🔭 Astronomy & Optics

ArcSec Matcher

Match telescope focal length and camera pixel pitch to atmospheric seeing for optimal deep-sky resolution

Optical & Sensor Setup

Image Scale & Sampling Verdict

0.55 arcsec / pixel
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Oversampled (finer than 0.57"/px)

Starlight is spread across 3.7 pixels of the 2" seeing disc, past the 3.5 pixel point where extra pixels stop adding detail. Exposures get longer and per-pixel SNR drops.

Effective Focal Length 1,422 mm f/7.0 focal speed
Effective Pixel Pitch 3.76 μm 1x1 binning
True Field of View (FOV) 56.8' × 37.9' 0.95° × 0.63° deg
Dawes Limit 0.57" arcsec Rayleigh 0.68" at 550 nm

Star Profile vs. Sensor Pixel Grid

Simulated 2.0" seeing FWHM star on pixel matrix
Sensor Pixel Star Profile (FWHM)

💡 Actionable Recommendation

Your image scale of 0.55"/px is oversampled. Try 2x2 hardware or software binning, or a focal reducer, to boost signal-to-noise per pixel.

Understanding Telescope Image Scale & Sampling

What is Image Scale (Arcseconds per Pixel)?

Image scale defines the angular size of the sky covered by a single camera pixel when attached to your telescope. It bridges optics (focal length) and sensors (pixel pitch) using the mathematical relationship:

S ("/px) = 206.265 × pixel pitch (μm) / effective focal length (mm)

The constant 206,265 is the number of arcseconds in one radian. A smaller image scale (e.g., 0.5"/px) gives higher magnification per pixel, while a larger image scale (e.g., 2.5"/px) provides a wider field of view and higher photon density per pixel.

The Atmospheric Seeing Limit (Nyquist Sampling)

Earth's turbulent atmosphere distorts point-source starlight into a blurred Gaussian disk measured in Full Width at Half Maximum (FWHM). This calculator models three cases: 1.2" (excellent), 2.0" (average) and 3.0" (poor).

According to the Nyquist-Shannon Sampling Theorem, to capture the finest detail resolved by your optical system without aliasing, the star profile must span at least 2 pixels across its FWHM, and past roughly 3.5 pixels the extra sampling buys no detail:

Sideal ("/px) = atmospheric seeing FWHM (") / (2 to 3.5)

The Three Sampling States

1. Undersampled (fewer than 2 pixels per FWHM)

Where the line sits: under average 2" seeing, any scale coarser than 1.00"/px; under poor 3" seeing, coarser than 1.50"/px.

Symptom: Square or blocky stars; faint nebula detail is lost across pixel boundaries.

Cause: Short focal length refractor paired with large camera pixels.

Solution: Use drizzling integration in stacking software (e.g., WBPP / Siril) or upgrade to a camera with smaller pixels.

2. Optimal Range (2 to 3.5 pixels per FWHM)

Where the line sits: 0.57"/px to 1.00"/px under average 2" seeing; 0.86"/px to 1.50"/px under poor 3" seeing.

Symptom: Smooth, round stars with maximum resolution and ideal signal-to-noise ratio.

Cause: Perfect match between optical focal length, sensor pixel pitch, and local seeing conditions.

Result: Crisp deep-sky detail with efficient exposure times.

3. Oversampled (more than 3.5 pixels per FWHM)

Where the line sits: under average 2" seeing, any scale finer than 0.57"/px; under excellent 1.2" seeing, finer than 0.34"/px.

Symptom: Bloated, soft stars; long exposure requirements; low signal-to-noise ratio per pixel.

Cause: Long focal length telescope (SCT/RC) with small camera pixels under average seeing.

Solution: Add a focal reducer (e.g., 0.7x) or utilize 2x2 camera binning.

Frequently Asked Questions

Image scale is the angular size of one pixel, in arcseconds, set by sensor pixel pitch and telescope focal length: 206.265 × pixel size in microns ÷ focal length in millimetres. Combined with sensor dimensions it gives the field of view, which determines whether a target fits the frame and whether the system is well sampled.

What image scale should I aim for?

There is no single number: the target scales with your seeing. Aim to spread the star FWHM across 2 to 3.5 pixels, so the ideal image scale is the seeing FWHM divided by 2 to 3.5. Under average 2 arcsecond seeing that is 0.57 to 1.00 arcseconds per pixel; under poor 3 arcsecond seeing it is 0.86 to 1.50. The commonly quoted 1 to 2 arcseconds per pixel is the same rule read against a total FWHM of 2 to 4 arcseconds, which is what many sites deliver once guiding error is included. Finer than the band is oversampling: the same photons spread over more pixels for no extra detail and worse signal-to-noise. Coarser undersamples and makes stars blocky.

What is the difference between image scale and resolution?

Image scale is the sampling rate of your sensor; resolution is the finest detail the system can actually record. Real resolution is limited by aperture (the Dawes or Rayleigh limit), atmospheric seeing, and guiding accuracy. Seeing usually dominates — a finer image scale cannot recover detail the atmosphere has already blurred away.

How do focal reducers and Barlows change the field?

They multiply effective focal length, so a 0.8× reducer shortens focal length by 20%, widening the field and coarsening image scale by the same factor. A 2× Barlow halves the field and halves the arcseconds per pixel. Reducers also alter the required back-focus distance, which affects star shapes at the corners.