# Input parameters for the reconstruction algorithm in Digital Holography

I've been browsing some Digital Holography papers these days, and have come across this fundamental question.

When you reconstruct the complex amplitude for the object image, you use e.g. Fresnel Transform to simulate diffraction.

The thing is, one of the parameters in this process is the distance, d, between the holographic plate (or CCD) and the object.

However, the whole point of Digital holography, I believe, is to find out the depth profile of the object, that is to say, the value of d.

We wouldn't have to do DH in the first place if we had known the precise (down to nanometric realm) value of the distance!

Could anyone clarify this for me?

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You can reconstruct the wavefront at any distance $z$. If you choose $z$ the same as the location of the object $d$, it will appear in focus. If you choose $z$ larger or smaller than $d$, it will look like out of focus (blurred). This has the same effect as changing the focus on a usual optical camera.
In fact this focus thing is equivalent to a lens: the the Fresnel transform includes a term identical to the phase modulation of a lens of focal length $z$. The image obtained is the same that a lens would provide.
So you can reconstruct at any depth (as long as it's not too far out of focus), then propagate forwards and backwards and find out what the focal distance actually is. SO the algorithm can infer $d$ - I believe this is what you're saying - it's just not spelt out. BTW I don't believe you have to delete anything - your answer is sound - just spell out the inference of $d$ bit as the OP was asking this. – WetSavannaAnimal aka Rod Vance Aug 23 '13 at 6:58
I used a wrong definition of $d$. Now corrected. You can reconstruct the wavefront at any distance $z$. If $z=d$ it is in focus. You may indeed be able to write an algorithm that finds $d$ by obtaining the best focus. – fffred Aug 23 '13 at 7:10