# 1 stop of DR -how important it is and for what kind of photography

Started Apr 7, 2012 | Discussions thread
Re: JPEG is limited to 8 stops

DigVis wrote:

No, that is not correct. We are still talking about the otherwise noise free case. The DR for an area of N samples (disregarding local clipping) can be defined as sum of saturation capacities / sum of noise. Uncorrelated noise sums as sqrt(N), which gives us a DR increase of N/sqrt(N) = sqrt(N) compared to the DR of the local sample. Quantization noise, however, is highly correlated and therefore sums as N. The DR increase becomes N/N=1, i.e. there is no increase in DR in this case.

This would be true in case of digitizing an analog signal. However, light is already "digitized" by photons. In this case the extent of the effect you are describing would depend on the efficiency of the sensor. For example, if a single photon is detected at exactly 1 LSB, 2 photons as 2 LSBs, etc, then there is no quantization noise in the sensor and the image can be downsampled for a higher DR, provided the sensor is not clipped in highlights.

(In the interest of a full disclosure, photons do not exist before the wave function of light actually hits the sensor. So the sensor does in fact quantize light, but not in the sense relevant to this discussion. It is just the weirdness of quantum mechanics.)

Take for example your example 1/3 LSB signal without noise. Without noise, this value will be quantized to 0 in each of the local samples. The larger the integration area, the larger the quantization error. (The correct value N/3 vs the actual value 0).

The truncation distortion.

In order to get around this, one can decorrelate the quantization noise by adding actual random noise. Once that is done, the DR will increase by a factor of sqrt(N). That by itself is a rather interesting result (add noise -> increase DR), and is basically what dithering is all about.

I do not think this technique actually increases DR. A random noise of 2 LSBs is usually added to the signal to eliminate the truncation distortion you described above. Because such random noise is bigger than the quantization noise, the DR and SNR are decreased, but the distortion is gone. If you then downsample, you would decrease the DR, but never below the original level, because once the random noise becomes less than the quantization noise, the truncation is back and you are back to where you were in the first place.

However, again, because photons are already quantized, with a high quantum efficiency sensor you do not need to add a random noise to remove the truncation error and can increase the DR by downsampling.

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