Camera And Optics Basics

Why this matters

Real-world computer vision performance starts with photons hitting a sensor. Understanding lenses, exposure, and sensors helps you design reliable pipelines, reduce noise and blur, size datasets correctly, and debug issues faster.

• Product CV: Choose lenses and exposure that keep barcodes or labels sharp on a conveyor.
• Robotics: Balance shutter speed against light to avoid motion blur during navigation.
• Mobile CV: Handle rolling shutter and wide-angle distortion in AR and SLAM.
• Research/ML: Collect cleaner data to improve training signal and reduce domain shift.

Who this is for

• Computer Vision Engineers and ML practitioners building vision systems.
• Data scientists labeling or curating image/video datasets.
• Developers integrating cameras into apps, robots, or embedded devices.

Prerequisites

• Basic linear algebra and trigonometry (angles, tangent, arctangent).
• Familiarity with coordinate systems and pixels.
• Optional but helpful: basic Python and NumPy for calibration tasks.

Concept explained simply

A camera turns light into numbers. The lens guides light; the aperture and shutter decide how much and how long; the sensor collects and converts it to pixel values.

• Focal length (f): how strongly the lens converges light. Short f = wide view; long f = narrow view.
• Field of View (FOV): how much of the scene is captured. Roughly: FOV ≈ 2 × arctan(sensor_size / (2f)).
• Aperture (f-number, e.g., f/2.8): affects brightness and depth of field. Smaller f-number = more light, shallower focus.
• Shutter speed (e.g., 1/250 s): exposure time. Faster shutter reduces motion blur but needs more light.
• ISO: sensor gain. Higher ISO brightens but adds noise.
• Sensor size and pixel pitch: larger pixels gather more light and have better signal-to-noise in low light.
• Distortion: wide lenses bend straight lines near edges (barrel); tele can pinch (pincushion). Corrected in calibration.
• Rolling vs global shutter: rolling reads line-by-line (can skew fast motion); global captures at once.
• Color filter array (Bayer): most sensors see through R/G/B filters; requires demosaicing and white balance.

Mental model

Imagine a pinhole camera. Shrink the hole: sharper but darker. Add glass (a lens) to get both sharpness and light. Now control three levers—aperture, shutter, ISO—to hit a target brightness while keeping blur and noise low. Finally, fix the quirks: distortion, color casts, and rolling-shutter artifacts.

Key formulas and quick checks

• Horizontal FOV ≈ 2 × arctan(sensor_width / (2f))
• Exposure change in stops: doubling exposure time = +1 stop; doubling ISO = +1 stop; f-number ×√2 = −1 stop of light
• Radial distortion (one form): r_d = r × (1 + k1 r^2 + k2 r^4 + ...), where r is normalized radius
• Motion blur distance ≈ scene_speed × shutter_time; in pixels ≈ blur_distance / scene_scale_per_pixel

Worked examples

Example 1: Compute horizontal FOV

Given sensor width = 6.3 mm and focal length f = 4.0 mm.

FOV ≈ 2 × arctan(6.3 / (2 × 4.0)) = 2 × arctan(0.7875) ≈ 2 × 38.4° ≈ 76.8°.

Result: about 77° horizontal FOV (wide).

Example 2: Exposure change in stops

From f/4, 1/200 s, ISO 100 to keep same brightness but increase shutter speed to 1/800 s (2 stops faster).

• Need +2 stops from aperture/ISO: options include f/2 (open 2 stops) or ISO 400 (+2 stops), or mix: f/2.8 (+1), ISO 200 (+1).

Result: f/2.8, 1/800 s, ISO 200 is one valid combination.

Example 3: Estimate motion blur in pixels

Object speed = 0.5 m/s, shutter = 1/250 s → blur distance ≈ 0.5 × 0.004 = 0.002 m = 2 mm. If each pixel covers 0.05 mm, blur ≈ 2 / 0.05 = 40 pixels. Too high—use a faster shutter or reduce speed.

Example 4: Distortion quick correction value

Normalized radius r = 0.5, k1 = -0.2, k2 = 0. r_d = 0.5 × (1 + (-0.2) × 0.25) = 0.5 × (1 - 0.05) = 0.475. Points move slightly toward center after correction.

Exercises

These mirror the tasks in the Exercises section below. Try them here first, then check the detailed solutions.

Exercise 1: Lens selection and FOV planning

You have a sensor with 6.4 mm horizontal size and want about 70° horizontal FOV. What focal length should you pick (approximate)? Use f ≈ sensor_width / (2 × tan(FOV/2)).

• Target: round to nearest 0.1 mm.
• Self-check: does a shorter focal length give wider FOV?

Exercise 2: Keep brightness, cut motion blur

Current settings: f/2.8, 1/200 s, ISO 100. You see blur and want 1/800 s (2 stops faster) but keep the same brightness. Propose two valid setting combinations.

• Constraint: noise should be moderate; prefer changing aperture before maxing ISO.

Exercise checklist

• I computed FOV with the correct sensor dimension (horizontal for horizontal FOV).
• I adjusted exposure by exact stops (no guesswork).
• I confirmed trade-offs: faster shutter increases noise or requires wider aperture.

Common mistakes and self-check

• Mixing sensor diagonal with width/height for FOV. Self-check: confirm which FOV you compute (H/V/Diagonal).
• Changing multiple exposure levers without tracking stops. Self-check: write each stop change explicitly.
• Ignoring rolling shutter when objects move fast. Self-check: inspect vertical edges for tilt or skew.
• Assuming higher resolution always helps. Self-check: compare noise and motion blur; sometimes faster shutter at lower resolution wins.
• Skipping lens distortion calibration for wide lenses. Self-check: do straight lines bow near edges? Run a checkerboard calibration if yes.

Practical projects

• Build a FOV calculator: input sensor size and focal length; output H/V/Diagonal FOV and suggested working distance for a target object width.
• Exposure triangle notebook: given desired blur limit (pixels), compute minimum shutter, then solve for aperture/ISO to keep brightness.
• Distortion demo: render a grid, apply simple barrel distortion with a k1 term, then undistort it and measure residual error.

Learning path

• Start: Camera model (pinhole), FOV, exposure triangle.
• Next: Distortion models and camera calibration (intrinsics and extrinsics).
• Then: Photometric effects (white balance, gamma, tone mapping) and RAW vs JPEG.
• Finally: Sensor timing (rolling vs global shutter) and synchronization for multi-camera setups.

Next steps

• Calibrate a real or synthetic camera to estimate focal length, principal point, and distortion.
• Design a data capture plan: choose lens, FOV, and exposure to meet blur and noise limits for your task.
• Document your assumptions (sensor width, pixel size, shutter type) alongside datasets.

Mini challenge

You must read 10 mm-wide text from 1 m away. Your sensor width is 7.2 mm and you want the text to occupy at least 400 pixels horizontally on a 1920 px-wide image. Choose an approximate focal length that satisfies both FOV and sampling. State your assumptions and trade-offs (depth of field vs light). There is no single right answer—justify yours.

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