An in-depth explanation of the optical, physical, and mathematical principles of image formation
Understanding how light behaves and interacts with surfaces
Wave–particle duality: Light behaves as both electromagnetic waves and as quantized particles (photons). It diffracts and interferes like a wave, yet in photoelectric/photochemical interactions it transfers energy in discrete quanta.
Reflection: When a light ray hits a surface, the angle of incidence equals the angle of reflection. Specular (mirror-like) surfaces reflect sharply, while rough or matte surfaces scatter light diffusely.
Refraction: At a boundary between media of refractive indices n₁, n₂, Snell’s law applies: n₁·sinθ₁ = n₂·sinθ₂. A convex lens focuses parallel rays; a concave lens diverges them. Dispersion through a prism separates wavelengths due to differential refraction.
Absorption: Light intensity decays in an absorbing medium by Beer–Lambert law: I = I₀·e^(–αx), where α is the absorption coefficient.
Scattering: Small particles cause Rayleigh scattering (intensity ∝ 1/λ⁴), explaining blue skies. Larger particles lead to wavelength-independent Mie scattering.
Diffusion (Lambertian reflection): Diffuse reflectors emit equally in all directions: L = E·R/π. Brightness appears constant from all angles on a matte surface.
Lens geometry and aperture control in cameras
Thin-lens equation:
1/f = 1/dₒ + 1/dᵢwhere f = focal length, dₒ = object distance, dᵢ = image distance
Magnification: m = -dᵢ / dₒ
Aperture: N = f / D, where D is aperture diameter. Smaller apertures (large N) increase depth-of-field (DOF); larger ones decrease it.
Field of view:
FOV = 2·arctan(H / 2f)For full-frame 35mm sensor (24×36mm), f = 50mm yields ~47° vertical FOV.
Image capture mechanisms in digital and film photography
CMOS/CCD sensors: Pixels generate charges when photons strike them. CCDs shift charges; CMOS amplifies in-pixel. Demosaicing interpolates Bayer-filter data (RGGB: 2 green, 1 red, 1 blue) into RGB images.
Film emulsion: Silver-halide crystals form latent images via photochemical reaction. Development converts latent to visible metallic silver.
Quantifying and understanding light intensity and exposure
Illuminance (Ev): Lux (lumens/m²). Point source: E ≈ I / d².
Luminance (Lv): Candela/m². L = (E_v · R) / π.
Exposure Value (EV):
EV = log₂(N² / t)ISO 100 baseline. 1 EV = 1 stop = 2× exposure change.
Color perception and adaptation in sensors and the human eye
Spectral Sensitivity: RGB filters have different curves from human cones; requires remapping.
Color Temperature: Expressed in Kelvin. Daylight ~5500–6500K (blue); tungsten ~2700–3200K (yellow).
Chromatic Adaptation: Simulated via white balance matrix/gains, matching colors across lights.
Predicting the image using light, optics, and sensor behavior
Lighting: Illuminance from a source: E = I / r², scaled by cosθ if off-axis.
Projection: Projected image height: ≈ (f / Z) × object height.
Sensor Exposure: Photons captured ∝ L × A × t, where A = effective aperture area ∝ (f / N)².
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