Does a "reflected" hologram produce a caustic in the shape of the original object?

Question

Imagine you make a transmission hologram, ala the standard picture. Now you take your photographic plate, and everywhere it is transparent, you put a thin reflective layer on, and everywhere it is opaque, you make it transparent (more accurately, you create a plate with R' = 1-R, T' = 1-T at every point).

What happens when you shine the reconstruction beam at this plate? Does it produce a caustic at the location of the (surface of the) original imaged object? Suppose I wanted to use this in 3-D printing with some, initially transparent, photosetting plastic. What happens?

Answer 1

You may illuminate the plate and observe what happens to the light in each side of it. As it has reflecting and transparent fringes, it would work as a transmission hologram. Babinet's principle assures you that the inverse/complementary plate generates the same image as the 'direct' one (it is locally a diffraction grating). Then you would see, when looking from the opposite side of the plate, a virtual image in the place the object was set. This is used in holographic interferometry.

But you are interested in the reflected light. The main difficulty for me in this question is that I am not completely sure, but almost, that transparent lines would work for this light as if they were opaque, as light arriving there would pass and interfere only affecting light in the other side. If this is true, then you can think the plate as the complementary one plus a mirror. This means the image would form in the opposite side of the mirror, being virtual too, and you would see it only when looking from the original object side of the plate. But there are many ways you can get a real image in the position you want, if that is the problem, for example just illuminating the master plate from the opposite side with the reference beam. If you do that and substitute the original object with a photosensitive material block, you will get the shape of the surface of the object recorded inside it, a 3-D print.

You can find easy to use information about holographic real images in:

[1] Hariharan, P. (2002). Basics of holography. Cambridge University Press.

[2] Saxby, G. (2010). Practical holography. CRC Press.