Choosing Binning for a Small-Telescope Survey
A 0.40 m f/10 telescope feeds a 1024×1024 CCD with 6.0 µm pixels. The site's median seeing is 2.5 arcsec FWHM. You are planning a survey of a 3.0 arcmin × 3.0 arcmin field, targeting faint point sources with a broadband V filter. The camera offers 1×1, 2×2, and 3×3 on-chip binning. Read noise is 5 e− per binned pixel, dark current is 0.01 e− pixel−1 s−1, and the sky background is 80 e− pixel−1 s−1 in the unbinned mode. Exposure overhead is 8 s per pointing. A colleague wants unbinned images to preserve the sharpest possible resolution; another wants 3×3 binning to cover the field faster. The telescope's tracking is good to 0.3 arcsec rms over a 10-minute exposure, and the filter wheel has both a broad V filter and a narrow Hα filter.
1. Compute the unbinned plate scale and field of view. Does the requested 3.0 arcmin square field fit?
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Focal length f = 0.40 m × 10 = 4.0 m. Unbinned plate scale = 206,265 × pixel size / f = 206,265 × 6.0×10^-6 m / 4.0 m = 0.309 arcsec/pixel. A 1024-pixel axis covers 1024 × 0.309 = 317 arcsec = 5.28 arcmin. The requested 3.0×3.0 arcmin field is 180 arcsec on a side, or about 582 unbinned pixels, so it fits comfortably with room for dithering. Binning changes the field coverage per pixel but not the total field of the CCD: 2×2 and 3×3 still cover the same 5.28 arcmin, just with coarser sampling and fewer pixels. So the field-size argument does not by itself force 3×3 binning.
2. Compare 1×1, 2×2, and 3×3 binning for sampling and faint-source signal-to-noise. What do you recommend?
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Sampling: the unbinned scale is 0.309 arcsec/pixel, about 8 pixels per 2.5 arcsec FWHM, which is oversampled. Nyquist-style sampling wants roughly 2–3 pixels per FWHM, or about 1 arcsec/pixel, so 3×3 (0.928 arcsec/pixel) is well matched; 2×2 (0.618 arcsec/pixel) is also acceptable. For faint point sources, binning increases signal and sky per pixel by the same factor while read noise stays per binned pixel. In a read-noise-limited case, 3×3 improves S/N per binned pixel; in a sky-limited case, total S/N is nearly unchanged. Since the sky is 80 e−/pixel/s and read noise is 5 e−, read noise is not dominant for long exposures, so the gain is modest. Recommendation: 2×2 or 3×3, not 1×1; 3×3 is reasonable for the faint survey if 0.93 arcsec sampling is acceptable.
3. How would your recommendation change for narrowband Hα imaging of an extended nebula?
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For narrowband Hα imaging of an extended nebula, resolution of fine structure and sky-background subtraction matter more than read noise. The narrow filter admits less continuum, so exposures are longer and the source may be faint and extended. Binning too aggressively (3×3) blurs small knots and makes accurate background modeling harder; 2×2 is a better compromise at 0.62 arcsec/pixel, still well sampled relative to 2.5 arcsec seeing. If the nebula is very faint and read-noise-limited, 3×3 may be justified, but only after checking that the filter bandpass excludes bright sky lines. Tracking error of 0.3 arcsec rms is below one unbinned pixel per short exposure but can smear over 10 minutes; that favors slightly coarser sampling, not finer.