Field of View Lab

Frame the sky with confidence.

Explore exact field geometry and see how image scale compares with your local seeing. Results update here in the browser.

Catalogue presets are sourced from MySQL and copied into local calculator state. Ordinary control changes never wait for the network; target illustrations are scaled from catalogue angles but remain visual guides rather than calibrated sky-survey imagery.

Current field

2.24 degrees horizontal by 1.50 degrees vertical134.6 arcminutes horizontal by 89.9 arcminutes vertical

Andromeda Galaxy (M31): extends beyond the centred sensor frame.

Diagonal field: 2.70 degrees161.9 arcminutes
Image scale: 1.29 arcseconds per output pixelEquivalent output pitch 3.76 micrometres

Proportional sky geometry

Target framing simulator

Compare the catalogue target footprint with the exact sensor field. North is up and east is left. Catalogue position angles run east from north; positive frame rotations are clockwise.

Display zoom

Magnifies only the drawing; field-of-view calculations and fit remain unchanged.

Frame rotation

Rotates the sensor outline around the centred target; it does not alter the calculated field dimensions.

Sensor orientation

LandscapePortrait

Portrait swaps the displayed sensor axes without changing the camera or optical calculation.

Extends beyond frameCentred total clearance: -37.8′ horizontal, -1.90° vertical. Negative values indicate cropping.

Illustrative representation. The target artwork is recognisable but is not a calibrated sky survey and does not represent surface brightness or faint extensions.

Target footprint: Andromeda Galaxy (M31), 3.33° × 1.18°; catalogue position angle 35 degrees east of north.
Displayed sensor field: 2.24° × 1.50°, landscape, frame rotated 0 degrees.
Centred geometric fit: Extends beyond the frame. This footprint estimate does not account for faint extensions, brightness, tracking, focus, or processing.
Display guide: 1.00× visual zoom only; 1.0° grid and 30′ scale bar. North is up and east is left.
Sources and credit: Astrotools target illustration, CC BY 4.0. Asset licence Angular-size source, verified 2026-07-30.

Calculated now

Imaging results

Full precision is retained; values below are rounded for display.

Sensor size: 23.50 × 15.70 mm28.26 mm diagonal
Effective optics: f/7.5600.00 mm focal length
Sampling: 1.55 output pixels per full width at half maximum2.0 arcseconds stated seeingLikely undersampled for the stated seeingTracking, focus, optics, processing, and target type also affect the useful sampling.

Effective optics

Effective focal length — symbolic

f_{e} = f_{n} \prod_{i = 1}^{n} m_{i}

Effective focal length — current values

600 mm \times 1 \approx 600 mm

Effective focal ratio — symbolic

N_{e} = \frac{f_{e}}{D}

Effective focal ratio — current values

\frac{600 mm}{80 mm} \approx 7.5

In words

Multiply native focal length by every optical factor, then divide the effective focal length by aperture to obtain the effective f-number.

Variables and units

f_n: Native telescope focal lengthUnit: millimetres
f_e: Effective focal length after every modifierUnit: millimetres
m_i: Each ordered reducer, flattener, Barlow, or custom factorUnit: dimensionless multiplier
i, n: Modifier index and total number of factors; an empty product equals oneUnit: integer index and count
D: Nominal telescope apertureUnit: millimetres
N_e: Effective focal ratioUnit: dimensionless f-number

Final result

600.00 mm effective focal length; f/7.5

Interpretation

This effective focal length drives both framing and sampling. Reducers shorten it and Barlows lengthen it. In direct-focal-length mode, aperture alone does not alter the field.

Achieved spacing can change the actual modifier factor and geometric f-number. Obstruction, transmission, and vignetting affect delivered light or usable field and are not modelled.

Sensor geometry

Supplied active dimensions — current values

d_{x} \approx 23.5 mm, d_{y} \approx 15.7 mm

Sensor diagonal — symbolic

d_{d} = \sqrt{{d_{x}}^{2} + {d_{y}}^{2}}

Sensor diagonal — current values

\sqrt{{23.5 mm}^{2} + {15.7 mm}^{2}} \approx 28.261989 mm

In words

Use the supplied active sensor width and height directly, then use Pythagoras for the diagonal.

Variables and units

d_x: Active sensor widthUnit: millimetres
d_y: Active sensor heightUnit: millimetres
d_d: Corner-to-corner sensor diagonalUnit: millimetres

Final result

23.50 mm × 15.70 mm; 28.26 mm diagonal

Interpretation

These are active physical sensor extents. Binning or software resampling changes output sampling, not sensor size or field of view. Pixel-derived dimensions assume square pixels.

