Optical Resolution Calculator
Determines the minimum resolvable distance between two point sources through a microscope or lens using the Rayleigh criterion. Essential for microscopists, optical engineers, and anyone specifying imaging system performance.
Last updated: September 2026
Formula below · 2 sources (optica.org, Wikipedia) · Updated Sep 2026
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About this calculator
The lateral resolution of a microscope objective is d = k·λ / NA, where NA = n·sin θ already includes the refractive index n of the immersion medium. The criterion constant k is 0.61 for Rayleigh (Airy-disk minimum on the neighbouring maximum), 0.5 for Abbe (λ/2NA) and 0.47 for Sparrow. Because NA already contains n, the immersion index is not divided in a second time; instead it caps the NA you can reach: about 0.95 in air, 1.2–1.33 in water and 1.4–1.49 in oil. That is why oil immersion improves resolution — it allows a larger NA. With λ = 550 nm and NA = 1.4 (oil), the Rayleigh limit is 0.61 × 550 / 1.4 = 240 nm.
How to use
Suppose you use a 60× air objective with NA = 0.85 and green light at λ = 550 nm. Step 1: Enter 550 in Light Wavelength. Step 2: Enter 0.85 in Numerical Aperture. Step 3: Select 'air' as Immersion Medium (refractive index = 1.0). The formula gives: d = 0.61 × 550 / 0.85 = (1.22 × 550) / (2 × 0.85) = 671 / 1.70 = 394.7 nm. So the minimum resolvable feature is approximately 395 nm, meaning details closer together than ~0.4 µm will appear merged.
Frequently asked questions
What is the Rayleigh criterion and how does it define optical resolution?
The Rayleigh criterion is a standard definition of the resolution limit for an optical system based on diffraction. It states that two point sources are just resolved when the central bright spot (Airy disk) of one coincides with the first dark ring of the other. At this separation, there is a small but detectable dip in intensity between the two peaks. Resolution better than this limit requires techniques like STED microscopy or structured illumination that circumvent classical diffraction limits.
How does numerical aperture affect the resolution of a microscope objective?
Numerical aperture directly appears in the denominator of the Rayleigh formula, so a higher NA produces a smaller (better) minimum resolvable distance. NA is increased by using objectives that collect light at wider angles and by employing immersion media with higher refractive indices. Oil-immersion objectives can reach NA values above 1.4, roughly doubling the resolution compared to air objectives of similar design. Choosing the right combination of NA and wavelength is the primary lever optical designers use to push imaging systems toward finer detail.
Why does immersion oil improve microscope resolution compared to air?
Immersion oil has a refractive index around 1.515, closely matching that of the glass coverslip, which eliminates refraction at the coverslip–medium interface and allows light to enter the objective at much steeper angles. Because NA = n · sin(α), the higher refractive index directly multiplies the effective NA even if the collection angle stays the same. In contrast, air (n = 1.0) caps the maximum achievable NA below 1.0. Oil immersion is routinely used in high-magnification microscopy (100× objectives) when sub-micron resolution is required for imaging cells, bacteria, or fine tissue structures.