# Spherical Aberation & Barrel Distortion

1. Jun 20, 2012

### SSJVegetto

Hello all,

Can someone explain why barrel distortion is present by lenses and if it is related to Spherical aberation yes or no? Descriptions tell us that this is caused by the magnification being less when the distance from the optical axis increases. What magnification how can i understand this clearly?

Kind Regards,

Bob Rots

2. Jun 20, 2012

### Andy Resnick

Distortion is not related to spherical aberration. Distortion is the aberration defined by a magnification that changes with image height, while spherical aberration is defined by the focal length changing with aperture height. Spherical aberration can be reduced by 'stopping down' a lens, while distortion does not change with aperture.

For distortion, if the change in magnification is positive, you get barrel distortion. If it's negative, you get pincushion distortion. More complicated changes are sometimes referred to as 'mustache distortion'.

These and other aberrations occur because the approximation sin(q) = q, the 'paraxial approximation', breaks down as rays move away from the optical axis.

Does this help?

3. Jun 20, 2012

### SSJVegetto

Hi Andy,

I'm sorry but i still don't quite understand the nature of the problem. What angle when sin(q) = q are we talking about here I think it should be the angle with the optical axis but i don't understand? Can you make it more clear with a picture or something? And where does the magnification come from can I somehow derive this or how does this exactly work?

Is there a way to easily and/or fast calculate the corrected image?

Kind Regards,

Bob Rots

4. Jun 20, 2012

### sophiecentaur

Aren't Barrel and pincushion distortion there because the film / sensor lie in a plane and distances from the lens, in the simple lens formulae are radial (polar coordinates)? So the parts of a rectangular object can't be relied upon to lie on a rectangle in a much reduced image. It's a 'coordinate projection' problem, I think.

5. Jun 20, 2012

### Andy Resnick

Ok, let's back up a bit. First, the paraxial approximation: analyzing (or designing) an imaging optical system tracing the path of light rays (geometrical optics) is greatly simplified when the angle a particular ray makes with the centerline of the optical system (q) is small enough so that sin(q) is almost equal to q- and the smaller q is, the more accurate the approximation. In addition to 'linear optics', there's third-order [sin(q) = q - 1/6 q^3], 5th order, etc.... all corresponding to adding the next successive term in the Taylor series expansion of sin(q). Third-order optics modifies perfect imaging by introducing 'aberrations'.

The approximation sin(q) = q also means that point objects are imaged as points, so-called 'perfect imaging'. When the paraxial approximation is not accurate, point objects are not imaged as points, but as *aberrated* points. For example, spherical aberration causes points to be imaged as fuzzy round blobs, and the aberration 'coma' causes off-axis points to be imaged as off-axis fuzzy elliptical blobs.

Distortion is exhibited by the effect on a line that does not pass through the center of the image. In object space, the line is straight, while in image space, the line is curved- outwardly, inwardly, or some more complex shape.