Before a computer can “see” an image, that image has to be created. This process starts with light. Light travels from a source, like the sun, bounces off objects in the world, and some of it streams into a camera. For our purposes, we can think of light as traveling in straight lines, called rays.

The simplest way to form an image is to let these rays pass through a tiny opening and project them onto a surface. This is the principle behind a camera obscura, or pinhole camera. It creates a naturally focused, but inverted, image of the outside world. This simple model is the foundation for understanding how all cameras, from your phone to a high-end DSLR, fundamentally work.

To work with images computationally, we need a mathematical model. The pinhole camera model provides a simple geometric description of how a 3D scene is projected onto a 2D image. Imagine a box with a tiny hole (the aperture) on one side and a light-sensitive sensor (the image plane) on the opposite side. A ray of light from a point in the 3D world travels through the aperture and strikes a single point on the image plane.

The geometry of this setup can be described using similar triangles. The relationship between a 3D point's coordinates $(X, Y, Z)$ in the world and its projected 2D coordinates $(x, y)$ on the image plane is defined by the camera's focal length, $f$.

The inversion is a real physical phenomenon, but for computational convenience, we often imagine a "virtual" image plane in front of the pinhole at a distance $f$. This gets rid of the negative sign in the equations, making the math a bit cleaner while representing the same geometric projection.

A pinhole creates a perfectly focused image, but it lets in very little light, making the image dim. To capture brighter images, we need to gather more light. This is where lenses come in. A lens is a piece of curved glass that can bend light rays, converging them to a single point of focus.

Unlike a pinhole which has an infinite depth of field (everything is in focus), a lens can only perfectly focus objects at a specific distance. The relationship between the object distance, the image distance, and the focal length of a simple, ideal lens is described by the thin lens equation.

Once light is focused onto the sensor, we need to measure it. The image sensor in a digital camera is a grid of millions of tiny light-sensitive elements called photosites. Each photosite measures the amount of light that hits it and converts that measurement into a digital value. This process is the domain of radiometry and photometry.

In simple terms, radiometry deals with the physics of light energy. Key quantities include:

• Radiant Flux ($\\\Phi$): The total energy radiated from a source per unit time, measured in watts (W).
• Irradiance ($E$): The radiant flux received by a surface per unit area, measured in W/m². This is what the camera sensor measures—how much light power falls on each pixel.
• Radiance ($L$): The radiant flux emitted or reflected by a point on a surface in a particular direction. This describes how bright a surface appears. An image is essentially a 2D map of the radiance of the scene from the camera's viewpoint.

Finally, to capture color, camera sensors use a color filter array. The most common is the Bayer filter, which places a red, green, or blue filter over each photosite, making it sensitive to only that color. The camera's processor then interpolates these values to create a full-color image. These fundamental principles of light, optics, and measurement are the building blocks of every image a computer vision system analyzes.

These concepts form the physical and mathematical basis for how digital images are created.