Why is my moving photo blurry?

The shutter is a time window

An exposure gathers light over an interval. It is not an infinitely short instant. In this lab the electronic exposure window is uniform; no moving mechanical shutter curtain is simulated.

Motion spreads the signal

Our toy image translates horizontally at a constant speed. At 800 image pixels per second, a 1/200-second exposure spans 4 pixels of motion. The feature has its own width, and each detector pixel also covers an area.

Rows can start at different moments

A rolling exposure staggers the row intervals. With a 20-millisecond delay from the first row to the last, our full-height stripe shifts 16 pixels from top to bottom. Many row intervals overlap; a scanning beam is not required.

Shorter is not the same as simultaneous

Shorten each exposure to 1/2000 second: its motion extent becomes 0.4 pixels. The 20-millisecond first-to-last delay is unchanged, so the full-height centerline displacement is still 16 pixels.

Stored values can be read later

Global exposure gives the rows a common exposure interval. The sensor can still transfer their stored values in sequence afterward. That transfer alone does not mean the rows captured different moments.

Focus is a different question

A stationary flat target can remain fuzzy when its image does not converge onto the detector plane. Our separate focus bench changes the ideal sensor distance and circular aperture footprint. Shorter exposure does not move the focus plane.

Collecting light and displaying brightness differ

A longer exposure can collect more detected electrons from a stationary patch. Brightness normalization divides by duration to help compare shapes; display gain can brighten the result. Neither operation creates more collected signal.

One capture is one observation

The noise loupe samples photon-count variation and independent read noise using a saved seed. A redraw or brightness change keeps the same sample. Take another sample to make a new observation.

Define the coordinate system

The reference detector has 640 columns and 360 rows, numbered from zero. Coordinates describe the final upright image. Relative motion is measured in image pixels per second, not a measured toy speed in meters per second.

Row timing convention

For row r, c(r) = (r/359 − 1/2)R; reversing scan changes its sign. Start is c − T/2 and end is c + T/2. R is explicitly the first-to-last center delay, not an unqualified manufacturer readout-time specification.

Three different quantities

Per-row motion extent is |v|T. The signed full-height center displacement is vR, with scan direction included. The full capture span is R + T, while the adjacent-row delay is R/359. None of these by itself establishes the frame rate.

A true image integral

The image operator integrates a continuous row signal over the chosen exposure and a one-pixel detector footprint. Toy source pixels are decoded from sRGB into premultiplied linear RGBA and reconstructed as constant cells. Moving foreground coverage and the stationary background are combined in that space. Encoding for display happens last.

Exact within a deliberately narrow model

Translation is constant, horizontal and parallel to a fixed orthographic image plane. Piecewise-polynomial primitives integrate the reconstructed source exactly, including fractional shifts. This does not represent spinning wheels, acceleration, moving perspective, depth-dependent motion or a general camera-shake kernel.

A measurable stripe fixture

The calibration bar is eight pixels wide before motion. At four pixels of motion, detector centers at offsets 0, 2, 4 and 6 receive normalized signals 1, 31/32, 1/2 and 1/32. At sixteen pixels of motion the central value is 1/2. The normalized bar area remains eight pixels, with enough image margin.

Not every feature spans every row

The full-height calibration bar has the complete vR center displacement. The shorter placard on the toy spans fewer row times. Do not attribute the full-image number to every short edge in the picture.

An ideal geometric focus footprint

For the stationary flat target, object distance is 1,000 mm, focal length 8 mm and detector pitch 0.01 mm. Focusing at 500 mm with f/2 produces a geometric footprint diameter of 400/123 ≈ 3.2520 pixels. At f/4 it is half as large. This is a circular footprint diameter, not a Gaussian blur setting.

Focus limits

The flat-target inspector convolves a normalized circular footprint, using 64 × 64 area samples per kernel cell. Diffraction, lens aberrations, color filters, lens breathing, autofocus and portrait-mode processing are omitted. The narrow geometric model does not mean that the smallest possible aperture always gives the sharpest photograph.

