Captured USAF-1951 MTF

KrakenOS has two different MTF paths:

• PSFCalc.calculate_mtf and the layout editor’s MTF analysis transform a simulated or ray-traced point-spread function.

• USAFMTF.analyze_usaf_image measures a real camera/lens capture of a USAF-1951 three-bar target.

The vector file attachment/USAF-1951.svg is target artwork, not a captured system response. Print or display it at a known physical scale, capture it through the machine-vision system without clipping highlights or shadows, and analyze the resulting raster image. Perspective-correct the chart first if it is not normal to the optical axis. This particular legacy SVG has unitless width/height values and declares its document units as pixels, so do not assume a printer or browser preserved its intended millimetre scale. Verify a bar with a microscope or calibrated ruler: its physical width should be 1 / (2 * f) mm for element frequency f in line-pairs/mm.

Method

For every selected USAF element, KrakenOS averages along the bars to obtain a one-dimensional intensity profile. It jointly fits the fundamental, third, and fifth square-wave harmonics while allowing a linear illumination trend. The fundamental image modulation is converted to MTF by

\[\mathrm{MTF}(f) = \frac{\pi}{4}\, \frac{M_{\mathrm{fundamental,image}}(f)}{C_{\mathrm{target}}}.\]

This Fourier-domain method is preferable to applying an infinite-square-wave series directly to the finite three-bar element. The result is a set of MTF samples at the USAF frequencies

\[f(g,e) = 2^{g + (e-1)/6}\quad\text{line-pairs/mm}.\]

Vertical bars measure x response and horizontal bars measure y response. The CSV retains both directions, the fitted cycles/pixel, pixels/cycle, fit \(R^2\), and an optional calibration consistency error. Inspect these diagnostics: fewer than roughly four pixels/cycle is undersampled, and a low \(R^2\) usually means the ROI contains a label, the orthogonal bars, severe noise, or incorrect rotation.

Python API

ROIs use (x0, y0, x1, y1) pixel bounds and should contain one complete three-bar element without its number or the adjacent orthogonal element.

import KrakenOS as Kos

rois = [
    Kos.USAFElementROI(0, 1, (120, 80, 240, 130), "vertical"),
    Kos.USAFElementROI(0, 1, (250, 70, 305, 190), "horizontal"),
    Kos.USAFElementROI(0, 2, (330, 90, 430, 132), "vertical"),
]

result = Kos.analyze_usaf_image(
    "capture.tif",
    rois,
    magnification=0.5,   # absolute image size / object size
    pixel_pitch_um=3.45,
    target_contrast=1.0,
)
result.save_csv("capture_mtf.csv")
figure, axes = result.plot(frequency_space="object")
figure.savefig("capture_mtf.png", dpi=160)

Object-space frequency comes directly from the USAF group and element. With magnification, image-space frequency is object frequency / abs(m). With pixel_pitch_um, KrakenOS also converts the fitted cycles/pixel to a measured image-space frequency. A large discrepancy between those two values indicates incorrect magnification, pixel pitch, ROI extent, or element labels.

Command line

Create a JSON file describing the same ROIs:

{
  "magnification": 0.5,
  "pixel_pitch_um": 3.45,
  "target_contrast": 1.0,
  "rois": [
    {"group": 0, "element": 1, "roi": [120, 80, 240, 130], "orientation": "vertical"},
    {"group": 0, "element": 1, "roi": [250, 70, 305, 190], "orientation": "horizontal"}
  ]
}

Then generate both outputs:

python -m KrakenOS.USAFMTFCLI capture.tif rois.json

The default files are capture_mtf.csv and capture_mtf.png. Use --csv, --plot, and --frequency-space image to override them.

Measurement limits

This is an end-to-end system MTF: lens, focus, motion, sensor aperture, demosaicing, sharpening, and compression can all affect it. Use linear raw or linearized image intensity where possible; gamma-encoded JPEG values bias contrast. The estimator does not automatically recognize the chart or remove perspective distortion. An SVG rasterization only tests the artwork/rendering chain and cannot measure the machine-vision system.

The Fourier treatment follows the finite three-/four-bar method described by G. D. Boreman and S. Yang, Applied Optics 34, 8050-8052 (1995), DOI 10.1364/AO.34.008050. The general bar-to-OTF correction is discussed by R. L. Lucke, Applied Optics 37, 7248-7252 (1998), DOI 10.1364/AO.37.007248.