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Imatest Documentation The plot on the right shows MTF70 through MTF10 displayed in polar coordinates. Spatial frequency (cycles per pixel in this case) increases with radius. (This is the opposite of the image itself, where spatial frequency is inversely proportional to radius.) This plot is most similar to the spider plot shown in Image Engineering digital camera tests and Digital Camera Resolution Measurement Using Sinusoidal Siemens Stars (Fig. 15), by C. Loebich, D. Wueller, B. Klingen, and A. Jaeger, IS&T, SPIE Electronic Imaging Conference 2007. MTF10 (the black octagon on the right) corresponds to the Rayleigh diffraction limit. MTF contours: rectangular and polar The plot on the right shows the MTF contours for each of the 8 segments. Spatial frequency is displayed on a linear scale, but a log scale may be selected and a color bar (see below) may be added. This plot contains information similar to the rectangular MTFnn plot, above. MTF70 – MTF10: Polar coordinates, Linear frequency on radius. MTF contours, rectangular display, Linear frequency scale. 216 of 451
Imatest Documentation The plot on the right shows the MTF contours for each of the 8 segments, displayed on a polar scale, where location (radius) on the plot corresponds to the image. This is the inverse of the polar MTFnn plot, above, where spatial frequency is the inverse of image radius. Most of the action in this image is near the center. If the Zoom box is checked you can zoom in by selecting a portion of the image or simply by clicking on it. Equations, algorithm, and issues MTF contours, polar display. Equations for analyzing the Siemens star are given in Digital Camera Resolution Measurement Using Sinusoidal Siemens Stars by C. Loebich, D. Wueller, B. Klingen, and A. Jaeger, IS&T, SPIE Electronic Imaging Conference 2007. The algorithms used for Imatest Star Charts are similar, differing only in details. The 32, 64, or 128 radii ri , located from just outside the inner circle to just inside the outer circle, are selected using a logarithmic scale that makes them more closely spaced near the inner circle. This makes the frequency spacing (proportional to 1/radius) more consistent than for uniformly spaced radii. For each of the 32 radii ri , all points are located with radii between ( ri-1+ri )/2 and ( ri+ri+1 )/2 pixels. ( ri−0.7 and ri+0.7 pixels, used prior to Imatest 2.7.2, caused significant bumps in the MTF response.) Spatial frequency is 1/(2π ri ) cycles/pixel. These points fit the curve, I(φ) = a + b1 sin(2π/g) φ ) + b2 cos(2π/g) φ ), where b = sqrt( b1 2 + b2 2 ) MTF = b/a The equation for I(φ) is recognized as a term in a Fourier series expansion, which can be solved using the standard Fourier series equation since each segment (there are 8, 12, or 24) has an integral number of cycles (of a total of 144, 120, 72, or 48 cycles on the chart). b1 = k mean( sin(2π/g) I(φ) ); b2 = k mean( cos(2π/g) I(φ) ); a = mean( I(φ) ) Since MTF is normalized to 1 at the lowest measured spatial frequency for each segment, k drops out of the final result. Algorithm issues Bumps in the MTF response curve caused by aliasing are visible in the image below. 217 of 451
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