This post is an excerpt from https://www.imatest.com/docs/nyquist-aliasing/#slant
Thanks to the ISO 12233 binning algorithm, slanted-edges can measure system response above the Nyquist frequency (fNyq = 0.5 cycles per pixel). As we have shown, response above the fNyq can lead to aliasing artifacts such as moiré, but there are some limitations to MTF measurements— especially with the slanted-edge MTF measurement, which is Imatest’s preferred method (in most instances) because of its speed and efficient use of space.
The limitations are
The standard output (processed; not raw) of most consumer cameras is sharpened, which significantly boosts response at high spatial frequencies. The amount and the range of frequencies where response is boosted depends on the sharpening amount, radius, and algorithm. Since sharpening has little effect on aliasing artifacts (which depend on the spatial frequency spectrum of the light reaching the sensor and the demosaicing algorithm), the response of sharpened images can be quite misleading.
Color moiré is difficult to see on slanted edges. It is actually present in the form of colored pixels close to the edge, but it’s difficult to see in non-repetitive patterns.
Moiré is much more visible on
hyperbolic wedges (a converging bar pattern),
Siemens stars, which unfortunately have a very limited area of high spatial frequencies, and
Log Frequency-Contrast, where moiré is quite visible but difficult to measure quantitatively.
Moiré is exceptionally visible on zone plate patterns (a kind of worst case pattern that can be created with the Imatest Test Charts module), but the zone plate is not suited for quantitative measurements.
Because it is difficult to correlate MTF measurements with visible aliasing, strong MTF response above Nyquist should be regarded only as a warning that aliasing might be an issue and hence needs to be explored further. It is not a definite indicator of aliasing. Imatest techniques for directly measuring the effects of aliasing are listed below.
Sinusoidal Patterns
Sinusoidal patterns on the Siemens Star and Log-F contrast target are alternatives to slanted edges, which are less sensitive to signal processing. The disadvantage is that they take up more space, take more time to analyze, and are difficult to analyze with extreme distortion.
Leader SFR-Fit MTF Measurement Software is an alternative measurement software that uses connected displays and live acquisition from a connected camera to display multiple fixed-frequency sinusoidal patterns in a localized area. This can enable more accurate high frequency MTF measurement of systems that are sharpened.
Textured Patterns
Spilled Coin (dead leaves) PatternDead leaves/Spilled Coins charts are interesting because their statistics resemble those of natural scenes; they are less affected by edge sharpening than other patterns (especially the slanted edge) and hence provide estimates of texture detail that correlate better with perceptual observations. They are also more susceptible to noise reduction, making analysis of random patterns valuable for evaluating the preservation of texture in processed images.
Wedges
Wedges, which are analyzed by Imatest’s Wedge and eSFR ISO modules, provide the best visual indication as well as measurement of aliasing. Wedges can be used to calculate
MTF (with limited accuracy because of high contrast and because subpixel variations of sampling phase can cause significant variation of MTF).
the onset of aliasing (also called “vanishing resolution”; the spatial frequency where the bar count starts decreasing).
the effects of aliasing, especially color moiré.
Wedges can be manually selected in the old ISO 12233:2000 chart with the Wedge module, which we don’t recommend because it’s inconvenient. (and the old chart is also not recommended by the current ISO 12233:2014+ standard). We strongly recommend using the eSFR ISO chart and module, which is compliant with the current standard and automatically detects wedges and other features. It measures a great many image quality factors (MTF, Lateral Chromatic Aberration, color, tonal response, noise, Signal-to-Noise Ratio, and more) in addition to color aliasing. Wedge moiré plots are identical in the Wedge and eSFR ISO modules. We illustrate eSFR ISO results below.
The Wedge moiré plot
The Wedge moiré plot below shows the mean CIELAB chroma (𝐶∗=𝑎∗2+𝑏∗2‾‾‾‾‾‾‾‾‾√ ) measured inside the wedge as a function of spatial frequency. Several other color aliasing-related metrics are listed in the table below.
