Correcting nonuniform illumination in slanted-edge MTF measurements

April 22, 2018
April 22, 2018

Slanted-edge regions are sometimes unevenly illuminated. While every effort should be made to achieve even illumination, it isn’t always possible (for example, in medical endoscopes). The uneven illumination causes an irregularity in MTF at low spatial frequencies (shown as the red ellipse in the MTF curve, below) that distorts MTF summary metrics like MTF50.

This page refers to nonuniformity perpendicular (normal) to the slanted-edge, not nonuniformity along the edge, which does not cause a systematic error, but sometimes adds a sawtooth (zigzag) component to the MTF at high spatial frequencies.

 

Figure 1. Original average edge and MTF.
The low frequency irregularity (red ellipse) affects summary metrics, such as MTF50.

Imatest 5.0+ has an option for dealing with this problem for all slanted-edge modules (SFR and Rescharts/fixed modules SFRplus, eSFR ISO, SFRreg, and Checkerboard. To do so, you need to check the Nonuniformity MTF correction checkbox in the settings (or More settings) window, shown on the right.

When this box is checked, a portion of the spatial curve on the light side of the transition (generally displayed on the right in Imatest) is used to estimate the nonuniformity. The light side is chosen because it has a much better Signal-to-Noise Ratio than the dark side. In the above image this would be the portion of the red curve (the complete edge profile) greater than about 6 pixels from the center. Imatest finds a first-order fit to the curve in this region. Set some limits on this curve (so it doesn’t drop below zero), then divide the average edge by the first-order function. 

 

Detailed algorithm

We assume that the illumination of the chart in the Region of Interest (ROI) approximates a first-order function, L(d) = k1 + k2d, where d is the horizontal or vertical distance nearly perpendicular to the (slanted) edge. The procedure consists of estimating k1 and k2, then dividing the linearized average edge by L(d). 

k1 and k2, are estimated using the light side of the transition starting at a sufficient distance dN from the transition center xcenter so the transition itself does not have much effect on the k1 and k2 estimate. To find  dN we first find the 20% width d20 of the line spread function (LSF; the derivative of the edge), i.e., the distance between the points where the LSF falls to 20% of its maximum value. 

dN = xcenter + 2 d20 

If the the edge response for x > dN has a sufficient number of points, it is used to calculate k1 and k2 using standard polynomial fitting techniques. The result, shown below, is a more accurate representation of the edge. Summary metrics like MTF50 are also more accurate.

Figure 2. Corrected average edge and MTF.
MTF50 is 18% higher than the uncorrected results.

Note that the nonuniformity is  multiplicative rather than additive. An additive signal would fog the shadow areas.  

Recommendations

MTF nonuniformity correction should not be turned on for most situation, since there may be unusual cases where it causes artifacts. It should only be checked for known nonuniform illumination, such as the case shown above.

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