Physics · Mirrors and Lenses

Optical Resolution / Imaging Limits

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What you learned

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Read next: Double-Slit InterferenceCompare another aperture pattern

Key takeaway

A finite aperture makes each focused point a diffraction blur with a measurable width.
A larger aperture or shorter wavelength narrows the blur; a longer wavelength or smaller aperture broadens it.
Two points are resolved only when their spacing is large enough compared with the Rayleigh blur scale.
Moving the detector sample reads the profile but does not change the optical resolution limit.

Common misconception

Correct focus is necessary, but it is not enough: diffraction from the finite aperture still limits how much detail the image can separate.

Correct focus removes defocus blur, but it does not remove diffraction from a finite aperture.

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Another aperture patternOptics

Double-Slit Interference

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Compare image systemsMirrors and Lenses

Lens Imaging

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Single-aperture limitOptics

Diffraction

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Equation snapshotResolution comparison · Image-plane spacingShow 3 equations

Read the point spacing and the Rayleigh blur scale together; neither one alone tells you whether the pair is resolved.

Resolution comparison
$θ_{R} \approx 1.22 \frac{λ}{D}$
Gives a practical angular scale for when two equal diffraction blurs are only just distinguishable.
Image-plane spacing
$s \approx f Δ θ$
Turns the object's angular separation into center-to-center spacing on the detector.
Image-plane blur radius
$r_{R} = f θ_{R} \approx 1.22 \frac{λ f}{D}$
Turns the same diffraction limit into the characteristic radius of one point-spread core on the detector.

Why it behaves this way

Explanation

Even a perfectly focused imaging system does not send one object point to a mathematically perfect point on the detector. Because the aperture is finite, each object point forms a diffraction blur with a real width.

Resolution is therefore a comparison between two distances on the same image plane: how far apart the two image centers are, and how wide each diffraction blur is. On this bench, wavelength and aperture set the blur width, point separation sets the center-to-center spacing, and the detector sample only reads one place on the finished profile.

Key ideas

01A finite aperture turns each object point into a diffraction blur, not a perfect point.

02A larger aperture or a shorter wavelength shrinks that blur, while a smaller aperture or a longer wavelength broadens it.

03Two points are easier to resolve when their detector spacing is large compared with the blur width.

04The Rayleigh limit gives a practical scale for when two equal point sources are only just distinguishable.

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Frozen walkthrough

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Frozen walkthrough

These examples use the live wavelength, aperture, and point spacing from the current image, so the algebra explains the same detector profile you are already seeing.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current wavelength lambda = 550 nm and aperture D = 2.4 mm, what diffraction-limited Rayleigh scale should you expect for two equal point sources?

l amb d a

Wavelength

550 nm nm

D

Aperture diameter

2.4 mm mm

t h e t a_{R}

Rayleigh limit

0.28 mrad mrad

1. Start from the diffraction limit

Use

θ_{R} \approx 1.22 λ / D

for a circular aperture.

2. Substitute the live wavelength and aperture

\theta_R \approx 1.22 \dfrac{550 nm}{2.4 mm} = 0.28 mrad.

3. Turn that angular limit into a detector blur size

With the fixed focal length, the same limit maps to an image-plane blur radius of 33.55 um.

Current diffraction scale

θ_{R} \approx 0.28 m r a d

and

r_{R} \approx 33.55 u m

The current pair is at or above the Rayleigh threshold, so the detector profile can sustain a visible dip between the peaks.

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Accessibility

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The simulation shows two distant point sources on the left, one finite lens aperture in the middle, and one detector strip on the right. Each source forms a diffraction-limited blur on the detector rather than a perfect point.

Optional overlays show the aperture diameter on the lens, the current point-spread centers on the detector, and the Rayleigh blur scale around those centers. A movable detector sample marks one detector position and reports the current normalized exposure there.

Graph summary

The graph shows normalized exposure against detector height, with one combined profile and two component profiles for the individual point-spread contributions.

Hovering the graph previews the matching detector position on the stage, so the profile stays linked to the same image plane rather than turning into a time plot.

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Starter track

Step 5 of 5

Wave Optics

Optical Resolution / Imaging Limits appears later in this track, so it is cleaner to start from the beginning first.

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