tonyr wrote: ↑Mon Jul 01, 2019 6:56 pm
Thanks lobaz that is extremely helpful, not just the result but how you derived it.
You are very welcome. However, note that I wanted to keep the formulas as simple as possible. As Dinesh correctly pointed, magnification should be calculated by taking d(xO)/d(xI) rather than my simplistic xO/xI. Anyway, if you understand the principle, you can derive it yourself or check the articles Dinesh mentioned:
Magnification and Third-Order Aberrations in Holography
Reinhard W. Meier
Journal of the Optical Society of America Vol. 55, Issue 8, pp. 987-992 (1965) doi: 10.1364/JOSA.55.000987
Nonparaxial Imaging, Magnification, and Aberration Properties in Holography
Edwin B. Champagne
Journal of the Optical Society of America Vol. 57, Issue 1, pp. 51-55 (1967) doi: 10.1364/JOSA.57.000051
(PM me if you don't have access)
Also note that the formulas (also posted by Dinesh) use different symbols than I used.
tonyr wrote: ↑Mon Jul 01, 2019 6:56 pm
So the bottom line is you can only get perfect magnification by stretching the holographic pattern, and even then you need to use either a higher diffractive order or different reconstruction wavelength.
Something like that. Note that in display holography, perfect magnification is not necessary; the formulas just give you insight what is actually happening.
tonyr wrote: ↑Mon Jul 01, 2019 6:56 pm
Separate wavelengths aren't that practical, at most ~2x magnification if you record with blue and playback with red.
Exactly. On the other hand, changing wavelength was the Gabor's original idea behing the holography.
tonyr wrote: ↑Mon Jul 01, 2019 6:56 pm
Not sure higher orders are practical either considering weakness like you said. 10x magnification sounds out of the question.
Agree.
tonyr wrote: ↑Mon Jul 01, 2019 6:56 pm
Not to mention, how would you even implement the stretch? Use a lens to magnify and reimage the holographic pattern onto a new plate? Has that been done?
I am not sure, but I think it something was done using "exotic" waves, like microwaves or sound waves. Maybe Dinesh knows more. Anyway, magnifying/reimaging fringes for display application sounds hard.