MVLscope CONCEPT 05 · 12–15 MINUTES
More pixels. More detail?
Sampling & Digital Images — When More Pixels Help
What the optics deliver
Ideal continuous intensity after diffraction. Same specimen and fixed display scale.
What the detector samples
From specimen to pixels
Named 3D optical pathSpecimen → objective → tube lens → camera pixels → digital image. Change the detector pitch above to see the recorded pattern.
3D loads on demand. All detector experiments work without it.
The objective and tube lens project the fluorescence image onto the camera. Each pixel integrates light over an area.
Your sampling evidence
Make a defensible acquisition
Your lesson record
Research notes · sampling, model limits & sources
Match the detector to the optical image
Specimen pixel pitch = camera pitch × binning / objective magnification, with a 1× relay. For ideal incoherent widefield fluorescence at 520 nm, optical cutoff f꜀ = 2NA/λ. The full-band sampling target is p ≤ 1/(2f꜀) = λ/(4NA). This is a spatial-frequency sampling bound, not the Rayleigh two-point separation criterion. In practice, leave margin and consider noise, aberrations and your measurement task.
The specimen is an original periodic fluorescent intensity pattern. Its two orthogonal sinusoidal components have amplitudes 0.32 and 0.16 around a mean of 0.5, at frequencies f = 1/period and 0.6f. The circular-pupil modulation transfer function is 2/π[acos(ρ) − ρ√(1−ρ²)] for ρ = f/f꜀ below one, and zero above. Pixel-area averaging multiplies each component by sinc(fp). This finite-pixel attenuation is not a perfect anti-alias filter.
The detector displays normalized area averages with a fixed linear green display scale, without photon noise, clipping, pixel gaps or a colour filter array. Binning means combining contiguous areas and normalizing by area; the lesson does not predict the SNR or readout speed of a particular camera. CCD charge binning and sCMOS digital binning behave differently. Small pixels do not recover frequencies the optics have removed.
A fixed 6 µm square teaching crop isolates sampling. A 2× or 4× digital view magnifies its centre without changing recorded values. Edge pixels are cropped. The illustrative 2048 × 2048 native detector has full field width 2048 × camera pitch / magnification; binning reduces output dimensions, not that full field. The 3D scene exaggerates dimensions and slows the light. Its detector grid represents this teaching crop, not all 2048 pixels. Uniform illumination and suitable emission filtering are assumed; this is not a scanned-laser microscope.
Scientific Volume Imaging · Widefield Nyquist sampling ↗
Nikon MicroscopyU · Match camera and microscope resolution ↗
TU Delft · Circular-pupil transfer function, chapter 2 ↗
Hamamatsu · Camera binning and noise ↗