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So I may be missing something but I cannot think what it can be.

I have a Sony compact hx9v and an NEX-6. the 16mm on the NEX is very similar to the compact at its widest, so I thought I would compare the shots. With the bigger sensor I thought the NEX would produce a brighter picture.

Both 16 megapixels Both set to f3.5, ISO 100, 1/80, exp 0.

Even with this, the compact produces a brighter picture. I thought that with the bigger sensor the NEX would produce a brighter picture?

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It is not. What you are referring to is sensitivity to light. That is the ISO sensitivity is for and while there is a standard that describes it, digital sensors do not match exactly the posted sensitivity. A site like DxOMark actually measures ISO equivalence as part of its sensor benchmarks and you can commonly see a difference of ±1/3 EVs.

The other independent variable here is that you may be looking at images rather than RAW data. If this is the case, the tone-curve applied to transform the sensor's linear-response can be different and it most likely is. Nearly all cameras have parameters which affect , this, like Contrast, Key and Brightness. Exact parameters and their impact is different between cameras so you cannot simply set them to the same levels and expect the same results.

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Theoretically both images should be the same brightness, even though the NEX sensor is larger, it stills receives same amount of light per unit area both lenses were set to f/3.5. The difference in brightness is due to different processing, there's nothing in the ISO standard that guarantee the same digital brightness values given the same exposure and ISO setting.

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