why does my georeferenced image end up distorted with transformation?

[JessamynBenshoof]

I have been georeferencing a number of historical CIR images to recent high resolution NRCS orthophotos for a project. We have been using a second order polynomial transformation with 20 control points. It works for most of the images I've been using just fine but I've had a coupled that have ended up curved and distorted once I jump from the first order to the second order transformation. The first time it happened I was able to fix the problem by using a 2nd copy of the image and starting over. I now have this one image that I have georeferenced 5 times and it ends up curved, it is not highly distorted but it is noticeable. I don't understand why the second order polynomial works with all my other images but not this one.

[DanPatterson_Retired]

If you are trying to register an image that has no distortion in it, then you only need a 1st order transformation normally (an affine transformation).  As you more to higher orders in an attempt to reduce rms error, you will effectively start to introduce distortion in the areas away from the control points.  Most people erroneously think that the higher the order the better... wrong.  The examples in the help file will give you some visuals and a good explanation.  If you examine your control point information and the rms data, you will find that you may have one or two control points are causing the 'issues'  but it is better to stick with a 1st order if it works well and if a 2nd order introduces distortion (particularly along the edges) you will know you have gone too far.  If you want to see some real fun stuff, ramp up the order and watch the warping increase.

So my recommendation, if the images don't contain distortions, then stick with registering and start with an affine (1st order) and only move up the order if you have ruled out erroneous control points and 2nd improves things.

Fundamentals of georeferencing a raster dataset—Help | ArcGIS for Desktop 

The next thing to read is 

Fundamentals of orthorectifying a raster dataset—Help | ArcGIS for Desktop 

when you know that simple rectification isn't going to cut it.

[JessamynBenshoof]

Thanks for the info. I will work it some more and see what I can do with the affine. I've been using the 2nd order polynomial because that's what the person I am doing the work for requested, per methods used by some other groups. I am digitizing river channels on each image and using geoprocessing methods to come up with river migration rates over time. We are attempting to keep the RMS low to reduce the error in the migration rates. The second order polynomial was effective and worked well for all the other historic images I've used. I think this one has presented problems because it is in a slightly different area where the satellite imagery has been taken from different angles and I'm working in Albers EA instead of NAD83. I can keep the RMS low with the affine/1st order but only with control points near the center of the image, points closer to the edge are not referencing well.