Radial Frequency Response Chart

In collaboration with Yanding, Fourier Image Lab developed an HDR spatial frequency response chart. This chart enables the analysis of modulation transfer at any angle and helps quantify blooming and processing artifacts like demosaicing, sharpening, and gamma adjustments.

Modern sensors with multiple photodiodes often calculate MTF from reflective charts, which typically reflect the performance of the best photodiode. However, the HDR MTF chart incorporates signals from all photodiodes, providing results that better replicate natural outdoor environments, where contrast ratios are thousands of times higher than those achievable with reflective charts.

The chart was created from a 100GB uncompressed file with a resolution of 10,000 x 10,000 pixels and a 32-bit depth. A specialized printing method was employed to achieve precise reproduction, even with printer dithering.

We offer both reflective and translucent chart versions; please get in touch with us for more information.

The waveform is sine(x²)

The digital version of the chart (you may still observe artifacts of resampling since your browser does resampling of the image)

Let's build a horizontal cross-section and plot the values along a horizontal vector from the chart's center, as displayed in the yellow line below.

The cross-section shows increasing frequency at the same amplitude. This is constant SFR, that real optical systems do not have.

Let's capture a chart and plot the cross-section. We have a translucent version of the chart for HDR chat attached to the lightbox.

The chart captured on the right with iPhone 12 Pro shows ghost images in the area around half Nyquist, but overall aliasing is suppressed quite smoothly.

Let's build a cross-section of a horizontal line and observe how the wave's amplitude reduces with frequency increase. The green line following the peaks of the curve can be interpreted as a spatial frequency response. Remember that we have a squared growth speed at the x-axis that defines how fast the frequency increases.

Additionally to SFR, the plot above provides a good way to observe (high and low) image clipping, quantization, and apparent variability at the higher frequencies. All of these influence the resulting MTF measurements.

Missing frequency bands usually appear as regular patterns on the captured image. Angles of straight segments in those patterns are linked to how the gradient is calculated in demosaicing. It is tough to extract smooth gradients from a color filter array without losing some resolution, and when those trade-offs

are not aligned with the lens frequency response, we can observe peaks of angular distribution of MTF functions indicating those angular biases in hardware.

We aim to control and adjust Nyquist and noise thresholds in demosaicing and sharpening in ISP and sensor. This chart can also be used to explore gamma function limits interactively.

Another valuable application of this chart is revealing the top layers of the convolutional network and finding out if generative AI was used to process the original image. Sometimes, we can see a ghost image of the ground truth data, which was used to train the system after capturing this chart.

Spatial frequency response is a key to object detection and detail reproduction.