by Din » Thu Mar 12, 2015 7:21 pm
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.
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.