Airy Disk & Pixel Sampling Simulator
Explore how wavelength, numerical aperture, magnification, pixel size, and binning affect the relationship between the Airy disk and Nyquist sampling. Click 📖 Learn for detailed explanations of each control and visualization.
📷 Camera Pixel Size
The camera’s physical pixel size determines how finely you sample the magnified image. Smaller pixels (3.7 µm) sample more densely but collect fewer photons per pixel.
The pixel size you see here is at the sensor plane—the objective’s magnification projects and enlarges the Airy disk onto these pixels.
🔬 Objective Selection
The objective sets two critical parameters: NA (determines Airy disk size) and Magnification (projects/enlarges that disk onto the camera).
High NA = smaller Airy disk = finer resolution. High magnification = larger projection onto camera = more pixels per Airy disk.
🌈 Emission Wavelength
The Airy disk diameter scales linearly with wavelength. Blue light (450 nm) produces a smaller disk than red light (700 nm), enabling finer resolution.
Set this to your fluorophore’s emission peak—this determines the actual size of point sources in your image.
🔆 Numerical Aperture
NA is the most critical factor for resolution. Airy disk ∝ 1/NA—doubling the NA halves the Airy disk diameter, dramatically improving resolution.
High-NA objectives (1.2–1.45) require immersion media and have shorter working distance, but provide the finest resolution possible.
NA does NOT affect magnification—two 60× objectives can have very different NA values and thus different resolution limits.
🔍 Magnification — The Optical Bridge
Magnification does NOT change resolution—it only enlarges the image (including the Airy disk) onto the camera sensor.
Its role is to match the optical resolution to the detector’s sampling. The Airy disk at the sample is projected onto the camera enlarged by this factor.
At the camera: Airy disk (projected) = Airy disk (sample) × Magnification
Pixel sampling at sample = Camera pixel size ÷ Magnification
🔲 Camera Pixel Size
This is the physical size of each pixel on the sensor. Smaller pixels sample more finely but collect fewer photons.
The effective sampling at the sample depends on magnification: Sample/pixel = Pixel size ÷ Magnification
For a 6.5 µm pixel at 25×: 6500 nm ÷ 25 = 260 nm per pixel at the sample.
🔳 Binning — Signal vs. Resolution Trade-off
Binning combines adjacent pixels into larger “super-pixels.” 2×2 binning combines 4 pixels; 4×4 combines 16 pixels.
Benefits: Larger effective pixel = more photons collected per readout = improved signal for weak samples.
Cost: Coarser sampling = reduced spatial resolution. Also, read noise adds from each physical pixel—4 pixels binned means 4× the read noise variance.
Best practice: Optically matching camera pixel to Airy disk (via magnification choice) is always preferable to binning. Use binning only when optical matching isn’t possible or when signal is critically weak.
📊 Understanding Nyquist Sampling
The Nyquist-Shannon theorem states you need at least 2 samples per cycle to reconstruct a signal. For microscopy, this means ≥2 pixels per resolution element (the Airy disk radius).
Undersampled (ratio < 2): Pixels are too large—you’re discarding optical resolution that the objective provides. Information is lost.
Optimal (ratio 2.0–2.5): Perfect match—capturing all the optical information while maximizing photons per pixel.
Oversampled (ratio > 3): Pixels are unnecessarily small—no extra information, but fewer photons per pixel = lower signal-to-noise.
🎯 What You’re Seeing
The colored disk is the Airy pattern—the fundamental image of a point source. The dashed gold circle shows the Nyquist sampling limit (2× pixel size)—the smallest feature your detector can resolve. For optimal sampling, the Airy disk should be about twice the diameter of the gold circle, spanning 4–5 pixels across. If the Airy disk is smaller than the gold circle, you’re undersampled and losing optical resolution.🔬 The Critical Relationship
This visualization shows the interplay between optical resolution (the Airy disk set by physics) and detector sampling (the pixel grid set by your camera + magnification).
The Airy disk is the smallest possible image of a point—determined entirely by wavelength and NA. No amount of camera or magnification change affects its size at the sample.
The pixel grid shows how your camera samples this pattern. Magnification projects and enlarges the Airy disk onto the camera—higher magnification = more pixels spanning the same Airy disk.
The Nyquist circle (gold dashed) represents 2× your sampling interval—the smallest feature your detector can resolve. For optimal sampling, the Airy disk should be larger than this circle (~2× diameter). If the Airy disk is smaller, your pixels are too coarse and you’re losing optical resolution.
🎯 Airy Disk Diameter
The full width of the central maximum: 1.22 × λ / NA
This is the physical size at the sample plane—the smallest resolvable point. It represents where ~84% of the light from a point source is concentrated.
📏 Rayleigh Resolution
The minimum separation to distinguish two points: 0.61 × λ / NA
This is half the Airy disk diameter—when two Airy disks are separated by this distance, their first minima align and you can just barely tell them apart.
🔲 Sample per Pixel
How much sample each pixel represents: Camera pixel ÷ Magnification
This is your effective sampling interval at the sample plane. Compare this to the resolution limit—ideally, the resolution should be ~2× this value.
📊 Nyquist Sampling Limit
The smallest feature your detector can resolve: 2 × Pixel size
Any feature smaller than this will be aliased or unresolved by your camera. The optical resolution should be ≥ this value—if the optics resolve finer than this, you’re undersampled and losing information.
🎯 Pixels per Airy Disk
How many pixels span one Airy disk diameter.
Optimal: 4–5 pixels across the Airy disk ensures Nyquist sampling while maximizing signal per pixel.
Too few (< 3): Undersampled. Too many (> 6): Oversampled.
🔳 Effective Pixel at Camera
Physical pixel size × binning factor.
With 2×2 binning, a 6.5 µm pixel becomes 13 µm effective. This collects 4× more photons but samples half as finely.
Note: Binning also means 4× read noise variance—problematic for very weak signals where read noise dominates.