🔭 Astronomy & Optics

ArcSec Matcher

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

Ad Space — 728×90
Ad Space — 320×50

Optical & Sensor Setup

Image Scale & Sampling Verdict

0.54 arcsec / pixel
⚠️
Oversampled

Starlight is spread over too many pixels, reducing signal-to-noise without adding detail.

Effective Focal Length 1,422 mm f/7.0 speed
Effective Pixel Pitch 3.76 μm 1x1 binning
True Field of View (FOV) 56.8' × 38.0' 0.95° × 0.63°
Dawes / Rayleigh Limit 0.57" arcsec Theoretical optical cutoff

Star Profile vs. Sensor Pixel Grid

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

💡 Actionable Recommendation

Your current scale is oversampled for 2.0" seeing. Consider using a focal reducer or 2x2 software binning to boost signal-to-noise ratio per pixel on faint deep-sky targets.

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:

$$\text{Scale } S = 206.265 \times \frac{\text{Pixel Size }(\mu\text{m})}{\text{Effective Focal Length }(\text{mm})}$$

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). Typical seeing ranges from 1.5" (excellent) to 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 to 3 pixels across its FWHM:

$$\text{Ideal Image Scale } S_{\text{ideal}} = \frac{\text{Atmospheric Seeing FWHM}}{2 \text{ to } 3.5}$$

The Three Sampling States

1. Undersampled (> 2.0"/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 (1.0" – 2.0"/px)

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 (< 1.0"/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.