Detected electrons, not incident photons

The separate stationary patch has an authored expected detected-electron rate of 20,000 per second at f/2 and illumination multiplier 1. Expected count μ = 20,000Tq(2/N)² already includes detection efficiency; it is not an incident-photon rate or a measurement of a real phone.

Shot noise and read noise

The patch uses P distributed as Poisson(μ), plus independent zero-mean Gaussian read noise with standard deviation 2 electrons. Before clipping, the mean is μ, variance is μ + 4 and input SNR is μ/√(μ + 4). At 10, 100 and 400 expected electrons the SNRs are approximately 2.673, 9.806 and 19.901.

Computational photographs

A phone may combine frames and apply denoising, sharpening, stabilization or other processing. Our display gain is not a complete ISO model, and our single-exposure image is not a reconstruction of a particular phone pipeline. A corrected source image is an estimate, not proof that arbitrary lost information can be recovered.

Sports and playful motion

A short exposure can reduce subject-motion blur. It does not by itself remove row-time distortion or fix missed focus.

Machine vision

Timing matters when cameras measure moving objects. Exposure synchronization, row timing and geometric calibration are separate design questions.

Everyday phone pictures

Steadying the phone can reduce camera motion. Scene light, focus and computational processing still matter; this is not a universal settings recipe.

Keep the motion and row delay fixed. What should a shorter exposure do?

• Shorten the motion smear.
• Refocus the lens automatically.
• Always remove rolling-shutter lean.

At 800 image pixels per second, how far does the image move in 1/200 second?

• 160,000 pixels
• 4 pixels
• 4 seconds

The stripe gets sharper but still leans. Why?

• The physical object must bend.
• This proves a damaged lens.
• Different rows still capture different moments.

A global-exposure sensor transfers its stored rows in sequence afterward. Must that bend a moving object?

• No: the exposure intervals matter.
• Yes: every sequential transfer bends an image.
• No: global exposure has no motion blur.

A stationary print stays fuzzy with the focus set to the wrong distance. What should you change first?

• First-to-last row delay
• Focus setting
• Only the exposure time

Display gain brightens a short capture. Did it collect more electrons?

• Yes: brighter always means more collected light.
• Yes: input SNR rises by the gain.
• No: the existing signal and noise were scaled.

Why is the sample mean not exactly the theoretical mean?

• A finite random sample can differ from its expectation.
• The expected value must be wrong.
• Changing screen size should fix it.

What are source Figure 16 panels c and d?

• New photographs proving perfect recovery
• Processed correction estimates
• The exact settings of our toy scene

Global and rolling exposure differ from subsequent transfer order.

Manufacturer explanation of exposure intervals and stored-value readout. Device-specific specifications are not generalized.

Row-dependent capture under motion changes image geometry.

Primary rolling-shutter geometry paper. Our parallel translation model is independently derived and narrower.

Expected signal, photon shot noise, read noise and gain are different quantities.

Primary sensor characterization standard; model assumptions are explicit. This lab is not an EMVA-compliant measurement.

Image noise is a distribution around an underlying signal.

Course-author imaging notes support the noise/observation distinction; no source diagrams are redistributed.

A camera model can sample light over shutter time and lens position.

Source-owned rendering reference. This implementation uses exact integration for a bounded reconstructed image field.

Thin-lens geometry supports the separate focus-plane calculation.

The geometric cone diameter is derived from the thin-lens relation; diffraction and aberrations are excluded.

Linear-light arithmetic requires decoding nonlinear sRGB.

Source definition of sRGB transfer functions. Display clipping and encoding occur after the signal calculation.

Actual calibration-board captures show motion blur and rolling distortion; correction panels are processed estimates.

Figures 12 and 16, original complete JPEGs, CC BY 4.0. They do not calibrate the authored simulation or establish a universal correction capability.