12 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Eyepiece | 3/7 | https://en.wikipedia.org/wiki/Eyepiece | reference | science, encyclopedia | 2026-05-05T09:47:24.682125+00:00 | kb-cron |
True or Telescope's field of view For a telescope or binocular, the actual angular size of the span of sky that can be seen through a particular eyepiece, used with a particular telescope, producing a specific magnification. It ranges typically between 0.1–2 degrees. For a microscope, the actual width of the visible sample on the slide or sample tray, usually given in millimeters, but sometimes given as angular measure, like a telescope. For binoculars it is expressed as the actual field width in feet or in meters at some standard distance (typically either 100 feet or 30 meters, which are very nearly the same: 30 m is only a 2% smaller than 100 feet). Apparent or Eye's field of view For telescopes, microscopes, or binoculars, the apparent field of view is a measure of the angular size of the image seen by the eye, through the eyepiece. In other words, it is how large the image appears (as distinct from the magnification). Unless there is vignetting by the telescope's or microscope's body tube, this is constant for any given eyepiece with a fixed focal length, and may be used to calculate what the true field of view will be when the eyepiece is used with a given telescope or microscope. For modern eyepieces, the measurement ranges from 30–110 degrees, with all current good eyepieces being at least 50°, except for a few special-purpose eyepieces, such as some equipped with reticles. It is common for users of an eyepiece to want to calculate the actual field of view, because it indicates how much of the sky will be visible when the eyepiece is used with their telescope. The most convenient method of calculating the actual field of view depends on whether the apparent field of view is known. If the apparent field of view is known, the actual field of view can be calculated from the following approximate formula:
T
F
O
V
≈
A
F
O
V
M
{\displaystyle T_{\mathsf {FOV}}\approx {\frac {\ A_{\mathsf {FOV}}\ }{M}}}
where:
T
F
O
V
{\displaystyle \ T_{\mathsf {FOV}}\ }
is the true field of view (on the sky), calculated in whichever unit of angular measurement that
A
F
O
V
{\displaystyle A_{\mathsf {FOV}}\ }
is provided in;
A
F
O
V
{\displaystyle \ A_{\mathsf {FOV}}\ }
is the apparent field of view (in the eye);
M
{\displaystyle \ M\ }
is the magnification. The formula is accurate to 4% or better up to 40° apparent field of view, and has a 10% error for 60°. Since
M
=
f
T
f
E
,
{\displaystyle \ M={\frac {\ f_{\mathsf {T}}\ }{f_{\mathsf {E}}}}\ ,}
where:
f
T
{\displaystyle \ f_{\mathsf {T}}\ }
is the focal length of the telescope;
f
E
{\displaystyle \ f_{\mathsf {E}}\ }
is the focal length of the eyepiece, expressed in the same units of measurement as
f
T
;
{\displaystyle \ f_{\mathsf {T}}\ ;}
The true field of view even without knowing the apparent field of view, given by:
T
F
O
V
≈
A
F
O
V
[
f
T
f
E
]
=
A
F
O
V
×
f
E
f
T
.
{\displaystyle T_{\mathsf {FOV}}\approx {\frac {A_{\mathsf {FOV}}}{\ \left[{\frac {f_{\mathsf {T}}}{\ f_{\mathsf {E}}\ }}\right]\ }}=A_{\mathsf {FOV}}\times {\frac {\ f_{\mathsf {E}}\ }{f_{\mathsf {T}}}}~.}
The focal length of the telescope objective,
f
T
,
{\displaystyle \ f_{\mathsf {T}}\ ,}
is the diameter of the objective times the focal ratio. It represents the distance at which the mirror or objective lens will cause light from a star to converge onto a single point (aberrations excepted). If the apparent field of view is unknown, the actual field of view can be approximately found using:
T
F
O
V
≈
57.3
d
f
T
{\displaystyle \ T_{\mathsf {FOV}}~\approx ~{\frac {\ 57.3\ d\ }{f_{\mathsf {T}}}}\ }
where:
T
F
O
V
{\displaystyle \ T_{\mathsf {FOV}}\ }
is the actual field of view, calculated in degrees.
d
{\displaystyle \ d\ }
is the diameter of the eyepiece field stop in mm.
f
T
{\displaystyle \ f_{\mathsf {T}}\ }
is the focal length of the telescope, in mm. The second formula is actually more accurate, but field stop size is not usually specified by most manufacturers. The first formula will not be accurate if the field is not flat, or is higher than 60° which is common for most ultra-wide eyepiece design. The above formulas are approximations. The ISO 14132-1:2002 standard gives the exact calculation for apparent field of view,
A
F
O
V
,
{\displaystyle \ A_{\mathsf {FOV}}\ ,}
from the true field of view,
T
F
O
V
,
{\displaystyle \ T_{\mathsf {FOV}}\ ,}
as:
tan
(
A
F
O
V
2
)
=
M
×
tan
(
T
F
O
V
2
)
.
{\displaystyle \ \tan \left({\frac {\ A_{\mathsf {FOV}}\ }{2}}\right)=M\times \tan \left({\frac {\ T_{\mathsf {FOV}}\ }{2}}\right)~.}
If a diagonal or Barlow lens is used before the eyepiece, the eyepiece's field of view may be slightly restricted. This occurs when the preceding lens has a narrower field stop than the eyepiece's, causing the obstruction in the front to act as a smaller field stop in front of the eyepiece. The exact relationship is given by
A
F
O
V
=
2
×
arctan
(
d
2
×
f
E
)
.
{\displaystyle A_{\mathsf {FOV}}~=~2\times \arctan \left({\frac {d}{\ 2\times f_{\mathsf {E}}\ }}\right)~.}
An occasionally used approximation is
A
F
O
V
≈
57.3
∘
×
d
f
E
.
{\displaystyle A_{\mathsf {FOV}}~~\approx ~~57.3^{\circ }\times {\frac {d}{\ f_{\mathsf {E}}\ }}~.}