lronacecho implements a correction designed to remove an echo effect from LROC NAC images. In the summer of 2011, an echo effect was discovered in the NAC detectors. The signal in each pixel is replicated to a smaller extent in the pixel on the same line 2 columns over, 1 collumn in summed NACs. MSSS was consulted and it was confirmed this is a detector effect related to the high speed (>3000 lines/second) of the NAC detectors. The even and odd columns of the detector have separate signal processing chains, so when one pixel is read out, the next pixel with the same signal processing chain is two columns over. There is no measurable effect 4 columns over; the echo has no echo.

The size of the echo effect was determined by analyzing the signal at the edge the detector mask on each side of many NAC images, and by analyzing images with stars that had well-defined ghosts offset by two pixels. The effect is large enough that an inverse technique is needed to correct it with sufficient accuracy. The analysis determined that the echo is a larger percent of the signal for signals less than 100 DN. However, the correction uses a fixed fraction equal to for all pixels of all images. This value was derived from many flight images and is optimized for signals greater than 100 DN. Using a larger echo fraction for lower DN values would degrade the signal-to-noise too much. To reduce any artifacts in the begining of the image, the SMOOTHINGROWS parameter is used to specify the number of visible samples, before the full constant is applied. This fractional delta constant is calculated by the function: for NACLs, with the offset being from 5064 rather than 0 in the NACR.

A brute force inverse technique derived from simple substitution was used early in the development of the echo correction. Let be the NAC-L ideal signal in column i of a line without the echo effect, and the actual signal including the echo effect. Consider an ideal case where the detector response is linear and uniform and we ignore the other calibration corrections. Then

So, we have the line of the actual image , which includes the echo, and we want to recover the ideal image line without the echo. To avoid confusion, let's call this new calculated value where is an approximation of the original dependent on the accuracy of . It's trivial for line 0. Then, for line 2 we just substitute the solution from line 0 for and solve for . Likewise, for line 4 substitute for using line 2 and solve for , etc. The result is

Note, however, that this equivalent to:

So we can calculate the new correction factors from the previously corrected pixels (the ); there is no need to calculate each fractional "echo" factor from the original image (the ).

In practice it has proven most successful to apply the echo correction after the flat field correction.
The effect of the echo correction on the flat field is not significant.