Exact field of view

Horizontal, vertical, and diagonal fields — symbolic

\begin{matrix} θ_{x} = 2 \arctan (\frac{d_{x}}{2 f_{e}}) \frac{180 °}{π} \\ θ_{y} = 2 \arctan (\frac{d_{y}}{2 f_{e}}) \frac{180 °}{π} \\ θ_{d} = 2 \arctan (\frac{d_{d}}{2 f_{e}}) \frac{180 °}{π} \end{matrix}

Horizontal, vertical, and diagonal fields — current values

\begin{matrix} θ_{x} \approx 2 \arctan (\frac{23.5 mm}{2 \times 600 mm}) \times \frac{180 °}{π} \approx 2.243798 ° \\ θ_{y} \approx 2 \arctan (\frac{15.7 mm}{2 \times 600 mm}) \times \frac{180 °}{π} \approx 1.499154 ° \\ θ_{d} \approx 2 \arctan (\frac{28.261989 mm}{2 \times 600 mm}) \times \frac{180 °}{π} \approx 2.698322 ° \end{matrix}

Educational small-angle approximation — not used

θ \approx \frac{d}{f_{e}} \frac{180 °}{π}

The small-angle approximation is shown only for education and is not used by the calculator. It increasingly overestimates the field as the angle widens.

In words

For each sensor axis, divide its physical extent by twice the effective focal length, take arctangent, double the angle, and convert radians to degrees.

Variables and units

θ_x, θ_y, θ_d: Horizontal, vertical, and diagonal angular fieldsUnit: degrees, with arcminute equivalents
d_x, d_y, d_d: Sensor width, height, and diagonalUnit: millimetres
f_e: Effective focal lengthUnit: millimetres
π: The circle constant piUnit: dimensionless
θ, d: Generic angle and sensor extent used only in the educational small-angle approximationUnit: degrees for θ; millimetres for d

Final result

2.24 degrees horizontal by 1.50 degrees vertical

134.6 arcminutes horizontal by 89.9 arcminutes vertical

Diagonal: 2.70 degrees, or 161.9 arcminutes

Interpretation

Horizontal and vertical values are ideal edge-to-edge angular spans; diagonal is corner-to-corner. The calculator uses exact arctangent geometry within this ideal rectilinear model.

Real focal length, active area, distortion, and vignetting can make a measured sky footprint differ.

Image scale

Equivalent output pitch — symbolic

s_{e} = s b

Equivalent output pitch — current values

3.76 µm \times 1 \approx 3.76 µm

Image scale — symbolic

ρ = \frac{206.265 s_{e}}{f_{e}}

Image scale — current values

\frac{206.265 \times 3.76}{600 mm} \approx 1.292594 arcsec/output px

In words

Multiply native pixel pitch by the grouping factor, then apply the conventional paraxial plate-scale relation using effective focal length.

Variables and units

s: Native square-pixel pitchUnit: micrometres per native pixel
b: Same grouping factor along each axisUnit: dimensionless positive integer
s_e: Equivalent output sampling pitchUnit: micrometres per output pixel
ρ: Conventional paraxial image scaleUnit: arcseconds per output pixel
206.265: Rounded radians-to-arcseconds factor including the micrometre-to-millimetre conversionUnit: arcsecond millimetres per micrometre
f_e: Effective focal lengthUnit: millimetres

Final result

3.76 µm equivalent output pitch; 1.29″ per output pixel

Interpretation

Near the optical axis, each output sample represents approximately 1.2926 arcseconds of sky. The rounded constant and ideal geometry make this an estimate; calibrated plate scale can vary across a distorted field.

Hardware binning and post-read software resampling have different noise behaviour. Software resampling does not create physically larger pixels, and neither operation changes sensor extent.

Seeing and sampling

Pixels per seeing FWHM — symbolic

P_{FWHM} = \frac{w_{seeing}}{ρ}

Pixels per seeing FWHM — current values

\frac{2 ″}{1.292594 arcsec/output px} \approx 1.547276 output px/FWHM

Qualified sampling assessment — current values

1.547276252249353 < 2 \Rightarrow Likely undersampled for the stated seeing

Qualified sampling assessment — default thresholds

\begin{matrix} Likely undersampled & if P_{FWHM} < 2 \\ Broadly appropriate & if 2 \leq P_{FWHM} \leq 4 \\ Likely oversampled & if P_{FWHM} > 4 \end{matrix}

In words

Divide stated atmospheric seeing FWHM by image scale to estimate how many output samples span that seeing width.

Variables and units

P_FWHM: Estimated output samples across the seeing FWHMUnit: output pixels per FWHM
w_seeing: User-stated atmospheric seeing full width at half maximumUnit: arcseconds
ρ: Image scaleUnit: arcseconds per output pixel

Final result

1.55 output pixels per seeing FWHM

Likely undersampled for the stated seeing

Interpretation

The thresholds are explanatory defaults, not universal laws: fewer than 2 is likely undersampled, 2 through 4 inclusive is broadly appropriate for many conditions, and more than 4 is likely oversampled for the stated seeing.

Tracking and guiding, focus, diffraction and optics, wavelength, exposure, processing method, and target type also affect measured stellar width and useful sampling.

Frame the sky with confidence.

Configure the optical path

Telescope

Optical modifiers

Camera

Capture conditions

Target

Target framing simulator

Imaging results

Equations and interpretation

Effective optics

In words

Variables and units

Final result

Interpretation

Sensor geometry

In words

Variables and units

Final result

Interpretation

Exact field of view

In words

Variables and units

Final result

Interpretation

Image scale

In words

Variables and units

Final result

Interpretation

Seeing and sampling

In words

Variables and units

Final result

Interpretation