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From: jbm@eos.arc.nasa.gov (Jeffrey Mulligan)
Newsgroups: sci.electronics
Subject: Re: ..but what about _output_ filtering for D/A's?
Message-ID: <7518@eos.arc.nasa.gov>
Date: 26 Oct 90 02:43:43 GMT
References: <1319@beguine.UUCP> <17660123@hpfcdj.HP.COM>
Organization: NASA Ames Research Center, California
Lines: 44

I wrote:

>>As Bob has pointed out, the key here is nonlinearities.  Interestingly,
>>the visual analog of this DOES work, i.e. the sum of two high frequency
>>gratings (which cannot be resolved) can produce a visible beat.

myers@hpfcdj.HP.COM (Bob Myers) writes:

>Uh, Jeff, I'm still not certain I go along with this - isn't the above
>phenomenon the result of interference (two items of slightly different
>wavelengths - or in this case, spacing - resulting in constructive and
>destructive addition of the signals at a much longer, and hence visible,
>wavelength) rather than intermodulation (the actual multiplication of
>sinusoids of different frequencies)?

You are right up to a point; what you describe is the formation
of a single interference grating.  In practice this is done
using two plane waves of the same frequency, but different orientations
in space.  Two focussed beams enter through different points
in the pupil, with the spacing of the entrance pupils controlling
the spatial frequency on the retina.  The upper limit on spatial
frequency produced is determined by how far apart the beams can
be spaced; sometimes drugs may be used to dilate the pupil.

In the experiments which demonstrated the nonlinearity, two pairs
of beams produced two interference gratings.  The beams were
pulsed so that only one pair was on at a time.  Thus there is
no interference between the beams making up each of the two gratings.
The pulse rate was high ( > 1KHz ), so the gratings were
superimposed as far as the visual system is concerned.

This is pretty much state-of-the-art research which has been
done at the University of Rochester.  The results about the
nonlinearity are still unpublished, although they have been
presented at several scientific meetings.  There are some
papers out of the same lab in which high-frequency laser
interference gratings generated visible low-frequency aliases
with the photoreceptor sampling array.

-- 

	Jeff Mulligan (jbm@eos.arc.nasa.gov)
	NASA/Ames Research Ctr., Mail Stop 262-2, Moffett Field CA, 94035
	(415) 604-3745