Measure spatial frequency response using Imatest^{®}
eSFR chart

measures the spatial frequency response (SFR) at all slanted edge regions of
interest (ROIs) of an Imatest`sharpnessTable`

= measureSharpness(`chart`

)^{®} Extended eSFR chart.
`sharpnessTable`

includes the frequency for each ROI at which
the response drops to 50% of the initial and peak values.

measures the SFR at all specified slanted edge ROIs, specifying additional
parameters.`sharpnessTable`

= measureSharpness(`chart`

,`Name,Value`

)

`[`

also returns the average SFR of vertical and horizontal ROIs, using the input
arguments of either of the previous syntaxes.`sharpnessTable`

,`aggregateSharpnessTable`

] = measureSharpness(___)

Slanted edges on a properly oriented chart are at an angle of 5 degrees from the horizontal or vertical. Sharpness measurements are not accurate when the edge orientation deviates significantly from 5 degrees.

Sharpness is higher toward the center of the imaged region and decreases toward the periphery. Horizontal sharpness is usually higher than vertical sharpness.

The SFR measurement algorithm is based on work by Peter Burns [1]
[2]. First,
`measureSharpness`

determines the edge position with sub-pixel
resolution for each *scan line*, or row or column of pixels
perpendicular to the edge, in the ROI. For example, each row of pixels is a scan line
for a near-vertical edge. Next, `measureSharpness`

aligns and averages
the scan lines to create an oversampled edge intensity profile. The function takes the
derivative of the intensity profile and applies a windowing function. The returned SFR
measurement is the absolute value of the Fourier transform of the windowed
derivative.

[1] Burns, Peter. "Slanted-Edge
MTF for Digital Camera and Scanner Analysis." *Society for Imaging Science and
Technology; Proceedings of the Image Processing, Image Quality, Image Capture
Systems Conference*. Portland, Oregon, March 2000, pp.
135–138.

[2] Burns, Peter. "sfrmat3: SFR evaluation for digital cameras and scanners." URL: http://losburns.com/imaging/software/SFRedge/sfrmat3_post/index.html.