Lack of proper gamma compression for the output

[Photosounder]

There's a major but common mistake which makes all the images look wrong. The images are naturally calculated using linear light values but saved as 8-bit sRGB values without any correct conversion from linear values to sRGB (gamma compressed) values. Here's how it should look once that problem is fixed:

This is quite radically different, and you can now see how the beams that cross into the shadows appear as bright as they should. The way to do it is to replace this:
p[0] = p[1] = p[2] = (int)(fminf(sample((float)x / W, (float)y / H) * 255.0f, 255.0f));
with this:
p[0] = p[1] = p[2] = (int)(255. * lsrgb(fminf(sample((float)x / W, (float)y / H), 1.f)));

and add somewhere a function lsrgb that does this:

double lsrgb(double linear)	// converts a [0.0, 1.0] linear value into a [0.0, 1.0] sRGB value
{
	if (linear <= 0.0031308)
		return linear * 12.92;
	else
		return 1.055 * pow(linear, 1.0/2.4) - 0.055;
}

Btw in the image above I also added Gaussian antialiasing which is achieved by adding a Gaussian jitter in the sample() function to x and y independently.

[miloyip]

Thank you for your info.
I am not sure if sRGB chunk is not avaliable in a PNG, how the color is intrepreted.

[Photosounder]

The default way a PNG is interpreted is sRGB. Besides you really wouldn't want an 8-bit linear image, you would see tons of banding in the darks, as if there were about only 4 bits,