Understand the relationship
The reasoning behind the result
Apparent field and true field describe different angles
TFOV≈AFOV/M
Apparent field AFOV is the angular width of the view presented by the eyepiece. True field TFOV is the angular width of sky included in that view. Dividing apparent field by angular magnification M gives a convenient estimate of the sky field.
The division assumes a simple angular mapping across the field. Real eyepiece distortion means it is not generally an exact identity, especially for wide apparent fields. The inverse apparent-field result is therefore an approximate requirement under the same mapping, not a manufacturer's specification or a guarantee of the desired sky field.
A field stop limits the visible focal-plane image
TFOVparaxial=(s/F)·180/π
The field stop bounds the circular portion of the telescope's focal-plane image admitted by the eyepiece. In the paraxial mapping, effective stop diameter s divided by effective telescope focal length F gives the field in radians; multiplying by 180/π converts it to degrees. Both lengths must be in the same unit, here millimetres.
The calculator also lists 2 arctan(s/(2F)) in degrees as a separate ideal rectilinear-projection comparison. This is not an automatic correction for a real telescope or eyepiece: its mapping assumption differs. The difference exposes the small-angle approximation and should not be mistaken for a measured field uncertainty. Optical distortion, vignetting and the meaning of a manufacturer's effective stop remain relevant.
Reverse solves retain the same assumptions
srequired=F·TFOVtarget·π/180; AFOVrequired≈M·TFOVtarget
A desired sky field and effective telescope focal length determine the required paraxial field-stop diameter. A desired field and magnification determine the approximate required apparent field. Each target is solved in its own method so a field-stop dimension is never confused with a viewing angle.
The result does not assert that an eyepiece with that stop fits a particular barrel or focuser. Housing dimensions, field-stop placement, telescope baffles, aberrations and illumination are not inferred. An apparent-field requirement reaching 180 degrees or more is reported as outside this ordinary eyepiece-field model.
Follow the numbers
Two starting measurements that need not give the same estimate
- An eyepiece with an entered 70-degree apparent field at 100x gives TFOV≈70/100=0.7 degrees, or 42 arcminutes.
- A separately entered effective field stop of 12 mm at a 1,000 mm focal length gives 0.012 radians, or about 0.687549354 degrees. The calculator does not silently force those different supplied descriptions to agree.
- For a one-degree target at 1,000 mm, the paraxial required field stop is 1,000×π/180≈17.4532925 mm.
Use the method supported by the actual available specification and retain its approximation.
Quick guide
How to use this calculator
- Choose the starting data that is actually known; field-stop and apparent-field methods use different inputs.
- Enter named rows using the format described next to the field. The two angle inputs always use degrees.
- Use effective telescope focal length after any independently known accessory factor, and an effective field-stop diameter appropriate to the eyepiece.
- Read the method and its assumptions. A calculated field does not establish sharpness, illumination, focus or a compatible physical eyepiece.
Calculation method
Calculation and interpretation
Keep apparent eyepiece field, angular magnification, focal-plane field stop and sky field distinct.
TFOV≈AFOV/M; TFOVparaxial=(180/π)·s/F; starget=F·TFOVtarget·π/180; AFOVtarget≈M·TFOVtarget.
Worked example
Two starting measurements that need not give the same estimate
Use the method supported by the actual available specification and retain its approximation.
TFOV≈AFOV/M; TFOVparaxial=(180/π)·s/F; starget=F·TFOVtarget·π/180; AFOVtarget≈M·TFOVtarget.
Supported inputs
Precision and limits
Optical mapping estimates
Apparent-field division and field-stop paraxial mapping are approximations. The alternate rectilinear projection is another ideal model, not a measured correction or uncertainty bound.
Field size is not image quality
The calculation does not establish edge sharpness, illumination, optical compatibility, eye relief, barrel fit or safe viewing. Actual camera sensor fields use a separate imaging workflow.
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