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Exactly the same happened to me as it did to you: I was reading the book, and quite following everything that I was reading, until that bit with the defocus blur. My issue was very specifically with the following bits: lower_left_corner: look_from - half_width*focus_dist*u - half_height*focus_dist*v - focus_dist*w, horizontal: 2.0*half_width*focus_dist*u, ...

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I didn't get this part: That way each ray would just multiply its solid angle by its radiance value, and you'd get an "Irradiance" value of W/m^2. I'll try to explain how the whole thing works though. You have a light source, it emits light rays. Those light rays bounce around the scene and eventually end up at your camera film. So at the end of the ...

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I have found the issue. The gamma correction was the correct value, the same as in the book (1/2), but the light source had the brightness of 1.0f. The book had set the light's brightness to 18.0f for all color channels. This would introduce color overflow if left at that, and the very light areas (above 1.0f, and subsequently when converted, outside the ...

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Since you seem to want an explanation in terms of irradiance, consider both the radiance and irradiance definitions: $$E = \frac{d\Phi}{dA}, \quad L = \frac{d^2\Phi}{d\omega dA^{\perp}}$$ We can reformulate the radiance definition as: $$d^2\Phi = L \cos\theta d\omega dA$$ Integrating both sides over the solid angle $d\omega$ (in the sense of Lebesgue-...

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The two cosine terms basically refer to the foreshortening effect which says: The irradiance falling onto a patch must be modified by the cosine of the angle of the patch to the source. Now from the definition of the irradiance: irradiance is flux per unit area, therefore: Reordering it gives: which is the definition of radiance, with the same cosine ...

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Your main idea is more or less correct. The cosine hidden in the projected area measure $dA^\perp = dA\cos(θ)$ compensates the weakening of irradiance due to incident angle (the Lambert's cosine law). This makes radiance independent from the incident angle. My guess is that the main motivation was to make it more practical to work with. The cosine in the ...

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