Using a Digital Fourier Lens Instead of a Physical Lens in Experimental Holography Examples

[OMozafar]

Hello,

In all examples of experimental holography, I noticed that a physical Fourier lens is used in the setup. I was wondering whether it is possible to replace the physical lens with a digital lens encoded on the SLM. Specifically, I’m interested in whether the calibration between the camera and the SLM would still work, and if the optimization loops for spot holography would operate correctly in this case.

If so, could you then comment on why you used a physical Fourier lens instead of a digital one in your optical setup?

Cheers,
Omid

[ichristen]

Hi @OMozafar ,

Sorry for my late reply. You raise an interesting question!

We actually previously implemented something similar to what you're saying in this paper (see figs 4 and 5, where the "microlenses" are digital Fourier lenses). Holography (and Fourier and wavefront calibration) still work in this case. The restrictions of this paper were more due to the smaller pixel aperture of the cropped lenses than the digital lens.

A main issue that you would run into is the achievable focal length of a digital lens: the focal length must be large to avoid blurring the Fresnel lens at its far extents (see fig 10 for an example of how this blurring occurs). For a microlens, smaller focal lengths more achievable because the lateral extent of the lens is smaller.

For a full SLM, a focal length of around half a meter is reasonable to achieve. However, to image the full farfield of this SLM configuration, one would need a very large camera sensor, larger than the size of the SLM. Such cameras are not super common, especially for the cheaper scientific cameras (though they do exist in medium or large format digital cameras and for some higher-end scientific cameras).

As a last thing to mention, a digital lens is not identical to a conjugate physical lens (a lens spaced at a focal length away from both the SLM and camera). Conjugate spacing has important properties that allow more perfect mapping of a nearfield to its farfield (see the below quick diagram). However, loss of these properties is surmountable, especially with software calibrations.

Hope this is informative, and sorry again for my late reply!

Best,
Ian