Holographyforum.org / holowiki.org

Another question, if anyone has time. I was reading about spherical aberration on Wikipedia.

http://en.wikipedia.org/wiki/Spherical_aberration

For spatial filtering using microscope objectives, I assume there is some correction for both chromatic and spherical aberration. But things may be more difficult for a simple lens (or a few simple lenses in series). It was said in the above article, that spherical aberration is reduced for approximately the middle 50% of the lens, while the other areas (going toward the edges of the lens) tend to produce spherical aberration, and don't focus to the "main" focal point. As a matter of practical spatial filtering, I was wondering if anyone has attempted to use a small lens, and found an improvement by reducing the input size of the beam. Say for example a ball lens 2mm in diameter (which is what I intend to try) and attempted to reduce spherical aberration by reducing the size of the input beam to 1mm.

The Wikipedia article on spherical aberration shows the following diagram as an example:

http://upload.wikimedia.org/wikipedia/c ... _2.svg.png

With the lens in the diagram, the rays incident on the central portion of the lens focus light further downstream, while the rays incident on the edges of the lens focus light further upstream. With the spatial filtering of co-linear blue, green, and red laser light (in my case just green and red), it has been recommended that the longer wavelength beam diameters be larger than the shorter wavelength ones. I'm wondering if chromatic aberration (as shown in the other diagram) and spherical aberration are two "competing" effects. That is, does the focal point of the smaller diameter beam (blue) get pushed downstream (because it's incident on more of the central portion of the lens, i.e., less spherical aberration) which "cancels out" it's tendency to focus upstream (i.e., chromatic aberration)?

I can't speak to the issue of spherical aberration in a spatial filter. It's why a microscope objective is generally used. To spread the beam more than what's possible with a 40x objective, I've used a small short focus double concave negative lens after the spatial filter, attached directly to the pinhole mount.

Thank you, I will definitely try that.

Ball lenses are attractice for their short focal lengths but will introduce major aberrations for sure...it is a sphere so will have speherical aberration as well as chromatic aberration. Microscope objectives are well corrected.

Launching into polarization preserving SM fiber for a spatial filter works great but you end up with 30% power loss if you are lucky; a high price to pay. But you can also get the lasers off the table.

Spatial filters cannot have aberrations. It's a filter, not a refractive element.

The reason for spherical aberrations is that the point of a lens is to alter a phase curvature of one curvature(the input to the lens) into a phase curvature of another curvature (the output from the lens). If you hit a lens with a collimated beam, then the incoming phase wavefront is flat (it's not really, but we can pretend, since it's pretty close). The lens takes this flat wavefront and converts it into a curved wavefront. Ideally, the curved wavefront is a perfect circle (in two dimensions), in which case, the curved wavefront will collapse onto a geometric point at the geometric centre of the circle (yes, I'm aware this violates conservation of energy, but we can pretend it actually is a geometric point.). Now, if you actually calculate the shape necessary to convert a flat wavefront into a circular wavefront, you'll find that the necessary shape is a parabola. But, parabolic lenses are not easy to make and so are fairly expensive. To make life easier, and cheaper, you may use a circular profile (in two dimensions). In this situation, the centre of the circle approximates to the centre of a parabola, and so the flat wavefront converts to a circular wavefront for rays close to the centre of curvature of the lens, near the axis (the paraxial rays). Thus, the beams near the axis focus to a point at the calculated distance. However, as you go up the y axis, ie up the face of the lens, the discrepancy between a circle and a parabola is increased.This increase in the discrepancy causes the wave to be not-quite-circular at the edges of the lenses at some distance from the axis. This not-quite-circular wavefront at the edges away from the axis converge to a "fuzzy" point some distance away from the actual focal point.