Re: How to "add" MTFs?

[T3D John Ohrt <johrt@xxxxxxx>]

T3D john bercovitz wrote:

>  I can see adding resolutions (eg in lines per mm) in quadrature as being
> at the least a very good approximation, but I can't see through to it
> for adding contrasts.  When I said I would think that contrasts would
> multiply (at each spatial frequency), I was thinking along the lines of
> how you find the transmission of a combined pair of filters by multiply-
> ing the transmission of each (in percent, eg) together at each wavelength.
> I guess you don't buy this as being similar?

Well, I assumed it was similar, but then I could be wrong.  My logic was that
resolution is equivalent to measuring the highest lpm at which a specific
modulation transfer could be achieved, whereas MTF measures the modulation
transfer for each of a range of lpm.  However the lines in resolution are
square wave am and the lines in MTF are sinewave am.  And I am close to
positive that you combine resolutions as RSS of the inverses.

>
>
> Could you illustrate with some numbers how you would add modulations
> in quadrature?  I'm not sure how to approach this.  I guess I follow a
> sample calculation better than an explanation sometimes.

Well, unlike the radio astronomy example where the combination is coherent,
here the combination is incoherent.

> > Comments from the pro's please.
>
> I'd settle for a good rationale.  8-)

Me too.  I can see how the argument of multiplicative combination might be
valid.

As for combining a sequence of lens subsystems, it is readily doable in
theory and in practise because the instrument that I worked on required both
the calculation and measurement as proof of workmanship.  Leitz easily met
all workmanship requirements, but as the optics engineer put it "He doesn't
know if anyone else could."

Maybe Peter can do all our research <grin>.

Regards,

--

John Ohrt * Toronto * ON * Canada






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