Diffraction Limit Discussion Continuation

Started Feb 21, 2014 | Discussions thread
gollywop Veteran Member • Posts: 8,279
Re: So is this one

TomFid wrote:

Sorry, couldn't resist.

Admittedly the cubic fits are problematic. But it's almost as silly to fit a quadratic and discuss significance, treating this as a noisy sampling process. These are engineering measurements with fairly high precision, so presumably the issues with the quadratic fit are due to systematic problems with the model, which we'd expect from first principles, not from underdetermination.

Probably best to stick to just eyeball the raw data, and be satisfied with its 1 stop interval. Or, build a model with a sensible functional form and fit it to a larger sample of body/lens combinations.

I'm hoping that the phrasing I used ("Even if you were to restrict yourself to a quadratic . . .") is not so subtle as to make you think I was suggesting it seriously. Please disabuse me of that hope if you thought otherwise.

As to inventing a curve by eyeballing the data, the results are completely without value. Indeed, the best estimate we have for a maximum is the maximum we have, not one based on speculation. You can then do some half hearted Bayesian modification by saying that you have a diffuse prior that, when taken into account, would suggest that that maximum could be in a range around the data maximum -- maybe even 1 stop. But there's no value to eyeballing a curve.

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