Field of View Calculator

Field of view is an angle, and it is computed two different ways depending on what sits at the focal plane. For a camera the geometry is exact: FOV = 2 arctan(w / 2f), where w is sensor width and f is focal length, giving 3.44 degrees for a 36mm full-frame sensor on a 600mm telescope. For visual use the working approximation is true field equals apparent field divided by magnification, with magnification being telescope focal length over eyepiece focal length. A 25mm eyepiece of 52 degrees apparent field in a 1200mm scope yields 48x and a 1.08-degree true field. The rigorous version instead uses the eyepiece field stop: true field equals 57.3 times field stop diameter divided by telescope focal length. The full Moon spans 0.52 degrees, or 31 arcminutes, which is the reference most observers judge fields against. Aperture governs everything else on this panel. The Dawes limit of 116 divided by aperture in millimeters gives resolution in arcseconds, the Rayleigh criterion of 138 divided by aperture is the stricter diffraction-based version, and useful magnification runs from about aperture divided by 7 to roughly twice the aperture in millimeters. Exit pupil, aperture divided by magnification, should stay under about 7mm or light spills past the observer iris. Two hard limits are easy to overlook: the AFOV-divided-by-magnification shortcut ignores eyepiece distortion and manufacturer figures are often optimistic, and barrel diameter caps the field stop at roughly 27mm for 1.25-inch eyepieces and 46mm for 2-inch, so no eyepiece design can exceed that maximum true field.

Field of view has been an eyepiece problem since the beginning. Christiaan Huygens introduced a two-element eyepiece in the 1660s that reduced chromatic error but delivered barely 30 degrees of apparent field. Jesse Ramsden design of 1782 and Carl Kellner achromatic version of 1849 improved correction incrementally, and the symmetric design associated with Georg Simon Plossl around 1860 reached roughly 50 degrees with good sharpness, which is why the Plossl remained the default eyepiece supplied with telescopes for over a century. Widening the field further required more glass and better correction of astigmatism at the edge, achieved in the Erfle designs developed at Zeiss during the First World War era, which pushed apparent fields into the 60 to 70 degree range. The modern ultra-wide era began when Al Nagler, who had designed wide-field simulator optics for the Apollo lunar module program, founded Tele Vue in 1977 and released the 82-degree Nagler eyepiece in the early 1980s, followed by the 100-degree Ethos in 2007. On the resolution side, William Rutter Dawes established his empirical limit in the 1860s by systematically testing how close a double star could be before his refractors merged the pair, deliberately fitting observation rather than theory. Lord Rayleigh derived the complementary diffraction-based criterion in 1879 from the condition that one Airy disk maximum falls on the first minimum of the other.