Re: Digital Holograms, Refarctive index distributions
Timo Nieminen
> I am working with a digital holographic microscope to obtain 3D refractive index distributions of biological cells and I am struggling to model even the basic case. I need to create a phase object (an object which retards or advances light waves velocity as travelling through the object) so that only the phase of the light and not the amplitude is altered. It is the refractive index (n=c/v) i.e a measure of how much slower the light is compares to a vacuum that determines the phase change. For simplicity I am trying to create a 2D array with two top hat functions in the center. One of the top hats is twice as big as the other. I somehow need to assing numbers (or functions?) to the two seprate top hats so that the outer top hat for instance could be air and the inside one glass (glass has a much higher optical density than air so light waves are slowed down lots leading to a high
> refractive index, air- low refractive index).
>
> I then need to 'propagate light' through the phase object (assuming zero scattering to simplify the problem) to determine the hologram? I am slightly confused as how exactly I am supposed to do this as my supervisor was a bit vague. I think the only way I can 'propagate light' through my matehamtically created object would be to take the Fourier transform of the 'aperture' to get the Fraunhoffer diffraction pattern. But can you treat a phase object as if it were an aperture? Any help or advice would be much appreciated as I find programming really tough!!!
Your phase mask is some function F(x,y). For a phase-only mask, |F| = 1.
For zero phase shift, such as outside your phase object, F = 1. If you
have, e.g., a 1/5 wave phase shift, you'll have F = exp((2*pi/5)*i) or
F=exp(-(2*pi/5)*i).
If the complex amplitude of the light before the phase mask is E(x,y),
you'll have F(x,y)*E(x,y) after it. That's the easy part.
How you want to calculate the propagation of light after the mask is up to
you. That's the hard part! Fourier transform might be OK, but in that
case, you don't want to find the transform of the mask itself - better the
product F*E than the equivalent convolution.
What you're asking is an optics question, not a Matlab question, so
perhaps an optics newsgroup is more appropriate?
--
Timo
Marco
atmosphere on the light of stars. The varying index is what makes stars
twinkle. Twinkling stars are great for lovers but astronomers hate them.
We create a model of the atmospheric volume above the telescope based on its
varying refractive index and 'propagate light' through the model along the
path to a star and use the projected phase delay to correct for the actual
phase delay.
The same technologies are also used to do that for vision optics studying
the retina in live subjects and for cellular biology as you described.
Are you trying to figure out how to create a model of the volume as a
function of refractive index or how to use such a volume to predict the
phase delay of light passing through it?
--
Marco
UCO Lick Observatory
Laboratory for Adaptive Optics
"Timo Nieminen" <ti...@physics.uq.edu.au> wrote in message
news:Pine.LNX.4.50.0912111057590.16936-100000@localhost...
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