes.

Emission-line wavelengths from NIST, why steep light cones shift filter passbands to the blue, and which f/2–f/4 telescopes in our data are fast enough to matter.

Where the 500 rule came from, how Frédéric Michaud's NPF rule adds f-number, pixel pitch and declination, and how the two compare on real camera bodies.

Why imagers put two to three pixels across a star's FWHM, how AAVSO, Diffraction Limited, Stan Moore, Atik and a PASA paper disagree, and what seeing to expect.

What bias, dark, flat and dark-flat frames record, why only (L − D) ÷ (F − O) removes vignetting and dust, what must match, and the disk space a library takes.

What drizzle integration does, why it needs dithered and undersampled frames, which camera and telescope pairs qualify, and what it costs in noise and disk space.

The CCD equation behind exposure planning: why S/N grows with the square root of total time, when read noise makes sub length matter, and what it costs in storage.

Magnification, exit pupil and true field formulas, why 50× per inch and the 7 mm pupil are conventions, and how the dark-adapted pupil shrinks with age.