How is an HDR radiance map constructed from exposures?

What's really being asked

The interviewer wants the algorithmic recovery of a radiance map and a precise statement of why the Camera Response Function is central.

The full answer

High Dynamic Range imaging represents the full range of light in a scene, far wider than a single 8-bit exposure can capture, by combining bracketed exposures. The core problem is that recorded pixel values are a nonlinear function of scene radiance times exposure time, defined by the Camera Response Function. The Debevec and Malik method recovers the inverse CRF by sampling pixels that appear across multiple exposures and solving a least-squares system, with a smoothness constraint on the response curve and a weighting that emphasizes mid-range values, to obtain a mapping from pixel value to log radiance. With the inverse CRF known, you linearize every exposure into radiance, divide by its known exposure time to put all frames on a common scale, and merge them pixel by pixel using a weighted average that gives well-exposed pixels high weight and suppresses near-saturated or near-black, noisy pixels. The output is a floating-point radiance map, the HDR image proper, which can then be tone mapped for display.

The mistakes people make

Averaging the raw, gamma-encoded pixel values, which ignores the nonlinear CRF and is physically wrong. Assuming the response is linear. Confusing the radiance map with the tone-mapped display image.

What usually comes next

Why the smoothness term and weighting matter, why RAW data can bypass CRF estimation, ghost removal for non-static scenes, and the choice of weighting function.

A concrete example

Given five bracketed shots of a cathedral interior with bright windows, you sample matching pixels, solve for the inverse CRF, linearize each frame, scale by exposure, and merge so the radiance map records both the dim pews and the brilliant stained glass in one floating-point image, ready to tone map.