To get the plot below, acquire an eSFR ISO chart image,then run eSFR ISO Setup, following the instructions here. eSFR ISO can also be run in batch-capable Auto mode. Under Display, select 18. Wedge moiré.
The curve in the plot is the mean of the selected metric (𝐶∗=𝑎∗2+𝑏∗2‾‾‾‾‾‾‾‾‾√ in this case), taken inside the wedge as illustrated below.
The table below lists the available metrics, which are selected in the Moiré dropdown menu on the right side of the image below Display. Only three of the metrics are recommended: the others are informative or experimental. The maximum value of each metric is displayed in the upper left of the plot (shown above). The maximum values for all the metrics can be saved in JSON and CSV results files. Here is a list of the metrics, emphasizing the recommended metrics.
mean(|R-B|) | This is a good metric since the Red and Blue channels are most affected by color aliasing. |
mean(|R-B|) / mean(R,B) | This is slightly more stable since it’s normalized to the mean value of R and B. |
mean(|R-G|) | These may be interesting to examine, but they tend to be less sensitive than R-B metrics because the green (G) channel has a higher Nyquist frequency. |
mean(|R-G|) / mean(R,G) | |
mean(|G-B|) | |
mean(|G-B|) / mean(G,B) | |
S(HSL) | These Saturation metrics are not recommended because they can have large values at low levels (L or S), hence can be misleading. They may not be kept. |
S(HSV) | |
Chroma 𝐶∗=𝑎∗2+𝑏∗2‾‾‾‾‾‾‾‾‾√ | CIELAB Chroma, 𝐶∗=𝑎∗2+𝑏∗2‾‾‾‾‾‾‾‾‾√ This is the primary (recommended) color aliasing metric. |
Color aliasing metric
The color aliasing metric is new in Imatest 5.1.12, released in October 2018. Prior to this release the color metrics did not correlate well with image appearance. The metric to display is selected in the Moiré dropdown menu, below Display.
Each wedge region is white-balanced prior to calculating the color aliasing metrics. The metrics are calculated inside the wedge. Smoothing (with a kernel of width 0.01 Cycles/Pixel) is recommended for consistent results. The color moiré metric is selected in the Moiré dropdown menu. Our primary recommended metric is Chroma (sqrt(a*^2 + b*^2)). This is the mean of the CIELAB chroma, C = sqrt(a*2 + b*2). Other useful color aliasing metrics are mean(|R-B|) and mean(|R-B|) / mean(R,B). |R-B| is useful because Red and Blue are more sensitive to aliasing then Green.
Clicking Save data (or running eSFR ISO setup with the appropriate boxes checked) saves data to CSV and JSON files. Here is a sample of JSON output for the color aliasing summary metrics (the maximum value for each metric shown in the above table). Recommended metrics are shown in boldface.
“color_aliasing_max_mean_R_minus_B”: [0.1327,0.1088,0.07527,0.07033],
“color_aliasing_max_mean_R_minus_B_normalized”: [0.391,0.2999,0.4362,0.3822],
“color_aliasing_max_mean_R_minus_G”: [0.09607,0.02452,0.08199,0.07815],
“color_aliasing_max_mean_R_minus_G_normalized”: [0.328,0.05977,0.4449,0.3945],
“color_aliasing_max_mean_G_minus_B”: [0.1041,0.1088,0.06335,0.03999],
“color_aliasing_max_mean_G_minus_B_normalized”: [0.2701,0.2991,0.2851,0.1786],
“color_aliasing_max_mean_S_HSL”: [0.6033,0.9159,0.4902,0.5427],
“color_aliasing_max_mean_S_HSV”: [0.3227,0.2781,0.4083,0.3311],
“color_aliasing_max_mean_CIELAB_chroma”: [16.61,16.48,10.69,11.19],