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Downsample it and then up sample and see how different (e.g. mean squared error over the pixels) it is? (Or equivalently (assuming anti-aliasing in the sampling version), apply a low pass filter and compare.

Those are just heuristics, you'd have to try it to see how well they work.

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thank you, I tried with downsample and up sample it with opencv using INTER_AREA then compare them with SSMI, but it still not work well. Could you tell me what low pass filter you applied?

Use the pixel MSE, not SSMI - I'm not really familiar with it, but it appears to be more about structure or perception. This is not what you care about, you want to see how much fine detail gets lost. You'll have to play around with it, I would just try to Gaussian blur with different radii to see what works.

Alternatively (though roughly equivalent) you could try some kind of edge detection (and then summing the output) - especially if you're talking about blurred text, I'd expect there to be fewer hard edges in a blurry image

woah, so SSMI is wrong metrics. thanks a lot. I will try it.

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