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Imatest Documentation The image is sharpened if ksharp > 0 and de-sharpened if ksharp < 0 (a bit different from standard blurring). For R = 2, the maximum change takes place at half the Nyquist frequency, f = fN /2 = dscan/4, where cos(2πR f /dscan) = cos(π) = -1. Sharpening with R = 2 has no effect on the response at the Nyquist frequency ( fN = dscan/2) because cos(2πR fN /dscan) = cos(2π) = 0. Raw MTF50, without standardized sharpening, produces the most accurate results for comparing lenses and for comparing the sharpness at the center and edge of a single image. MTF50P is somewhat better when comparing cameras with strong sharpening. MTF50P equals MTF for slightly to moderately sharpened images, but it is lower for oversharpened images. It is a good sharpness indicator when images will not be post-processed, for example, in video cameras. Standardized sharpening is the best approach for comparing different cameras. Examples An undersharpened image The 11 megapixel Canon EOS-1Ds DSLR is unusual in that it has very little built-in sharpening (at least in this particular sample). The average edge (with no overshoot) is shown on top; the MTF response is shown on bottom. The black curves are the original, uncorrected data; the dashed red curves have standardized sharpening applied. Standardized sharpening results in a small overshoot in the spatial domain edge response, about what would be expected in a properly sharpened image. It is relatively consistent for all cameras. Oversharpening or undersharpening is the degree to which the uncorrected pulse is over- or undersharpened, i.e., sharpened relative to the standard sharpening value. It is equal to 100% (MTF( feql )-1). It if is negative (the case for the EOS-1Ds), sharpening is applied to the original response; if it is positive, de-sharpening is applied. (I use "de-sharpening" instead of "blurring" because the inverse of sharpening is, which applied here, is slightly different from conventional blurring.) Note that it is not the actual sharpening applied by the camera and software. An oversharpened image 28 of 451
Imatest Documentation The image to the right is for the 5 megapixel Canon G5, which strongly oversharpens the image— typical for a compact digital camera. The uncorrected 10-90% edge rise distance of the G5 is considerably better than the 11 megapixel EOS-1Ds (1940 vs. 1511 per PH), but the corrected 10-90% rise (with standard sharpening) is 76% of the EOS-1Ds. Based on pixels alone, the expected percentage ratio would be 100% (1944/2704) = 72%. MTF50P is not shown on the left. It is displayed when Standardized sharpening is turned off; it can also be selected as a Secondary readout (in place of MTF30 on the left). For this camera MTF50P is 345 cycles/pixel or 1340 LW/PH, almost 8% lower than MTF50. It's a slightly better sharpness indicator for strongly oversharpened cameras, especially in cases like video cameras where the image will not be post-processed. The raw MTF50 of the G5 is close to the EOS-1Ds, but the corrected MTF50 (with standard sharpening) is 73% of the EOS-1Ds, very close to the ratio of vertical pixels. These results illustrate how uncorrected rise distance and MTF50 can be misleading when comparing cameras with different pixel sizes and degrees of sharpening. MTF50P is slightly better for comparing cameras when strong sharpening is involved. Uncorrected MTF50 is, however, appropriate when comparing lens performance (different focal lengths, apertures, etc.) on a single camera. Unsharp masking "Unsharp masking" (USM) and "sharpening" are often used interchangeably, even though their mathematical algorithms are different. The confusion is understandable and far from serious because the end results are visually similar. But when sharpening is analyzed in depth the differences become significant. "Unsharp masking" derives from the old days of film when a mask for a slide, i.e., positive transparency, was created by exposing the image on negative film slightly out of focus. The next generation of slide or print was made from a sandwich of the original transparency and the fuzzy mask. This mask served two purposes. It reduced the overall image contrast of the image, which was often necessary to get a good print. It sharpened the image by increasing contrast near edges relative to contrast at a distance from edges. Unsharp masking was an exacting and tedious procedure which required precise processing and registration. But that has changed. USM can now be accomplished with only a few mouse clicks in an image editor. Thanks to the central limit theorem, blur can be expressed by the Gaussian function (Bell curve). Blur = exp(-x 2 /2σx 2 ) / sqrt(2πσx 2 ) σx corresponds to the sharpening radius, R. The unsharp masked image can be expressed as the original image summed 29 of 451
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